CRITICAL CURRENTS IN GRANULAR HIGH
TEMPERATURE SUPERCONDUCTORS
Anthony Roger Jones
Christs College
Cambridge
A Dissertation submitted for the Degree of Doctor of Philosophy
at the University of Cambridge
March 1995
" U n l i k e
T . V . ,
w e c a n n o t h a v e
t o o
m u c h o f
s c i e n c e , d e s p i t e
i t s n u c l e a r
q u i r k s .
W i t h s c i e n c e ,
i d e a s c a n
g e r m i n a t e
w i t h i n
a
b e d o f
t h e o r y ,
f o r m
a n d
p r a c t i s e
t h a t
a s s i s t s t h e i r
g r o w t h .
B u t
w e ,
a s
g a r d e n e r s , m u s t
b e w a r e .
F o r
s o m e s e e d s a r e t h e
s e e d s
o f
R u i n , a n d t h e m o s t i r i d e s c e n t
b l o o m s a r e
o f t e n
t h e
m o s t
d a n g e r o u s .
"
' V ' ,
i n
" V f o r
V e n d e t t a "
b y A l a n M o o r e a n d D a v i d
L l o y d
1
A c k n o w l e d g e m e n t s
A C K N O W L E D G E M E N T S
T h e w o r k p r e s e n t e d
i n
t h i s
t h e s i s w a s c a r r i e d
o u t
i n
t h e
I n t e r d i s c i p l i n a r y
R e s e a r c h
C e n t r e
i n
S u p e r c o n d u c t i v i t y
( I R C ) ,
U n i v e r s i t y o f
C a m b r i d g e ,
a s p a r t o f
t h e
J c
g r o u p .
F i r s t l y , I w o u l d l i k e t o t h a n k
m y
s u p e r v i s o r
D r . A . M .
C a m p b e l l a n d
m y
A D R
D r .
D . A . C a r d w e l l f o r t h e i r
c o n t i n u i n g
a d v i c e a n d s u p p o r t
t h r o u g h o u t
t h e
c o u r s e
o f m y
w o r k . T h e y
h e l p e d
t o k e e p
m e
p o i n t i n g
i n
t h e
r i g h t
d i r e c t i o n a n d e x p l a i n
t h e
r e s u l t s I
o b t a i n e d .
A l s o i n
t h i s
v e i n
I a c k n o w l e d g e D r . S . P . A s h w o r t h a n d
D r . R . A . D o y l e
f o r
i n v a l u a b l e
a s s i s t a n c e
a n d d i s c u s s i o n s d u r i n g t h e c o u r s e m y e x p e r i m e n t s .
T h a n k s
a l s o
g o
t o D r . J . D .
J o h n s o n ,
D r .
D . - N .
Z h e n g a n d
M r
C . D .
D e w h u r s t
f o r
c a r r y i n g
o u t t h e
m a g n e t i c
m e a s u r e m e n t s
d e t a i l e d
i n c h a p t e r s
3 ,
5
a n d s e c t i o n 6 . 4 . 4
r e s p e c t i v e l y ,
D r . A . M .
C a m p b e l l
f o r
p e r f o r m i n g
t h e
t h e o r e t i c a l l o c a l f i e l d
c a l c u l a t i o n s u s e d
i n
s e c t i o n 3 . 4 . 5 a n d l i k e w i s e M r C . D .
D e w h u r s t
a n d M r P . D . H u n n y b a l l
f o r t h e
e l e c t r o n
m i c r o g r a p h s
p r e s e n t e d i n
c h a p t e r 4 .
A l l o f
t h e
w o r k d e t a i l e d i n t h i s t h e s i s c o u l d
n o t
h a v e b e e n c a r r i e d
o u t
w i t h o u t t h e
c o r r e c t
s a m p l e s .
T h e r e f o r e I m u s t a l s o
a c k n o w l e d g e
I . C . I . S u p e r c o n d u c t o r s ,
t h e H i t a c h i
C o r p o r a t i o n a n d D r . A . P .
B a k e r f o r
p r o v i d i n g
m e w i t h
t h e
s a m p l e s u s e d i n
c h a p t e r s
4 ,
5
a n d
6 o f
t h i s
t h e s i s
r e s p e c t i v e l y .
O n t h e t e c h n i c a l
s i d e ,
I
w o u l d
l i k e
t o
a c k n o w l e d g e
M r A . G .
L a w r e n c e ,
M r S .
S m i t h ,
M r S . W i l l i s a n d M r
P .
H u n n y b a l l f o r
t h e i r
h e l p
i n d e s i g n i n g
a n d b u i l d i n g
t h e
v a r i o u s p i e c e s
o f
a p p a r a t u s
u s e d
i n m y e x p e r i m e n t s ,
a n d
i n
t h e
p r e p a r a t i o n o f t h e
s a m p l e s
m e a s u r e d .
F i n a n c i a l l y ,
I
w o u l d
l i k e
t o t h a n k O x f o r d I n s t r u m e n t s
f o r
p r o v i d i n g m e w i t h a
C A S E
A w a r d d u r i n g t h e c o u r s e
o f m y P h . D . ,
a s
w e l l a s C h r i s t s
C o l l e g e
a n d
t h e I R C f o r
p r o v i d i n g
m e w i t h t h e f i n a n c i a l
s u p p o r t
w h i c h a l l o w e d m e
t o
c o n t i n u e
w r i t i n g a f t e r I
o v e r - r a n .
I w o u l d l i k e
t o t h a n k D r . R . A . D o y l e ,
D r . J . D .
J o h n s o n ,
D r .
S . P .
A s h w o r t h
a n d
D r .
D . A . C a r d w e l l
a s e c o n d t i m e f o r t h e i r
p a t i e n c e a n d t o l e r a n c e i n
r e a d i n g t h e
v a r i o u s
i i
Acknowledgements
drafts of the chapters of this thesis and for providing a great deal of helpful advice and
comments on how they might be improved.
My friends in the Cambridge University Role-Playing Society past and present,
too numerous to name individually, also deserve a mention for keeping me sane during
the course of this thesis. A special mention goes to Iain Walker for providing me with
incentive by showing what happens if you overrun for too long.
Lastly, I would like to thank my parents, Allan and Ruth, for their continued
support over the total of six years of student life I have had.
I hereby declare that this thesis is the result of my own original work and contains
nothing that is the result of collaboration except for the magnetic measurements carried
out in chapter 3, chapter 5 and section 6.4.4 which were carried out by Dr. J.D. Johnson,
Dr. D.-N. Zheng and Mr C.D. Dewhurst respectively. The work included in this thesis
has not been previously submitted in part or whole to any university for any degree,
diploma or other qualification. Some of the work contained in this thesis has been
published or submitted for publication. A list of these papers is contained in the
Appendix. The length of this thesis is within the word limit set by the Physics and
Chemistry Degree Committee.
Anthony R. Jones
March 1995
iii
S u m m a r y
S U M M A R Y
O F
P H . D .
D I S S E R T A T I O N
T h e w o r k d e s c r i b e d i n t h i s
t h e s i s c o n s i s t s
o f a n i n v e s t i g a t i o n
i n t o t h e
b e h a v i o u r o f
t h e c r i t i c a l c u r r e n t
d e n s i t y
(
J c
)
o f s e v e r a l d i f f e r e n t
h i g h
t e m p e r a t u r e
s u p e r c o n d u c t o r s
( H T S C s )
a s
a f u n c t i o n o f t e m p e r a t u r e a n d
a p p l i e d
m a g n e t i c
f i e l d .
T h e
f o c u s o f
t h i s
r e s e a r c h h a s
b e e n t o i n v e s t i g a t e t h e d i s c r e p a n c i e s w h i c h
g e n e r a l l y
e x i s t
b e t w e e n
m a g n e t i c
a n d
t r a n s p o r t m e a s u r e m e n t s
o n
H T S C s . I n
o r d e r t o
d o
t h i s
a
n u m b e r
o f
s y s t e m s
w e r e
s e l e c t e d
w i t h d i f f e r e n t w e a k
l i n k
s t r e n g t h s , o v e r a l l
a l i g n m e n t
a n d
p i n n i n g
c h a r a c t e r i s t i c s .
S y s t e m a t i c
s t u d i e s w e r e c a r r i e d o u t o n
t h e s e
s y s t e m s
u s i n g
b o t h
t r a n s p o r t
a n d
m a g n e t i c
t e c h n i q u e s .
T h e
r e s u l t s o b t a i n e d w e r e c o m p a r e d
t o o b t a i n
a c o h e r e n t
p i c t u r e o f t h e r e l a t i o n b e t w e e n c r i t i c a l c u r r e n t s
i n
H T S C s ,
t h e i r
g r a n u l a r i t y
a n d
s t r u c t u r e ,
a n d h o w t h i s a c c o u n t s f o r t h e
d i f f e r e n c e s i n
m a g n e t i c a n d
t r a n s p o r t
m e a s u r e m e n t s .
T h e
J c
o f g r a n u l a r b u l k
s i n t e r e d Y B C O w a s m e a s u r e d a s a
f u n c t i o n
o f
m a g n e t i c
f i e l d a n d
o r i e n t a t i o n ,
a n d
a t t e m p t s m a d e t o f i t t h e r e s u l t s o b t a i n e d
t o t h e o r y .
T h e
r e s u l t s
o b t a i n e d i n d i c a t e t h a t
h y s t e r e s i s
o f
J c
w i t h f i e l d
c a n n o t
b e
e x p l a i n e d
b y f l u x
t r a p p i n g
a l o n e .
J c
m e a s u r e m e n t s w e r e c a r r i e d
o u t o n
t h e
' h u b - a n d - s p o k e 1 ( H - S )
g r a i n s
o f
m e l t - p r o c e s s e d
Y B C O t h i c k
f i l m s .
T h e s e
i n d i c a t e d t h a t w i t h i n e a c h
H - S g r a i n
t h e c u r r e n t
i s
c o n s t r a i n e d t o r a d i a l p a t h s
t h r o u g h t h e c e n t r e
o f
t h e g r a i n .
T h i s h a s m a j o r
i m p l i c a t i o n s
;
;
M
f o r t h e a n a l y s i s
o f
a n y
m e a s u r e m e n t s c a r r i e d o u t o n t h e s e
s a m p l e s , a s w e l l
a s
f o r
a p p l i c a t i o n s , a s o n l y a s m a l l
f r a c t i o n o f t h e
s a m p l e
c a r r i e s t h e
a p p l i e d
c u r r e n t .
S i l v e r - c l a d
t a p e s o f T l : 1 2 2 3 a n d T l : 2 2 2 3 w e r e m e a s u r e d
i n d i f f e r e n t
t e m p e r a t u r e s ,
a p p l i e d m a g n e t i c f i e l d s a n d
o r i e n t a t i o n s . T h e v a r i a t i o n o f
J c
a l o n g
t h e
t a p e l e n g t h w a s
a l s o m e a s u r e d t o
p r o v i d e
a n
e s t i m a t e o f t h e i r h o m o g e n e i t y . I t
w a s f o u n d t h a t
t h e
p r o c e s s i n g r o u t e
u s e d
i n
t h e
p r o d u c t i o n o f t h e s e t a p e s h a d n o t a l i g n e d
t h e
s u p e r c o n d u c t o r
w i t h i n
t h e m ,
a n d
a l s o
t h a t
t h e
t a p e
p r o p e r t i e s w e r e n o t h o m o g e n o u s
a l o n g
t h e i r l e n g t h .
T h i s
p r o b a b l y
a r i s e s
f r o m t h e c r y s t a l
s t r u c t u r e
o f
t h e t h a l l i u m
m a t e r i a l s .
T h e
J c
s
o f
m e l t - p r o c e s s e d t h i c k f i l m s o f B i : 2 2 1 2 o n
s i l v e r
s u b s t r a t e s
w e r e
m e a s u r e d a s a f u n c t i o n o f t e m p e r a t u r e
a n d
a p p l i e d
m a g n e t i c
f i e l d ,
a n d
c o m p a r e d
w i t h
r e s u l t s
o b t a i n e d f r o m m a g n e t i c
m e a s u r e m e n t s o b t a i n e d f r o m a V S M .
A t t e m p t s
w e r e
m a d e t o f i t t h e s e
r e s u l t s
t o t h e o r y . T h e
r e s u l t s
o b t a i n e d s h o w c l e a r s c a l i n g
b e h a v i o u r o f
J c
w i t h
T a t
c o n s t a n t
B a n d i m p l y t h a t
t h e v a r i a t i o n i n
t h e
f o r m o f t h e
J c
v e r s u s T c u r v e s
i s
d u e
s i m p l y t o t h e
s u p p r e s s i o n o f
T c
w i t h i n c r e a s i n g
a p p l i e d f i e l d .
I V
C o n t e n t s
C O N T E N T S
1 S U P E R C O N D U C T I V I T Y
1
1 . 1 I N T R O D U C T I O N
1
1 . 1 . 1
O r g a n i s a t i o n
o f t h i s T h e s i s
1
1 . 2 S U P E R C O N D U C T I V I T Y I N D I F F E R E N T
S Y S T E M S
3
1 . 3
D E V E L O P M E N T
O F
T H E
T H E O R Y
O F S U P E R C O N D U C T I V I T Y
3
1 . 4
B E H A V I O U R
O F
S U P E R C O N D U C T O R S
I N
M A G N E T I C
F I E L D S
7
1 . 4 . 1
T y p e
I
S u p e r c o n d u c t o r s
8
1 . 4 . 2 T y p e I I S u p e r c o n d u c t o r s
8
1
. 5 T H E B E H A V I O U R O F F L U X I N
A T Y P E I I
S U P E R C O N D
U C T O R
1 2
1 . 5 . 1 F l u x P i n n i n g
1 2
1 . 5 . 2 I n t e r a c t i o n o f
F l u x L i n e s , P i n n i n g
C e n t r e s a n d A p p l i e d
C u r r e n t s
1 2
1
. 6
T H E
C R I T I C A L S T A T E
M O D E L
1
3
1 . 6 . 1 M a g n e t i s a t i o n
1 6
1 . 7
T H E R M A L
E F F E C T S O N
F L U X
L I N E S
1 8
1 . 7 . 1 F l u x
C r e e p
2 0
1 . 7 . 2 T h e r m a l l y A s s i s t e d F l u x F l o w
( T A F F )
2 0
1 . 7 . 3
T h e r m a l D e p i n n i n g a n d t h e I r r e v e r s i b i l i t y L i n e
2 0
1 . 8
T H E F A M I L I E S
O F
H I G H
T C
S U P E R C O N D U C T I N G O X I D E S
2 1
1 . 8 . 1 T h e
L a - S r - C u - 0 S y s t e m
2 2
1 . 8 . 2
T h e
Y - B a - C u - 0 S y s t e m
2 2
1 . 8 . 3 T h e
B i - S r - C a - C u - 0
S y s t e m
2 4
1 . 8 . 4 T h e T l - B a - C a - C u - 0 S y s t e m
2 4
1 . 8 . 5
O t h e r
H i g h - T c S y s t e m s 2 5
1 . 9 T H E M I C R O S C O P I C T H E O R Y O F
H I G H - T C
S U P E R C O N D U C T I V I T Y
2 7
1 . 1 0
T H E
E F F E C T S O F A N I S O T R O P Y
2 8
l . l l
G R A N U L A R
S U P E R C O N D U C T O R S
3 0
1 . 1 1 . 1 T h e
J
o s e p h s o n
E f f e c t
3
1
1 . 1 1 . 2 G r a n u l a r
S u p e r c o n d u c t o r s
i n
G e n e r a l
3 4
1
. 1 1 . 3
G r a n u l a r i t y i n H i g h
T c
S u p e r c o n d u c t o r s
3 4
v
Contents
1.12 REFERENCES 39
EXPERIMENTAL TECHNIQUES 47
2.1 INTRODUCTION 47
2.2 RESISTANCE MEASUREMENTS 48
2.3 TRANSPORT Jc MEASUREMENTS 51
2.3.1 Major Considerations 51
2.3.2 D.C. Measurements 64
2.3.3 Pulsed Measurements 66
2.4 MAGNETIC MEASUREMENTS 72
2.4.1 D.C. Magnetic Measurements 73
2.4.2 A.C. Inductive Measurements 78
2.5 REFERENCES 81
MEASUREMENTS OF HYSTERESIS OF JC IN SINTERED YBCO 85
3.1 INTRODUCTION 85
3.2 EXPERIMENTAL TECHNIQUE 91
3.2.1 Sample Preparation 91
3.2.2 Transport Measurements 92
3.2.3 Magnetic Measurements 93
3.3 RESULTS 94
3.3.1 Transport Measurements 94
3.3.2 Magnetic Measurements 95
3.4 DISCUSSION 96
3.4.1 Self-Field Effects 96
3.4.2 Amount of Hysteresis 96
3.4.3 Demagnetising Factor 97
3.4.4 Further Investigation 99
3.4.5 Fitting Results to Theory 105
3.5 CONCLUSIONS 106
3.6 REFERENCES 107
vi
C o n t e n t s
4
C R I T I C A L C U R R E N T S
I N
M E L T
P R O C E S S E D Y B C O T H I C K
F I L M S
1 0 9
4 . 1 I N T R O D U C T I O N
1 0 9
4 . 1 . 1
S a m p l e P r e p a r a t i o n
1 1 0
4 . 1 . 2
T h e
H u b - a n d - S p o k e
G r a i n
S t r u c t u r e
1 1 0
4 . 2 E X P E R I M E N T A L
T E C H N I Q U E
1 1 2
4 . 2 . 1 T r a n s p o r t M e a s u r e m e n t s
1 1 2
4 . 2 . 2 M a g n e t i c
M e a s u r e m e n t s
1 1 6
4 . 2 . 3
M i c r o s t r u c t u r a l O b s e r v a t i o n s
1 1 7
4 . 3 R E S U L T S A N D D I S C U S S I O N
1 1 7
4 . 3 . 1
T r a n s p o r t M e a s u r e m e n t s
1 1 7
4 . 3 . 2 M a g n e t i c
M e a s u r e m e n t s
1 2 4
4 . 3 . 3
E l e c t r o n M i c r o s c o p y
1 2 6
4 . 3 . 4
C o m p a r i s o n
o f
T r a n s p o r t a n d M a g n e t i c
M e a s u r e m e n t s
1 2 9
4 . 3 . 5 C o r r e l a t i o n
o f
R e s u l t s
a n d
M i c r o s t r u c t u r e
-
H u b a n d
S p o k e M o d e l
1 2 9
4 . 3 . 6 T e s t i n g t h e H u b a n d S p o k e
M o d e l
1 3 0
4 . 3 . 7 I m p l i c a t i o n s o f t h e H u b a n d S p o k e M o d e l
1 3 2
4 . 4
C O N C L U S I O N S
1 3 5
4 . 5 R E F E R E N C E S
1 3 5
5 M E A S U R E M E N T S O N
T H A L L I U M - B A S E D
S U P E R C O N D U C T I N G T A P E S
1 3 8
5 . 1 I N T R O D U C T I O N
1 3 8
5 . 1 . 1
T a p e
F a b r i c a t i o n
1 3 9
5 . 2 E X P E R I M E N T A L
T E C H N I Q U E
1 4 0
5 . 2 . 1 T r a n s p o r t M e a s u r e m e n t s
1 4 0
5 . 2 . 2 M a g n e t i c
M e a s u r e m e n t s
1 4 1
5 . 3
R E S U L T S
A N D
D I S C U S S I O N
1 4 2
5 . 3 . 1 L o w F i e l d
T r a n s p o r t
M e a s u r e m e n t s
1 4 2
5 . 3 . 2 M e a s u r e m e n t s o n L o n g
T a p e s i n Z e r o
F i e l d
1 4 3
5 . 3 . 3
M e a s u r e m e n t s o n
L o n g
T a p e s i n
M a g n e t i c
F i e l d s
1 4 5
5 . 3 . 4 H i g h F i e l d T r a n s p o r t
M e a s u r e m e n t s
1 4 7
5 . 3 . 5 M a g n e t i c
M e a s u r e m e n t s
1 5 1
5 . 3 . 6 C o m p a r i s o n o f T r a n s p o r t a n d
M a g n e t i c
R e s u l t s
1 5 4
5 . 4 C O N C L U S I O N S
1 5 5
v i i
Contents
5.5 REFERENCES 155
6 MEASUREMENTS ON BSCCO THICK FILMS 158
6.1 INTRODUCTION 158
6.1.1 Sample Preparation and Processing 159
6.2 EXPERIMENTAL TECHNIQUE 159
6.2.1 Transport Measurements 159
6.2.2 Magnetic Measurements 161
6.3 RESULTS 162
6.3.1 Initial Sample Characterisation 162
6.3.2 Transport Measurements 165
6.3.3 Magnetic Measurements 173
6.4 DISCUSSION 111
6.4.1 Transport Measurements 111
6.4.2 VSM Measurements 183
6.4.3 Comparison of Transport and Magnetic Measurements 184
6.4.4 Comparison of Results with Single Crystal Data 191
6.5 CONCLUSIONS 192
6.6 REFERENCES 193
7 OVERALL CONCLUSIONS AND FUTURE WORK 195
7.1 CONCLUSIONS 195
7.2 FUTURE WORK 197
APPENDIX 198
viii
C h a p t e r
1
: S u p e r c o n d u c t i v i t y
C H A P T E R 1 : S U P E R C O N D U C T I V I T Y
1 . 1 I N T R O D U C T I O N
I n
1 9 1 1 ,
t h r e e
y e a r s
a f t e r f i r s t
l i q u e f y i n g
h e l i u m ,
K a m e r l i n g h
O n n e s
u n e x p e c t e d l y
f o u n d w h i l e i n v e s t i g a t i n g t h e r e s i s t i v i t y
o f
m e r c u r y
a t l o w t e m p e r a t u r e s
t h a t a t
~ 4 . 2 K t h e
r e s i s t i v i t y
o f
h i s
s a m p l e
s u d d e n l y
d r o p p e d
d r a m a t i c a l l y
[ 1 . 1 ] .
F u r t h e r
i n v e s t i g a t i o n
s h o w e d t h a t
t h e r e s i s t a n c e h a d a c t u a l l y
d r o p p e d
t o
z e r o a n d n o t
j u s t
t o a
v e r y
l o w v a l u e .
T h i s m a r k e d t h e f i r s t
o b s e r v a t i o n o f s u p e r c o n d u c t i v i t y i n a
m a t e r i a l
w h i c h
h a d
b e e n
c o o l e d t o b e l o w
a
c e r t a i n
t e m p e r a t u r e , i t s t r a n s i t i o n t e m p e r a t u r e
(
T c
) .
W i t h i n
s e v e r a l
y e a r s
s u p e r c o n d u c t i v i t y w a s f o u n d i n a l a r g e n u m b e r
o f m e t a l s . T h e
a b r u p t n e s s
o f
t h e
d r o p t o z e r o
r e s i s t a n c e a t
T c
s u g g e s t e d t h a t t h e t r a n s i t i o n t o t h e
s u p e r c o n d u c t i n g
s t a t e
w a s
i n f a c t a
p h a s e
t r a n s i t i o n ,
a n d t h i s w a s l a t e r c o n f i r m e d
b y
m e a s u r e m e n t s
o f
s p e c i f i c
h e a t .
I t w a s i n i t i a l l y
h o p e d t h a t s u p e r c o n d u c t o r s w o u l d
a l l o w t h e
c o n s t r u c t i o n
o f
l o w - p o w e r
h i g h - f i e l d
m a g n e t s .
H o w e v e r ,
i t
w a s s o o n d i s c o v e r e d t h a t
s u p e r c o n d u c t o r s
h a v e
a
c r i t i c a l c u r r e n t
( / c )
a n d a
c r i t i c a l m a g n e t i c f i e l d ( H c )
a b o v e w h i c h
t h e y r e v e r t
t o
t h e n o r m a l
s t a t e . I n e l e m e n t a l
s u p e r c o n d u c t o r s t h e s e p a r a m e t e r s a r e
t o o l o w t o
a l l o w t h e i r
u s e
i n
h i g h c u r r e n t
o r
h i g h
f i e l d a p p l i c a t i o n s .
1 . 1 . 1
O R G A N I S A T I O N O F T H I S
T H E S I S
T h e
w o r k d e s c r i b e d i n t h i s t h e s i s
c o n s i s t s
o f a n i n v e s t i g a t i o n i n t o
t h e
b e h a v i o u r o f
t h e c r i t i c a l c u r r e n t d e n s i t y o f
s e v e r a l
d i f f e r e n t
H T S C s
u n d e r
t h e i n f l u e n c e
o f
m a g n e t i c
f i e l d s .
T h e f o c u s o f t h i s r e s e a r c h
h a s b e e n t o
i n v e s t i g a t e
t h e d i s c r e p a n c i e s w h i c h
g e n e r a l l y
e x i s t b e t w e e n
m a g n e t i c
a n d
t r a n s p o r t m e a s u r e m e n t s
o n
H T S C s .
I n
o r d e r
t o
d o
t h i s a n u m b e r o f s y s t e m s
w e r e
s e l e c t e d w i t h
d i f f e r e n t w e a k
l i n k
s t r e n g t h s , o v e r a l l
a l i g n m e n t a n d
p i n n i n g c h a r a c t e r i s t i c s .
S y s t e m a t i c
s t u d i e s
w e r e
c a r r i e d
o u t o n t h e s e
s y s t e m s
u s i n g b o t h t r a n s p o r t a n d m a g n e t i c
t e c h n i q u e s .
T h e
r e s u l t s o b t a i n e d w e r e
c o m p a r e d t o o b t a i n a c o h e r e n t p i c t u r e o f t h e r e l a t i o n b e t w e e n c r i t i c a l c u r r e n t s
i n
H T S C s ,
t h e i r
g r a n u l a r i t y a n d
s t r u c t u r e ,
a n d
h o w t h i s a c c o u n t s
f o r t h e
d i f f e r e n c e s i n m a g n e t i c a n d
t r a n s p o r t m e a s u r e m e n t s .
T h i s c h a p t e r
b r i e f l y
r e v i e w s
t h e
t y p e s
o f m a t e r i a l s i n w h i c h
s u p e r c o n d u c t i v i t y
o c c u r s t h e n g i v e s a n
o v e r v i e w o f t h e
d e v e l o p m e n t o f
t h e t h e o r y
o f
s u p e r c o n d u c t i v i t y i n
l o w
t e m p e r a t u r e
s u p e r c o n d u c t o r s
( L T S C ) ,
c u l m i n a t i n g i n
t h e
B C S t h e o r y
o f 1 9 5 7 .
N e x t ,
1
Chapter 1 : Superconductivity
the distinction between type I and II superconductors is made by considering their
behaviour in magnetic fields. The factors controlling the distribution of flux in a
superconductor are then considered, followed by a discussion of the critical state model
and details of the behaviour of flux in a type II superconductor in different field and
temperature regimes. Once this is done, the various families of high-Tc oxide
superconductors (HTSC) are listed. The theory of high-Tc superconductivity is then
briefly discussed, followed by the effects of anisotropy in superconductors, particularly
HTSCs. The chapter then delves more deeply into granular superconductivity. First,
Josephson effects are outlined for their relevance to granular superconductors, before
moving on to consideration of superconductivity in granular materials in general then in
granular HTSCs.
Chapter 2 describes the experimental techniques common to the majority of
measurements performed on the materials investigated in the course of this thesis. These
include resistance versus temperature measurements, D.C. and pulsed transport critical
current measurements (as a function of field and temperature) along with relevant
considerations for these measurements, magnetisation measurements and A.C.
susceptibility measurements.
Chapter 3 consists of measurements of the hysteresis of transport critical current
carried out on samples of bulk sintered YBa2Cu307_g (YBCO) with low critical current
density (Jc). These were done as a function of temperature, magnetic field and orientation
with respect to magnetic field to determine the mechanism which controls the hysteresis
of Jc in a system of randomly oriented 'weak' weak links.
Chapter 4 describes transport and magnetic measurements carried out on thick
films of YBCO laid down on yttria-stabilised zirconia substrates to determine the
systematics of current flow within them. These samples formed a partially aligned system
of 'strong' weak links due to their melt processing.
Chapter 5 shows results obtained from transport and magnetic measurements on
silver and gold-palladium clad tapes of TlSr2Ca2Cu30s (Tl:1223) and Tl2Sr2Ca2Cu30s
(Tl:2223) superconductors as a function of applied field, temperature and orientation.
This system forms an array of weak links which have been partially textured by the tape
production process.
Chapter 6 includes results from transport and magnetic measurements on
Bi2Sr2CaCu208+5 (Bi:2212) thick films laid down on silver substrates as a function of
field and temperature. Because of the production technique used these samples form a
system of 'strong' and textured weak links.
2
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
T h e
o v e r a l l
c o n c l u s i o n s
o f t h i s t h e s i s
a r e p r e s e n t e d
i n
c h a p t e r
7 .
1 . 2 S U P E R C O N D U C T I V I T Y I N M E T A L S ,
A L L O Y S
A N D
C O M P O U N D S
O v e r
t h e
y e a r s t h e n u m b e r o f m a t e r i a l s
i n
w h i c h
s u p e r c o n d u c t i v i t y
o c c u r r e d
e x p a n d e d g r e a t l y . I n
a d d i t i o n
t o p u r e
m e t a l s ,
s u p e r c o n d u c t i v i t y
w a s
d i s c o v e r e d
i n a l l o y s ,
o x i d e s ,
o r g a n i c c o m p o u n d s ,
C g o
f u l l e r e n e c o m p o u n d s
a n d
h e a v y - f e r m i o n
i n t e r m e t a l l i c
s y s t e m s .
A l s o ,
a s
t i m e
p a s s e d , t h e
h i g h e s t
k n o w n
T c
r o s e .
B y
1 9 7 3
t h e
m a t e r i a l w i t h
t h e
h i g h e s t
T c
k n o w n
w a s
N t g G e ,
w i t h
a
T c
o f
a p p r o x i m a t e l y
2 3 . 2 K .
F o l l o w i n g
t h e
d i s c o v e r y o f
N b 3 G e , t h e
h i g h e s t
k n o w n
T c
d i d
n o t
c h a n g e
u n t i l
1 9 8 6 . T a b l e 1 . 1
s h o w s t h e
m a x i m u m
T c s
f o r t h e d i f f e r e n t
c l a s s e s o f s u p e r c o n d u c t o r a t t h e
t i m e o f
w r i t i n g .
C l a s s
o f S u p e r c o n d u c t o r
C u r r e n t
M a x i m u m
T c
( K )
P u r e M e t a l
- 9
A l l o y
~ 2 3
O x i d e
- 1 6 4
( u n d e r
p r e s s u r e )
O r g a n i c C o m p o u n d
- 1 3
C 6 0
F u l l e r e n e C o m p o u n d
- 4 0
H e a v y - F e r m i o n
I n t e r m e t a l l i c
S y s t e m
- 1 . 5
T a b l e 1 . 1 :
M a x i m u m
T 0 s
o f
t h e
d i f f e r e n t
c l a s s e s
o f
s u p e r c o n d u c t o r .
I n
1 9 8 6 ,
B e d n o r z
a n d M u l l e r w e r e
i n v e s t i g a t i n g
s u p e r c o n d u c t i v i t y
i n
t h e
p e r o v s k i t e f a m i l y o f
o x i d e s .
T h e y
d i s c o v e r e d t h a t a
c o m p o u n d
i n
t h e
B a - L a - C u - 0
s y s t e m ,
L a i . 8 5 B a o . i 5 C u 0 4 - y ,
b e c a m e s u p e r c o n d u c t i n g a t 3 5 K
[ 1 . 2 ] .
S i n c e
t h e n ,
a n u m b e r
o f
f a m i l i e s
o f h i g h - T c
o x i d e
s u p e r c o n d u c t o r s
h a v e b e e n d i s c o v e r e d ,
b a s e d o n
t h e
Y - B a - C u - O ,
B i - S r - C a - C u - O ,
T l - B a - C a - C u - 0 a n d H g - B a - C a - C u - 0
s y s t e m s .
T h e
m a x i m u m k n o w n
T c
h a s r i s e n
d r a m a t i c a l l y
f r o m 3 5 K t o m o r e t h a n
1 6 0 K . F i g u r e 1 . 1
s h o w s
a
p l o t
o f t h e m a x i m u m
T c
a g a i n s t
t i m e f o r s e v e r a l
f a m i l i e s o f s u p e r c o n d u c t o r s .
1 . 3 D E V E L O P M E N T
O F
T H E
T H E O R Y O F
S U P E R C O N D U C T I V I T Y
I n i t i a l l y ,
s u p e r c o n d u c t i v i t y w a s t h o u g h t t o
b e o n l y a s t a t e
o f i n f i n i t e
c o n d u c t i v i t y .
T h e
f i r s t a t t e m p t s
t o
e x p l a i n
i t
u s e d M a x w e l l s e q u a t i o n s
i n t h e
l i m i t o f
i n f i n i t e
c o n d u c t i v i t y
a n d f o c u s e d o n t r y i n g
t o
e l u c i d a t e w h y t h e
e l e c t r o n s
i n
t h e
s u p e r c u r r e n t
d i d
n o t
s c a t t e r a s t h e y d i d i n t h e
n o r m a l s t a t e .
H o w e v e r ,
i n
1 9 3 3
M e i s s n e r a n d O c h s e n f e l d
d i s c o v e r e d t h a t
i f a
s u p e r c o n d u c t o r
w a s c o o l e d
t o b e l o w
T c
i n
a
l o w
m a g n e t i c f i e l d
i t
w o u l d
e x p e l a l l m a g n e t i c
f l u x
f r o m w i t h i n i t
[ 1 . 3 ] .
T h i s p e r f e c t d i a m a g n e t i s m
a l l o w e d
3
Chapter 1 : Superconductivity
them to show that a superconductor does not merely possess infinite conductivity, which
would tend to trap flux if cooled in a magnetic field, but is a completely new state with
unique magnetic properties. This discovery of what became known as the Meissner effect
shifted the focus of investigation to the nature of the phase transition of the electrons
within the material which leads to superconductivity.
Figure 1.1 : Maximum Tc versus time for a number of families of superconductor.
The reversibility of the superconducting transition as the applied magnetic field is
cycled indicated that the onset of superconductivity is thermodynamically related to the
free energy difference between the normal and superconducting states. It occurs when the
free energy of the superconducting state at a given temperature is less than the free
energy of the normal state at the same temperature [1,4]. This observation explains the
existence of both a critical temperature and a critical field in superconductors. The critical
temperature is the point where the free energy of the superconducting state becomes less
than that of the normal state, and the critical field is that at which the magnetic energy
overcomes the free energy difference between the normal and superconducting states.
In 1934 Gorter and Kasimir [1.5-7] showed that several properties of
superconductors could be accounted for by a 'two-fluid' model. This considered a
superconductor to be a mixture of two fluids, one superconducting and one normal. The
superconducting fluid is a Bose condensate which possesses greater order than the normal
4
C h a p t e r
1 :
S u p e r c o n d u c t i v i t y
f l u i d ,
a n d
i s i d e n t i f i e d
w i t h
t h e d e n s i t y o f
s u p e r c o n d u c t i n g
e l e c t r o n s
n s .
F r o m
t h e
f a c t
t h a t
t h e
s u p e r e l e c t r o n s
a r e c o n d e n s e d
i n t o t h e l o w e s t e n e r g y
s t a t e
t h e y
s h o w e d
t h a t
t h e
s u p e r e l e c t r o n s a r e n o t d i s o r d e r e d a n d t h u s
a
s u p e r c u r r e n t c a r r i e s n o
e n t r o p y [ 1 . 8 ] .
I n 1 9 3 5
F .
L o n d o n
a n d
H . L o n d o n
a p p l i e d
M a x w e l l s
e q u a t i o n s
t o
s u p e r c o n d u c t o r s .
T h e y u s e d t h e a s s u m p t i o n s t h a t
n s ,
t h e
d e n s i t y o f
s u p e r c o n d u c t i n g
e l e c t r o n s ,
w a s z e r o a t
T c
a n d
e q u a l
t o t h e
t o t a l n u m b e r o f
e l e c t r o n s
i n
t h e
s y s t e m
a t
7 = 0 ,
a n d a p p l i e d
t h e m
t o N e w t o n s s e c o n d l a w . T h i s
a l l o w e d t h e m t o
r e l a t e t h e
s u p e r c u r r e n t
d e n s i t y
t o
t h e m a g n e t i c
f i e l d a n d s h o w t h a t f o r a s t e a d y
s u p e r c u r r e n t n o e l e c t r i c
f i e l d
i s
r e q u i r e d .
F r o m t h i s t h e y
d e r i v e d
t h e
M e i s s n e r e f f e c t
m a t h e m a t i c a l l y
[ 1 . 9 ] .
T h e y
a l s o
s h o w e d t h a t i n a s u p e r c o n d u c t o r i n t h e M e i s s n e r s t a t e t h e
c u r r e n t s w h i c h
s h i e l d
t h e
i n t e r i o r f r o m a n
a p p l i e d f i e l d f l o w i n a s u r f a c e l a y e r o f a v e r a g e
t h i c k n e s s g i v e n b y
a
p e n e t r a t i o n d e p t h
A ,
d e t e r m i n e d b y t h e
d e n s i t y
o f
s u p e r c o n d u c t i n g
e l e c t r o n s
n s .
F .
L o n d o n
l a t e r
s u g g e s t e d t h a t s u p e r c o n d u c t i v i t y i s a
q u a n t u m
p h e n o m e n o n
a s s o c i a t e d
w i t h t h e r i g i d i t y o f
t h e w a v e f u n c t i o n d e s c r i b i n g t h e
r e s p o n s e o f
t h e s u p e r c o n d u c t o r
t o
c h a n g e s i n
t h e
m o m e n t u m o f
e l e c t r o n s i n
a
m a g n e t i c f i e l d .
H e
e m p h a s i s e d t h a t t h i s
r i g i d i t y c o u l d
a r i s e f r o m a l o n g - r a n g e
o r d e r i n
t h e
m o m e n t u m
d i s t r i b u t i o n
o f
t h e
e l e c t r o n s
[ 1 . 1 0 ] ,
I n 1 9 5 3
P i p p a r d
[ 1 . 1 1 ]
f o u n d t h a t
A
i n c r e a s e s
a s i m p u r i t i e s
a r e
a d d e d ,
i . e . a s t h e
s c a t t e r i n g
m e a n f r e e
p a t h
o f
t h e n o r m a l e l e c t r o n s d e c r e a s e s . H e
p r o p o s e d t h a t
t h i s c o u l d
b e
e x p l a i n e d
b y
c o n s i d e r i n g a m o d i f i c a t i o n o f
t h e L o n d o n
t h e o r y w h e r e t h e
s u p e r c o n d u c t i n g
c a r r i e r s
w e r e
e n t i t i e s e x t e n d e d o v e r a
d i s t a n c e d e t e r m i n e d b y a
c o h e r e n c e
l e n g t h ,
£ ,
w h i c h
a l s o d e t e r m i n e s
t h e
r a t e a t w h i c h
n s
c a n
v a r y
i n s p a c e .
T h i s
c o h e r e n c e
l e n g t h
i s g i v e n b y
r ÿ t f + r 1
( U )
w h e r e l i s t h e e l e c t r o n m e a n
f r e e p a t h a n d
£ o
i s t h e c o h e r e n c e d i s t a n c e
i n
t h e
p u r e
m e t a l .
T h i s g i v e s r i s e t o
t h e
c o n c e p t
o f ' c l e a n '
a n d ' d i r t y '
s u p e r c o n d u c t o r s , w h e r e
a ' c l e a n '
m a t e r i a l i s c l o s e t o a p u r e
m e t a l
s o
£ ,
=
a n d a ' d i r t y ' m a t e r i a l
h a s a s h o r t m e a n f r e e p a t h
g i v i n g
E ,
—
>
0 .
A t
a l m o s t t h e s a m e
t i m e ,
G i n z b u r g a n d L a n d a u
[ 1 . 1 2 ]
p r o p o s e d a d i f f e r e n t
m o d i f i c a t i o n o f t h e L o n d o n
t h e o r y t o e x p l a i n
t h e e n e r g y
d i f f e r e n c e s a r i s i n g f r o m
t h e
m a c r o s c o p i c p e n e t r a t i o n o f f l u x i n t o e l e m e n t a l s u p e r c o n d u c t o r s w i t h
n o n - z e r o
d e m a g n e t i s i n g
f a c t o r s
( t h e
i n t e r m e d i a t e
s t a t e ) .
I n t h e s e
m a t e r i a l s ,
a t t h e
b o u n d a r y
b e t w e e n
t h e
n o r m a l a n d s u p e r c o n d u c t i n g
d o m a i n s ,
n s
c h a n g e s
f r o m
z e r o
t o
i t s
e q u i l i b r i u m
v a l u e o v e r
a
d i s t a n c e d e t e r m i n e d
b y E ,
a n d A .
I n o r d e r
t o a c h i e v e t h i s
t h e y
d e v i s e d
a
p h e n o m e n o l o g i c a l
t h e o r y t o d e s c r i b e
c h a n g e s
o f
n / r )
i n s p a c e .
T h e y p r o p o s e d
5
Chapter 1 : Superconductivity
that superconductivity is a macroscopic quantum state described by an order parameter, a
complex function with amplitude and phase which vanished at Tc, given by
'F(r) = |4/(r)| eif’(r) (1.2)
This gives expressions for the density and velocity of the superconducting
electrons and lead to the concept of flux quantisation, which arises from the condition
that xF(r) must be single-valued. The flux quantum has a value equal to
d>0 = h / q = 2.07 X 10~15 Wb (where q is the charge on the superconducting carriers).
In 1950 it was discovered that the Tc of a superconductor depends on its isotopic
mass [1.13, 14]. This led to the suggestion by Frohlich [1.15] that superconductivity
arises from interactions between electrons and vibrations of the crystal lattice (phonons).
However, superconductivity could not be explained by considering the change in energy
of individual electrons by interaction with phonons [1.16], though Bardeen and Pines
[1.17] found that the electron-phonon interaction could lead to an attractive interaction
between electrons.
In 1957 Bardeen, Cooper and Schrieffer proposed what has since become known
as the BCS theory [1.18, 19]. This is based on the pairing of electrons in a
superconducting ground state, with pairing occurring so as to take advantage of the
attractive interaction between electrons arising from the electron-phonon interaction with
the crystal lattice. These coupled electrons are known as Cooper pairs. They are Bosons
in which the electrons each have opposite spin and the centre-of-mass momentum is zero.
The Cooper pairs form a Bose condensate in their lowest possible energy state, which
allows them to move through the superconductor without being scattered. A review of the
BCS and related theories by Bardeen is given in [1.8].
The BCS theory indicates that a temperature dependent energy gap A(T) appears
at the Fermi surface in a superconductor, in agreement with heat capacity and thermal
conductivity experiments, for example those of Meservey and Schwarz [1.20]. This
energy gap successfully accounts for many of the properties of LTSCs, for example
persistent currents, the Meissner effect, the isotope effect and the second order phase
transition at the onset of superconductivity.
A property of superconductors which derives from their having a coherent
superconducting wave function is what is known as the proximity effect. This arises from
the concept of the smooth, rather than abrupt, change in the density of supercurrent
carriers ns over the range of the coherence length E, at the interface between a
superconductor and a normal metal, insulator, or different superconductor [1.11]. This
was first described by Meissner in 1958 [1.21], It leads to the suppression of the
6
C h a p t e r
1 :
S u p e r c o n d u c t i v i t y
s u p e r c o n d u c t i n g
w a v e
f u n c t i o n i n
t h e
s u p e r c o n d u c t o r
n e a r
t h e
b o u n d a r y ,
a n d
i t s
p e n e t r a t i o n
i n t o
t h e n o r m a l o r
i n s u l a t i n g r e g i o n , i n d u c i n g
s u p e r c o n d u c t i n g
b e h a v i o u r
i n
t h e
n o r m a l
m e t a l o r i n s u l a t o r
n e a r t h e
i n t e r f a c e ,
o v e r
a
d i s t a n c e
d e t e r m i n e d b y
a
d e c a y
l e n g t h £ , N .
I f
a n o r m a l m e t a l
l a y e r
f o r m s
a t h i n b a r r i e r b e t w e e n
t w o s u p e r c o n d u c t o r s
t h e n
i t
i s p o s s i b l e f o r
t h e w a v e f u n c t i o n t o
p e n e t r a t e
e n t i r e l y
f r o m
o n e s u p e r c o n d u c t o r
t o t h e
o t h e r ,
l e a v i n g t h e b a r r i e r o n l y a s a
r e g i o n
o f d e p r e s s e d
s u p e r c o n d u c t i n g
p r o p e r t i e s .
A
r e v i e w
o f
t h e
p r o x i m i t y
e f f e c t b y
D e u t s c h e r
c a n b e
f o u n d i n
[ 1 . 2 2 ] .
T h e
p r o x i m i t y
e f f e c t
i s
a
m a j o r f a c t o r i n t h e b e h a v i o u r o f
s u p e r c o n d u c t i n g - n o r m a l - s u p e r c o n d u c t i n g
J o s e p h s o n
j u n c t i o n s
( s e e
s e c t i o n
1 . 1 1 . 1 , b e l o w ) .
( a )
N o r m a l S u p e r c o n d u c t i n g
P e n e t r a t i o n
D e p t h
a n d C o h e r e n c e L e n g t h
a t B o u n d a r y
( b )
N o r m a l
S u p e r c o n d u c t i n g
P e n e t r a t i o n D e p t h a n d
C o h e r e n c e L e n g t h
a t
B o u n d a r y
F r e e
E n e r g y
D e n s i t y
E l e c t r o n -
O r d e r i n g
E n e r g y
C o n t r i b u t i o n s
t o F r e e E n e r g y
T o t a l F r e e E n e r g y T o t a l F r e e
E n e r g y
F i g u r e
1 . 2 :
H o w
( a )
p o s i t i v e
a n d
( b )
n e g a t i v e
s u r f a c e e n e r g i e s
i n
s u p e r c o n d u c t o r s
a r i s e
f r o m d i f f e r e n c e s
i n
t h e v a l u e s
o f
A
a n d
E , .
1 . 4 T H E
B E H A V I O U R O F
S U P E R C O N D U C T O R S
I N
M A G N E T I C F I E L D S
S u p e r c o n d u c t o r s
c a n b e
d i v i d e d i n t o t w o d i s t i n c t
t y p e s
d e p e n d i n g
o n h o w
t h e y
r e a c t t o a m a g n e t i c f i e l d
[ 1 . 2 3 ] .
T h i s b e h a v i o u r i s
g o v e r n e d
b y
t w o f u n d a m e n t a l
m a t e r i a l
p a r a m e t e r s ;
A ,
t h e L o n d o n
p e n e t r a t i o n d e p t h , a m e a s u r e o f t h e
d i s t a n c e w h i c h a n a p p l i e d
m a g n e t i c
f i e l d
p e n e t r a t e s a
s u p e r c o n d u c t o r , a n d
£ ,
t h e c o h e r e n c e l e n g t h
( t h e
e f f e c t i v e
s i z e
7
Chapter 1 : Superconductivity
of the Cooper pair). These can be combined together into a single variable known as the
Ginzburg-Landau parameter, K[ 1.12], defined as
Although both A and t, vary with temperature, they have similar temperature
dependencies, making K generally independent of temperature.
It can be shown [1.23] that if K is less than 1A/2 the superconductor is
characterised by a positive energy between the superconducting and normal states. If K is
greater than '/\/2 then there is a negative energy between the two states. The origin of
this is shown schematically in figure 1.2. Depending on the value of K superconductors
react very differently to applied magnetic fields, allowing the classification of
superconductors into two distinct groups, known as type I and type II, depending on
whether their K is smaller or larger than VA/2 [1.23],
1.4.1 TYPE I SUPERCONDUCTORS
In superconductors where K is less than VA/2, in samples with a zero
demagnetising factor (such as a long thin rod parallel to the applied field),
superconductivity disappears abruptly on application of a field greater than Hc, the
thermodynamic critical field. This field can arise purely from the self-field (current)
alone, or from the sum of the self-field and an externally applied field and was first
explained in this way by Silsbee in 1916 [1.24], Such materials tend to be pure metals
and are known as Type I superconductors. These tend to have very low overall Jcs,
making them unsuitable for applications [1.25],
In samples with a non-zero demagnetising factor, demagnetising effects cause the
appearance of what is known as the intermediate state in which the sample splits up into
macroscopic superconducting and normal laminae to minimise its Gibbs free energy.
1.4.2 TYPE II SUPERCONDUCTORS
If K is greater than V-\/ 2 the superconductor is classified as Type II [1.23], The
negative energy between the superconducting and normal states in these materials means
that, below an external field HCi there is complete flux exclusion, i.e. a perfect Meissner
state. Hr is known as the lower critical field and is given by
8
C h a p t e r
1 :
S u p e r c o n d u c t i v i t y
( I n * :
+
0 . 0 8 )
( 1 . 4 )
A t
H c r
f l u x b e g i n s
t o e n t e r t h e s u p e r c o n d u c t o r a n d
i t
i s
e n e r g e t i c a l l y
a d v a n t a g e o u s f o r a
t y p e
I I
s u p e r c o n d u c t o r t o d i v i d e i t s e l f
i n t o a
m i x e d
s t a t e
o f
s u p e r c o n d u c t i n g
a n d m i c r o s c o p i c n o r m a l r e g i o n s .
B e c a u s e t h e
s u p e r c o n d u c t o r
d o e s n o t
h a v e t o e x p e n d
s o m u c h
e n e r g y
i n e x c l u d i n g
f l u x ,
s u p e r c o n d u c t i v i t y
p e r s i s t s
t o
a
f i e l d
,
t h e u p p e r c r i t i c a l
f i e l d ,
w h i c h i s h i g h e r
t h a n
H c
a n d i s g i v e n b y
H C I = ÿ 2 K H C
( 1 . 5 )
B e c a u s e s u p e r c o n d u c t i v i t y c a n
p e r s i s t t o
m u c h
h i g h e r
f i e l d s
a n d
c u r r e n t s
i n
t y p e I I s u p e r c o n d u c t o r s t h e s e m a t e r i a l s c a n b e u s e d f o r
p r a c t i c a l
a p p l i c a t i o n s
i n
t h e s e
r e g i m e s
[ 1 . 2 5 ] .
F i g u r e 1 . 3 s h o w s a
s c h e m a t i c
d i a g r a m
o f m a g n e t i s a t i o n
v e r s u s
a p p l i e d
f i e l d f o r
t y p e I
a n d
I I
s u p e r c o n d u c t o r s .
F i g u r e
1 . 3 : S c h e m a t i c
d i a g r a m o f m a g n e t i s a t i o n
v e r s u s a p p l i e d f i e l d f o r
a
t y p e
I
( d a s h e d
l i n e )
a n d
t y p e
I I
( s o l i d
l i n e )
s u p e r c o n d u c t o r
s h o w i n g
t h e
u p p e r ,
l o w e r
a n d
t h e r m o d y n a m i c
c r i t i c a l
f i e l d s .
I t w a s
o r i g i n a l l y
t h o u g h t t h a t f l u x e n t e r e d
t y p e I I s u p e r c o n d u c t o r s
a s i t d o e s
t y p e
I
s u p e r c o n d u c t o r s i n
t h e
i n t e r m e d i a t e
s t a t e ,
i . e .
t h r o u g h t h i n
n o r m a l l a y e r s .
H o w e v e r ,
A b r i k o s o v
[ 1 . 2 6 ]
d e r i v e d a n o t h e r
s o l u t i o n
f r o m t h e G i n z b u r g - L a n d a u
e q u a t i o n s w h e r e
t h e n o r m a l r e g i o n s a r e q u a n t i s e d f l u x
v o r t i c e s o r
f l u x
l i n e s e a c h c o n t a i n i n g
o n e
f l u x
q u a n t u m
( < J > o ) .
T h e o r d e r p a r a m e t e r f a l l s t o z e r o o n t h e
a x i s o f e a c h
f l u x l i n e .
T h e
n o r m a l
r e g i o n
h a s
a
r a d i u s o f
a p p r o x i m a t e l y
t h e
c o h e r e n c e
l e n g t h
£ , a n d
i s
s u r r o u n d e d
b y
a
r e g i o n o f
c i r c u l a t i n g
s u p e r c u r r e n t w i t h a r a d i u s o f
a p p r o x i m a t e l y
t h e
L o n d o n
p e n e t r a t i o n
d e p t h
X .
T h i s s c r e e n i n g
s u p e r c u r r e n t i s
j u s t
s u f f i c i e n t
t o
g e n e r a t e
f l u x e q u a l t o
d ? 0 .
F i g u r e 1 . 4
s h o w s
a
s c h e m a t i c d i a g r a m
o f
a s i n g l e f l u x
v o r t e x .
9
Chapter 1 : Superconductivity
Centre of
Flux Vortex
Figure 1.4 : Structure of flux vortex showing the normal core, where the
superconducting order parameter ¥/ is suppressed to zero, with a radius of
and the field h sustained by supercurrents circulating over a radius ~A
around the flux line.
As the applied field H increases so does the density, n, of the flux lines. Within
the superconductor, the flux density B = nOg. In the absence of any interaction between
the vortices and the microstructure of the superconductor, the vortices interact among
themselves to form a minimum-energy arrangement [1.26]. This state usually consists of
a triangular lattice of flux lines (though a square lattice is possible in, for example, an
anisotropic superconductor when B is not parallel to H [1.27]). These flux lines are each
separated by a distance
Below H there is no flux in the superconductor. As the applied field increases
above HCi the flux lines become closer together until at H , B —> Bÿ
At this point the normal cores of the flux lines overlap and the entire
superconductor reverts to the normal state.
The flux line lattice can be imaged by a number of different techniques including
neutron diffraction [1.28], which gives details of the flux structure in the interior of a
(1.6)
v c2 y
(1.7)
10
C h a p t e r
1 : S u p e r c o n d u c t i v i t y
s u p e r c o n d u c t o r ,
d e c o r a t i o n o f t h e
s u p e r c o n d u c t o r
b y
f e r r o m a g n e t i c
p a r t i c l e s o r
t h e
u s e
o f
B i t t e r
p a t t e r n s , b o t h
o f w h i c h
g i v e t h e s t r u c t u r e o f f l u x l i n e s a t t h e
s u r f a c e o f
t h e
s u p e r c o n d u c t o r . F o r
a r e v i e w o f t h e s e
t e c h n i q u e s s e e B i s h o p e t a l .
[ 1 . 2 9 ] .
S i n c e
i n a d d i t i o n t o d e c r e a s i n g
£
a n d
i n c r e a s i n g X , a l l o y i n g
d e c r e a s e s l , t h e
m e a n
f r e e p a t h o f
a
m a t e r i a l ,
a l l o y s t e n d t o h a v e
n e g a t i v e
s u r f a c e
e n e r g i e s
a n d s o t o
b e
t y p e I I
s u p e r c o n d u c t o r s . B e c a u s e o f t h i s a l l o y i n g
a m a t e r i a l
c a n c a u s e i t t o c h a n g e
f r o m
t y p e I t o
t y p e
I I
s u p e r c o n d u c t i v i t y .
F i g u r e 1 . 5
:
P h a s e
d i a g r a m s h o w i n g r e l a t i o n s h i p s
b e t w e e n
h
,
h H ,
h c ÿ
a n d
K
I n a d d i t i o n t o
H
„
a n d
H „
,
w h i c h a r e b u l k
e f f e c t s ,
i t w a s s h o w n
b y
S a i n t - J a m e s
a n d d e
G e n n e s
[ 1 . 3 0 ]
t h a t
s u p e r c o n d u c t o r s
c a n a l s o e x h i b i t s u r f a c e e f f e c t s . T h e s e
o c c u r
i f
K >
0 . 4 2 a s
a
s h e a t h o f
t h i c k n e s s
o n
s u r f a c e s
p a r a l l e l t o t h e a p p l i e d f i e l d
a n d
p e r s i s t
u p
t o
a f i e l d
H
=
1 . 6 9 H
f o r a
t y p e
I I
s u p e r c o n d u c t o r .
T h e
p r e s e n c e o f
c a n b e
d e d u c e d f r o m
d i f f e r e n c e s b e t w e e n r e s i s t i v e m e a s u r e m e n t s
a t
l o w
c u r r e n t s
( d o m i n a t e d
b y
t h e s m a l l f r a c t i o n
o f m a t e r i a l
w h i c h r e m a i n s s u p e r c o n d u c t i n g ) a n d
m a g n e t i c
m e a s u r e m e n t s
( w h i c h
a r e
s e n s i t i v e
t o
t h e
b u l k o f t h e
s a m p l e ) . F i g u r e
1 . 5 s h o w s
a
s c h e m a t i c
p h a s e d i a g r a m
o f
H c ,
H
,
a n d
H c
v e r s u s K . U n d e r c e r t a i n
c i r c u m s t a n c e s
s u p e r c o n d u c t i v i t y p e r s i s t s
e v e n a b o v e H o n
t h e e d g e s
a n d
c o r n e r s
o f
a
s a m p l e ,
d i s a p p e a r i n g a t H a n d
H c
r e s p e c t i v e l y . T h e s e s u r f a c e
e f f e c t s a r e
m e n t i o n e d
o n l y
f o r
c o m p l e t e n e s s
a n d
a r e
n o t
c o n s i d e r e d
f u r t h e r
i n
t h i s t h e s i s .
1 1
Chapter 1 : Superconductivity
1.5 THE BEHAVIOUR OF FLUX IN A TYPE II SUPERCONDUCTOR
1.5.1 FLUX PINNING
In a type II superconductor above H a (usually triangular) flux line lattice is
formed due to repulsive interactions between flux lines [1.26]. As shown in section 1.4.2,
a flux line is a magnetic field and a depression of the order parameter to zero. In an
imperfect superconductor there are other places where the order parameter is depressed.
This can be to zero in, for example, a non-superconducting precipitate, or simply to
below that of the bulk of the material in, for example, impurities, crystal dislocations and
grain boundaries within the sample. If the flux line moves so that the flux line core
intersects with one of these imperfections, then the energy of the superconductor is
reduced. This gives an attractive force between flux lines and imperfections. Because
these imperfections tend to 'pin' flux lines to them they are known as pinning centres.
However, pinning is strongest if the size of the pinning centre is approximately the same
as £ It can be shown [1.31] that the pinning force density is related to the critical current
density as F = Jcx B, or, in one dimension, Fp = JCB. The surface of a superconductor
can also act as a pinning centre as this is a region where the order parameter is depressed.
1.5.2 INTERACTION OF FLUX LINES, PINNING CENTRES AND APPLIED CURRENTS
In the absence of pinning flux lines move immediately a transport current is
applied to the sample, generating an electric field which leads to dissipation of energy in
the sample, i.e. a resistance. A theory which attempts to explain the behaviour of a
superconductor under these circumstances is that of Bardeen and Stephen [1.32], which
considers the dissipation process when a single vortex moves in the absence of flux
pinning. This has become known as the Bardeen-Stephen model.
In a sample with pinning, a transport current density perpendicular to the flux
lines produces a Lorentz force density on the flux line lattice equal to JxB. When this
becomes sufficient to remove flux lines from their pinning centres, i.e. > Fp, the pinning
force density, the flux lines and flux lattice begin to move and start to produce
dissipation. This current density is known as the critical current density Jc and is
dependent on the sample microstructure.
The interaction of the flux line lattice (FLL) with the underlying pinning
microstructure of a superconductor helps to determine how Jc varies in a sample in the
mixed state [1.31]. The potential energy of a vortex lattice is a sum of the potential
12
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
e n e r g y
o f t h e
i n d i v i d u a l
f l u x
l i n e s a n d t h a t o f
t h e p i n n i n g
c e n t r e s
[ 1 . 3 1 ] ,
T h e
l a r g e r
t h e
p o t e n t i a l
e n e r g y
o f
t h e f l u x
l i n e s ,
t h e s t i f f e r t h e f l u x
l a t t i c e .
A c c o r d i n g
t o
L a b u s c h
[ 1 . 3 3 ] ,
t h e r e
a r e f o u r
p i n n i n g r e g i m e s
w h i c h c a n b e
c o n s i d e r e d ,
d e p e n d i n g o n t h e
r i g i d i t y
o f
t h e
f l u x l i n e l a t t i c e
( w h i c h
i s a l s o d e p e n d e n t o n
T
a n d
B )
:
( i )
F L L c o m p l e t e l y r i g i d . T h e n e t p i n n i n g
f o r c e
o n t h e
F L L
i s
z e r o
a s ,
o n
a g i v e n
f l u x
l i n e ,
t h e p i n n i n g
f o r c e f r o m
a
r a n d o m
a r r a y
o f p o i n t p i n n i n g
s i t e s
c a n c e l s t o
z e r o .
T h i s
g i v e s a c r i t i c a l c u r r e n t
d e n s i t y
o f
z e r o ,
b u t i s u n l i k e l y t o o c c u r
i n r e a l i t y .
( i i )
F L L s t i f f .
O n l y
w e a k i n t e r a c t i o n s o c c u r b e t w e e n
p i n s a n d
F L L a s i t i s
d i f f i c u l t
f o r
a
r e g u l a r r i g i d
l a t t i c e t o p i n
t o r a n d o m
a r r a y .
O n l y
a
s m a l l
n u m b e r o f f l u x
l i n e s a r e
p i n n e d
a t
a n y
o n e
t i m e ,
g i v i n g a l o w
J c .
A s s o o n a s
t h e
F L L b e c o m e s
f l e x i b l e i t
i s p o s s i b l e
t o
h a v e ‘ b u n d l e s ’ o f
i n t e r a c t i n g
f l u x
l i n e s
‘ p i l i n g
u p ’ b e h i n d
p i n n i n g
b a r r i e r s
a n d
m o v i n g
p a s t t h e m b y
t h e r m a l a c t i v a t i o n .
( i i i )
F L L
f l e x i b l e .
I n t h i s c a s e t h e F L L
a d j u s t s
i t s s h a p e b y
p l a s t i c
d e f o r m a t i o n t o p i n
t h e m a x i m u m n u m b e r o f f l u x
l i n e s . I n t h i s c a s e
J c
i s d e t e r m i n e d b y
p i n
b r e a k i n g .
F l u x
w i l l
b e
p i n n e d b y g r a i n
b o u n d a r i e s .
( i v )
F L L
v e r y
f l e x i b l e . S h e a r i n g o f t h e f l u x l a t t i c e
c a n o c c u r
d o w n g r a i n
b o u n d a r i e s .
I n
t h i s
c a s e
J c
i s d e t e r m i n e d
b y p i n a v o i d a n c e .
l . 6
T H E C R I T I C A L S T A T E M O D E L
F l u x
p i n n i n g
i s
t h e
m a j o r f a c t o r
c o n t r o l l i n g t h e
b e h a v i o u r o f
s u p e r c o n d u c t o r s i n
m a g n e t i c
f i e l d s
[ 1 . 3 1 ] ,
T h e p r e s e n c e o f
p i n n i n g
c e n t r e s
s t o p s
f l u x
r e a d i l y
m o v i n g
i n
o r
o u t
o f
t h e
s a m p l e ,
l e a d i n g
t o a f l u x g r a d i e n t f r o m t h e o u t s i d e o f t h e
s a m p l e
t o i t s c e n t r e
a n d g i v i n g
r i s e t o i r r e v e r s i b l e m a g n e t i s a t i o n a n d h y s t e r e s i s
[ 1 . 3 4 ] ,
F l u x
p i n n i n g
i m p l i e s
t h e
p r e s e n c e
o f g r a d i e n t s
i n t h e i n d u c e d c u r r e n t
d e n s i t y
a n d i n t e r n a l f i e l d
a n d c a n l e a d
t o
a
c o m p l e x
i n t e r n a l f l u x
d i s t r i b u t i o n
f o r
a s a m p l e
i n
a n
a l t e r n a t i n g m a g n e t i c f i e l d
[ 1 . 3 1 ] .
S e v e r a l
m o d e l s h a v e b e e n p u t f o r w a r d
t o
e x p l a i n t h e I - V a n d m a g n e t i c
c h a r a c t e r i s t i c s o f t y p e
I I
s u p e r c o n d u c t o r s .
A c c o r d i n g
t o t h e s e m o d e l s a n y c h a n g e
i n
t h e
m a g n e t i c f i e l d
a p p l i e d
t o
a s u p e r c o n d u c t o r
( i n c l u d i n g
t h e s e l f - f i e l d o f a
c u r r e n t
t h r o u g h
t h e
s a m p l e ) i n d u c e s s c r e e n i n g c u r r e n t s
i n i t s
b u l k w i t h
v a l u e s o f t h e l o c a l
J c .
B e c a u s e o f
f l u x p i n n i n g
t h i s
f i e l d
d o e s n o t
i m m e d i a t e l y
p e n e t r a t e
t h e
w h o l e
s a m p l e
b u t i s
c o n f i n e d
t o
a
r e g i o n
n e a r t h e s u r f a c e . W h e n
t h e l o c a l
f i e l d
b e c o m e s
l a r g e
e n o u g h
t h a t i t
d r i v e s
a
p o i n t
i n
t h e s a m p l e a b o v e t h e
l o c a l
J c
t h e n t h e
f i e l d
p e n e t r a t e s f u r t h e r
i n t o t h e s a m p l e , i n d u c i n g
c u r r e n t s a t g r e a t e r
a n d
g r e a t e r
d e p t h s u n t i l
f i n a l l y
t h e c e n t r e o f
t h e
s a m p l e
i s r e a c h e d .
1 3
Chapter 1 : Superconductivity
Reversing the applied field leads to a set of negative currents penetrating from the
surface. This means that at a given time all parts of the sample have a current density of
either zero, +JC or -Jc.
The distribution of fields and currents inside type II superconductors has been
calculated using several models under a variety of conditions. These all assume that flux
penetrates into a superconductor as described above, but have different dependences of Jc
on local field which significantly affect the results obtained.
The model describing the behaviour of superconductors under the influence of
applied currents and magnetic fields which is now known as the Bean model was
independently proposed by Bean [1.35] and London [1.36] in 1964. This model assumes
that Jc is independent of applied magnetic field.
The model of Kim [1.37], in contrast, assumes that Jc varies with field as
B + p'
Thirdly, the model of Campbell and Evetts [1.31], and also of Yeshurun et al.
Fourthly, the model of Doyle and Doyle [1.39] assumes that Jc exp +/3.
In all these cases ft and e are constants.
These models allow the calculation of field and current distributions inside a slab
when a current is passed through it, a field applied to it, and with combinations of these
conditions. Examples of these calculations for the Bean model are shown in figures 1.6(a)
to 1.6(d) below. They assume that the slab is infinite in the y and z directions so there are
no end effects. Similar calculations can be performed for the other models described.
The critical state model has been confirmed experimentally by several groups via
the direct detection of flux profiles within superconductors [1.40, 41], by magnetisation
and transport measurements.
1
14
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
F i g u r e
1 . 6 ( b )
:
U n i f o r m
a p p l i e d
f i e l d f o r
t h e
B e a n
M o d e l .
A B
J c
\
I I
- J c
B i n
S l a b
C u r r e n t i n S l a b
F i g u r e
1 . 6 ( c )
: A p p l i e d
f i e l d f o l l o w e d b y
a n a p p l i e d
c u r r e n t
f r o m
t h e B e a n M o d e l .
\
A B
J °
r
V
■
- J c
B i n S l a b
C u r r e n t
i n
S l a b
F i g u r e
1 . 6 ( d )
:
A p p l i e d
c u r r e n t
f o l l o w e d
b y
a n
a p p l i e d f i e l d
f r o m
t h e B e a n M o d e l .
1 5
Chapter 1 : Superconductivity
When the half thickness of the superconductor is comparable to the penetration
depth X, the applied field or the self-field of an applied current immediately penetrates the
entire sample. For the geometry used in figure 1.6 this increases Hc by a factor of
A fa \T1/21--tanh — , where a is the half thickness of the sample, and reduces Jc by aa \A,J_
factor tanh(a/A). This is covered in more detail by Rose-Innes and Rhoderick in [1.42]
but is mentioned here only for completeness.
1.6.1 MAGNETISATION
The average Jc in a magnetisation measurement is directly proportional to the
width of the observed hysteresis loop if current flows on the length scale of the sample.
This allows the calculation of Jc(magnetic ) for a sample using a critical state model
[1.35].
The magnetic moment of a current loop is given by m - ids where i is the current
flowing around the loop and ds is the area of the loop. Therefore, the total magnetic
moment of a sample, which can be considered to be a combination of many such loops, is
given by
= jids (1.8)
If a sample is fully penetrated by an applied magnetic field, then the whole sample
will be carrying its maximum possible superconducting screening current, i.e. Jc.
Assuming that Jc is independent of field (the Bean Model), i in equation 1.8 becomes Jc
t dr where t dr is the cross-sectional area of the current loop ( t = thickness of the disc,
dr = radial thickness of loop).
This allows the calculation of the magnetisation of a fully penetrated
superconducting sample. The exact form of ds in equation 1.8 depends on the shape of
the sample for which the calculation is being carried out.
For a disc of radius a, ds is nr2, so the total magnetic moment is
m =|Jctnr2dr = — Jct.nai (1.9)
o
Magnetisation is defined as magnetic moment per unit volume. The volume of the
disc is n t a2, therefore its magnetisation becomes :
16
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
( 1 . 1 0 )
T h i s
a s s u m e s
f u l l
p e n e t r a t i o n
o f
t h e s a m p l e
b y t h e
a p p l i e d m a g n e t i c
f i e l d
s o
t h a t
t h e
i n d u c e d c u r r e n t s f l o w
h o m o g e n e o u s l y o v e r
t h e
e n t i r e
s a m p l e
a n d
t h a t
J c
i s
i n d e p e n d e n t
o f
a p p l i e d f i e l d
( f o r
H T S C s t h i s g e n e r a l l y
o c c u r s o n l y a t
h i g h
f i e l d s
( > 1 T )
[ 1 . 4 3 ] ) .
A f u r t h e r a s s u m p t i o n
c a n o f t e n
a l s o
b e
m a d e ,
t h a t t h e h y s t e r e s i s
l o o p w i d t h
i s
s y m m e t r i c a l
a b o u t t h e
r e v e r s i b l e f i e l d c u r v e
( t h a t
f o r a p e r f e c t
p i n n i n g - f r e e
s p e c i m e n
o f
t h e
s a m e
m a t e r i a l )
s o t h a t t h e
l o o p
w i d t h A m
=
2 m
,
a l l o w i n g
t h e
c a l c u l a t i o n
o f
J c
f o r
a
d i s c
J c
=
3 A m
2 n a i t
( 1 . 1 1 )
T h i s d o e s n o t t a k e i n t o a c c o u n t
a n y
d e m a g n e t i s i n g
e f f e c t s ,
a l t h o u g h
t h e s e w i l l
b e
i n s i g n i f i c a n t
i n t h e r e g i m e s w h e r e
t h i s e q u a t i o n i s u s e d
i n t h i s t h e s i s d u e
t o i t s
o n l y b e i n g
u s e d w e l l a b o v e t h e
f i e l d f o r f u l l p e n e t r a t i o n o f t h e
s a m p l e .
J c ( m a g n e t i c )
f o r
s q u a r e
p l a n a r s a m p l e s
m a y
a l s o
b e
c a l c u l a t e d
u s i n g
t h e s a m e
a s s u m p t i o n s
a s f o r a d i s c t o b e
J
=
3 A
m
t w 3
w h e r e w i s t h e
s a m p l e
w i d t h
( 1 . 1 2 )
I t c a n b e
s h o w n
t h a t
f o r
a l o n g c y l i n d e r
o r s l a b t h e
m a g n e t i s a t i o n
i s
a l s o e q u a l t o
t h e
a v e r a g e d i f f e r e n c e
i n
f i e l d
f r o m t h e
i n s i d e
t o t h e
o u t s i d e o f t h e s a m p l e .
A
d i f f i c u l t y
i n c o m p a r i n g m a g n e t i s a t i o n a n d
t r a n s p o r t
J c
m e a s u r e m e n t s
i s t h a t
t r a n s p o r t
m e a s u r e m e n t s
a r e
p e r f o r m e d
i n
t h e
l o w p e n e t r a t i o n r e g i m e
( i . e .
b e f o r e t h e f i e l d
h a s
p e n e t r a t e d a l l
t h e w a y
t o t h e c e n t r e o f t h e
s l a b ,
w h i c h f o r
a h o m o g e n e o u s
m a t e r i a l
o c c u r s
w h e n
t h e e n t i r e s a m p l e i s a t o r
a b o v e
J c
) .
I n t h i s
c a s e ,
r a t h e r
t h a n i n t e g r a t i n g
a c r o s s
t h e e n t i r e
s a m p l e ,
t h e i n t e g r a t i o n
m u s t b e p e r f o r m e d o n l y i n t h e r e g i o n
p e n e t r a t e d
b y
f l u x . T h i s
i s m o r e c o m p l e x a s t h e e x t e n t o f t h i s
r e g i o n
c a n b e
d i f f i c u l t
t o d e t e r m i n e .
A l s o ,
m a g n e t i c
m e a s u r e m e n t s o f
J c
u s e
a n
e f f e c t i v e
v o l t a g e
c r i t e r i o n
w h i c h c a n b e
m o r e
t h a n a n o r d e r o f m a g n i t u d e
l e s s t h a n
t h a t
f o r a t r a n s p o r t
m e a s u r e m e n t ,
g r e a t l y
a f f e c t i n g
t h e
m e a s u r e d
J c
d u e t o t h e n o n - l i n e a r i t y o f
t h
e l - V c u r v e s o f
m o s t s u p e r c o n d u c t o r s [ 1 . 4 4 ] .
I t
i s a l s o p o s s i b l e t o u s e t h e c r i t i c a l
s t a t e
m o d e l t o
c a l c u l a t e
t h e
l o s s e s
i n
a
s u p e r c o n d u c t o r
u n d e r t h e i n f l u e n c e o f a n a l t e r n a t i n g f i e l d
o r c u r r e n t .
T h i s i s
r e v i e w e d
b y
1 7
Chapter 1 : Superconductivity
Campbell in [1.45] but has not been done in the course of this thesis and is only
mentioned for completeness.
1.7 THERMAL EFFECTS ON FLUX LINES
The existence of flux pinning leads to the phenomenon known as flux creep. This
occurs when flux lines are thermally activated between pinning centres in a steady field,
causing the distribution of flux to gradually equilibrate, as first described by Anderson in
1962 [1.46]. Although this behaviour generates an electric field and therefore a voltage,
in the absence of a transport current the flux lines move randomly and so give a net
voltage of zero. When a transport current is applied to a superconductor in the mixed state
this adds an energy gradient Aw to it so as to favour the movement of flux vortices in one
direction over the other, as shown in figure 1.8. This implies a density gradient of flux
lines, which in turn implies a driving force on the flux lines. This force is given by
Figure 1.8 : Schematic representation of flux creep before (dashed line )
and after the application of an external driving force (e.g. an applied
transport current). Aw is the energy gradient added to the system by the
driving force causing flux lines to tend to creep to the left and Up is the
pinning energy.
In this case the behaviour of the flux line lattice is a balance between three
different forces acting on the individual flux lines :
(i) Lorentz Force (interaction with current) FL = Jx @0
In the D.C. case this will be a steady force at right angles to the applied current
and field. In an A.C. case this force will reverse direction with the reversal of the current,
resulting in no overall motion of flux.
J= 0-
/> 0
Aw
18
C h a p t e r 1 : S u p e r c o n d u c t i v i t y
( i i )
V i s c o u s
F o r c e
F v
=
r \ v
( v
=
v e l o c i t y o f
f l u x m o t i o n )
T h i s a r i s e s
f r o m
d y n a m i c
i n t e r a c t i o n s
w i t h
t h e
s u p e r c o n d u c t o r a n d
b e t w e e n
f l u x
l i n e s . I t h a s
d i f f e r e n t e f f e c t s d e p e n d i n g o n w h e t h e r t h e
s y s t e m
i s
a n A . C . o r
D . C .
o n e .
I n a
D . C . c a s e i t t e n d s
t o
l i n k
t h e f l u x
l i n e s t o g e t h e r s o t h a t a n u m b e r o f
f l u x
l i n e s
c a n
b e
p i n n e d b y
o n l y o n e p i n n i n g
c e n t r e ,
a p r o c e s s
k n o w n a s ' c o l l e c t i v e
p i n n i n g ' .
T h e n u m b e r
o f
f l u x
l i n e s
w h i c h f o r m
s u c h a
' b u n d l e ' d e p e n d s o n t h e t h e r m a l e n e r g y
o f
t h e
s y s t e m
a n d
t h e r e l a t i v e s i z e
o f t h e L o r e n t z
f o r c e o n
t h e f l u x
l i n e s .
I n a n
A . C .
c a s e t h e
v i s c o s i t y
s i g n i f i c a n t l y
a f f e c t s t h e b e h a v i o u r o f t h e f l u x l i n e s . I n c r e a s i n g
v i s c o s i t i e s
i n c r e a s i n g l y
d a m p e n
t h e
A . C .
e f f e c t s o n t h e f l u x
l i n e s . A s
t h e
f r e q u e n c y
i n c r e a s e s t h e
a m o u n t
o f
d a m p e n i n g a l s o
i n c r e a s e s d u e t o t h e h i g h e r a v e r a g e
v e l o c i t y o f t h e f l u x
l i n e s .
( i i i )
P i n n i n g F o r c e
( i n t e r a c t i o n
w i t h
m i c r o s t r u c t u r e
o f
s u p e r c o n d u c t o r )
F p
=
J c x < P 0
E a c h
p i n n i n g
c e n t r e i n t h e
s u p e r c o n d u c t o r
e x e r t s a n
a t t r a c t i v e
f o r c e o n a
f l u x l i n e
n e a r
i t ,
w h i c h d e p e n d s o n t h e
t e m p e r a t u r e ,
c u r r e n t a n d m a g n e t i c
f i e l d .
B e l o w
J c
t h i s f o r c e
i s
g r e a t e r t h a n
o r
e q u a l
t o t h e L o r e n t z
f o r c e o n
t h e f l u x l i n e s
a n d
J c
c a n b e
d e f i n e d a s t h e
p o i n t
a t w h i c h t h e
p i n n i n g
f o r c e
i s e x c e e d e d .
W h e n t h e
s u p e r c o n d u c t o r i s
i n e q u i l i b r i u m
( f o r
e x a m p l e ,
b e l o w
J c )
F L + F V + F P =
0
F l u x w i l l
m o v e i f
F L >
F p
=
J c x
< P 0 ,
i . e . f o r
J
>
J c \
v
=
( J -
J c ) x —-
n
T h e n e t m o v e m e n t
o f
f l u x
i n o n e
d i r e c t i o n i m p l i e s t h e
p r e s e n c e o f a
n e t n o n - z e r o
e l e c t r i c f i e l d a n d l o s s i n t h e m a t e r i a l .
T h i s i s
g i v e n b y E = v x B
w h e r e v
i s t h e f l u x
l i n e
v e l o c i t y , g i v e n b y
v
=
•
d n
a n d
d n
i s t h e
d i s t a n c e m o v e d
b y
t h e f l u x l i n e
a s i t ' h o p s '
b e t w e e n p i n n i n g s i t e s . F r o m F a r a d a y s l a w
o f
i n d u c t i o n
E
=
v x B
d >
( J - J c ) x —
x B ( 1 . 1 3 )
N o t e
t h a t
E i s
i n
t h e s a m e d i r e c t i o n a s J .
R e v i e w s
o f f l u x m o t i o n
i n
s u p e r c o n d u c t o r s
b y
G r i e s s e n a n d
E v e t t s a r e g i v e n
i n
[ 1 . 4 7 ]
a n d
[ 1 . 4 8 ]
r e s p e c t i v e l y . T h e r e
a r e
t h r e e r e g i m e s i n w h i c h
f l u x
m o t i o n o c c u r s .
T h e s e a r e d e s c r i b e d
b e l o w .
1 9
Chapter 1 : Superconductivity
1.7.1 FLUX CREEP.
In this regime the thermal energy kBT « Up where Up is the pinning energy, and
the additional energy provided by an applied current is JCBVC < Up where Vc is the
volume of a bundle of flux lines. Due to the small kBT a high current density is necessary
to unpin the flux lines. A theory explaining this behaviour was first put forward by
Anderson in 1962 [1.46]. In LTSCs flux creep occurs logarithmically with time [1.49],
but so slowly that it cannot be measured in a magnetic field due to creep in the magnet
itself. However, it can be measured in the decay of the remnant magnetisation in a
material [1.50, 51]. Because of the much higher creep rate in HTSCs [1.52, 53] flux creep
has been measured in them in applied fields.
1.7.2 THERMALLY ASSISTED FLUX FLOW (TAFF).
In this case kBT < Up and JCBVC « Up and a small applied current density will
supply enough energy to unpin the flux line. However, the limits of the regime in which
thermally activated flux flow is important are very field and material dependent.
Figure 1.9 shows the differences between the flux creep and the thermally activated flux
flow regimes.
Flux Creep Regime Thermally Assisted Flux Flow Regime
Figure 1.9 : The distinction between flux creep and thermally activated flux flow
regimes in a type II superconductor by the relative sizes of kBT and JCBVC with
respect to Up.
1.7.3 THERMAL DSPINNING AND THE IRREVERSIBILITY LINE.
At this point kBT> Up so that flux lines become decoupled from the pinning sites
and from each other. When this occurs a magnetic hysteresis loop measured for the
sample collapses, implying that the Jc falls to zero as there is no effective flux pinning,
although the material remains superconducting. The field at which this occurs varies with
20
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
t e m p e r a t u r e
a n d w h e n p l o t t e d
i n H - T
s p a c e i s
k n o w n a s t h e
i r r e v e r s i b i l i t y
l i n e [ 1 . 5 4 ] .
I n
h i g h - t e m p e r a t u r e
s u p e r c o n d u c t o r s t h i s
d e p i n n i n g
t r a n s i t i o n
c a n o c c u r
w e l l
b e l o w
B c
a n d
s i g n i f i c a n t l y l i m i t
t r a n s p o r t
p r o p e r t i e s . I n
L T S C s
i t
g e n e r a l l y
o c c u r s
s u f f i c i e n t l y
c l o s e
t o
t h a t t r a n s p o r t p r o p e r t i e s a r e u n a f f e c t e d .
O n c e t h e r m a l
e f f e c t s o n
f l u x
l i n e s a r e
i n c l u d e d
i n a s y s t e m ,
J c ,
a s a
p a r a m e t e r ,
l o s e s i t s
s h a r p n e s s
b e c a u s e r e g a r d l e s s
o f
t h e v a l u e
o f J t h e r e
i s
a l w a y s
s o m e
f l u x
m o t i o n
a n d
t h e r e f o r e
s o m e l o s s .
T h i s a l s o a f f e c t s
m a g n e t i c
m e a s u r e m e n t s
a s
i t
t e n d s
t o s m o o t h
o u t
a n y f l u x
g r a d i e n t s
i n t h e m a t e r i a l .
H o w e v e r ,
i t
i s p o s s i b l e t o
d e f i n e a
J c
f r o m t h e
B e a n
M o d e l a s
t h e
c u r r e n t d e n s i t y f o r w h i c h
n o f l u x m o t i o n i s
o b s e r v e d o v e r
t h e
t i m e o f a n
e x p e r i m e n t .
l . 8
T H E
F A M I L I E S O F H I G H -
T C
O X I D E
M A
T E R I A L S
S i n c e t h e
d i s c o v e r y o f
h i g h - 7 ] - .
s u p e r c o n d u c t i v i t y i n 1 9 8 6
[ 1 . 2 ]
a
n u m b e r
o f b r o a d
f a m i l i e s
o f h i g h
t e m p e r a t u r e
s u p e r c o n d u c t i n g o x i d e
m a t e r i a l s h a v e b e e n
d i s c o v e r e d .
A l t h o u g h t h e
H T S C s s h a r e m a n y
c o m m o n p r o p e r t i e s
w i t h
t h e
L T S C s ,
t h e y
a l s o h a v e a
n u m b e r
o f s i g n i f i c a n t
d i f f e r e n c e s f r o m t h e m . F i r s t l y , t h e y a r e
h i g h l y
a n i s o t r o p i c , a
f e a t u r e
w h i c h
a r i s e s
f r o m
t h e i r
l a y e r e d s t r u c t u r e . T h i s c a u s e s g r e a t
d i f f e r e n c e s
i n t h e i r
p r o p e r t i e s
d e p e n d i n g o n w h e t h e r a
m e a s u r e m e n t i s c a r r i e d o u t p a r a l l e l o r
p e r p e n d i c u l a r
t o t h e
C u C > 2
l a y e r s
w i t h i n i t .
S e c o n d l y , t h e c o h e r e n c e l e n g t h o f t h e
s u p e r c u r r e n t c a r r i e r s
i n t h e
H T S C s i s m u c h
l e s s t h a n i n m o s t L T S C s . T h i s m e a n s t h a t t h e
H T S C s a r e e x t r e m e
t y p e
I I
s u p e r c o n d u c t o r s w i t h
v e r y
l a r g e v a l u e s
o f K
a n d 7 7 - 1 0 0 T .
T h i r d l y ,
t h e s e
m a t e r i a l s a r e
s u p e r c o n d u c t i n g a t
t e m p e r a t u r e s w e l l
a b o v e t h o s e
o f t h e
L T S C s ,
m a k i n g
t h e r m a l
e f f e c t s
a r i s i n g
f r o m
t h e
h i g h e r t h e r m a l
e n e r g y
k B T
m u c h m o r e
s i g n i f i c a n t
i n t h e m . D a t t a
p r e s e n t s
a r e v i e w o f t h e s e
p r o p e r t i e s
i n
[ 1 . 5 5 ] .
T h e m a j o r i t y
o f t h e h i g h - T c o x i d e s u p e r c o n d u c t o r s
c o n s i s t o f
a
h i g h l y a n i s o t r o p i c
l a y e r e d
o r t h o r h o m b i c o r
t e t r a g o n a l c r y s t a l
s t r u c t u r e m a d e
u p
o f
C u C > 2
p l a n e s
( k n o w n
a s
t h e a b -
p l a n e s ) s e p a r a t e d b y
p l a n e s
o f o t h e r
o x i d e s .
T h e
C u C > 2
p l a n e s
c o n s i s t o f
C u a t o m s
i n a
r e c t a n g u l a r
a r r a y , e a c h
s u r r o u n d e d
b y
f o u r
O a t o m s i n a
s i m i l a r
a r r a n g e m e n t . I t
i s
b e l i e v e d
t h a t
t h i s l a y e r e d
s t r u c t u r e i s e s s e n t i a l
t o t h e
e x i s t e n c e o f
h i g h - 7 ] :
s u p e r c o n d u c t i v i t y . C h a r g e
t r a n s p o r t
i s
m a i n l y
c o n f i n e d
t o w i t h i n t h e
C u C > 2
p l a n e s
[ 1 . 5 6 -
5 9 ]
w h i l e d o p a n t s i n t h e l a y e r s o f o t h e r
o x i d e s p r o v i d e
a
r e s e r v o i r o f
c h a r g e
t o
t h e
Q 1 O 2
l a y e r s . I n m o s t
o f
t h e h i g h - T c
o x i d e
c o m p o u n d s
i t
h a s b e e n f o u n d
t h a t
T c
c a n
b e
c h a n g e d
b y v a r y i n g
t h e
h o l e
c o n t e n t
[ 1 . 6 0 - 6 2 ] ,
T h i s i s a c h i e v e d
b y
o x y g e n a t i o n ,
r e d u c t i o n o r
2 1
Chapter 1 : Superconductivity
changing the doping of the material using cation substitution [1.63-65]. The following
sections give details on some of the families of high-Tc oxide superconductors.
The materials described above are known as p-type superconductors, as
conduction within them is carried out by holes. However, n-type HTSCs are also known
where conduction arises from the movement of electrons.
/.8.1 THE La-Sr-Cu-0 SYSTEM.
This was the first family of high temperature superconductors, discovered by
Bednorz and Muller in 1986 [1.2]. They found superconductivity at 35K in
Laj 85Bao.15CuO4.-y. Since then superconductivity has been extended to the more general
family La2-xMxCu04.-y where M signifies Ba, Sr, or Ca, x ~ 0.15 and y is small. Chemical
changes to the system have extended its Tc to as high as 60K in (La2-xSrx)CaCÿOÿ.
Table 1.2 summarises this information.
Compound Maximum Tc (K)
(La2-xSrx)Cu04 38
(La2-xSrx)CaCu20fi 60
Table 1.2 : Compounds in the La-Sr-Cu-0 family.
1.8.2 THE Y-Ba-Cu-0 SYSTEM.
The Y-Ba-Cu-O (YBCO) system was the second class of high temperature
superconductors to be discovered, by Wu et al. in 1987 [1.66]. Changes in oxygenation
have been found to have a strong effect on superconductivity in this system, with the
maximum Tc of the most commonly used compound in this system, YBa2Cu307_5
(YBCO) being 94K. This is considerably higher than the maximum Tc in the La-Sr-Cu-0
system, and above the boiling point of liquid nitrogen, so that since its discovery the
YBCO system has been intensively investigated for potential technological applications.
At low oxygen concentrations a structural phase change from orthorhombic to disordered
tetragonal occurs and Tc drops to zero. These compounds have the advantage that they
can be synthesised reliably and reproducibly. Other superconducting compounds
consisting of the same elements also exist, such as YBa2Cu407-g (Y:124) and
Y2Ba4Cu707_5 (Y:247), with varying Tc, oxygen stability and other properties.
22
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
<
—
a
—
> ~
F i g u r e
1 . 1 0
:
A
s c h e m a t i c
r e p r e s e n t a t i o n o f
t h e c r y s t a l
s t r u c t u r e
o f
Y B a 2 C u s O j . § s o w i n g
t h e
C u C > 2
p l a n e s
a n d c h a i n s .
F o r t h e
h i g h
o x y g e n
c o n c e n t r a t i o n o r t h o r h o m b i c p h a s e a
=
3 .
8 5 9 1
A ,
b
=
3 . 9 1 9 5 A ,
c
=
1 1 . 8 4 3 1 A . F o r
t h e l o w e r
o x y g e n
c o n c e n t r a t i o n t e t r a g o n a l
p h a s e
a
=
b
=
3 . 8 6 3
A ,
c
=
1 1 . 8 3 0 A .
C o m p o u n d
M a x i m u m
T c
( K )
Y B a 2 C u 3 0 7 - 8
( Y : 1 2 3 )
9 4
Y B a 2 C u 4 O 7 . f i
( Y : 1 2 4 )
8 0
Y 2 B a 4 C u 7 O 7 . f i
( Y : 2 4 7 )
4 0
L a B a 2 C u 3 O 7 . f i
9 1
N d B a 2 C u 3 O 7 . f i
9 1
S m B a 2 C u 3 O 7 . f i
9 4
E u B a 2 C u 3 O 7 . f i
9 4
G d B a 2 C u 3 O 7 . f i
9 5
H 0 B a 2 C u 3 O 7 . f i
9 3
E r B a 2 C u 3 O 7 . f i
9 4
T m B a 2 C u 3 O 7 . f i
8 6
L u B a 2 C u 3 O 7 . f i
9 1
P r B a 2 C u 3 O 7 . f i
I n s u l a t i n g
T a b l e 1 . 3
:
C o m p o u n d s i n t h e Y B C O
f a m i l y .
2 3
Chapter 1 : Superconductivity
There is a family of other superconducting compounds with compositions based
on YBCO but in which the yttrium atom is replaced by another rare earth element (e.g.
La, Nd, Sm, Eu, Gd, Ho, Er, Tm or Lu) which have Tcs of ~90K. There are also related
compounds such as PrBa2Cu307_5 which are non-superconducting but which, due to their
almost identical crystal structures, have potential applications, with YBCO, for the
construction of thin film multilayers and devices. Figure 1.10 shows a schematic
representation of the YBCO crystal structure while table 1.3 summarises the Tcs of
compounds in the YBCO family. A review of the electronic structure of the high-7ÿ oxide
superconductors is given by Pickett in [1.56], from which the dimensions listed in
figure 1.9 are taken.
1.8.3 THE Bi-Sr-Ca-Cu-0 SYSTEM.
Superconductivity at ~30K in the Bi-Sr-Cu-0 system was first discovered by
Michel et al. in 1987 [1.67]. In 1988 Maeda et al. discovered superconductivity in the
Bi-Sr-Ca-Cu-O (BSCCO) system [1.68]. Since then a family of related high-temperature
superconductors have been discovered [1.69]. Table 1.4 lists the compounds in the
BSCCO system along with their Tcs. As with the YBCO system the BSCCO system has
been subjected to intense scrutiny for possible technological applications due to the high
Tcs of the Bi:2212 and Bi:2223 compounds. The Bi:2212 system is one of the most
anisotropic of the HTSCs, making its properties very sensitive to the alignment of the
ab-planes relative to applied fields and currents.
Compound Maximum Tc (K)
Bi2Sr2CuC>6+x (Bi:2201) 28
Bi2Sr2CaCu2C>8+x (Bi:2212) 94
Bi2Sr2Ca2Cu30io+x (Bi:2223) 110
Table 1.4 : Compounds in the BSCCO family.
1.8.4 THE Tl-Ba-Ca-Cu-0 SYSTEM.
The first thallium-based HTSC was discovered by Sheng and Hermann in 1988
[1.70], Since then a number of related superconducting compounds have been discovered
[1.71-74]. There has been a high degree of interest expressed in the technological
potential of these compounds due to their very high Tcs (up to 125K) and high
irreversibility lines [1.75], but this has been dampened by the problems of working with
highly toxic thallium compounds. These compounds all belong to the same group of
24
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
s t r u c t u r e s a s t h e
B i - b a s e d
H T S C s . T a b l e
1 . 5 s u m m a r i s e s
t h e
s u p e r c o n d u c t i n g
m a t e r i a l s
i n
t h e t h a l l i u m
s y s t e m .
C o m p o u n d
M a x i m u m
T c
( K )
T l B a 2 C u 0 5
( T l : 1 2 0 1 )
5 0
T l B a 2 C a C u 2 0 7
( T l : 1 2 1 2 )
8 0
T l B a 2 C a 2 C u 3 0 9
( T l : 1 2 2 3 )
1 1 0
T I B
a 2 C a 3 C u 4 0 i 1
( T l : 1 2 3 4 )
1 2 2
T l 2 B a 2 C u 0 6
( T l : 2 2 0 1 )
8 0
T l 2 B a 2 C a C u 2 0 8
( T l : 2 2 1 2 )
1 0 8
T l 2 B a 2 C a 2 C u 3 0 i o
( T l : 2 2 2 3 )
1 2 5
T a b l e
1 . 5 : C o m p o u n d s
i n t h e T l - B a - C a - C u - 0
f a m i l y .
1 . 8 . 5
O T H E R
H I G H - T C
S Y S T E M S .
T h e r e a r e
s e v e r a l
o t h e r o x i d e s y s t e m s w h i c h
a r e
s u p e r c o n d u c t i n g
a t h i g h
t e m p e r a t u r e s . T h e s e a r e m e n t i o n e d h e r e f o r t h e s a k e o f
c o m p l e t e n e s s b u t
h a v e n o t
b e e n
i n v e s t i g a t e d
i n
t h e
c o u r s e o f t h i s
P h . D .
T h e f i r s t o f t h e s e s y s t e m s
c o n s i s t
o f t h e c o m p o u n d s o f t h e m e r c u r y - b a s e d
s y s t e m ,
f o r
e x a m p l e
H g B a 2 C a 2 C u 2 0 g + § ,
w h i c h
w e r e
d i s c o v e r e d b y P u t i l i n e t
a l . i n 1 9 9 1
[ 1 . 7 6 ] .
A l t h o u g h
t h e
T c s
o f t h e s e m a t e r i a l s w e r e
o r i g i n a l l y
l o w ,
t h e y n o w
i n c l u d e
t h o s e
w i t h ,
c u r r e n t l y ,
t h e
h i g h e s t
k n o w n
T c
o f 1 6 4 K u n d e r
p r e s s u r e .
T h e s e c o m p o u n d s
b e l o n g
t o t h e
s a m e
g r o u p
o f
s t r u c t u r e s a s
t h e
B i
a n d T l - b a s e d
H T S C s ,
a n d l i k e t h e
T l - b a s e d
c o m p o u n d s
a r e h i g h l y
t o x i c .
S e c o n d l y ,
s u p e r c o n d u c t i v i t y
h a s b e e n
o b s e r v e d
i n w h a t a r e
k n o w n a s
i n f i n i t e - l a y e r
c o m p o u n d s ,
w h i c h h a v e a s t r u c t u r e
c o n s i s t i n g o f a n i n f i n i t e a r r a y
o f
C u 0 2
p l a n e s
s e p a r a t e d
b y i n s u l a t i n g l a y e r s . T h e s y n t h e s i s o f
( S r , C a ) C u C > 2
w a s f i r s t r e p o r t e d b y
G r e a v e s
[ 1 . 7 7 ]
a n d S i e g r i s t e t
a l . [ 1 . 7 8 ]
i n 1 9 8 8 . I n
1 9 9 1
t h e f i r s t i n f i n i t e l a y e r
s u p e r c o n d u c t o r ,
( S r i _ x N d x ) C u 0 2 ( T c
=
4 0
K ) ,
w a s s y n t h e s i s e d b y S m i t h e t
a l . [ 1 . 7 9 ] .
T h i s
w a s s o o n f o l l o w e d b y t h e d i s c o v e r y o f
s u p e r c o n d u c t i v i t y a t
t e m p e r a t u r e s o f u p t o 1 1 0
K
i n
h o l e - d o p e d s a m p l e s w i t h t h e
n o m i n a l
c o m p o s i t i o n
( S r o . 7 C a o . 3 ) o . 9 C u 0 2
[ 1 . 8 0 ] .
T h e s e
m a t e r i a l s a r e
i n t e r e s t i n g
i n
t h a t
t h e y
d o n o t c o n t a i n a s e p a r a t e d o p a n t l a y e r
t o p r o v i d e
c h a r g e
t o t h e
C u C > 2
p l a n e s .
F i g u r e
1 . 1 1 s h o w s
a
s c h e m a t i c r e p r e s e n t a t i o n
o f t h e
s t a c k i n g
s e q u e n c e o f t h e
m e t a l o x i d e
l a y e r s p e r p e n d i c u l a r
t o t h e
c - a x i s
w h i c h a r e
c o m m o n
t o a l l
t h e
2 5
Chapter 1 : Superconductivity
(Tl, Bi or Hg)m(Can.])(Ba or Sr)2Cun02n+m+2 compounds (for Bi, m = 2, n = 1, 2, 3; for
Tl, m = 1, 2, n = 1, 2, 3; for Hg, m = 1, n = 1, 2, 3).
m= 1
Tl/HgO
Ba/SrO
n= 1 CuC>2
Ba/SrO
Tl/HgO
m= 2
Tl/BiO
Tl/BiO
Ba/SrO
CuC>2
Ba/SrO
Tl/BiO
Tl/BiO
Tl/HgO
Ba/SrO
CUO2
n= 2 Ca
Cu02
Ba/SrO
Tl/HgO
Tl/HgO
Ba/SrO
Ca
n“ 3 CuOj
Ca
CUQ2
Ba/SrO
Tl/HgO
« i • o
» • • •
0-•-O-O-O-•-0
• • • t
Tl/BiO
Tl/BiO
Ba/SrO
Cu°2
Ca
Cu°2
Ba/SrO
Tl/BiO
Tl/BiO
— >— h— C-- — —1
i . • f, o
• e • ©
Tl/BiO
Tl/BiO
Ba/SrO
CUQ2
Ca
CuCÿ
Ca
Cu O2
Ba/SrO
Tl/BiO
Tl/BiO
-0-o-0—0—o
Figure 1.11 : Schematic representation of the stacking sequence of the
metal oxide layers perpendicular to the c-axis in
(Tl, Bi or Hg)m(Can.])(Ba or Sr)2Cun02n+m+2 compounds.(for Bi, m = 2,
n = 1,2,3; for Tl, m - 1,2, n = 1,2,3; for Hg, m = 1, n = 1,2,3).
Thirdly there are the compounds of the (Pb,Cd)-Sr-(Y,Ca)-Cu-0 system, for
example (Pbo.5Cdo.5)Sr2(Yi_xCax)Cu207. These too are superconducting at high
temperatures and belong to a family of materials with the same structures as a number of
the Tl and Hg-based HTSCs.
26
C h a p t e r 1 :
S u p e r c o n d u c t i v i t y
F o u r t h l y a
n u m b e r
o f
H T S C
c o m p o u n d s h a v e b e e n
s y n t h e s i s e d
b y
s u b s t i t u t i n g
l e a d
i n t o
t h e B S C C O
a n d T l - S r - C a - C u - 0
s y s t e m s
i n
p l a c e o f a
p e r c e n t a g e
o f t h e
B i
o r
T 1
a t o m s i n o r d e r
t o s t a b i l i s e
t h e m .
L a s t l y t h e r e a r e t h e n - t y p e
H T S C s ,
w h e r e
c o n d u c t i o n
o c c u r s v i a
e l e c t r o n s r a t h e r
t h a n
h o l e s .
T h e f i r s t o f
t h e s e ,
N d 2 - x C e x C u 0 4 + 5 , w a s d i s c o v e r e d b y
T o k u r a e t
a l . i n
1 9 8 9
[ 1 . 8 1 ]
a n d h a s
a
T c
o f
~ 2 4 K .
1 . 9
T H E
M I C R O S C O P I C T H E O R
Y
O F
H I G H -
T c
S U P E R C O N D
U C T I V I T Y
A l t h o u g h m a n y
t h e o r i e s h a v e b e e n p u t f o r w a r d t o
e x p l a i n t h e
p r o p e r t i e s o f
H T S C s ,
t h i s i s a n a r e a o f g r e a t
c o n t r o v e r s y a s
t h e r e i s a s
y e t
n o
g e n e r a l l y
a c c e p t e d
t h e o r y
w h i c h f u l l y e x p l a i n s t h e i r b e h a v i o u r .
F r o m t h e
B C S t h e o r y
M c M i l l a n
[ 1 . 8 2 ]
p r e d i c t e d
a
m a x i m u m
p o s s i b l e
T c
f o r
s t r o n g - c o u p l e d
s u p e r c o n d u c t o r s
g i v e n
b y
( 1 . 1 4 )
w h e r e M i s t h e
a v e r a g e
m a s s o f t h e a t o m s i n
t h e
m a t e r i a l
i n
q u e s t i o n
a n d C
i s
a
c o n s t a n t f o r a g i v e n
c l a s s
o f
m a t e r i a l s .
U n f o r t u n a t e l y t h e
c r i t i c a l
t e m p e r a t u r e s o f
m a n y o f
t h e
H T S C s e a s i l y
e x c e e d
r c m a x ,
i n d i c a t i n g t h a t t h e y
r e q u i r e a t l e a s t a n
e x t e n s i o n
t o t h e
B C S t h e o r y
b e f o r e t h e i r
p r o p e r t i e s
c a n b e
f u l l y e x p l a i n e d . T h i s i s c o n f i r m e d
b y , f o r
e x a m p l e ,
m e a s u r e m e n t s o f
2 A ( 0 )
/
k s T c ,
w h i c h ,
a c c o r d i n g t o t h e
B C S t h e o r y
i s 3 . 5 2
b u t
i s c o n s i d e r a b l y h i g h e r
i n
m o s t H T S C s
[ 1 . 5 5 ] ,
A
n u m b e r o f
t h e o r i e s h a v e b e e n p u t f o r w a r d w h i c h a t t e m p t
t o
e x p l a i n
h i g h - T c
s u p e r c o n d u c t i v i t y .
A s
y e t
n o n e o f t h e s e
h a s
b e e n i n c o n t r o v e r t i b l y
p r o v e n
t o a c c o u n t f o r
a l l
t h e i r
p r o p e r t i e s a n d t h e r e
i s
s t i l l
c o n s i d e r a b l e
d e b a t e
a s t o w h i c h
i s t h e
c o r r e c t
e x p l a n a t i o n .
T h e
e l e c t r o n - p h o n o n
i n t e r a c t i o n h a s
n o t p l a y e d a l a r g e
r o l e
i n
t h e
t h e o r y o f
H T S C s ,
u n l i k e t h e
c a s e i n L T S C s . T h e e l e c t r o n - e l e c t r o n i n t e r a c t i o n
h a s b e e n f o u n d t o
a c c o u n t f o r
o b s e r v e d m a g n e t i c
e f f e c t s a n d u n u s u a l
n o r m a l
s t a t e
p r o p e r t i e s
b u t t h e
e l e c t r o n i c
s t r u c t u r e o f H T S C s m u s t b e u n d e r s t o o d
b e f o r e
a c l e a r t h e o r y c a n
e m e r g e .
I t h a s b e e n s h o w n b y G o u g h e t
a l .
[ 1 . 8 3 ]
t h a t t h e
s u p e r c u r r e n t
c a r r i e r s i n
H T S C s
a r e p a i r e d e l e c t r o n s o r
h o l e s .
T h e
e x a c t m e c h a n i s m
b y
w h i c h
t h e
e l e c t r o n s a r e
p a i r e d
i s
a s s u m e d
t o b e
s i m i l a r t o t h a t o f
t h e B C S
t h e o r y ,
b u t
i t s
d e t a i l s a r e
s t i l l
u n c l e a r .
E v i d e n c e
h a s b e e n p u b l i s h e d w h i c h
s u p p o r t s a n u m b e r o f c o m p e t i n g
t h e o r i e s
[ 1 . 8 4 ,
8 5 ] ,
2 7
Chapter 1 : Superconductivity
In addition to this lack of a single unifying theory, there are also many problems
which limit the application of accepted models, such as the Bean model, to the behaviour
of HTSCs. These include uncertainty about the nature of the behaviour of the flux line
lattice in HTSC materials as a function of field and temperature, and also the effects of
the severe anisotropy in the structure of the HTSCs.
1.10 THE EFFECTS OF ANISOTROPY
Most known high-Tc oxide superconductors are anisotropic layer structures (see
section 1.8). For example, the c-axis of a unit cell of YBCO is approximately three times
longer than the a or b axes. This and the very short coherence length in the HTSCs means
the properties of HTSCs within the ah plane are very different to those along the c axis
[1.55, 86]. A few of these properties are listed below as examples.
(i) The c-axis resistivity is much greater than that along the airplanes, so that
Pcÿ Pab ~ 100. Also, the normal electron mean free path is only about twice the c-axis
spacing.
(ii) HC2 is much larger along the ab plane than along the c-axis, with
Hcÿ (BLc - axis) > H ( Bile - axis). B, is approximately equal to the carrier separation so
there is very little overlap of Cooper pairs both within and between aÿ-planes. This
means that superconductivity is mainly in the ab planes, which are only weakly coupled
to each other.
(iii) The penetration depth and coherence lengths show similar behaviour. The
BSCCO system has the largest anisotropy of X and £, with, for Bi:2212 [1.55, 87],
~ 500 and ~ 8
This means that flux lines penetrate between the ab planes much more easily than
they cut across them. For a field at an angle to the ab planes this leads to the situation
shown in figure 1.12, where the flux lines in a HTSC, rather than being parallel to the
applied field, are 'stepped' with 'treads' along the ab plane and 'risers' along the c-axis.
The relative sizes of the 'treads' and 'risers' are determined by the angle of the field to the
ab plane.
In particularly anisotropic materials such as BSCCO the ab-plane shows metallic
behaviour while the c-axis is Josephson coupled [1.88] as first proposed by Lawrence and
Doniach for LTSC layer structures [1.89], In HTSCs it leads to the existence of 'pancake'
28
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
v o r t i c e s ,
a s f i r s t
c o n s i d e r e d
b y C l e m
i n
1 9 9 1
[ 1 . 9 0 ] .
I n t h i s
m o d e l ,
r a t h e r
t h a n
a
c y l i n d e r
o f
c u r r e n t
c i r c u l a t i n g
a r o u n d a f l u x
l i n e
p e r p e n d i c u l a r
t o t h e
a b p l a n e ,
d i s k s
o f
c u r r e n t
c i r c u l a t e
i n
e a c h
a b p l a n e
a n d a r e o n l y
w e a k l y c o u p l e d t o t h e
c o r r e s p o n d i n g
d i s k s
i n
a d j a c e n t
p l a n e s .
W h e n
t h e t h e r m a l
e n e r g y
o f e a c h p a n c a k e
b e c o m e s
g r e a t e r
t h a n
t h e
i n t e r p l a n e c o u p l i n g
e n e r g y , t h e
' p a n c a k e s '
o n e a c h l a y e r
d e c o u p l e a n d
m o v e
w i t h i n
t h e
p l a n e i n d e p e n d e n t l y o f t h o s e
i n t h e o t h e r l a y e r s ,
t u r n i n g
t h e
s u p e r c o n d u c t i v i t y
f r o m a
3 d
p h e n o m e n o n t o
o n e o c c u r r i n g
i n a
c o l l e c t i o n o f 2 d
s h e e t s .
F i g u r e
1 . 1 3
s h o w s
s c h e m a t i c
d i a g r a m s
o f
3 d c o u p l e d
a n d 2 d
d e c o u p l e d f l u x
p a n c a k e s .
B
F l u x
L i n e s
( a )
F i g u r e 1 . 1 2 :
B e h a v i o u r
o f f l u x
l i n e s i n
a H T S C
w i t h t h e
f i e l d
a p p l i e d
a t
a n
a n g l e t o
t h e
a b - p l a n e s .
' V o r t e x
L i n e s '
( b )
A T
F l u x
P a n c a k e s
F i g u r e
1 . 1 3 : S c h e m a t i c
d i a g r a m o f f l u x
p a n c a k e s
s h o w i n g
( a )
3 d c o u p l e d
p a n c a k e s a n d
(
b
)
2 d d e c o u p l e d p a n c a k e s .
T h i s
b e h a v i o u r
h a s b e e n
o b s e r v e d ,
f o r e x a m p l e ,
i n
B i : 2 2 1 2
b y
C u b b i t e t a l .
[ 1 . 9 1 ]
a n d i m p l i e s
t h a t t h e
s a m e
a r r a n g e m e n t
o f p i n n i n g c e n t r e s w o u l d b e
n e e d e d o n a l l l a y e r s
t o
c o m p l e t e l y
p r e v e n t
v o r t e x m o v e m e n t
i n
t h e
2 d
s t a t e . W i t h
B
a t a n a n g l e
t o t h e
c - a x i s ,
2 9
Chapter 1 : Superconductivity
decoupling is even more likely to occur due to the already-weak interplane coupling of
the 'stepped' flux lines (see figure 1.12).
Because the energies to move the flux pancakes independently on each plane are
much lower than those to move a whole 'vortex line', the irreversibility line and thus the
Jc of a material in the 2d state is much lower than that in the 3d state. Attempts have been
made to explain this transition in terms of the theory of Kosterlitz and Thouless [1.92],
but incontrovertible evidence for this has not yet been found.
l.ll GRANULAR SUPERCONDUCTORS
Granular superconductors are a composite consisting of an array of
superconducting particles separated from each other by a weakly or non-superconducting
medium. The original interest in these materials stemmed from the observation of an
enhanced Tc in granular aluminium films, but many types of material show granular
behaviour, from fine multi-filamentary superconducting wires to sintered HTSCs. In
some materials granularity is intrinsic to the superconductor, arising at weakly or
non-superconducting regions due to, for example, a short coherence length. In others it is
an extrinsic property. Goldman and Wolf, and Gubser et al. [1.93, 94] describe granular
superconductivity in LTSCs while Finnemore gives a general review including HTSCs
[1.95].
A basic feature of granular superconductivity is that, although the grains within
the superconductor may be individually below Tc, H or Jc, the sample will not show
bulk superconductivity until the intergranular regions also become superconducting. This
occurs when the temperature, field or current fall sufficiently for the intergrains become
superconducting, or when the proximity effect from the grains becomes large enough to
link the grains together. Because of this, in a granular material the overall transport
properties are determined by the intergranular regions.
Granular materials tend to show a two-stage transition to superconductivity. In a
resistive transition there is an initial drop in resistance arising from loss of resistance in
the grains, followed by a further drop to zero resistance as the intergrains start to
superconduct and phase coherence is established over the whole superconductor. In an
ACS a drop in %' occurs when the individual grains become superconducting and enter
the Meissner state, followed by a slower drop as grains link together in local
phase-locked loops which grow until a single loop is formed over the entire sample when
bulk diamagnetism arises. This is shown in figures 2.3 and 2.27.
30
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
l . l l . l
J O S E P H S O N
E F F E C T S
I n 1 9 6 2 J o s e p h s o n
p r e d i c t e d
t h a t C o o p e r
p a i r s
s h o u l d
b e
c a p a b l e
o f
t u n n e l l i n g
t h r o u g h
n o r m a l o r
i n s u l a t i n g
b a r r i e r s
i n
t h e s a m e w a y
a s
s i n g l e
e l e c t r o n s [ 1 . 9 6 ] .
H e
a l s o
p r e d i c t e d t h a t t h i s t u n n e l l i n g
s u p e r c u r r e n t ,
i f
d r i v e n
b y a
D . C . v o l t a g e ,
w o u l d
b e
a n
a l t e r n a t i n g
c u r r e n t . T h e s e e f f e c t s w e r e c o n f i r m e d e x p e r i m e n t a l l y
a n d
n o w
b e a r
h i s
n a m e .
A l t h o u g h
J o s e p h s o n b a s e d h i s p r e d i c t i o n s o n a
m i c r o s c o p i c
t h e o r e t i c a l
a n a l y s i s
o f
q u a n t u m
m e c h a n i c a l t u n n e l l i n g o f e l e c t r o n s t h r o u g h
a b a r r i e r l a y e r ,
i t
h a s s i n c e
b e c o m e
c l e a r t h a t t h e s e e f f e c t s a r e
v e r y g e n e r a l a n d o c c u r
w h e n e v e r t w o
s t r o n g l y
s u p e r c o n d u c t i n g
e l e c t r o d e s a r e c o n n e c t e d b y a w e a k e r o r
n o n - s u p e r c o n d u c t i n g
l i n k . T w o
g e n e r a l
r e v i e w s
o f t h i s s u b j e c t a r e
p r e s e n t e d b y L i k h a r e v i n
[ 1 . 9 7 ]
a n d b y
T i n k h a m i n
[ 1 . 9 8 ] .
T y p e s o f W e a k L i n k s
T h e r e a r e
s e v e r a l t y p e s o f w e a k
l i n k s
( W L s ) .
T h e s e a r e
l i s t e d b e l o w .
( i )
A n
i n s u l a t i n g
l a y e r
b e t w e e n t w o
s u p e r c o n d u c t o r s
( a s
J o s e p h s o n
o r i g i n a l l y
p r o p o s e d ) ,
n o t n e c e s s a r i l y
o f
t h e
s a m e t y p e .
T h i s
i s k n o w n a s
a n S I S j u n c t i o n
i f
t h e t w o
s u p e r c o n d u c t o r s a r e o f t h e
s a m e t y p e , o r S I S '
i f n o t . I n t h i s c a s e
t h e w a v e
f u n c t i o n s o f t h e
t w o s u p e r c o n d u c t o r s a r e
s e p a r a t e f r o m e a c h o t h e r a n d t h e j u n c t i o n
m u s t
b e v e r y
t h i n
( ~ l n m )
t o
s h o w a n y
s u p e r c o n d u c t i n g p r o p e r t i e s .
( i i )
A
n o r m a l
m e t a l l a y e r .
T h i s t y p e o f
j u n c t i o n
i s
k n o w n a s
S N S
i f t h e t w o
s u p e r c o n d u c t o r s
a r e o f t h e s a m e
t y p e , o r
S N S '
i f
n o t .
I n t h i s c a s e
t h e
p r o x i m i t y e f f e c t
( s e e
s e c t i o n
1 . 3 )
c a u s e s t h e
e x t e n s i o n o f a
r e d u c e d
s u p e r c o n d u c t i n g
s t a t e
a c r o s s t h e n o r m a l
l a y e r a n d t h e
p a r t i a l s u p p r e s s i o n
o f
t h e
s u p e r c o n d u c t i n g s t a t e
i n
t h e
s u p e r c o n d u c t o r
c l o s e
t o
t h e
W L .
B e c a u s e
o f
t h e p r o x i m i t y e f f e c t t h e b a r r i e r l a y e r c a n b e
m u c h
t h i c k e r t h a n i n a
S I S j u n c t i o n
( ~ 5 0 n m ) .
( i i i )
A
s h o r t
c o n s t r i c t i o n
i n a c o n t i n u o u s
b o d y o f s u p e r c o n d u c t o r .
T h i s i s k n o w n
a s
a
S c S
j u n c t i o n .
I n t h i s c a s e
t h e r e
i s n o r e d u c t i o n i n t h e s u p e r c o n d u c t i n g
w a v e f u n c t i o n a t
t h e
W L ,
b u t
i n s t e a d a n
i n c r e a s e i n
t h e
s u p e r c u r r e n t
c a r r i e r v e l o c i t y
v s .
( i v )
O t h e r
t y p e s o f m u l t i - l a y e r
W L
s t r u c t u r e s
a r e p o s s i b l e ,
f o r
e x a m p l e
S N I N S , o r
S N I S ' .
T h e s e a r e m e n t i o n e d o n l y f o r c o m p l e t e n e s s a n d w i l l n o t
b e
d i s c u s s e d f u r t h e r
i n
t h i s t h e s i s .
3 1
Chapter 1 : Superconductivity
The Jr- of a Weak Link
As stated in section 1.3 a superconductor is a macroscopic quantum system
described by an order parameter with amplitude and phase, given by equation 1.2.
In zero magnetic field the phase of this wave function, (p, varies with position as
the supercurrent carrier velocity vs and the inverse of the supercurrent carrier density ns,
i.e
d (p 1
(1.15)
dx ns
This implies that when ns drops to near zero, as in the vicinity of an insulating or
normal metal WL, or becomes high, as in a constriction, then (p changes very rapidly
with position as compared to the bulk of the superconductor. If the link is weak enough
its phase gradient becomes so large that the phase gradient in the bulk of the material can
be neglected and the current is determined only by the total phase difference A(p between
the strong superconductors on each side of the WL, not the local details of the phase
gradient. This is an essential property of Josephson junctions.
If a constriction WL is longer than the coherence length E, the supercurrent in the
link scales with A(p until Jc is reached. If the WL is shorter than then A(p varies within
the range ±TC due to the higher energy cost of a larger difference so that the supercurrent
in the link is determined by Acp within the bounded and periodic range I2tcI. The simplest
generalisation of this is
This is known as the D.C. Josephson effect. There is also an A.C. Josephson
effect, but this is not relevant to the results taken here and is not discussed further.
From these concepts relations for the critical currents of weak links can be
derived. Ambegaokar and Baratoff [1.99, 100] found, neglecting suppression of the
superconducting energy gap by the supercurrent, that the critical current due to tunnelling
between two superconductors is
Is = Ic sin(Atp) (1.16)
(1.17)
where A(T) is the energy gap parameter from BCS theory, and
32
C h a p t e r
1 : S u p e r c o n d u c t i v i t y
( 1 . 1 8 )
w h e r e t
i s
t h e r e d u c e d
t e m p e r a t u r e
T / T c ,
i s t h e
t h i c k n e s s
o f
t h e
n o r m a l
m e t a l
b a r r i e r a n d
i s
t h e
d i s t a n c e e l e c t r o n
p a i r s
p e n e t r a t e t h e b a r r i e r
( s e e
s e c t i o n 1
. 3 ) .
T h e e f f e c t o f a m a g n e t i c f i e l d
o n a J o s e p h s o n j u n c t i o n
i s d e p e n d e n t
o n t h e
t y p e o f
j u n c t i o n i n v o l v e d . F o r a
l o o p
o f
s u p e r c o n d u c t o r w i t h
t w o
i d e n t i c a l w e a k
l i n k s
i n
i t ,
a s
s h o w n
i n
f i g u r e
1 . 1 4 ,
a n
a p p l i e d m a g n e t i c f i e l d
c a u s e s a
m o d u l a t i o n o f t h e
I c
o f t h e
l o o p
a s
a
w h o l e .
w h e r e
I c
i s t h e c r i t i c a l
c u r r e n t o f e a c h
W L ,
< t >
t h e
a p p l i e d f l u x
a n d
O o
t h e f l u x
q u a n t u m .
T h i s
r e l a t i o n p e r m i t s t h e
m e a s u r e m e n t o f
f l u x
d o w n t o s m a l l
f r a c t i o n s o f
< t > o
a s
t h i s
i s
t h e
p e r i o d o f t h e i n t e r f e r e n c e
p a t t e r n , a n d
f o r m s
t h e
b a s i c
p r i n c i p l e o f t h e
s u p e r c o n d u c t i n g
q u a n t u m i n t e r f e r e n c e d e v i c e
( S Q U I D ) .
F o r a s i n g l e
e x t e n d e d r e c t a n g u l a r j u n c t i o n p e n e t r a t e d b y
f l u x i n t h e
p l a n e o f t h e
j u n c t i o n t h e
m a x i m u m c u r r e n t
r e m a i n s
p e r i o d i c i n
f i e l d b u t i s
r e d u c e d a t
i n c r e a s e d f i e l d s
T h i s i s
t h e
s a m e f o r m a s
t h a t o f t h e F r a u n h o f e r
d i f f r a c t i o n
p a t t e r n f o r l i g h t p a s s i n g
t h r o u g h a
n a r r o w r e c t a n g u l a r
s l i t .
T
2
F i g u r e
1 . 1 4 :
S c h e m a t i c
d i a g r a m , o f
a l o o p o f s u p e r c o n d u c t o r
w i t h
t w o
w e a k
l i n k s
c o n t a i n i n g
f l u x
0 .
T h i s a r r a n g e m e n t
f o r m s
t h e
b a s i s
o f
t h e
s u p e r c o n d u c t i n g q u a n t u m i n t e r f e r e n c e
d e v i c e
( S Q U I D ) .
T h e m a x i m u m
c u r r e n t t h r o u g h
t h e l o o p i s t h e n g i v e n b y
( 1 . 1 9 )
a s
( 1 . 2 0 )
3 3
Chapter 1 : Superconductivity
If the local critical supercurrent density Jc(x) is non-uniform this result is replaced
by a Fourier transform of Jc(x). Also, if the junction area is circular instead of rectangular
then an Airy diffraction pattern is obtained.
1.11.2 GRANULAR SUPERCONDUCTORS IN GENERAL
Because the intergrains act as weak links, a granular superconductor can be
considered an array of Josephson junctions, which can be anything from completely
regular to completely random. A granular superconductor can be approximated as an
array of identical superconducting grains coupled by Josephson junctions [1.101], If these
grains are arranged on a cubic lattice with a lattice constant of a0 then Jc is given by
J = (1.21)
where IQ is given by equation 1.17 for a SIS junction and equation 1.18 for a SNS
junction. The interactions between Josephson junctions are reviewed by Bindslev Hansen
in [1.102] but are not considered further in this thesis.
Because the intergrains are weak links flux can penetrate into the material more
easily through these paths than if it had to penetrate a bulk sample of the same
dimensions. This leads to very inhomogenous distributions of flux, especially in fields
decreasing from values high enough to penetrate the grains, when flux can be trapped in
the grains [1.103] and makes any interpretation using a critical state model (see
section 1.6) very complex, as flux penetrates the inter- and intra-granular regions
differently. This means that to calculate a magnetic Jc the length scale over which the
induced current flows must be measured or assumed. This can be done by analysis of
hysteresis loops [1.104], or via ACS measurements [1.105].
1.11.3 GRANULARITY IN HIGH TC SUPERCONDUCTORS
Very soon after HTSCs were discovered it became obvious that most processing
routes for them produce extremely granular materials. However, the granularity in
HTSCs has a number of differences from that in LTSCs. Most significant is that for
granular LTSCs the grain size (~8nm) is smaller than the bulk coherence length
(~100nm). In HTSCs the grain size (~l(im) is larger and the coherence length (~lnm)
shorter than in LTSCs, significantly affecting many of their properties. For example it
increases their sensitivity to defects and impurities within grains [1.55], makes them
34
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
h i g h l y
s e n s i t i v e
t o
a p p l i e d
f i e l d s
w h i c h
r a p i d l y s u p p r e s s t h e w e a k l y l i n k e d
i n t e r g r a i n s
a n d
c a u s e s
l a r g e
t h e r m a l
f l u c t u a t i o n s
w h i c h ,
f o r e x a m p l e ,
b r o a d e n
t h e
r e s i s t i v e
t r a n s i t i o n
[ 1 . 5 5 , 1 0 6 ] .
I t h a s a l s o
b e e n
p r o p o s e d t h a t
t h e g r a i n
b o u n d a r i e s o f
H T S C s a r e
c o n s i d e r a b l y
m o r e c o m p l e x
t h a n
t h o s e
o f L T S C s
[ 1 . 1 0 7 ] ,
f u r t h e r
c o m p l i c a t i n g
m a t t e r s .
G e r b e r c o m p a r e s
g r a n u l a r i t y
i n L T S C s a n d H T S C s i n
[ 1 . 1 0 8 ] .
M o s t
H T S C s
a r e
i n t r i n s i c a l l y
g r a n u l a r d u e t o t h e
a n i s o t r o p y
o f
t h e i r
p h y s i c a l
p r o p e r t i e s . T h i s t u r n s
t h e m i n t o a
s e r i e s o f s u p e r c o n d u c t i n g
p l a n e s
( t h e
C u O l a y e r s )
w h i c h a r e o n l y w e a k l y l i n k e d . A t a g i v e n
p o i n t i n
a L T S C t h e
w a v e
f u n c t i o n s o f
m i l l i o n s
o f C o o p e r p a i r s
a r e
o v e r l a p p i n g ,
s t r o n g l y l i n k i n g t h e
p h a s e o f t h e
s u p e r c o n d u c t i n g w a v e
f u n c t i o n a c r o s s
t h e w h o l e s u p e r c o n d u c t o r . I n a H T S C w h e r e t h e
c o h e r e n c e l e n g t h
a l o n g
t h e
o a x i s , ~ l n m ,
i s l e s s t h a n t h e
c - a x i s
s i z e o f t h e u n i t
c e l l ,
o n l y
~ 1 0 C o o p e r
p a i r s
o v e r l a p
a t a n y g i v e n p o i n t .
T h i s m a k e s
t h e
p h a s e
o f
t h e w a v e
f u n c t i o n i n a
H T S C
m u c h
m o r e
w e a k l y l i n k e d a n d e a s i l y
d i s r u p t e d
b y
l o c a l d i s t o r t i o n s
w h i c h b r e a k i t
u p i n t o
a
s e r i e s
o f w e a k l y l i n k e d r e g i o n s w i t h
d i f f e r e n t p h a s e s t o
t h e i r
w a v e
f u n c t i o n s .
T h i s m e a n s
t h a t t h e m a t e r i a l s b e h a v i o u r i s g o v e r n e d b y t h e
J o s e p h s o n c o u p l i n g o f
t h e
C u O l a y e r s
[ 1 . 8 9 ] .
A l s o ,
t h e
s h o r t c - a x i s c o h e r e n c e l e n g t h m e a n s t h a t
u n d e r c e r t a i n c o n d i t i o n s ,
u s u a l l y a t
t e m p e r a t u r e s
n e a r
T c ,
t h e
C u - 0 p l a n e s
i n
a H T S C c a n
d e c o u p l e d f r o m e a c h
o t h e r a s
d e s c r i b e d i n s e c t i o n 1 . 1 0 .
M o s t
b u l k p r o c e s s i n g r o u t e s f o r H T S C s a l s o
p r o d u c e
e x t r i n s i c a l l y g r a n u l a r
m a t e r i a l s ,
c o n s i s t i n g o f g r a i n s , e a c h
w i t h ,
p o s s i b l y ,
h i g h - q u a l i t y
s u p e r c o n d u c t i n g
p r o p e r t i e s ,
b u t
v a r y i n g
a l i g n m e n t r e l a t i v e t o
e a c h
o t h e r ,
s e p a r a t e d b y g r a i n
b o u n d a r i e s o f
m u c h
l o w e r
q u a l i t y
m a t e r i a l w i t h
a t h i c k n e s s
g r e a t e r
t h a n t h e
a f r - p l a n e
o r c - a x i s
c o h e r e n c e l e n g t h s o t h a t t h e y f o r m w e a k l i n k s
[ 1 . 1 0 9 ] .
T h i s m e a n s t h a t t h e
a c t u a l
t r a n s p o r t
J c
i n
a m e a s u r e m e n t c a n b e
c o n s i d e r a b l y
h i g h e r
t h a n
t h a t
c a l c u l a t e d
b y
a s s u m i n g t h e c u r r e n t f l o w s
e v e n l y
t h r o u g h o u t t h e e n t i r e
c r o s s - s e c t i o n o f t h e s a m p l e
a s
i t
d e p e n d s o n
t h e
c o n t i n u o u s p a t h
t r a v e r s i n g
t h e
s t r o n g e s t
o f
t h e
w e a k
l i n k s ,
u s u a l l y
o n l y
a
f r a c t i o n o f
t h e
t o t a l c r o s s - s e c t i o n a l a r e a . C a l c u l a t i o n s h a v e f o u n d t h a t > 1 7 %
o f s t r o n g
g r a i n
b o u n d a r i e s
w i l l
f o r m a t l e a s t o n e c o n t i n u o u s
h i g h
c u r r e n t p e r c o l a t i v e
c o n d u c t i o n
p a t h
t h r o u g h a g r a n u l a r
H T S C
[ 1 . 1 1 0 ] .
T h e o v e r a l l
J c
i s
d e t e r m i n e d
b y t h e
w e a k e s t l i n k
o n t h i s p a t h . I n
a g r a n u l a r s u p e r c o n d u c t o r t h e
i n t r a - g r a i n
J c
i s d e t e r m i n e d b y f l u x
p i n n i n g
w i t h i n t h e g r a i n s , w h i l e t h e i n t e r - g r a i n ( t r a n s p o r t )
J c
i s d e t e r m i n e d
b y
t h e w e a k l i n k s
b e t w e e n
g r a i n s .
U s i n g
t h i s c o n c e p t
a t t e m p t s
h a v e b e e n m a d e t o e x p l a i n
t h e
I - V f o r
H T S C s
i n t e r m s o f d i s t r i b u t i o n s o f i n t e r g r a i n
7 c s
[ 1 . 1
1
1 ] .
A l s o , t h e a l i g n m e n t
b e t w e e n a d j a c e n t
g r a i n s
h a s
a
s i g n i f i c a n t
e f f e c t o n t h e
J c
o f
t h e
g r a i n
b o u n d a r y . I n g e n e r a l ,
t h e l a r g e r
t h e
m i s o r i e n t a t i o n t h e
l o w e r t h e
J c
o f
t h e
b o u n d a r y . D i m o s
a n d
C h a u d h a r i
[ 1 . 1 1 2 , 1 1 3 ]
p e r f o r m e d e x p e r i m e n t s
o n e p i t a x i a l t h i n
f i l m s
o n
b i c r y s t a l
s u b s t r a t e s
w i t h d i f f e r e n t
d e g r e e s
o f a & - p l a n e
m i s o r i e n t a t i o n . T h e y
3 5
Chapter 1 : Superconductivity
found that Jc for an ad-plane misalignment angle of 10° fell by a factor of fifty from that
in a perfectly aligned sample, indicating that grain misalignment is a major factor limiting
the Jc of bulk HTSC materials. Field et al. found similar behaviour in bicrystals of
melt-textured YBCO [1.1141. However, it has also recently been suggested by Kroeger
et al. [1.115, 116] that low angle (<10°) grain boundaries are the main current carrying
paths through high quality bulk HTSCs. This supports the work of Shi [1.117], who finds
that the Jc-B characteristics of a material are determined mainly by the portion of strongly
coupled regions at grain boundaries and not necessarily by their overall orientation.
Two models have been proposed to explain current flow in textured HTSCs.
These are the 'Brick Wall' model of Malozemoff et al. [1.118, 119] and the 'Railway
Switchyard' model of Hensel et al. [1.120]. Both models imply that, regardless of the
relative directions of overall current flow and applied magnetic field, there is never a
'force-free' situation where the current is always parallel to the applied field.
The 'Brick Wall' Model
This model assumes that in an aligned superconductor the superconducting grains
are regularly arranged, as in a brick wall, with a common c-axis but misalignment in the
ad-plane. This means the ah plane intergranular junctions form weak links to current
flow, forcing current to meander from grain to grain via c-axis coupling. Figure 1.15
shows this schematically.
This has been extended to take into account different sizes of 'bricks' in the
system, and to include the possibility of misalignment between bricks [1.121].
The 'Railway Switchyard' Model
This model, in contrast, assumes a considerable degree of c-axis misalignment
between grains, but that low angle ad-plane intergranular junctions form strongly
conducting current paths. These link the grains in the ad-planes and also, indirectly, in the
c-direction, forming a complex three-dimensional superconducting network. This means
that current meanders along the superconductor while remaining within the ad-planes of
the grains. Figure 1.16 shows this schematically.
36
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
F i g u r e
1 . 1 5
:
S c h e m a t i c
r e p r e s e n t a t i o n
o f
t h e
b r i c k w a l l
m o d e l ,
s h o w i n g
m e a n d e r i n g
c u r r e n t
f l o w
v i a c - a x i s
i n t e r g r a n u l a r
c o n t a c t s .
F i g u r e
1 . 1 6
:
S c h e m a t i c
r e p r e s e n t a t i o n
o f
t h e
r a i l w a y s w i t c h y a r d m o d e l ,
s h o w i n g
c u r r e n t
f l o w
v i a
l o w - a n g l e a b - p l a n e i n t e r g r a n u l a r
c o n t a c t s
( m a r k e d * ) .
T h e
a b - p l a n e
i s
p a r a l l e l t o
t h e
l o n g
a x i s
f o r
a l l
g r a i n s
.
T h e
r a i l w a y
s w i t c h y a r d
m o d e l i s
s u p p o r t e d
b y
a
n u m b e r
o f i t e m s o f e v i d e n c e .
F i r s t ,
t h e r e i s t h e
m i c r o s t r u c t u r e o f
t h e
t a p e s
t h e m s e l v e s ,
a s
s h o w n ,
f o r
e x a m p l e , i n
3 7
Chapter 1 : Superconductivity
[1.1201- This shows no noticeable sign of any brick wall-type structure, but transmission
electron microscopy (TEM) does show many small-angle c-axis grain boundaries [1.122,
123]. TEM investigation also shows that these low-angle grain boundaries have a high
degree of crystalline perfection [1.124], implying that they form good-quality conduction
paths. This agrees with the work of Field et al. and Kroeger et al., mentioned above
[1.114-116],
A problem with any model of conduction which includes a distribution of
misalignment angles through the sample is that Nakamura, in experiments on BSCCO
single crystals, has shown that the suppression of Jc with B is determined by the c-axis
component of the applied field [1.125]. This means that as long as any misalignment
exists in a sample there will be areas where the applied field has a c-axis component, and
thus in which the Jc is suppressed, leading to the most misaligned grain determining the
overall Jc of a sample in a magnetic field.
Peterson and Ekin [1.126] have argued that an Airy diffraction pattern (of the
form |/1(x)|/(x/2), where J\ is the first Bessel function) should be used instead of a
Fraunhofer diffraction pattern (of the form |sin(x)|/x, as shown in equation 1.20) to
model the Jc-B dependence of granular HTSCs [1.98, 127]. They consider it more likely
that random intergranular contacts are circular or ellipsoidal rather than the rectangles
necessary for a Fraunhofer diffraction pattern. In both cases it is assumed that the random
intergranular junction areas smear out the periodic modulation of Jc with B, leaving only
the envelope dependence of Jc versus B ( l/(;r <$/<!>„) «= \/H for rectangular contacts,
l/(7r<f>/<I>0) l/H312 for circular or ellipsoidal contacts). This helps to account for the
large reduction of Jc with field in HTSCs.
Because of their high degree of granularity the bulk of a HTSC can easily be
penetrated by magnetic flux even though individual grains may be excluding flux. This
causes Jc to drop faster with applied field than the Jc versus B characteristic of the grains
alone would indicate. However, it has also been found that many granular HTSCs, after
an initial sharp drop in Jc, reach a plateau where the material continues to have a
measurable Jc even out to high fields. For example, Matsuda et al. found this behaviour in
Tl:1223 [1.128]. This has been explained in a number of ways, including the persistence
of a number of very strong conduction paths through the sample [1.129, 130], the result
of a random spatial distribution of grain boundary Jc in a sample [1.131], or from the
Josephson coupling of grains which are in the mixed state [1.132].
Meilikhov reviews the effects of various structural features on the Jc and I-V
characteristics of HTSCs in [1.133],
38
C h a p t e r
1
:
S u p e r c o n d u c t i v i t y
1 . 1 2
R E F E R E N C E S
[ 1 . 1 ]
H . K a m e r l i n g h
O n n e s ,
A k a d . v a n
W e t e n s c h a p p e n
(
A m s t e r d a m
) , 1 4 ,
8 1 8
( 1 9 1 1 ) .
[ 1 . 2 ]
J . G . B e d n o r z a n d K . A .
M u l l e r ,
Z .
P h y s . ,
B 6 4 ,
1 8 9
( 1 9 8 6 ) .
[ 1 . 3 ]
W . M e i s s n e r a n d
R .
O c h s e n f e l d ,
N a t u r w i s s . ,
2 1 ,
7 8 7
( 1 9 3 3 ) .
[ 1 . 4 ]
F .
R e i f ,
F u n d a m e n t a l s
o f
S t a t i s t i c a l a n d T h e r m a l
P h y s i c s ,
M c G r a w H i l l ,
N e w
Y o r k
( 1 9 6 5 )
[ 1 . 5 ]
C . J .
G o r t e r
a n d
H . G . B .
K a s i m i r ,
P h y s i c a ,
1 ,
3 0 6
( 1 9 3 4 ) .
[ 1 . 6 ]
C . J . G o r t e r a n d H . G . B .
K a s i m i r ,
P h y s .
Z . ,
3 5 ,
9 6 3
( 1 9 3 4 ) .
[ 1 . 7 ]
C . J .
G o r t e r a n d H . G . B .
K a s i m i r ,
Z . T e c h .
P h y s . , 1 5 ,
5 3 9
( 1 9 3 5 ) .
[ 1 . 8 ]
J . B a r d e e n
i n C o n c i s e E n c y c l o p a e d i a o f M a g n e t i c
a n d
S u p e r c o n d u c t i n g
M a t e r i a l s
,
p p
5 5 4 ,
e d i t e d b y J . E .
E v e t t s ( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 1 . 9 ]
F . L o n d o n a n d H . L o n d o n ,
P r o c . R o y .
S o c . ,
A 1 4 9 ,
7 1
( 1 9 3 5 ) .
[ 1 . 1 0 ]
F .
L o n d o n
i n
S u p e r f l u i d s ,
p p
1 5 2
( W i l e y
1 9 5 0 )
[ 1 . 1 1 ]
A . B .
P i p p a r d , P r o c .
R o y .
S o c .
( L o n d o n ) , A 2 1 6 ,
5 4 7
( 1 9 5 3 ) .
[ 1 . 1 2 ]
V . L . G i n z b u r g
a n d L . D .
L a n d a u ,
Z h . E k s p .
T e o r . F i z . ,
2 0 ,
1 0 6 4
( 1 9 5 0 ) .
[ 1 . 1 3 ]
E .
M a x w e l l ,
P h y s .
R e v . ,
7 8 ,
A l l
( 1 9 5 0 ) .
[ 1 . 1 4 ]
C . A .
R e y n o l d s ,
B .
S e r i n ,
W . H . W r i g h t
a n d L . B .
N e s b i t t ,
P h y s .
R e v . ,
7 8 ,
4 8 7
( 1 9 5 0 ) .
[ 1 . 1 5 ]
H .
F r o h l i c h ,
P h y s .
R e v . ,
1 9 ,
8 4 5
( 1 9 5 0 ) .
[ 1 . 1 6 ]
H .
F r o h l i c h ,
P r o c .
R o y .
S o c .
( L o n d o n ) , A 2 1 5 ,
2 9 1
( 1 9 5 2 ) .
[ 1 . 1 7 ]
J . B a r d e e n a n d D .
P i n e s ,
P h y s .
R e v . ,
9 9 ,
1
1 4 0
( 1 9 5 5 ) .
[ 1 . 1 8 ]
J .
B a r d e e n ,
L . N .
C o o p e r a n d
J . R . S c h r i e f f e r , P h y s .
R e v . ,
1 0 6 ,
1 6 2
( 1 9 5 7 ) .
[ 1 . 1 9 ]
J .
B a r d e e n ,
L . N .
C o o p e r
a n d J . R .
S c h r i e f f e r ,
P h y s .
R e v . ,
1 0 8 ,
1 1 7 5
( 1 9 5 7 ) .
[ 1 . 2 0 ]
M e s e r v e y a n d
S c h w a r z
i n
S u p e r c o n d u c t i v i t y ,
e d i t e d
b y
R . D .
P a r k s
( M a r c e l
D e k k e r N e w
Y o r k
1 9 6 9 )
3 9
Chapter 1 : Superconductivity
[1.21] H. Meissner, Phys. Rev., 109, 686 (1958).
[1.22] G. Deutscher in Concise Encyclopaedia of Magnetic and Superconducting
Materials, pp 82, edited by J.E. Evetts (Pergammon Press 1992)
[1.23] P.G. de Gennes , Superconductivity of Metals and Alloys, Pages, Benjamin,
New York (1966) p207
[1.24] F.B. Silsbee, J. Wash. Acad. ScL, 6, 597 (1916).
[1.25] J.E. Evetts and P.H. Kes in Concise Encyclopaedia of Magnetic and
Superconducting Materials, pp 88, edited by J.E. Evetts (Pergammon Press
1992)
[1.26] A.A. Abrikosov, Zh. Eksp. Teor. Fiz. (Sov. Phys. JETP), 32 (5), 1442 (1174)
(1957).
[1.27] V.G. Kogan, Phys. Rev. B, 38, 7049 (1988).
[1.28] D. Cribier, B. Jacrot, L. Madhav Rao and B. Farnoux in Progress in Low
Temperature Physics, pp 161, edited by C.J. Gorter (North Holland Amsterdam
1967)
[1.29] D.J. Bishop, P.L. Gammel, D.A. Huse and C.A. Murray, Science, 255, 165
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2 : E X P E R I M E N T A L
T E C H N I Q U E S
2 . 1 I N T R O D U C T I O N
T h e r e a r e
a
n u m b e r
o f
e x p e r i m e n t a l t e c h n i q u e s
w h i c h
a r e
c o m m o n
t o t h e
m e a s u r e m e n t s
d e s c r i b e d
b e l o w ,
a n d w h i c h c a n b e
d i v i d e d i n t o
t w o
c o m p l e m e n t a r y
c a t e g o r i e s . T h e s e a r e t r a n s p o r t m e a s u r e m e n t s
( w h i c h
c a n b e
f u r t h e r
s u b - d i v i d e d
i n t o t h o s e
u s i n g
h i g h
a n d
l o w
c u r r e n t s )
a n d
m a g n e t i c
m e a s u r e m e n t s
( w h i c h
c a n b e
d i v i d e d
i n t o D . C .
o r
A . C .
f i e l d
t e c h n i q u e s ) .
T h i s
c h a p t e r d e s c r i b e s t h e t e c h n i q u e s u s e d
f o r
c a r r y i n g
o u t
t h e s e
t y p e s o f m e a s u r e m e n t s
o n
s u p e r c o n d u c t i n g s a m p l e s .
T h e f i r s t
s e c t i o n s o f t h i s c h a p t e r d e a l w i t h
t r a n s p o r t m e a s u r e m e n t s ,
b e g i n n i n g w i t h
t h o s e
a t l o w
c u r r e n t s ,
u s e d t o
m e a s u r e
r e s i s t a n c e ,
a n d m o v i n g
o n t o
t h o s e a t h i g h c u r r e n t s ,
u s e d
t o
m e a s u r e
t h e c r i t i c a l c u r r e n t d e n s i t y
J c .
T h i s
i n c l u d e s
i m p o r t a n t
c o n s i d e r a t i o n s
f o r
J c
m e a s u r e m e n t
s y s t e m s .
J c
m e a s u r e m e n t s
a r e d i v i d e d
i n t o D . C . a n d
p u l s e d
c u r r e n t
t e c h n i q u e s a n d
t h e
d e t a i l s
o f
t h e s e s y s t e m s , a l o n g w i t h t h e i r
p r o b l e m s a n d
a d v a n t a g e s ,
a r e
o u t l i n e d .
T h e l a t e r
s e c t i o n s o f t h e c h a p t e r d e a l w i t h t h e
D . C . a n d A . C .
m a g n e t i c
m e a s u r e m e n t s o n s u p e r c o n d u c t o r s .
T h e s e
a r e
d e s c r i b e d w i t h r e f e r e n c e
t o t h e
e x p e r i m e n t s
c a r r i e d o u t
i n
t h i s
t h e s i s ,
i n
p a r t i c u l a r
t h e
m a g n e t i c
m e a s u r e m e n t o f
J c
a n d
T c .
T h e
m a i n
p a r t s o f
t h i s c h a p t e r
a r e
c o n c e r n e d
w i t h
c r i t i c a l c u r r e n t
d e n s i t y
(
J c
)
m e a s u r e m e n t s . A l l
J c
m e a s u r e m e n t s a r e s i m i l a r i n t h a t t h e y
m e a s u r e t h e c u r r e n t d e n s i t y
r e q u i r e d
t o p r o d u c e a v o l t a g e
i n
t h e s a m p l e .
H o w e v e r ,
i n a
t r a n s p o r t
m e a s u r e m e n t t h e
c u r r e n t i s i n j e c t e d i n t o t h e
s a m p l e
f r o m a n e x t e r n a l
s o u r c e ,
w h i l e i n a m a g n e t i c
m e a s u r e m e n t t h e
c u r r e n t i s i n d u c e d i n t o
t h e
s a m p l e
b y a n
a p p l i e d m a g n e t i c
f i e l d . T h i s
a l l o w s
m a g n e t i c
m e a s u r e m e n t s o n g r a n u l a r s a m p l e s t o d i s t i n g u i s h
b e t w e e n c u r r e n t s
f l o w i n g
o n
t h e
s c a l e o f
t h e
w h o l e s a m p l e
a n d c u r r e n t s f l o w i n g w i t h i n
i n d i v i d u a l g r a i n s ,
a n d
i n
a n i s o t r o p i c
s a m p l e s t o
d e t e r m i n e c u r r e n t s f l o w i n g
i n
d i f f e r e n t
d i r e c t i o n s .
T r a n s p o r t
m e a s u r e m e n t s ,
o n
t h e
o t h e r h a n d ,
a r e b e t t e r
a t
p r o b i n g
t h e
p r o p e r t i e s o f t h e
s a m p l e
a s a
w h o l e ,
a n d t h u s f o r d e t e r m i n i n g t h e s u i t a b i l i t y o f
a
s a m p l e f o r a g i v e n
a p p l i c a t i o n .
D e p e n d i n g o n
t h e
s a m p l e , c u r r e n t s o f
u p
t o h u n d r e d s
o f
a m p e r e s m a y
b e
n e e d e d t o r e a c h
J c .
A
h i g h
q u a l i t y t h i n f i l m s a m p l e ,
w i t h a
J c
o f ~ 1 0 7 A c n r 2 b u t a n a r e a o f o n l y
~ 1 0 ' 8 c m 2
w o u l d n e e d a c u r r e n t o f - 0 . 1 A
t o
d r i v e
i t i n t o
t h e f l u x f l o w
s t a t e . A b u l k
m e l t - p r o c e s s e d
s a m p l e ,
o n t h e o t h e r
h a n d ,
m i g h t
h a v e a
J c
o f
o n l y
~ 2 0 0 0 A c n r 2 ,
b u t a
c r o s s - s e c t i o n a l
a r e a
o f ~ 0 . 0 5 c m 2 . I n t h i s c a s e a c u r r e n t o f
- 1 0 0 A
w o u l d
b e
n e c e s s a r y
t o r e a c h
l c .
T a p e o r t h i c k
4 7
Chapter 2 : Experimental Techniques
film samples lie somewhere between these two extremes. Obviously, methods which allow
the injection of current into the sample need to be optimised for different forms of HTSCs.
2.2 RESISTANCE MEASUREMENTS
Low-current resistance measurements can give a great deal of information about a
sample [2.1]. In addition to simply measuring the variation of a samples resistance or
resistivity as a function of temperature (the R-T curve), thus indicating the superconducting
transition temperature, Tc, further information can be gained from (i) the width of the
resistive transition, (ii) the linearity of the R-T curve above Tc and (iii) the residual
resistance (the value of resistance gained by extrapolating the R-T characteristic above Tc to
T = 0). These can indicate, for example, the presence of de-oxygenation, inhomogeneity
or impurity phases, superconducting fluctuations, vortex-glass transitions and flux flow
effects.
Samples are always measured using a four-point technique in order to eliminate the
resistance of the current leads from the measurement. A.C. or reversing D.C. methods are
used to eliminate any spurious contributions to the measured voltage due to, for example,
thermoelectric effects at the contacts. The A.C. technique uses a lock-in amplifier to detect
the resistive (i.e. in-phase) part of the voltage signal arising from an alternating current
passed through the sample. The reversing D.C. technique uses a computerised D.C. supply
and D.C. nano-voltmeter; the current direction through the sample is reversed on each
measurement cycle and the two signals subtracted and divided by two to calculate the
resistance. Figure 2.1 shows schematic diagrams of systems of these types.
Figure 2.1 : Block diagrams of (a) A.C. and (b) reversing D.C. resistance
versus temperature measurement systems
48
C h a p t e r
2 :
E x p e r i m e n t a l
T e c h n i q u e s
T h e r e a r e
s e v e r a l w a y s i n
w h i c h t h e
r e s i s t i v e
T c
c a n
b e
d e f i n e d
f r o m
a n
R - T
c u r v e .
E i t h e r t h e
o n s e t o f t h e f a l l i n
r e s i s t a n c e
(
T c ( o n s e t
) ) ,
t h e
m i d p o i n t
o f
t h e
t r a n s i t i o n
( '
T
c ( m i d p o i n t
) ,
d e f i n e d b y e i t h e r
r e s i s t a n c e o r t e m p e r a t u r e )
o r
t h e
t r a n s i t i o n t o
z e r o
r e s i s t a n c e
(
T c ( z e r o
) ,
d e f i n e d a s b e l o w
t h e
m i n i m u m
d e t e c t a b l e
r e s i s t a n c e )
m a y
b e
u s e d .
I n
a l o w
- T c
s u p e r c o n d u c t o r
t h e s e
v a l u e s
a r e
u s u a l l y c o m p a r a b l e
a s t h e
r e s i s t i v e
t r a n s i t i o n
i s
s h a r p .
I n a h i g h - 7 ) .
s u p e r c o n d u c t o r , o n t h e
o t h e r
h a n d ,
t h e
t r a n s i t i o n
i s
a l w a y s
b r o a d
d u e
t o
f l u c t u a t i o n
e f f e c t s ,
e v e n
f o r p u r e s a m p l e s , a n d
b r o a d e n s
f u r t h e r
w i t h
a p p l i e d
m a g n e t i c
f i e l d . T h i s c a n
l e a d
t o
g r e a t
d i f f e r e n c e s i n
T c
d e f i n e d b y
t h e s e d i f f e r e n t
t e c h n i q u e s
a s
s h o w n
i n f i g u r e 2 . 2 .
F i g u r e
2 . 2 :
T h e
d i f f e r e n t
m e t h o d s u s e d t o
d e f i n e T c f r o m
e i t h e r t h e
o n s e t
o f
t h e s u p e r c o n d u c t i n g t r a n s i t i o n ,
i t s
m i d p o i n t
o r t h e r e a c h i n g o f
t h e
z e r o
r e s i s t a n c e
s t a t e . N o t e h o w
T c
v a r i e s
d e p e n d i n g
o n
w h i c h m e t h o d i s
u s e d .
O h m s
l a w
s h o w s t h a t t h e v a l u e o f
m e a s u r i n g
c u r r e n t h a s n o
e f f e c t
o n
t h e
r e s i s t a n c e .
H o w e v e r ,
t h e
c h o i c e o f m e a s u r i n g c u r r e n t c a n a f f e c t t h e
r e s u l t s ,
a s t h e
R - T c u r v e i s r e a l l y a
v o l t a g e
v e r s u s t e m p e r a t u r e
a t
c o n s t a n t c u r r e n t m e a s u r e m e n t .
T h e
s a m p l e
w i l l r e a c h
' z e r o
r e s i s t a n c e ' w h e n
i t s
I c
r i s e s a b o v e
t h e v a l u e o f t h e m e a s u r e m e n t
c u r r e n t ,
s o t h e h i g h e r t h e
m e a s u r e m e n t
c u r r e n t
t h e l o w e r
t h e
m e a s u r e d
T c ,
r e g a r d l e s s o f t h e
d e f i n i t i o n
o f
T c .
A l s o ,
t h e v a l u e
o f
c u r r e n t c a n a f f e c t t h e
t e m p e r a t u r e
o f t h e
s a m p l e t h r o u g h
r e s i s t i v e
h e a t i n g
a t
t h e
c u r r e n t c o n t a c t s a n d w i t h i n t h e b u l k
o f
t h e
s a m p l e .
A g a i n ,
t h i s
c a n
s i g n i f i c a n t l y
s h i f t
t h e
a p p a r e n t
T c .
H o w e v e r ,
t h e s e f a c t o r s m u s t
b e b a l a n c e d a g a i n s t
t h e n e e d f o r a
d e t e c t a b l e
v o l t a g e
a c r o s s t h e
s a m p l e .
T h e
o p t i m u m
c u r r e n t m a y v a r y
f r o m
m i c r o a m p s
i n h i g h
r e s i s t a n c e s a m p l e s s u c h
a s p a t t e r n e d
t h i n
f i l m s ,
t o t e n s
o f
m i l l i a m p s f o r l o w - r e s i s t a n c e
4 9
Chapter 2 : Experimental Techniques
samples such as bulk melt-processed YBCO. In all cases the value of measuring current
should be balanced between the need for a sensitive measurement and the need to avoid
heating and broadening of the resistive transition.
In granular or inhomogenous superconductors the resistive transition can be broad
and display structure. In a weak linked granular material, for example, the R-T curve often
shows a two-stage transition. As the sample cools there is an initial drop in resistance as the
grains become superconducting, followed by a second (usually broad) drop to zero
resistance at a lower temperature when the intergranular regions become superconducting.
This is shown in figure 2.3 and discussed in more detail in section 1.11.2. These effects
make it difficult to define an absolute Tc in materials of this kind, although from the point
of view of Jc measurements and applications Tc(zero) is the most relevant. However, this
can be difficult to define exactly due to the low voltages involved and more often a criterion
of some kind is used. It should be noted that if there is enough of the higher Tc component
or a continuous strongly linked intergranular path, it will short out the lower Tc phase so
that it will not be detected. These problems are commonly dealt with using percolation or
effective medium theory, although these were not used in this thesis and will not be
discussed further.
Temperature (K)
Figure 2.3 : An R-T curve for a YBCO thick film showing granularity and
structure near the onset ofTc.
The R-T curve can also show an anomalous peak and/or trough just above Tc, as
shown in figure 2.3. This can be explained by the superposition of several different R-T
50
C h a p t e r
2
: E x p e r i m e n t a l
T e c h n i q u e s
c u r v e s w i t h
a
d i s t r i b u t i o n o f
T c s ,
s o m e o f w h i c h s h o w
a n
i n c r e a s e i n R
w i t h
d e c r e a s i n g
T
a b o v e
T c ,
s o m e a
d e c r e a s e
o f
R
w i t h T .
A n
a l t e r n a t i v e
e x p l a n a t i o n
i s
g i v e n
b y
M o s q u e i r a
e t
a l .
[ 2 . 2 ]
i n t e r m s o f a n o n - u n i f o r m
d i s t r i b u t i o n o f i n h o m o g e n e i t i e s
i n
T c
o v e r
l o n g
l e n g t h
s c a l e s t h r o u g h o u t t h e s a m p l e .
I n
t h e A . C .
t e c h n i q u e c o r r e c t p h a s i n g
o f
t h e
l o c k - i n
a m p l i f i e r
t o
t h e
r e s i s t i v e
p a r t
o f
t h e
s i g n a l i s
e s s e n t i a l
f o r a n
a c c u r a t e
m e a s u r e m e n t . I f t h e l o c k - i n
i s i n c o r r e c t l y
p h a s e d
t h e n
t h e s i g n a l
w i l l i n c l u d e a n i n d u c t i v e
c o m p o n e n t
w h i c h w i l l
a d d a
s p u r i o u s
c o n t r i b u t i o n
t o t h e
m e a s u r e d
r e s i s t a n c e . T h i s i s e s p e c i a l l y
s i g n i f i c a n t w i t h
l o w - r e s i s t a n c e
s a m p l e s w h e r e
t h e
r e s i s t i v e
a n d i n d u c t i v e
s i g n a l s
a t r o o m
t e m p e r a t u r e
( a r i s i n g
f r o m t h e
s a m p l e
a n d i m p e r f e c t
s h i e l d i n g o f t h e l e a d s t o t h e
s a m p l e , r e s p e c t i v e l y ) c a n
b e
c o m p a r a b l e i n
s i z e . C o r r e c t
p h a s i n g
c a n b e e n s u r e d
i n
t w o
w a y s . F i r s t l y , t h e i n d u c t i v e
s i g n a l
i n
t h e
s y s t e m
c a n b e
r e d u c e d a s m u c h
a s p o s s i b l e
( s e e
s e c t i o n
2 . 3 . 1 , b e l o w ) .
A l t e r n a t i v e l y , t h e
l o c k - i n c a n
b e
p h a s e d u s i n g t h e s i g n a l f r o m
a
r e s i s t o r i n s e r i e s
w i t h
t h e
s a m p l e . T h i s
i s
g e n e r a l l y t h e
e a s i e r o p t i o n .
F o r a l l R - T
m e a s u r e m e n t s t h e
r a t e a t w h i c h t h e
t e m p e r a t u r e i s
s w e p t
s h o u l d b e
k e p t
a s
l o w a s
p r a c t i c a l l y
p o s s i b l e .
A
f a s t s w e e p
r a t e c a n
c a u s e s i g n i f i c a n t
t e m p e r a t u r e
l a g
b e t w e e n
t h e s a m p l e a n d t h e
t e m p e r a t u r e
s e n s o r ,
s h i f t i n g
t h e
R - T c u r v e
a n d l e a d i n g
t o a n
i n c o r r e c t
v a l u e f o r
T c .
T h i s c a n b e
m o n i t o r e d b y m e a s u r i n g t h e
s a m p l e o n
b o t h
i n c r e a s i n g
a n d
d e c r e a s i n g
t e m p e r a t u r e
s w e e p s .
A s t h e
t r a n s i t i o n a t
T c
i s
s e c o n d o r d e r
t h e r e
s h o u l d b e
n o
d i f f e r e n c e
b e t w e e n t h e d i f f e r e n t
d i r e c t i o n s o f s w e e p .
A n y
s i g n i f i c a n t
d i f f e r e n c e
i n d i c a t e s
t h a t t h e
t e m p e r a t u r e s w e e p
r a t e
w a s
t o o h i g h a n d
t h e m e a s u r e m e n t
s h o u l d b e
r e p e a t e d
m o r e
s l o w l y .
2 . 3
T R A N S P O R T
J c
M E A S U R E M E N T S
J c
i s m e a s u r e d
r e s i s t i v e l y
b y a p p l y i n g a c u r r e n t t o a
s a m p l e a n d i n c r e a s i n g i t
u n t i l a
v o l t a g e
a p p e a r s
a n d
a
c h o s e n c r i t e r i o n i s
e x c e e d e d .
D e p e n d i n g o n
t h e
s a m p l e
I c
a n d
s y s t e m
u s e d
t h e
c u r r e n t
c a n e i t h e r b e
r a m p e d
D . C .
o r p u l s e d
i n o r d e r t o r e d u c e
s a m p l e h e a t i n g .
2 . 3 . 1 M A J O R C O N S I D E R A T I O N S
C r i t e r i a f o r D e t e r m i n i n g
A -
A
s a m p l e
w i t h f l u x p i n n i n g i n a n
a p p l i e d
f i e l d o r c u r r e n t h a s a g r a d i e n t o f
f l u x
i n s i d e i t . D e p e n d i n g
o n
t h e f i e l d a n d
t e m p e r a t u r e
r e g i m e t h i s f l u x w i l l
m o v e
b y
f l u x
c r e e p
o r
t h e r m a l l y
a c t i v a t e d
f l u x f l o w t o
s m o o t h
o u t a n y u n e v e n
f l u x
d i s t r i b u t i o n . B e c a u s e f l u x
5 1
Chapter 2 : Experimental Techniques
motion is always taking place, even below the nominal Jc, there will always be a non-zero
voltage signal and the transition at Jc is smoothed. This makes the determination of 7,-
somewhat harder (see figure 2.4(a)) and is especially significant in HTSCs where the
higher temperatures at which measurements can be carried out mean that thermal energies
of the flux lines can be much larger than in LTSCs, giving superconducting fluctuations
above and below Tc [2.3]. The activation energies for flux motion are also lower in
HTSCs, making flux creep more likely to occur (see section 1 .7). Inhomogeneities also
have a larger effect in HTSCs due to their small coherence lengths. These processes
broaden and smooth the transition at Jc so an arbitrary criterion becomes necessary to
determine when Jc has actually been reached. The choice of criterion has a large effect on
the measured value of Jc and on the specification of a material [2.4, 5], A review of the
specification of superconductors is given by Ekin in [2.6]. The different forms of I-V
curves are discussed by Evetts in [2.7]. These include those for ideal flux flow with flux
pinning, homogenous and inhomogenous superconductors, the effects of flux motion, and
the effects of a defective flux lattice or regular pinning potential. Correlations between the
results obtained from the different techniques used to measure Jc are given by Kroeger
et al. in [2.8], and by Campbell and Evetts in [2.9].
(a) The Electric Field Criterion
In this method Jc is defined as the point where the electric field measured along the
sample exceeds a fixed criterion (often defined as \jlV/cm) above any constant background
voltage signal arising from, for example, thermal gradients along the voltage leads (see
below). This method has the advantage of simplicity, but will give a Jc value (however
small) even for a non-superconducting sample, requiring the examination of the sample I-V
curves to ensure that it is really superconducting. Even in a superconducting sample the
choice of criterion can have a very significant effect on the apparent value of Jc [2.10, 11],
Lastly, this technique is hard to apply to small samples such as single crystals as the
voltage corresponding to a given criterion can be very small, making it difficult to extract
from background voltages within the system, especially for high current measurements.
(b) The Resistance Criterion
This method is similar to the electric field criterion method, but measures the sample
resistance or resistivity rather than the electric field along it. Jc is defined as the point at
which a specified resistivity, for example 10pf2cm, is exceeded. This technique is often
52
Chapter 2 : Experimental Techniques
used in magnet applications, where true zero resistance is not expected [2.12], as it relates
directly to the overall dissipation of a system.
(c) The Offset Criterion
In this method Jc is defined as the current where the tangent to the I-V curve at a
given voltage criterion extrapolates to zero voltage [2.10], This has the advantage of
distinguishing actual superconductivity from high-conductivity normal materials,
eliminating much of the arbitrariness and variability of the voltage and resistivity criterion
methods, and is also useful for measurements near Tc or HC1 when the I-V characteristic
begins to approach ohmic behaviour. However, in a sample with an I-V characteristic
which shows significant curvature at all values of current from Jc to the maximum applied it
can be difficult to determine the correct point at which to take the tangent to the I-V curve.
This is the case with most HTSCs and so this method is included only for completeness.
(d) The n-value Method
The overall quality of the resistive transition can be determined using the n-value
method, described, for example, by Evetts et al. in [2.13]. This measures the 'sharpness'
of a resistive transition by fitting the I-V curve in the vicinity of the resistive transition to a
power law, i.e. V I" , giving an estimate of the inhomogeneity of a sample and the spatial
distribution of Jc [2.14, 15]. For a fully resistive material n = 1, while for commercial
LTSC cables n ~ 20-100. The n-value varies with applied field, and with field cycling
[2.11], For granular superconductors and HTSCs n is generally much less than the values
for LTSCs, and can be as low as two [2.16].
In all the transport critical current results shown in this thesis, unless mentioned
otherwise Jc was determined using an electric field criterion of lpV/cm.
Figure 2.4 shows two diagrams demonstrating the determination of Jc via the
voltage criterion, resistance criterion and offset techniques. Note that depending on the
form of the I-V curve these techniques can give quite different results.
53
Chapter 2 : Experimental Techniques
Figure 2.4 : Two examples of different forms ofl-V curves showing how
the choice of criterion for Jc can affect the results obtained, (a) is the case
with most HTSCs, while (b) is generally the case in LTSCs.
Contacts to High 77 Superconductors
For transport Jc measurements it is often necessary to pass high currents,
sometimes of hundreds of amperes, through a sample. If the contact resistance is too high
then heating at the contacts can locally drive the superconductor into the normal state before
Ic is reached. This produces further heating and can eventually drive all of the
superconductor normal, causing an under-estimate of Jc or rendering its measurement
impossible [2.17]. In addition, heating effects can cause significant hysteresis in the I-V
curves for increasing and decreasing current. Low-resistance contacts are therefore
essential to minimise this resistive heating of the sample.
In addition to the variation in contact quality found between the different
techniques, different superconducting compounds give different results for the same
technique. For example, evaporated silver contacts (technique (ii) in table 2.1) give
excellent results when used on bulk YBCO. However, on bulk BSCCO very little silver
appears to be actually laid down on the sample and contacts of very low quality result.
Likewise, although soldering directly to the silver sheath of a silver-coated tape gives a
low-resistance contact, it can cause problems due to thermal degradation of the
superconductor close to the contact region. Conversely, silver paint gives a higher contact
resistance, but does not expose the sample to high temperatures and can give completely
satisfactory results in low Ic samples.
In general, each individual material should be investigated to determine the
technique which gives the best results.
54
C h a p t e r
2 :
E x p e r i m e n t a l
T e c h n i q u e s
A
n u m b e r o f
d i f f e r e n t
c o n t a c t
t e c h n i q u e s h a v e
b e e n
i n v e s t i g a t e d
b y
d i f f e r e n t
g r o u p s .
T h e s e a r e
s u m m a r i s e d ,
a l o n g w i t h
t h e r e l e v a n t
r e f e r e n c e s ,
i n
t a b l e
2 . 1 .
M e t h o d
N o . R e f . A n n e a l e d
T y p i c a l
R e s i s t i v i t y
C o m m e n t s
R o o m - t e m p e r a t u r e
d r y i n g
s i l v e r p a i n t
( i ) [ 2 . 1 8 ]
N o
I C E 1
Q c m 2
E a s i e s t
m e t h o d t o
u s e a n d
l e a s t
l i k e l y
t o
d a m a g e t h e
s a m p l e , b u t
h i g h
r e s i s t a n c e .
E v a p o r a t e d o r
s p u t t e r e d
s i l v e r
p a d s
( i i )
[ 2 . 1 8 ]
[ 2 . 1 9 ]
[ 2 . 2 0 ]
N o
I C E 7
£ 2 c m 2
L a b o r i o u s
t o p r o d u c e
w i t h a l o w
s u c c e s s
r a t e
o n
n o n - Y B C O s a m p l e s .
Y e s
l ( E 1 0 Q c m 2
M e l t e d - i n s i l v e r o r
g o l d
c o n t a c t p a d s
( i i i ) [ 2 . 2 1 ]
[ 2 . 2 2 ]
Y e s
5
x 1 0 - 7 £ 2 c m 2
R u g g e d
b u t n o t
s i m p l e
t o p r o d u c e .
P r o d u c t i o n
r e q u i r e s
h e a t i n g
o f t h e
s a m p l e t o
t e m p e r a t u r e
o f
m e l t i n g
p o i n t
o f
c o n t a c t
p a d .
M e l t e d - i n s i l v e r
p o w d e r
( i v ) [ 2 . 2 3 ]
Y e s
2
x
I C E 7 £ 2 c m 2
R e q u i r e s
u s e o f h i g h
t e m p e r a t u r e
a n n e a l i n g .
P l a s m a - s p r a y i n g
( v ) [ 2 . 2 4 ]
N o 1 ( E 8
Q c m 2
D o e s
n o t r e q u i r e t h e
s a m p l e
t o b e
h e a t t r e a t e d a f t e r
t h e
a p p l i c a t i o n o f
t h e
c o n t a c t .
P a i n t e d - o n s i l v e r
e p o x y ( e . g .
d u P o n t
4 9 2 9 )
( v i ) [ 2 . 2 5 ]
Y e s
1 0 - 2 Q c m 2
F i r e d - o n s i l v e r
p a i n t ( e . g . d u P o n t
6 8 3 8 )
( v i i )
N o
R e q u i r e s h e a t i n g
o f
s a m p l e t o
4 0 0 - 5 0 0 ° C
E l e c t r i c a l d i s c h a r g e
s p o t
w e l d i n g
( v i i i ) [ 2 . 2 6 ]
Y e s
2
x
I C E 7
Q c m 2
U s e s
b o t h
s e r i e s
a n d p a r a l l e l
w e l d i n g
t e c h n i q u e s .
A p p e a r s
t o
r e n d e r
s a m p l e
s e m i c o n d u c t i v e .
A n n e a l i n g n e c e s s a r y
t o
r e s t o r e
s u p e r c o n d u c t i v i t y .
U l t r a s o n i c a l l y
b o n d e d S i l v e r
w i r e
( i x )
[ 2 . 2 6 ]
Y e s
3
x
l O 8
£ 2 c m 2
“
U l t r a s o n i c a l l y
b o n d e d I n d i u m
p a d s
( x )
[ 2 . 2 7 ]
[ 2 . 2 8 ]
N o
A r g u a b l y
t h e b e s t
t e c h n i q u e .
E a s y
t o u s e .
G i v e s l o w
r e s i s t i v i t i e s .
A p p a r e n t l y m u c h
b e t t e r
i f
i n d i u m
p a d s
a p p l i e d t o s i l v e r ,
e i t h e r
s h e a t h i n g
o f
p r o c e s s e d
t a p e s / w i r e s
o r s i l v e r
p a d s
o n
b u l k
s p e c i m e n s .
T a b l e 2 . 1 :
S u m m a r y
o f
c o n t a c t
t e c h n i q u e s
t o
H T S C s .
T e c h n i q u e s
( i ) , ( i i )
a n d
( v i i )
h a v e b e e n u s e d t h i s
t h e s i s ,
a n d
e x p e r i m e n t s
m a d e
w i t h
t e c h n i q u e s
( i i i )
a n d
( i v ) .
S a m p l e
M o u n t i n g
H o w
t h e s a m p l e
i s
a c t u a l l y
m o u n t e d i n
t h e m e a s u r e m e n t
s y s t e m c a n
a l s o
a f f e c t t h e
r e s u l t s
o b t a i n e d . S p e c i a l m o u n t i n g
t e c h n i q u e s
a r e n e c e s s a r y ,
f o r e x a m p l e , i f t h e s a m p l e
i s
i n t e n d e d
t o
b e c o o l e d
b y
i m m e r s i o n i n
a
l i q u i d
c r y o g e n
( a s
i n a
s i m p l e d i p p r o b e ) o r
i f
i t i s
t o
b e u s e d
i n a c o n t i n u o u s f l o w
s y s t e m a n d c o o l e d
b y a
s t r e a m o f a g a s e o u s c r y o g e n .
5 5
Chapter 2 : Experimental Techniques
The heat capacity of the cryogen to be used will also affect how the sample should
be mounted. For cryogens with a large heat capacity, such as liquid nitrogen, a
considerable amount of heating at the sample can be tolerated without significantly affecting
the sample temperature as the cryogen boils only in places on the sample surface ("nucleate
boiling"). For cryogens with a lower heat capacity, such as liquid helium, a much lower
amount of heating will cause significant boiling at the sample, surrounding it with a sheath
of gas, insulating it from the cryogen and allowing further heating to occur ("film boiling").
The heat flux at which the transition from nucleate to film boiling occurs, Qc , is given by
Qc = 0-16{ÿPV2[CT£(PL -P,F} C2-1)
where 1 = latent heat of vaporisation, pL = liquid density, pv = vapour density,
a= surface tension of the liquid and g = the Gibbs function of the cryogen. Figure 2.5
shows schematic diagrams of the heat transfer rate versus the surface superheat, defined as
the difference between the temperature of the superconductor and the temperature of the
cryogen, for liquid helium and liquid nitrogen. The sample cooling rate should be such that
the sample is always below Qc [2.12],
Figure 2.5 : Schematic diagrams of rate heat transfer to coolant versus
superheating at sample surface for liquid helium and nitrogen cryogens
showing regions in which cooling takes place by different mechanisms and
Qc, the point where there is a change between them, (a) nucleate boiling,
(b) film boiling.
For liquid helium equation 2.1 gives Qc ~ 104Wm'2, while for liquid nitrogen
Qc ~ l()5Wm'2. This is covered in more detail by Van Sciver in [2.29], If the Jc-T
dependence of a given superconductor is known then the suppression of Jc for a given
surface superheat can be calculated, and an estimate made of the minimum superheat which
can be tolerated.
56
C h a p t e r
2 : E x p e r i m e n t a l
T e c h n i q u e s
T h e r e
a r e t w o b r o a d
c l a s s e s
o f
m o u n t i n g
t e c h n i q u e
w h i c h
c a n
u s e d
f o r
a
s a m p l e .
F o r
i m m e r s i o n
i n
a
b a t h
o f l i q u i d
c r y o g e n
a s m u c h o f t h e
s a m p l e s h o u l d
b e
i n c o n t a c t
w i t h
c r y o g e n
a s
p o s s i b l e t o
m a x i m i s e i t s c o o l i n g e f f e c t . F i g u r e
2 . 6
s h o w s a
t a p e
s a m p l e
m o u n t e d i n
o r d e r
t o a c h i e v e t h i s . I t
i s
s u p p o r t e d a w a y
f r o m t h e
s a m p l e
h o l d e r
b y
t h e
c u r r e n t l e a d s . E a c h l e a d
c o n s i s t s o f
a
l o o p o f
w i r e w i t h t h e
e n d
f l a t t e n e d
a n d b e n t
i n t o a ' U '
s h a p e .
T h e
t a p e
i s
s l i p p e d i n t o t h e
' U '
a n d
f i x e d
i n
p l a c e w i t h
s i l v e r
p a i n t .
V o l t a g e
c o n t a c t s
a r e m a d e b y
w r a p p i n g
f i n e g o l d w i r e
a r o u n d t h e
t a p e
a n d f i x i n g
i t i n
p l a c e
w i t h
s i l v e r p a i n t .
T h e
u s e
o f
a
' U '
s h a p e d c u r r e n t
l e a d a l s o
a l l o w s
c o n t a c t
t o
a
l a r g e
a r e a
o f t h e
s a m p l e ,
m a x i m i s i n g
c u r r e n t
t r a n s f e r
t o i t .
F i g u r e
2 . 6
: E x a m p l e o f s u p e r c o n d u c t i n g s a m p l e
m o u n t i n g
t e c h n i q u e
f o r
i m m e r s i o n i n l i q u i d c r y o g e n , s h o w i n g m u l t i p l e
v o l t a g e
c o n t a c t s
f o r
m e a s u r i n g
t h e
J c
o f d i f f e r e n t
s e c t i o n s
o f t h e
s a m p l e
a n d a
c e n t r a l s u p p o r t
.
L o n g e r
s a m p l e s , s u c h
a s
t h e
o n e s h o w n i n
f i g u r e
2 . 6 ,
r e q u i r e t h e
u s e o f a t
l e a s t
o n e
c e n t r a l
s u p p o r t f o r t w o r e a s o n s . F i r s t l y , t o
p r e v e n t
t h e
s a m p l e f r o m s a g g i n g ,
a n d m o r e
i m p o r t a n t l y
t o h e l p
p r e v e n t
t h e
s a m p l e
f r o m b u c k h n g w h e n
c a r r y i n g a
c u r r e n t
i n
a
m a g n e t i c
f i e l d . T h i s i s n e c e s s a r y
a s t h e f o r c e s o n a c u r r e n t c a r r y i n g
c o n d u c t o r
i n
a f i e l d c a n b e
s u b s t a n t i a l .
T h i s f o r c e i s g i v e n b y
F
=
I - l - B s i n #
( 2 . 2 )
w h e r e /
i s t h e c u r r e n t t h r o u g h
t h e
c o n d u c t o r ,
l t h e l e n g t h o f
t h e
c o n d u c t o r ,
B t h e
a p p l i e d
f i e l d
a n d 0 t h e a n g l e b e t w e e n c u r r e n t
a n d
f i e l d . F o r
e x a m p l e ,
a n
8 c m
l o n g
c o n d u c t o r c a r r y i n g 1 0 A
i n a f i e l d o f
5 T
p e r p e n d i c u l a r
t o t h e c u r r e n t
w i l l e x p e r i e n c e a f o r c e
o f 4 N
p e r p e n d i c u l a r t o b o t h t h e f i e l d a n d c u r r e n t .
F o r
a s i l v e r - c l a d s u p e r c o n d u c t i n g t a p e
t h i s
i s
m o r e t h a n s u f f i c i e n t
t o
b e n d
t h e
s a m p l e
a n d s i g n i f i c a n t l y d e g r a d e
J c .
I n a c o n t i n u o u s f l o w
s y s t e m w h e r e
t h e
s a m p l e i s c o o l e d
b y
c o n d u c t i o n t o a t h e r m a l
s i n k
r a t h e r
t h a n a
c r y o g e n o r
b y
c o n v e c t i o n ,
i t i s
n e c e s s a r y
t h a t t h e
s a m p l e
b e
w e l l
t h e r m a l l y
a n c h o r e d t o t h e
p r o b e
h e a d ,
f o r
e x a m p l e b y
u s i n g
d o u b l e - s i d e d
a d h e s i v e
t a p e .
5 7
Chapter 2 : Experimental Techniques
There are two reasons for this, first to maximise cooling by conduction to the probe head,
and second so that the temperatures of the sample and probe head remain as close as
possible. Thermally anchoring the sample to the probe head is achieved in two ways, both
of which are most applicable to samples with flat geometries. The first is to anchor the
sample itself to the probe head. Secondly, the current leads should be arranged so as to
maximise their thermal contact with the probe head. This both prevents heat build-up in the
leads and means that the leads assist in heat sinking the sample. Current leads of copper or
silver foil which, like the sample, can be firmly fixed to the probe head are ideal for this.
Figure 2.7 shows a diagram of a sample mounted in this fashion.
Figure 2.7 : Schematic plan view of sample mounting arrangement on the
head of a continuous flow cryostat probe.
The forces on the system when it carries a current should be considered when
measuring a sample under these circumstances. Ideally the field and current should be
oriented such that the force on the current pushes the sample back onto the probe head
rather than away from it.
Samples without a long flat face, such as extruded fibres of HTSC, can be
measured in a continuous flow system using a similar technique. This differs from that
shown in figure 2.7 as the sample is placed in 'U'-shaped holders formed from the
folded-over ends of the foil current leads and held there using, for example, silver paint.
58
C h a p t e r 2 : E x p e r i m e n t a l
T e c h n i q u e s
N o i s e
N o i s e ,
a s
a
t e r m ,
c a n b e a p p l i e d t o a n y s i g n a l w h i c h
o b s c u r e s
t h e
d e s i r e d s i g n a l .
T h i s i s
a m a j o r
p r o b l e m
i n
l o w v o l t a g e
( l e s s
t h a n 1 f i V ) m e a s u r e m e n t s o f
a l l
k i n d s . F o r
t h i s
r e a s o n a s
m a n y
s o u r c e s o f n o i s e a s p o s s i b l e h a v e
t o
b e c o n s i d e r e d a n d
e l i m i n a t e d .
I n
g e n e r a l
t h e s u m o f a l l
t h e
c o n t r i b u t o r y s i g n a l s
s h o u l d
b e
m u c h l e s s t h a n a n y
c r i t e r i o n
u s e d .
N o i s e
c a n b e e i t h e r a r a n d o m s i g n a l
i n t r i n s i c t o t h e m e a s u r e m e n t
s y s t e m
( r e f e r r e d
t o
a s
n o i s e
b e l o w ) ,
o r s o m e n o n - r a n d o m e x t e r n a l s i g n a l
w h i c h
i s p i c k e d u p b y i t
( r e f e r r e d
t o
a s
i n t e r f e r e n c e
b e l o w ) .
S i g n a l s
d e f i n e d a s
n o i s e
a r e r a n d o m
i n
n a t u r e a n d
u n c o n n e c t e d
t o t h e
i n t e n t i o n a l
s i g n a l .
T h u s
t h e y
c a n b e e l i m i n a t e d f r o m a
s y s t e m
b y s i g n a l
a v e r a g i n g .
T h e r e
a r e
s e v e r a l
t y p e s
o f
n o i s e .
T h e
f i r s t
o f
t h e s e
i s
J o h n s o n
n o i s e ,
c a u s e d b y
t h e r a n d o m
m o t i o n
o f
e l e c t r o n s i n a n o r m a l
c o n d u c t o r .
T h i s h a s a
R M S
v a l u e o f
~ 1 0 n V f o r a 1 £ 2
r e s i s t o r a t
r o o m
t e m p e r a t u r e ,
a n d
d e c r e a s e s w i t h t e m p e r a t u r e t o b e l o w t h e
v o l t a g e
r e s o l u t i o n o f
t h e
e q u i p m e n t u s e d
h e r e .
S h o t
n o i s e ,
a
r e s u l t
o f
c u r r e n t
b e i n g
m a d e
u p o f
d i s c r e t e
c h a r g e s ,
c a u s e s
s m a l l
f l u c t u a t i o n s i n t h e c u r r e n t
t h r o u g h
a
c o n d u c t o r .
F o r t h e
c u r r e n t s
u s e d h e r e
t h e s e
f l u c t u a t i o n s
a r e i n s i g n i f i c a n t
c o m p a r e d
t o t h e m e a s u r e m e n t
c u r r e n t s
( a p p r o x i m a t e l y
± 1 0 " 8 A
o n
a 1
A
c u r r e n t ) [ 2 . 3 0 ] .
L a s t l y , t h e r e
i s
l / / o r
f l i c k e r n o i s e .
T h i s
i s a n ' e x c e s s '
n o i s e o v e r
J o h n s o n a n d
s h o t
n o i s e ,
a n d
a r i s e s f r o m t h e c o n s t r u c t i o n o f a
p a r t i c u l a r
r e s i s t i v e
c o m p o n e n t .
I t
h a s
a
1
I f
s p e c t r u m , g i v i n g e q u a l p o w e r p e r
d e c a d e o f
f r e q u e n c y .
F o r
w i r e - w o u n d r e s i s t o r s
t h i s
n o i s e i s
- T O O n V ,
a n d
i t
i s t o b e e x p e c t e d t h a t t h e v a l u e s f o r
l o w - r e s i s t a n c e
s y s t e m s
w i l l
b e
l e s s
t h a n
t h i s ,
t a k i n g t h e
1 / /
n o i s e b e l o w
t h e v o l t a g e r e s o l u t i o n
o f t h e
s y s t e m s
u s e d h e r e .
I n t e r f e r e n c e
I n t e r f e r e n c e
i n a
m e a s u r e m e n t
s y s t e m
i s
v e r y
d e p e n d e n t o n t h e
l o c a l e n v i r o n m e n t
[ 2 . 3 0 ] .
T h e
m o s t c o m m o n
i n t e r f e r e n c e
p i c k e d
u p
b y a s y s t e m i s f r o m t h e
m a i n s
e l e c t r i c a l
s u p p l y .
A l t h o u g h t h i s
m a y
n o t
a f f e c t
a n A . C .
o r p u l s e d
m e a s u r e m e n t
i f
a n
a p p r o p r i a t e
f r e q u e n c y i s
c h o s e n ,
i t c a n c a u s e p r o b l e m s b y , f o r
e x a m p l e ,
o v e r l o a d i n g t h e
i n p u t
s t a g e
o f
a n
a m p l i f i e r .
O t h e r
e l e c t r i c a l
e q u i p m e n t
i n
t h e v i c i n i t y c a n
a l s o i n t e r f e r e w i t h
m e a s u r e m e n t s .
I n t e r f e r e n c e
c a n
e n t e r
a s y s t e m
i n
a
n u m b e r
o f
w a y s .
T h e s e i n c l u d e v i a
t h e
s y s t e m p o w e r
l i n e
a n d t h e s i g n a l i n p u t
o r o u t p u t
l i n e s .
S i g n a l s
c a n a l s o
c a p a c i t i v e l y c o u p l e
i n t o t h e
c i r c u i t ,
i n d u c t i v e l y c o u p l e i n c l o s e d l o o p s
i n
t h e
c i r c u i t a n d
e l e c t r o m a g n e t i c a l l y
c o u p l e v i a
w i r e s a c t i n g a s a n t e n n a e f o r
e l e c t r o m a g n e t i c r a d i a t i o n .
A l l o f t h e s e
m e c h a n i s m s
5 9
Chapter 2 : Experimental Techniques
can also couple signals from one part of a circuit to another. Lastly, signals can couple
between parts of a circuit via earth or power supply connections.
Capacitative effects occur when the electric field generated by the sample current
leads induces an electric field on the sample voltage leads. Inductive effects can arise when
the magnetic field generated by the sample current induces a spurious voltage signal into the
voltage measuring loop connecting the sample to the voltmeter as shown in figure 2.8. A
loop such as this will also pick up interference from the general laboratory environment
[2.30]. Inductive voltages also arise from motion of the sample or the sample leads in an
applied magnetic field. This motion can arise from a varying (A.C. or pulsed) current, or
from bubbling in a liquid cryogen.
/+ V I-
Figure 2.8 : Example of a source of pickup - a sample with
voltage leads forming a pick-up loop
It should also be taken into account that even in D.C. measurements, a high level of
A.C. noise can cause a D.C. voltmeter to display incorrect readings. This can lead to
effectively two sources of spurious voltages - actual high frequency voltages, which can be
measured on an oscilloscope, and lower frequency voltages which are purely an effect of
high frequency noise on a D.C. meter. These components can be eliminated by
measurements of the amounts of spurious voltages, location of their sources, and the
insertion of a low-pass filter such as a capacitor at an appropriate point in the system.
Thermoelectric Effects
Thermoelectric voltages arise from three sources during transport measurements
[2.31] and add an offset to the measured voltage signal. Differences in resistance between
the sample current contacts lead to different resistive losses at each contact and so to a
temperature gradient along the sample. This generates a voltage along the sample via the
Thomson effect, independent of the direction of current flow. Secondly, the Peltier effect
across the junctions between the sample and the current leads can also establish a
temperature gradient and therefore a voltage which is dependant on the direction of current
60
C h a p t e r
2 : E x p e r i m e n t a l
T e c h n i q u e s
f l o w
[
2 . 1 7 ] .
B o t h
o f
t h e s e e f f e c t s v a r y w i t h t h e
a p p l i e d
c u r r e n t .
T h i r d l y , t h e S e e b e c k
e f f e c t
c a n g e n e r a t e
v o l t a g e s
a l o n g t h e
l e a d s
f r o m
t h e s a m p l e d u e t o
t h e
t e m p e r a t u r e g r a d i e n t
a c r o s s
t h e
j u n c t i o n s
b e t w e e n
m a t e r i a l s a t t h e h i g h a n d l o w
t e m p e r a t u r e e n d s
o f t h e
v o l t a g e
l e a d s . T h i s i s i n d e p e n d e n t o f t h e a p p l i e d c u r r e n t a n d
d e p e n d s
o n l y
o n t h e
t e m p e r a t u r e
d i f f e r e n c e a l o n g
t h e
v o l t a g e
l e a d s . T h e r m o e l e c t r i c e f f e c t s
i n
s u p e r c o n d u c t o r s
t h e m s e l v e s
a r e r e v i e w e d i n
[ 2 . 3 2 ]
a n d
[ 2 . 3 3 ]
b u t w i l l n o t b e
d i s c u s s e d f u r t h e r
h e r e .
F i g u r e
2 . 9 s h o w s
t h e I - V
c u r v e s f o r a Y B C O t h i c k f i l m
w i t h
a
D . C .
a p p l i e d
c u r r e n t
i n
o p p o s i t e
d i r e c t i o n s ,
p l u s t h e
d i f f e r e n t i a l c u r v e e x t r a c t e d f r o m
t h e
t w o
m e a s u r e d
c u r v e s .
I t
m a y b e s e e n t h a t t h e
T h o m s o n e f f e c t i s a d d i n g a v o l t a g e
t o t h e
m e a s u r e d s i g n a l s .
F i g u r e
2 . 9
: A n e x a m p l e o f
t h e
d i s t o r t i o n
o f
I - V c u r v e s
d u e t o t h e
T h o m s o n
e f f e c t a r i s i n g
f r o m ,
t h e
d i f f e r e n t
r e s i s t a n c e s
o f t h e
c u r r e n t
c o n t a c t s .
T h e s e
p a r t i c u l a r
I - V c u r v e s w e r e c h o s e n a s
t h e y
a r e
f r o m
a p a r t i c u l a r l y
h a d
e x p e r i m e n t
w i t h ,
a
t e m p e r a t u r e d i f f e r e n c e
o f
~ 1 0 K ,
a n d
s o h a v e a
p a r t i c u l a r l y l a r g e d e g r e e o f
d i s t o r t i o n
i n
t h e
I - V
c u r v e s .
N o t e t h a t
t h e
c u r r e n t .
a n d v o l t a g e
f o r
t h e r e v e r s e
c u r r e n t h a v e b o t h
b e e n m u l t i p l i e d b y - 1
t o
a l l o w
c o m p a r i s o n
w i t h t h e
f o r w a r d
c u r r e n t .
U n f o r t u n a t e l y
c u r r e n t r e v e r s a l
i s l a b o r i o u s t o
a c h i e v e w i t h h i g h
s a m p l e
c u r r e n t s ,
a s
t h e c u r r e n t
s u p p l i e s u s e d a r e u n a b l e t o d i r e c t l y
s u p p l y
n e g a t i v e
c u r r e n t s ,
a n d
s o i s
g e n e r a l l y
o n l y
d o n e a
s m a l l
n u m b e r
o f t i m e s a t t h e
s t a r t
o f
a
g i v e n
s e t
o f
m e a s u r e m e n t s
t o d e t e r m i n e
w h e t h e r a n y
s u c h
e f f e c t s a r e a c t u a l l y
p r e s e n t .
6 1
Chapter 2 : Experimental Techniques
In an A.C. or pulsed current system the effect of thermoelectric voltages will
depend on the rate of heat dissipation from the sample. At one extreme the heat may be
dissipated as fast as it is generated, leading to (for example) a Thomson voltage at the same
frequency and phase as the applied current with a waveform proportional to the square of
the current waveform. At the other extreme heat dissipates from the sample only very
slowly leading to an essentially D.C. Thomson voltage. This is unlikely to be significant
compared to the other problems caused by heat building up in the sample, such as
suppression of Jc with increasing temperature.
Earthing
Earth loops are a serious problem if they exist in a system since a fraction of the
current can drain back through earth into areas where it is not wanted. Figure 2.10 shows
a schematic diagram of such a loop.
Figure 2.10 : Schematic diagram of circuit arrangement giving an earth
loop. The value of Re determines the precise effect of the earth loop, as
described in the text.
Regardless of tire value of Re an earth loop can pick up interference in the same way
as that shown in figure 2.8. If Re is low then the sample can also be partially shorted by
the earth loop. The current which is shorted can generate spurious voltages as it passes
through the resistance to earth. In a system with a number of connected stages multiple
earths can allow spurious signals to travel from, for example, high voltage outputs to low
voltage inputs. In a D.C. measurement the voltage which appears on the measuring
62
C h a p t e r
2
: E x p e r i m e n t a l
T e c h n i q u e s
i n s t r u m e n t
c a n
b e t h e
s u m o f
t h e
s a m p l e v o l t a g e
p l u s t h e
v o l t a g e
a l o n g
t h e
e a r t h
w i r e s .
I n
a
p u l s e d
c u r r e n t o r
A . C . c a s e i n d u c e d
c u r r e n t s c a n
a l s o a p p e a r
i n t h e
e a r t h
l e a d s
i f
t h e r e
i s
a
l o o p b e t w e e n
s e p a r a t e
c o m p o n e n t s o f t h e s y s t e m . I n e i t h e r c a s e
t h e
o v e r a l l
r e s u l t
i s
a n
o f f s e t
v o l t a g e o n t h e
m e a s u r e d
s i g n a l ,
w h i c h c a n e a s i l y b e
l a r g e e n o u g h
t o
d r o w n
t h e
d e s i r e d s i g n a l .
E a r t h
l o o p s
c a n b e
e l i m i n a t e d
b y c o n s i d e r i n g
t h e t o t a l
c i r c u i t d e s i g n
o f
t h e
s y s t e m ,
a n d
e i t h e r m a k i n g
s u r e
t h a t t h e w h o l e s y s t e m
h a s
o n l y a s i n g l e
e a r t h c o n n e c t i o n ,
o r f l o a t i n g
t h e w h o l e s y s t e m w i t h o u t a n y e a r t h c o n n e c t i o n s ( a l t h o u g h
t h i s i s
u s u a l l y
v e r y n o i s y ) .
D e p e n d i n g
o n
t h e
e q u i p m e n t t o b e u s e d
i t
i s n o t a l w a y s p o s s i b l e
t o
r e m o v e
a l l t h e e a r t h
l e a d s ,
i n
w h i c h c a s e i s o l a t i o n
d e v i c e s ,
s u c h
a s o p t o - i s o l a t o r s ,
s h o u l d b e
p l a c e d
i n t h e
s y s t e m
[ 2 . 3 0 ] .
S h i e l d i n g
B e f o r e t e s t i n g t h e
s y s t e m
f o r
n o i s e ,
i t
i s
p o s s i b l e t o
m i n i m i s e t h e
i n i t i a l
n o i s e
l e v e l
b y
u s i n g
l o w n o i s e p o w e r
s u p p l i e s
a n d
a m p l i f i e r s ,
a n d
t w i s t e d
a n d
s h i e l d e d
l e a d s .
C a p a c i t a t i v e e f f e c t s c a n b e r e d u c e d o r e l i m i n a t e d b y
s e p a r a t i n g t h e
v o l t a g e
a n d c u r r e n t
l e a d s .
I n d u c t i v e
e f f e c t s c a n b e r e d u c e d b y m i n i m i s i n g t h e a r e a
o f a n y
p i c k - u p l o o p s
i n
t h e
s y s t e m a n d t w i s t i n g e a c h s e t o f
w i r e s
t o g e t h e r .
C o a x i a l
o r
t w i s t e d p a i r
c a b l e s
( a t
l e a s t
o n
t h e
v o l t a g e
s i d e )
f u i t h e r r e d u c e t h e i n t e r f e r e n c e
f r o m
t h e
c u r r e n t
l e a d s . C o a x i a l
c a b l e h a s a
g e n e r a l l y
s u p e r i o r p e r f o r m a n c e t o t w i s t e d
p a i r s ,
i n
t h a t t h e
c o a x i a l c o n f i g u r a t i o n
c a n c e l s
t h e
s e l f f i e l d o f t h e o u t e r
s h e a t h a n d s c r e e n s t h e
i n n e r
c o r e
f r o m a n y e x t e r n a l
s i g n a l s .
H o w e v e r ,
i t
t e n d s t o b e i n f l e x i b l e a n d o f l a r g e
d i a m e t e r ,
m a k i n g i t
u n s u i t a b l e f o r
s o m e
a p p l i c a t i o n s .
T w i s t e d p a i r s h a v e r e d u c e d m a g n e t i c
p i c k u p a s
t h e y
e n c l o s e
o n l y a
s m a l l
a r e a ,
a n d t h e i n d u c e d s i g n a l s
i n
a d j a c e n t
t w i s t s
c a n c e l o u t
[ 2 . 3 0 ] .
B y
a d j u s t i n g t h e
t w i s t
p i t c h
t h e y
c a n b e m a d e i n s e n s i t i v e t o t h e o r i e n t a t i o n
o f
a n y
a p p l i e d f i e l d . A l t h o u g h
m o r e
s e n s i t i v e
t o s e l f a n d a p p l i e d
f i e l d s
t h a n c o a x i a l
c a b l e s ,
t w i s t e d p a i r s h a v e t h e
a d v a n t a g e t h a t t h e y
c a n
b e m a d e
f r o m a n y g a u g e o f w i r e a n d
t h u s
f i t
i n t o p l a c e s
w h e r e
c o a x i a l
c a b l e s c a n n o t .
B e c a u s e
o f t h e
c o m p l e x i t y o f m o s t m e a s u r e m e n t
s y s t e m s i t i s
d i f f i c u l t t o d e t e r m i n e
a l l p o t e n t i a l s o u r c e s o f
n o i s e
b e f o r e h a n d . F o r t h i s r e a s o n
t h e r e
e x i s t s e v e r a l
t e s t s
w h i c h c a n
b e u s e d t o d e t e r m i n e t h e n a t u r e o f a n y n o i s e e n c o u n t e r e d . T h e s e a r e d i v i d e d i n t o t w o
c a t e g o r i e s ,
f i n i t e - r e s i s t a n c e t e s t s
a n d
z e r o - r e s i s t a n c e
t e s t s ,
a s
s h o w n i n
f i g u r e
2 . 1 1 .
I n a
f i n i t e
r e s i s t a n c e t e s t
t h e
s u p e r c o n d u c t i n g s a m p l e i s r e p l a c e d
b y a n o r m a l
c o n d u c t o r
( s u c h
a s c o p p e r ) w i t h
a k n o w n
r e s i s t i v i t y , o f t e n o n e
w h i c h
g i v e s
v o l t a g e s o f
s i m i l a r
m a g n i t u d e
t o
t h o s e o b t a i n e d
w h e n
m e a s u r i n g
a n a c t u a l s u p e r c o n d u c t o r .
B e c a u s e
t h e r e w i l l b e n o
v o l t a g e s
a r i s i n g
f r o m t h e s u p e r c o n d u c t i n g
p r o p e r t i e s
o f t h e
s a m p l e a n d t h e
6 3
Chapter 2 : Experimental Techniques
I-V characteristic of the sample should be Ohmic it is then possible to determine whether
noise is present in the system.
The zero-resistance test uses a superconducting sample, but with one voltage lead
connected to the superconductor and the second voltage lead attached to the first close to the
sample. Obviously the voltage detected in this configuration should be zero. Any voltage
which is in fact detected is interfering noise from somewhere in the measuring system.
Figure 2.11 : Arrangements for (a) Finite resistance test and
(b) Zero-resistance tests.
A critical current simulator such as that shown in figure 2.12 can be useful in
running initial tests, in the calibration of computerised measurement systems, and to
determine whether a system performs as expected. It consists of a resistor and diode
network with a voltage-current characteristic similar to that of a superconductor [2.34], The
apparent 'critical current' for this particular device is approximately one ampere.
1+0- AA/V
ion
IN4Q04 diode
0.35Q- 0.035n<
I- o-
Figure 2.12 : Circuit diagram of critical current simulator.
Adjusting the components of the measuring system one at a time and using these
tests allows any sources of noise to be located and eliminated.
2.3.2 D.C. MEASUREMENTS
The simplest way to determine the D.C. I-V behaviour of a sample uses the
equipment shown in figure 2.13. A manually ramped current is applied to the sample. This
is measured by an I-V transducer (usually a resistor across which a voltage is measured)
64
C h a p t e r
2
: E x p e r i m e n t a l
T e c h n i q u e s
a n d p r o v i d e s
t h e x - a x i s i n p u t f o r a
x - y
r e c o r d e r . T h e
s a m p l e
v o l t a g e
i s
a m p l i f i e d a n d
p r o v i d e s
t h e
y - a x i s
i n p u t f o r
t h e
r e c o r d e r . A s
t h e
s a m p l e c u r r e n t
i n c r e a s e s
i t
e v e n t u a l l y
e x c e e d s
I c
a n d r e s u l t s
i n
t h e
a p p e a r a n c e o f
a
v o l t a g e .
O n c e
t h e m e a s u r e m e n t
i s
c o m p l e t e d
t h e r e s u l t i n g I - V
p l o t m u s t b e
d i g i t i s e d
o r i n s p e c t e d t o p r o d u c e a
v a l u e o f
I c
f r o m
w h i c h
J c
c a n b e c a l c u l a t e d .
F i g u r e
2 . 1 3
:
B l o c k
d i a g r a m o f
b a s i c
D . C . t r a n s p o r t
c r i t i c a l c u r r e n t
m e a s u r e m e n t
s y s t e m .
M o r e
s o p h i s t i c a t e d e x p e r i m e n t s a r e
e a s i l y
c o n s t r u c t e d u s i n g
c o m m o n l y a v a i l a b l e
G P I B a n d o t h e r
c o m p u t e r
i n t e r f a c i n g
t e c h n i q u e s t o c o n t r o l t h e
p o w e r
s u p p l y a n d r e p l a c e
t h e c h a r t r e c o r d e r b y t a k i n g
d a t a d i r e c t l y . T h r e e p o s s i b i l i t i e s
h a v e b e e n
e x p l o r e d
i n t h i s
t h e s i s a n d w e r e u s e d t o
m e a s u r e s a m p l e s i n
d i f f e r e n t f i e l d
a n d
t e m p e r a t u r e r e g i m e s .
T w o
u s e d a n u m b e r o f
c o m m o n c o m p o n e n t s
i n c l u d i n g a
v a r i a b l e g a i n
( x l O 3
t o
x l O 5 )
v o l t a g e
a m p l i f i e r c o n n e c t e d t o a G P I B - c o n t r o l l e d K e i t h l e y 1 9 9
D M M / S c a n n e r w h i c h
m e a s u r e s t h e
s a m p l e
v o l t a g e .
H i g h C u r r e n t
R a m p e d
M e a s u r e m e n t s
T h i s
s y s t e m
i s d e s i g n e d t o
m e a s u r e s a m p l e s
w i t h a
m o d e r a t e l y h i g h
I c .
I t
u s e s
a
H e w l e t t - P a c k a r d 6 0 3 1
A
1 2 0
A ,
2 0 V
s y s t e m
p o w e r
s u p p l y
( P S )
c o n t r o l l e d v i a a G P I B
i n t e r f a c e t o a n I B M - P C
c o m p u t e r .
T h i s
s t e p s
t h e P S
a t
a
c o n t r o l l e d
p r e d e t e r m i n e d
r a m p r a t e
a n d
a l s o
r e a d s
t h e
o u t p u t
c u r r e n t f r o m i t .
I t
s i m u l t a n e o u s l y
r e a d s
t h e
a m p l i f i e d v o l t a g e
a c r o s s
t h e
s a m p l e
f r o m
t h e K e i t h l e y
1 9 9
a n d c o n v e r t s i t
i n t o t h e
a c t u a l
s a m p l e
v o l t a g e .
T h i s
6 5
Chapter 2 : Experimental Techniques
information is saved as a file of I-V data. The system is limited in its measurement of
samples with low Ics as the output current resolution of the PS is only 30mA.
Low Current Ramped Measurements
The low-current measurement system uses a GPIB-controlled Farnell LB 30-4
Power Supply capable of providing a current of up to 4A with a resolution of 4mA. The
current from this is measured across a resistor and this voltage passed through a xlO gain
isolation amplifier into one channel of the Keithley 199. The sample voltage was passed
through a xlO5 gain voltage amplifier and into a second channel on the Keithley 199. The
data from the Keithley 199 was read in sequence, converted into actual values of current
and voltage and saved as a file of I-V data.
Very Low Current Ramped Measurements
For extremely low current measurements, an entirely different system was used.
This consisted of a Keithley 220 programmable current source and a Keithley 182 D.C.
nanovoltmeter. These were operated together under computer control to measure samples
with Ics of up to 100mA with a resolution of at least 50|iA. No voltage amplifier or current
measuring resistor was used as the current could be measured directly from the
Keithley 220 and the Keithley 182 was sensitive enough to make amplification of the
voltage signal unnecessary.
2.3.3 PULSED MEASUREMENTS
There are several problems associated with quasi-D.C. transport Jc measurements.
These include Ohmic heating in the current contacts, which can cause a significant drop in
Jc due to the heat diffusing into the bulk of the sample, and the problems of attaching leads
capable of carrying high currents to small or delicate samples. Because of these problems,
it was decided to construct a system, based on one built by Colclough et al. [2.35], to
perform routine computerised Jc measurements using a pulsed current technique.
A pulsed current has the advantage of enabling much higher sample currents to be
used without causing significant heating. This is possible because the power dissipation is
reduced by the ratio of the width of the current pulses to the spacing between them. It also
allows an average value of Jc to be found by measuring over many pulses. Although
66
C h a p t e r
2 : E x p e r i m e n t a l
T e c h n i q u e s
a v e r a g i n g
c a n ,
o f
c o u r s e ,
a l s o
b e c a r r i e d
o u t o n
a
D . C . s y s t e m ,
i t
i s m u c h
s l o w e r
a n d m o r e
l a b o r i o u s
t h a n o n a p u l s e d s y s t e m .
E f f e c t s
w h i c h h a v e t o b e t a k e n
i n t o c o n s i d e r a t i o n w h e n
c o n s t r u c t i n g
a p u l s e d
J c
m e a s u r e m e n t
s y s t e m
i n c l u d e v o l t a g e
t r a n s i e n t s c a u s e d
b y
t h e r a p i d
c h a n g e s
i n c u r r e n t ,
f o r c e s b e t w e e n
t h e
c u r r e n t
a n d
a p p l i e d
m a g n e t i c
f i e l d s ,
f l u x
m o t i o n ,
a n d t h e
s e l f - f i e l d
o f
t h e a p p l i e d c u r r e n t .
V o l t a g e
t r a n s i e n t s a r i s e
f r o m t h e
s u d d e n c h a n g e
i n
f l u x
i n d u c e d b y
t h e
c h a n g i n g
c u r r e n t a t t h e l e a d i n g a n d t r a i l i n g e d g e s o f t h e
p u l s e ,
w h i c h
i n d u c e v o l t a g e s
i n t h e
s a m p l e .
T h e s e a r e p r o p o r t i o n a l t o
d l /
d t a n d
c a n b e m u c h l a r g e r t h a n t h e
v o l t a g e s i g n a l
f r o m t h e
s u p e r c o n d u c t i n g s a m p l e , e s p e c i a l l y
w h e n
s q u a r e
p u l s e s h a p e s a r e
u s e d
( s e e
f i g u r e 2 . 1 4 ) .
T h i s ' r i n g i n g '
t y p i c a l l y
d e c a y s w i t h i n ~ 1 0 0 | l s o f t h e s t a r t
o f t h e p u l s e
i n t h e
a p p a r a t u s
u s e d
h e r e
b u t c a u s e s p r o b l e m s b e c a u s e
i t
i s c o n v o l u t e d w i t h i n t h e
m e a s u r e d v o l t a g e
s i g n a l .
T h i s
c a n b e
c o m p e n s a t e d f o r i n
t w o w a y s . F i r s t l y ,
t h e e n t i r e w a v e f o r m
i s
c a p t u r e d a n d o n l y
t h e
d a t a f r o m a f t e r t h e v o l t a g e h a s
s t a b i l i s e d i s u s e d .
T h i s
h a s p r o b l e m s
i f
t h e
v o l t a g e
a m p l i f i e r
i s
s a t u r a t e d
b y t h e ' r i n g i n g ' v o l t a g e .
S e c o n d l y , a m o r e
g r a d u a l
i n c r e a s e
i n
t h e
c u r r e n t c a n
b e
u s e d ,
w h i c h
r o u n d s
t h e e d g e s o f
t h e c u r r e n t
p u l s e .
T h i s
r e d u c e s t h e
r i n g i n g t o
t h e p o i n t
w h e r e i t c a n
b e s a f e l y i g n o r e d o r r e m o v e d
f r o m
t h e t o t a l s i g n a l .
A u s e f u l
f u n c t i o n f o r
s m o o t h i n g
t h e
p u l s e
e d g e s
w a s f o u n d t o b e
s i n 2 ( 0 )
f o r
9
f r o m 0
t o
7 1
1
2 -
T h i s
h a s a g r a d i e n t
d l
/
d t
=
0 a t
t h e
b e g i n n i n g a n d e n d
p o i n t s ,
r e m o v i n g a n y
s u d d e n c h a n g e s
i n c u r r e n t a n d
s o s i g n i f i c a n t l y r e d u c i n g
r i n g i n g .
F i g u r e
2 . 1 4
: S c h e m a t i c
d i a g r a m
o f
a ' t o p
h a t ' c u r r e n t p u l s e
a n d
c o r r e s p o n d i n g
v o l t a g e p u l s e s h o w i n g ' r i n g i n g ' .
*
R e g i o n s
w h e r e
r i n g i n g
i s
o c c u r r i n g .
6 7
Chapter 2 : Experimental Techniques
It should be remembered that even if the pulse edges are smoothed, any pulsed Jc
measurement system which uses computer-controlled ramping of the current will have
some degree of ringing present. This arises because the computers output to the current
supply, even if via a digital-to-analogue converter, is stepped rather than a smooth ramp.
However, the steps in current this produces are much smaller than that involved in the
square current pulse shown in figure 2.14 and so only produce limited ringing. This occurs
in both of the systems described below.
As mentioned in section 2.3.1 Lorentz forces have to be taken into consideration
when mounting and measuring a sample. Controlling the configuration so that the sample
is pressed onto the sample mount rather than pulled away from it is more important for
pulsed current measurements than a D.C. measurements (where it is also a factor) because
in a pulsed measurement the currents are generally larger and thus give many large 'jolts'
rather than a continuous smaller 'pull' on the sample.
The self-field of a sample significantly effects the results obtained in a number of
regimes. First, when the self-field is high compared to the applied field, the self-field limits
Jc [2.36]. Secondly, if the self-field is greater than Hc , Hpen (the field for full penetration
of the sample), H , or Hj (the field for full penetration of the intergranular regions in a
granular material) it will drive the sample from one regime of behaviour to another. The
self-field will generally have an insignificant effect when much less than the applied field,
except where it moves the total field over a boundary such as H . For a pulsed
measurement thermal effects also need to be included due to the short time scale compared
to quasi-D.C. measurements, which limits the amount of flux motion and so can lead to an
over-estimate of Jc [2.28], though this is unlikely to be significant compared to the effects
of the amplitude of the self-field.
The first pulsed Jc system developed here is shown in figure 2.15. It uses an
IBM PC computer connected to a current supply and current-voltage transducer. The
voltages are generated and measured by a 12-bit analogue-to-digital/digital-to-analogue
(ADDA) card. The current supply is an Oxford Instruments superconducting magnet power
supply, modified to pulse up to a maximum of ~70A within a time of ~lms. The computer
controls this via the sweep control input of the power supply to give a smoothed square
current pulse. The current through the sample is measured using a standard resistor. A
Datalab DL905 Transient Recorder is connected to the computer via a DIO card and
triggered from it to capture the entire voltage pulse across the sample. Two opto-isolated
amplifiers with gains of 105 and 10 respectively isolate both the sample from the transient
68
C h a p t e r
2 : E x p e r i m e n t a l
T e c h n i q u e s
r e c o r d e r
a n d
t h e c u r r e n t m e a s u r i n g
r e s i s t o r
f r o m
t h e
A D D A
c a r d
i n p u t
a n d
a l s o
s e r v e t o
a m p l i f y t h e m e a s u r e d
v o l t a g e
s i g n a l s .
V o l t a g e A m p l i f i e r
( I s o l a t i o n
A m p l i f i e r )
F i g u r e 2 . 1 5 :
B l o c k d i a g r a m
o f
t h e f i r s t p u l s e d t r a n s p o r t
J c
m e a s u r e m e n t
s y s t e m .
T h e c o m p u t e r
c o n t r o l s t h e e n t i r e p u l s i n g
a n d
d a t a
a c q u i s i t i o n
p r o c e s s . A
q u a s i - D . C . t e c h n i q u e i s u s e d
i n
w h i c h t h e h e i g h t o f e a c h v o l t a g e
p u l s e
i s a n a l y s e d a n d
c u r r e n t
p u l s e s r e p e a t e d a t
h i g h e r m a x i m u m c u r r e n t s u n t i l t h e
s p e c i f i e d v o l t a g e
c r i t e r i o n
f o r
J c
i s
r e a c h e d ,
g i v i n g a n I - V
c h a r a c t e r i s t i c
f o r
t h e s a m p l e . T h i s i s s h o w n
s c h e m a t i c a l l y
i n
f i g u r e 2 . 1 6 .
F i g u r e
2 . 1 6 : S c h e m a t i c d i a g r a m
o f
c u r r e n t
p u l s e s
u s e d i n t h e
q u a s i - D . C .
t e c h n i q u e
d e s c r i b e d
a b o v e .
6 9
Chapter 2 : Experimental Techniques
Although the pulsed current system described above was adequate, it was too slow,
the DL905 transient recorder was too unreliable, and the system did not allow measurement
at high enough currents to form the basis of a general-use pulsed Jc measurement system.
For this reason a second system was constructed using completely different equipment.
This system consists of a Hewlett-Packard 6031A 120A, 20V system power supply
(PS), a Hewlett-Packard 54601A digital storage oscilloscope (DSO) and a voltage amplifier
built in the I.R.C. with a gain variable between xlO3 to xlO5 and a bandwidth variable
from 1Hz to 1000Hz. A resistor is connected in series with the sample to measure the
current accurately. The voltage across the resistor is fed into the x input of the DSO. The
voltage across the sample is amplified and fed into the y input to the DSO. The DSO
simultaneously records the current and voltage waveforms, post-event triggering on the
descending edge of the current signal. The current and voltage signals are typically
averaged over 64 current pulses to obtain a statistically significant average, although
depending on noise conditions as few as eight or as many as 256 averagings can be used.
Experimental control and data capture are carried out by a 386 IBM PC computer. This
system is shown schematically in figure 2.17.
Voltage Amplifier
(Isolation
Figure 2.17 : Block diagram, of the second pulsed transport Jc system.
The second system uses a 'saw tooth' shaped waveform, rather than a set of square
pulses of increasing amplitude, with a constant ramp of the current to a maximum value and
70
C h a p t e r
2
:
E x p e r i m e n t a l
T e c h n i q u e s
a
s h a r p
d r o p
t o
z e r o ,
a s
s h o w n
i n
f i g u r e
2 . 1 8 ( b ) .
T h u s t h e
f u l l T V
c o u l d
b e
g a t h e r e d
i n a
s i n g l e
p u l s e .
A l t h o u g h r i n g i n g
o c c u r r e d a t t h e e n d o f t h e
p u l s e
t h i s
c o u l d b e s a f e l y i g n o r e d
f o r
t h e
p u r p o s e s
o f t h e e x p e r i m e n t s i n c e
I c
w a s o b t a i n e d
f r o m t h e
i n c r e a s i n g
p a r t
o f
t h e
w a v e f o r m .
F i g u r e
2 . 1 8
: C u r r e n t v e r s u s
t i m e
w a v e f o r m s
u s e d
f o r
p u l s e d
J c
m e a s u r e m e n t ,
( a )
S q u a r e p u l s e ,
( b )
' S a w t o o t h '
p u l s e .
T h e
o p t i m u m p u l s e
l e n g t h f o r a
p u l s e d
J c
s y s t e m c a n
b e
c h o s e n
a s
f o l l o w s .
T h e
v a r i a t i o n o f
s a m p l e
t e m p e r a t u r e
( o r
v o l t a g e )
i s m o n i t o r e d
a s
a
f u n c t i o n o f
t i m e
a t a f i x e d
c u r r e n t .
T h i s g i v e s
a f a m i l y
o f
p l o t s
o f
t e m p e r a t u r e
v e r s u s t i m e f o r
e a c h
v a l u e
o f c u r r e n t
a s
s h o w n s c h e m a t i c a l l y
i n
f i g u r e
2 ,
1
9 .
F i g u r e
2 . 1 9
:
M e t h o d
o f
o p t i m i s i n g
c u r r e n t
p u l s e
w i d t h .
F r o m t h i s
i n f o r m a t i o n i t s h o u l d
b e
p o s s i b l e t o d e t e r m i n e
t h e o p t i m u m
p u l s e w i d t h
f o r a g i v e n
c u r r e n t ,
t h o u g h t h e a c t u a l v a l u e s o f
t e m p e r a t u r e v e r s u s t i m e
f o r a
g i v e n
c u r r e n t
v a r y
b e t w e e n
s y s t e m s .
7 1
Chapter 2 : Experimental Techniques
2.4 MAGNETIC MEASUREMENTS
In any superconducting material in the presence of an applied magnetic field there is
an induced supercurrent giving rise to a magnetic moment which varies with applied field.
If there is no flux pinning this moment is fully reversible, while with flux pinning it is
hysteretic. If flux motion occurs then the moment will also change with time, though exact
form of this variation depends on the magnetic history of the sample.
All magnetic measurement techniques involve detecting the voltage generated by the
change in flux in a search coil due to the change in flux in a magnetised sample. There are a
number of ways of producing an inductive signal [2.1], for example varying the applied
field, or moving the sample in a constant but inhomogenous applied field. Neither of these
is a truly D.C. system, although the latter is usually referred to as such. In all magnetic
measurements the shape of the sample can significantly affect the results obtained, due to
demagnetising effects [2.37] and should be taken into consideration when analysing any
magnetic data.
In a sample with flux pinning which has been fully penetrated by the applied field,
the width of an observed magnetic hysteresis loop is directly proportional to the average
critical current density if current flows on the length scale of the whole sample [2.38], For
this reason Jc may be determined by a critical state model (see section 1.6) after measuring
the magnetisation curve of a sample at fixed temperature. Because the sample is fully
penetrated by the applied field demagnetising and geometry-dependant factors can be
assumed to be insignificant. In situations where the sample is not fully penetrated by the
applied field these effects cannot be ignored and the data requires careful interpretation.
There are four sample geometries where the detected signal can be directly related to
the sample magnetisation regardless of the current distribution in the sample as shown in
figure 2.20(a) to (d) [2.1, 39]. The first three of these involve loose inductive coupling
between sample and search coil. This increases the noise and background signals in the
system, but has the advantage of allowing a reasonably simple interpretation of the results
obtained.
For optimum sensitivity per turn of search coil, however, the search coil should be
wound on the surface of the sample as shown in figure 2.20(d). For samples of arbitrary
shape this presents more practical difficulties and difficulties of interpretation than for the
loosely-coupled geometries above. However, results can be obtained by using tables of
mutual inductances or by calibrating the system with a reference sample of bulk type I
superconductor, although in this case an error is introduced because the current flows
entirely on the surface in these materials.
72
C h a p t e r
2
: E x p e r i m e n t a l
T e c h n i q u e s
S e a r c h
C o i l s
o o o o o o o o o o o o o o o o o
S a m p l e -
• C D
o o o o o o o o o o o o o o o o o
F i g u r e
2 . 2 0
( a )
:
S m a l l
s a m p l e
e n c l o s e d
b y
a l o n g
s o l e n o i d a l
c o i l .
O
S a m p l e
\
S e a r c h C o i l
C D
\
o
F i g u r e
2 . 2 0
( b )
: S a m p l e
s m a l l
c o m p a r e d
t o
t h e
d i s t a n c e
f r o m
i t
t o t h e
s e a r c h c o i l
w i n d i n g s .
S a m p l e
\
S e a r c h
C o i l
\
o
F i g u r e
2 . 2 0
( c )
:
S m a l l
s a m p l e
i n s i d e
a l a r g e
c o i l .
S a m p l e
S e a r c h C o i l s
\
o o o o o
o o o o o
F i g u r e
2 . 2 0
( d )
: C o i l
w o u n d
r o u n d a
c y l i n d r i c a l
s a m p l e
a w a y
f r o m
i t s e n d s .
2 . 4 . 1 D . c . M A G N E T I C
M E A S U R E M E N T S
T h e r e a r e a n u m b e r o f w a y s t o m e a s u r e t h e m a g n e t i s a t i o n
o f a
s a m p l e
[ 2 . 1 ] .
T h e
c o m m o n e s t
w a y
p r o d u c e s
a n i n d u c t i v e s i g n a l
b y
m o v i n g
t h e s a m p l e e i t h e r
o u t o f t h e
s e a r c h
c o i l
o r b e t w e e n t w o
s e p a r a t e
s e a r c h
c o i l s .
C a r e
m u s t
b e t a k e n
i f
t h e r e
i s
a n y
i n h o m o g e n e i t y
i n
t h e a p p l i e d D . C .
f i e l d s i n c e
m o v i n g
t h e s a m p l e
w i l l t h e n t a k e i t
i n t o r e g i o n s
o f h i g h e r o r
l o w e r
f i e l d ,
t r a p p i n g o r e x p e l l i n g f l u x
a n d m o d i f y i n g t h e
m a g n e t i s a t i o n .
F o r s a m p l e s w i t h a
s m a l l
h y s t e r e s i s
t h e f i e l d c h a n g e s u f f i c i e n t
t o
i r r e v e r s i b l y a l t e r m
c a n b e
a s l o w a s a f e w
m i l l i T e s l a .
B e c a u s e o f
t h i s ,
s m a l l s a m p l e d i s p l a c e m e n t s a t a
r e l a t i v e l y h i g h
f r e q u e n c y
( ~ 1 0 0 H z )
a r e
p r e f e r a b l e . S y s t e m s w h i c h
u s e t h i s
m o d e
o f o p e r a t i o n a r e k n o w n
a s v i b r a t i n g
s a m p l e
m a g n e t o m e t e r s
( V S M s ) ,
a n d w e r e
f i r s t d e s i g n e d b y F o n e r
i n 1 9 5 9
[ 2 . 4 0 ] .
7 3
Chapter 2 : Experimental Techniques
An alternative technique was developed by Kiirti and Simon [2.41], In it the sample
remains stationary and the signal on the search coils is integrated as the applied field is
swept up from zero. Force or torque magnetometry, in which the forces on a
superconducting sample in a magnetic field are measured, can also provide useful
information on a superconducting sample [2.42], Superconducting quantum interference
device (SQUID) systems use much lower frequencies (~0.1Hz) and are about three orders
of magnitude more sensitive than a VSM. In a SQUID the sample is moved slowly through
search coils connected to the SQUID detector, and the output voltage is proportional to the
total flux passing through the coils [2.43]. Because of this SQUIDs are very susceptible to
any field inhomogeneity. These techniques are not used in this thesis and are mentioned
here only for completeness.
Calculation of Jr- from Magnetisation Measurements
A sketch of a typical hysteresis loop (determined, for example, by vibrating sample
magnetometry), for a type II superconducting material with flux pinning in fields much
less than H is shown in figure 2.21. Analysis of a curve such as this can be used to
obtain Jc(magnetic) as a function of B and T (see section 1.6).
Figure 2.21 : A sketch of a typical hysteresis loop for a type II
superconductor infields much less than Hc . Arrows indicate direction of
field sweep.
At fields greater than that required to fully penetrate the sample (so that the
hysteresis loop width is symmetrical about the reversible field curve, i.e. that for a perfect
pinning-free specimen of the same material) the magnetisation can be taken as half the
hysteresis loop width at a given field. Jc can then be estimated using an appropriate critical
state model. Bean [2.38] and London [2.44] were the first to consider this (see section
1.6). Calculations at fields near to H are very difficult due to the incomplete flux
CZ)
74
C h a p t e r
2 :
E x p e r i m e n t a l
T e c h n i q u e s
p e n e t r a t i o n
o f
t h e
s a m p l e
i n t h i s r e g i m e .
A
m a g n e t o m e t e r
w h i c h
h a s b e e n
c a l i b r a t e d a g a i n s t
a k n o w n
s t a n d a r d ,
s u c h a s
l e a d ,
i s u s e d ,
a l o n g w i t h t h e e q u a t i o n
2 . 3 . T h i s
r e l a t i o n s h i p i s
a p p l i c a b l e
t o a n i n f i n i t e c y l i n d r i c a l
s a m p l e
i n a
p a r a l l e l m a g n e t i c
f i e l d
w h e r e
J c
i s
i n d e p e n d e n t o f B , b u t g i v e s
u s a b l e
r e s u l t s f o r s a m p l e s w h i c h a r e f u l l y
p e n e t r a t e d
b y
t h e
a p p l i e d f i e l d s o t h a t g e o m e t r y - d e p e n d a n t
f a c t o r s c a n
b e
s a f e l y
n e g l e c t e d .
w h e r e a
=
s a m p l e r a d i u s
( 2 . 3 )
J
=
s c r e e n i n g
c u r r e n t
d e n s i t y
=
J c
l
=
s a m p l e
l e n g t h
m
=
m e a s u r e d s a m p l e m a g n e t i s a t i o n
T h e s c r e e n i n g
c u r r e n t
i s e q u a l t o
J c
a s t h e s a m p l e i s f u l l y
p e n e t r a t e d
b y
t h e
a p p l i e d
f i e l d
( s e e
s e c t i o n
1 . 6 ) .
=
j
J 7 t r 2 M r
=
n J a t
J c
m a y b e
c a l c u l a t e d
u s i n g
t h e f o l l o w i n g
e q u a t i o n s
( d e r i v e d
f r o m
e q u a t i o n
2 . 3 )
f o r
d i f f e r e n t g e o m e t r i e s , a s s u m i n g t h a t a
u n i f o r m c u r r e n t d e n s i t y
f l o w s
t h r o u g h o u t
t h e e n t i r e
w i d t h o f t h e
s a m p l e .
J c
=
J c
=
3 A m
I n
f t
3 A
m
t w
3
f o r a
d i s c
f o r a s q u a r e
p l a n a r
s a m p l e
( 2 . 4 )
( 2 . 5 )
w h e r e A m
=
w i d t h
o f h y s t e r e s i s
l o o p
=
2 m
f r o m e q u a t i o n
2 . 3
( t h i s
i s o n l y v a l i d
i f
t h e s a m p l e
i s
f u l l y
p e n e t r a t e d
b y
t h e
a p p l i e d
f i e l d ) ,
w
=
s a m p l e
w i d t h ,
t
=
s a m p l e
t h i c k n e s s ,
r
=
s a m p l e r a d i u s . F i g u r e 2 . 2 2
s h o w s t h e s e
t w o
c o n f i g u r a t i o n s
s c h e m a t i c a l l y .
F i g u r e
2 . 2 2
: S c h e m a t i c
d i a g r a m
o f
t h e
c o n f i g u r a t i o n s
u s e d f o r c a l c u l a t i n g
J c f r o m
h y s t e r e s i s
l o o p s
f o r
( a )
a d i s c a n d
( b )
a
s q u a r e p l a n a r
s a m p l e .
L a s t l y ,
a n
i m p o r t a n t f a c t o r w h i c h s h o u l d
a l w a y s
b e
c o n s i d e r e d i s
t h e d i f f e r e n c e
b e t w e e n
J c s
d e t e r m i n e d b y
t r a n s p o r t
a n d
m a g n e t i c m e t h o d s
i n g r a n u l a r a n d
a n i s o t r o p i c
s y s t e m s ,
s u c h a s
H T S C s . I n
g r a n u l a r
m a t e r i a l s t h e
t r a n s p o r t
J c
f o l l o w s a m e a n d e r i n g
p a t h
a l o n g t h e
m o s t
s t r o n g l y
s u p e r c o n d u c t i n g
r o u t e t h r o u g h
t h e
s a m p l e
a n d
i s l i m i t e d b y t h e
7 5
Chapter 2 : Experimental Techniques
weakest links along this 'strongest' route. As a magnetic field is applied the transport Jc of
the weak links will be suppressed by the field, leading to a rapid fall in the measured
transport Jc. A magnetic measurement of Jc, however, detects the induced currents within
the sample. At high fields in a weak-linked sample the intergranular Jc is suppressed and
the magnetic Jc is dominated by the currents induced within the grains rather than the much
smaller currents between them as shown schematically in figure 2.23. This gives rise to a
much higher apparent Jc than a corresponding transport measurement in these samples.
Most current HTSC samples fall into this category [2.45].
Figure 2.23 : Schematic diagram of the induced currents in a granular
superconductor showing the intra- and inter-granular J(S. At high fields the
intra-granular Jc will dominate the measured magnetisation.
Figure 2.24 : Schematic diagram of the flow of induced currents in an
anisotropic HTSC sample with the applied field into the plane of the paper
where Jc(ab-planes) > Jc(c-axis). The thin lines indicate the boundaries of
regions where current flow occurs in different directions.
In an anisotropic superconductor a magnetic measurement will be sensitive to the
alignment of the applied field with the superconductors crystal structure. In HTSCs this
means alignment with the CuO planes. If the applied field induces currents along the c-axis
of a HTSC this significantly reduces the measured Jc due to their weaker c-axis properties.
It also leads to the induced current loops being elongated along the direction with better
transport properties, the ab-planes, as shown in figure 2.24.
76
C h a p t e r
2 : E x p e r i m e n t a l
T e c h n i q u e s
L a s t l y , w h e n c a r r y i n g
o u t
a m a g n e t i c
J c
m e a s u r e m e n t
i t
s h o u l d b e
r e m e m b e r e d
t h a t ,
d u e
t o t h e
d i f f e r e n t v o l t a g e
l e v e l s
i n v o l v e d ,
t h e
e f f e c t i v e
e l e c t r i c f i e l d
c r i t e r i o n c a n e a s i l y b e
c h o s e n
t o
b e
~ 1 0 n V / c m ,
r a t h e r t h a n
t h e ~ l p V / c m
c o m m o n l y
u s e d
i n
t r a n s p o r t
J c
m e a s u r e m e n t s
[ 2 . 5 ] .
G i v e n t h e
n o n - l i n e a r s h a p e o f
T V
c u r v e s t h i s
d i f f e r e n c e
i n
c r i t e r i o n
c a n s i g n i f i c a n t l y a f f e c t t h e m e a s u r e d
J c .
V i b r a t i n g
S a m p l e
M a g n e t o m e t r v S y s t e m s
A s c h e m a t i c d i a g r a m
o f
a V S M s y s t e m
i s s h o w n
i n
f i g u r e
2 . 2 5 .
T h e
s y s t e m
u s e d
f o r t h e w o r k
d e s c r i b e d i n
t h i s
t h e s i s ,
a n
O x f o r d I n s t r u m e n t s
3 0 0 1
1 2 T
V S M ,
i s f u l l y
c o m p u t e r i s e d ,
a l l o w i n g
s e t s o f
h y s t e r e s i s
l o o p s t o b e
a u t o m a t i c a l l y
m e a s u r e d
a t f i x e d
t e m p e r a t u r e
f r o m 4 . 2 K
t o 3 0 0 K
i n f i e l d s o f u p
t o
± 1 2 T .
1 0
K e y
1
:
N e e d l e
V a l v e
2
:
S a m p l e
3
:
V i b r a t i n g
H e a d
4 :
1 2 T
S u p e r c o n d u c t i n g M a g n e t
C o i l s
5
:
P i c k - U p
C o i l s
6 : A u - F e
T h e r m o c o u p l e
7
:
P r e - A m p l i f i e r
8
:
L o c k - I n
A m p l i f i e r
9 :
S y s t e m
C o n t r o l l e r
1 0
:
T e m p e r a t u r e C o n t r o l l e r
1 1
:
T o P u m p i n g
S y s t e m
1 2
:
H e l i u m B a t h
F i g u r e
2 . 2 5 : S c h e m a t i c d i a g r a m
o f
V S M
s y s t e m .
T y p i c a l l y
a
V S M
o p e r a t e s a t a
f i x e d f r e q u e n c y
( ~ 6 0 H z )
a n d
t e m p e r a t u r e
w h i l e
s w e e p i n g
t o t h e
m a x i m u m
s e t
f i e l d a t
~ 1 0 0 m T / s e c .
A f t e r e a c h h y s t e r e s i s
l o o p
i s
m e a s u r e d
t h e s a m p l e i s h e a t e d t o w e l l
a b o v e i t s
T c
a n d c o o l e d t o
t h e
n e x t s e t
t e m p e r a t u r e
i n
z e r o f i e l d
i n
o r d e r t o r e m o v e a n y
t r a p p e d
f l u x w i t h i n t h e s a m p l e .
I n a d d i t i o n t o
m e a s u r e m e n t s o f
h y s t e r e s i s
l o o p s , i t
i s a l s o p o s s i b l e
f o r a V S M t o
m e a s u r e
f l u x
c r e e p
i n H T S C s
[ 2 . 4 6 ]
b y
m o n i t o r i n g t h e
c h a n g e i n m a g n e t i s a t i o n
a s
a
f u n c t i o n
o f t i m e a t c o n s t a n t
f i e l d a n d
t e m p e r a t u r e ,
o r t o
d e t e r m i n e t h e l e n g t h
s c a l e o n
w h i c h
7 7
Chapter 2 : Experimental Techniques
current flows in a superconductor [2.47], although these types of measurement are
mentioned here only for completeness.
2.4.2 A.C. INDUCTIVE MEASUREMENTS
Several parameters can be measured by applying A.C. fields to a superconductor,
including Jc and %, the magnetic susceptibility. A.C. inductive techniques are affected by
many of the same problems as D.C. techniques such as field inhomogeneity. The simplest
A.C. technique measures the change in impedance of a coil containing the sample as a
function of temperature or magnetic field. Although the signal from this configuration may
be small, superconductivity can be distinguished by detecting either its diamagnetic
response or the third harmonic of the drive frequency, as only superconductors generate a
signal at such a frequency [2.38]. Most A.C. systems, however, use a mutual inductance
technique (see below). As in D.C. methods, the drive coil should generate a uniform field
over all the sample, and the pickup coils should be such that the signal detected is easily
related to the magnetisation.
Susceptibility Measurements
A.C. Susceptibility (ACS) is a technique used in the study of the magnetic
properties of materials [2.48]. It does this by measuring the differential magnetic
susceptibility, % = dM / dH, the effect of a sample on the magnetic flux within a sensing
coil around the specimen. ACS can measure a sample at constant A.C. field and frequency
as a function of temperature, or at constant temperature as a function of field. The latter of
these is the same as is done in a VSM. A review of A.C. susceptometry and related topics
by Goldfarb et al. is given in [2.48], although in this thesis A.C. techniques have been
used only for determining the position and quality of the superconducting transition.
X can be measured by applying a small A.C. magnetic field of constant amplitude to
the sample and monitoring the induced voltage on a sense coil around the sample. To
simplify interpretation of the detected signal and increase sensitivity this sense coil is
usually wound in series opposition with an identical empty coil. In this arrangement the
induced voltages from the two coils cancel when they contain identical susceptibilities, so a
net signal is only observed when one coil contains a para- or diamagnetic sample. The
commercial ACS system used here is a Lakeshore Cryophysics model 7000A. A schematic
diagram of an ACS system is shown in figure 2.26.
78
C h a p t e r
2
: E x p e r i m e n t a l
T e c h n i q u e s
F i g u r e
2 . 2 6
:
S c h e m a t i c
d i a g r a m o f a n
A . C . s u s c e p t i b i l i t y
s y s t e m .
I n t e r p r e t a t i o n o f
t h e
r e a l a n d i m a g i n a r y
p a r t s
o f
t h e A C S s i g n a l
a s a
f u n c t i o n
o f
t e m p e r a t u r e i n a n
a p p l i e d f i e l d c a n b e c a r r i e d o u t u s i n g
a c r i t i c a l
s t a t e
m o d e l
( s e e
s e c t i o n
1 . 6 ) [ 2 . 4 9 , 5 0 ] ,
a l t h o u g h
t h i s
h a s n o t
b e e n
c a r r i e d o u t
i n
t h e
c o u r s e o f
t h i s
t h e s i s .
T h e
b e h a v i o u r i n s m a l l A . C .
f i e l d s
i s
s i m i l a r
t o
t h a t
i n t h e
D . C .
c a s e ,
b u t
l e s s
e a s y
t o
e x p l a i n
i n
a q u a l i t a t i v e m a n n e r .
F u l l d i a m a g n e t i s m ,
a n u n a m b i g u o u s
m a n i f e s t a t i o n
o f
s u p e r c o n d u c t i v i t y ,
c o r r e s p o n d s t o
a
s u s c e p t i b i l i t y
o f
- 1 .
T h e n o r m a l s t a t e o f a
H T S C ,
a b o v e
T c ,
i s
w e a k l y
p a r a m a g n e t i c ,
w i t h
x
~
1 0 “ 4 ( a l t h o u g h
t h i s
i s v e r y
v a r i a b l e ) .
W h e n t h e
t e m p e r a t u r e
o f
t h e
s a m p l e
i s m u c h
l e s s t h a n
T c
a n d t h e
s a m p l e
d i m e n s i o n s
m u c h
g r e a t e r t h a n
t h e p e n e t r a t i o n
d e p t h
X ,
a
s m a l l
( i . e .
l e s s
t h a n
H C I )
a p p l i e d A . C . f i e l d
i n d u c e s s u p e r c o n d u c t i n g s c r e e n i n g
c u r r e n t s o n t h e s u r f a c e o f t h e s u p e r c o n d u c t o r . I n
t h i s
c a s e t h e
s a m p l e h a s o n l y a s m a l l
h y s t e r e s i s
s o
x '
r e m a i n s
n e a r l y
c o n s t a n t a n d
% "
=
0 a t l o w
t e m p e r a t u r e s . W h e n a
b u l k
s h i e l d i n g
p a t h i s
e s t a b l i s h e d i n
a
s u p e r c o n d u c t o r
o n c o o l i n g
i n c o n s t a n t f i e l d a t
c o n s t a n t
f r e q u e n c y ,
t h e
s o - c a l l e d c o u p l i n g o n s e t w h e r e
t h e
i n d u c e d c u r r e n t s
f i r s t f l o w o n t h e
s c a l e
o f
t h e
w h o l e s a m p l e , t h e r e a l
p a r t
o f
t h e
A . C . s u s c e p t i b i l i t y ( x ' ) s t a r t s t o f a l l b e l o w
z e r o . T h i s
c o r r e s p o n d s t o t h e o n s e t o f
z e r o r e s i s t a n c e i n
a n R - T
m e a s u r e m e n t
( s e e
s e c t i o n
2 . 2 . 1 )
a n d
i s r o u t i n e l y
u s e d
f o r
m e a s u r i n g t h e t r a n s i t i o n t e m p e r a t u r e o f s u p e r c o n d u c t o r s .
I n
g r a n u l a r
m a t e r i a l s t w o d i s t i n c t
f e a t u r e s
o c c u r ,
c o r r e s p o n d i n g t o i n t r i n s i c
( i . e .
i n t r a g r a n u l a r )
a n d
c o u p l i n g
( i . e .
i n t e r g r a n u l a r ) e f f e c t s
a s s h o w n i n
f i g u r e
2 . 2 7 . T h e
d e c o n v o l u t i o n o f
t h e s e
t w o c o n t r i b u t i o n s t o
x
i s
p a r t i c u l a r l y
i m p o r t a n t
i n
m e a s u r e m e n t s o n p o l y c r y s t a l l i n e H T S C
s a m p l e s d u e t o t h e
h i g h l y g r a n u l a r
n a t u r e o f
t h e s e
m a t e r i a l s
( s e e
s e c t i o n
1 . 1 2 . 2 ) .
7 9
Chapter 2 : Experimental Techniques
Figure 2.27 : The ACS response of (Bi,Pb)2Sr2Ca2Cu30x in a O.lmT,
100HzA.C. applied field showing the effects of the intrinsic (intragranular)
response and the coupling (intergranular) response on %' and From
Goldfarb et al. [2.48]. %' does not extrapolate to -1 due to demagnetising
effects.
Information on inherent losses in a sample can be obtained from ACS because the
imaginary (out of phase) part of the signal (%") is proportional to the loss in the sample
[2.39]. This loss is small when FI « HCi (i.e. well below Tc) as the field penetrates only a
little way into the superconductor. As the temperature increases HCI and Jc fall and
screening currents begin to penetrate the sample; hysteresis appears and the sample
magnetisation becomes irreversible. This loss appears as an increase of above zero and a
drop in As the temperature increases further %" increases until the losses reach a
maximum just below Tc at H ~ Hc when the field penetrates to the centre of the sample.
When H » Hc (i.e. very close to Tc) the maximum field is well above that required for
full penetration so that the M-H loop collapses and the samples enters a reversible
(Abrikosov) magnetisation state, causing the losses to vanish and %" to return to zero. As
with in a granular material %" shows two distinct peaks, a higher temperature intrinsic
signal, and a lower temperature coupling signal, as seen in figure 2.27.
Other losses may contribute to %' and such as those associated with flux creep
and flux flow, but these have not been considered in the course of this thesis.
80
C h a p t e r
2
: E x p e r i m e n t a l
T e c h n i q u e s
T h e r e
a r e a l s o s e v e r a l
d i f f e r e n t A . C .
i n d u c t i v e
t e c h n i q u e s w h i c h
a r e u s e d t o
m e a s u r e
J c
[ 2 . 3 8 ,
3 9 , 5 1 - 5 4 ] ,
a l t h o u g h t h e s e h a v e n o t
b e e n
u s e d h e r e
a n d a g a i n a r e
m e n t i o n e d
o n l y f o r c o m p l e t e n e s s .
2 . 5 R E F E R E N C E S
[ 2 . 1 ]
A . M . C a m p b e l l
i n
C o n c i s e E n c y c l o p a e d i a
o f
M a g n e t i c
a n d
S u p e r c o n d u c t i n g
M a t e r i a l s
,
p p
3 0 5 ,
e d i t e d b y J . E .
E v e t t s
( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 2 . 2 ]
J . M o s q u e i r a ,
A .
P o m a r ,
A .
D i a z ,
J . A . V e i r a a n d
F .
V i d a l ,
P h y s i c a
C ,
2 2 5 ,
3 4
( 1 9 9 4 ) .
[ 2 . 3 ]
G .
D e u t s c h e r i n
C o n c i s e E n c y c l o p a e d i a o f M a g n e t i c
a n d
S u p e r c o n d u c t i n g
M a t e r i a l s , p p
8 2 ,
e d i t e d b y J . E . E v e t t s ( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 2 . 4 ]
J . E .
E v e t t s ,
I E E E
T r a n s .
M a g n . ,
1 9 ,
1 1 0 9
( 1 9 8 3 ) .
[ 2 . 5 ]
A . D .
C a p l i n ,
L . F .
C o h e n ,
G . K .
P e r k i n s
a n d A . A . Z h u k o v ,
S u p e r c o n d .
S c i .
T e c h n o l . ,
7 ,
4 1 2
( 1 9 9 4 ) .
[ 2 . 6 ]
J . W .
E k i n i n C o n c i s e
E n c y c l o p a e d i a o f M a g n e t i c
a n d
S u p e r c o n d u c t i n g
M a t e r i a l s ,
p p
5 7 8 ,
e d i t e d b y J . E . E v e t t s ( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 2 . 7 ]
J . E . E v e t t s
i n C o n c i s e
E n c y c l o p a e d i a
o f M a g n e t i c
a n d
S u p e r c o n d u c t i n g
M a t e r i a l s ,
p p
4 7 8 ,
e d i t e d b y J . E .
E v e t t s
( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 2 . 8 ]
D . M . K r o e g e r , C . C .
K o c h a n d J . P .
C h a r l e s w o r t h ,
/ . L o w
T e m p .
P h y s . ,
1 9 ,
4 9 3
( 1 9 7 5 ) .
[ 2 . 9 ]
A . M . C a m p b e l l a n d J . E .
E v e t t s ,
A d v a n c e s i n
P h y s i c s ,
2 1 ,
1 9 9
( 1 9 7 2 ) .
[ 2 . 1 0 ]
J . W .
E k i n ,
A p p l . P h y s .
L e t t . ,
5 5 ,
9 0 5
( 1 9 8 9 ) .
[ 2 . 1 1 ]
J . E . E v e t t s a n d
B . A .
G l o w a c k i ,
C r y o g e n i c s ,
2 8 ,
6 4 1
( 1 9 8 8 ) .
[ 2 . 1 2 ]
M . N . W i l s o n
,
S u p e r c o n d u c t i n g M a g n e t s , P a g e s ,
C l a r e n d o n
P r e s s ,
O x f o r d
( 1 9 8 3 )
[ 2 . 1 3 ]
J . E .
E v e t t s ,
B . A .
G l o w a c k i ,
P . L . S a m p s o n , M . G .
B l a m i r e ,
N . M .
A l f o r d
a n d
M . A .
H a r m e r ,
I E E E
T r a n s a c t i o n s o n M a g n e t i c s ,
2 5 ,
2 0 4 1
( 1 9 8 9 ) .
8 1
Chapter 2 : Experimental Techniques
[2.14] W.H. Warnes and D.C. Larbalestier, Appl. Phys. Lett., 48, 1403 (1986).
[2.15] C.J.G. Plummer and J.E. Evetts, IEEE Trans. Magn., 23, 1179 (1987).
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Superconducting Materials, pp 88, edited by J.E. Evetts (Pergammon Press
1992)
[2.17] H. Jones, L. Cowey and D. Dew-Hughes, Cryogenics, 29, 795 (1989).
[2.18] J.W. Ekin, A.J. Panson and B.A. Blankenship, Mat. Res. Soc. Symp. Proc.,
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Lett, 54, 666 (1989).
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[2.28] B.A. Glowacki (1991), Personal Communication
[2.29] S.W. Van Sciver , Helium Cryogenics, Pages, Plenum Press, New York (1986)
[2.30] P. Horowitz and W. Hill , The Art of Electronics, Pages, Cambridge University
Press, Cambridge (1989)
82
C h a p t e r
2
:
E x p e r i m e n t a l
T e c h n i q u e s
[ 2 . 3 1 ]
W .
J o n e s a n d
N . H . M a r c h
,
N o n - E q u i l i b r i u m
a n d
D i s o r d e r ,
P a g e s .
D o v e r
P u b l i c a t i o n s
I n c . ,
N e w Y o r k
( 1 9 8 5 )
[ 2 . 3 2 ]
V . L . G i n z b u r g
a n d G . F .
Z h a r k o v ,
S o v .
P h y s .
U s p . ,
2 1 ,
3 8 1
( 1 9 7 8 ) .
[ 2 . 3 3 ]
D . J .
v a n
H a r l i n g e n ,
P h y s i c a
B ,
1 0 9 - 1 1 0 ,
1 7 1 0
( 1 9 8 2 ) .
[ 2 . 3 4 ]
L . F .
G o o d r i c h ,
C r y o g e n i c s ,
3 1 ,
7 2 0
( 1 9 9 1 ) .
[ 2 . 3 5 ]
M . S . C o l c l o u g h , J . S .
A b e l l ,
C . E . G o u g h , J .
R i c k e t t s ,
T .
S h i e l d s ,
F .
W e l l h o f e r ,
W . F . V i n e n ,
N . M . A l f o r d a n d T .
B u t t o n ,
C r y o g e n i c s , 3 0 ,
4 3 9
( 1 9 9 0 ) .
[ 2 . 3 6 ]
M .
N a k a m u r a ,
G . D .
G u a n d N .
K o s h i z u k a ,
P h y s i c a
C ,
2 2 5 ,
6 5
( 1 9 9 4 ) .
[ 2 . 3 7 ]
A . M .
C a m p b e l l a n d F . J .
B l u n t ,
S u p e r c o n d .
S c i .
T e c h n o l . ,
3 ,
4 5 0
( 1 9 9 0 ) .
[ 2 . 3 8 ]
C . P .
B e a n ,
R e v .
M o d .
P h y s . ,
3 6 ,
3 1
( 1 9 6 4 ) .
[ 2 . 3 9 ]
A . M . C a m p b e l l
i n
P r o c e e d i n g s o f
M a g n e t i c S u s c e p t i b i l i t y
o f S u p e r c o n d u c t o r s
a n d O t h e r S p i n
S y s t e m s ,
p p
1 2 9 , C o o l f o n t ,
W e s t V i r g i n i a ,
U . S . A . ,
1 9 9 1
( P l e n u m P r e s s ,
N e w
Y o r k )
[ 2 . 4 0 ]
S .
F o n e r ,
R e v . S c i .
I n s t r u m . ,
3 0 ,
5 4 8
( 1 9 5 9 ) .
[ 2 . 4 1 ]
N . K u r t i a n d F .
S i m o n ,
P r o c .
R o y .
S o c . ,
1 5 5 A ,
6 1 0
( 1 9 3 5 ) .
[ 2 . 4 2 ]
C . W .
H a g e n
a n d R .
G r i e s s e n ,
P h y s .
R e v .
L e t t . ,
6 2 ,
2 8 5 7
( 1 9 8 9 ) .
[ 2 . 4 3 ]
G . B .
D o n a l d s o n ,
J . C l a r k e a n d J . C . M a c F a r l a n e
i n
C o n c i s e E n c y c l o p a e d i a o f
M a g n e t i c
a n d S u p e r c o n d u c t i n g
M a t e r i a l s ,
p p
5 0 1 ,
e d i t e d b y J . E . E v e t t s
( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 2 . 4 4 ]
H .
L o n d o n ,
P h y s .
L e t t . ,
6 ,
1 6 2
( 1 9 6 3 ) .
[ 2 . 4 5 ]
L .
G a o ,
R . L .
M e n g ,
Y . Y .
X u e ,
P . H . H o r
a n d
C . W .
C h u ,
A p p l . P h y s .
L e t t . .
5 8 ,
9 2
( 1 9 9 1 ) .
[ 2 . 4 6 ]
Y . Y e s h u r u n a n d A . P .
M a l o z e m o f f ,
P h y s .
R e v . L e t t . ,
6 0 ,
2 2 0 2
( 1 9 8 8 ) .
[ 2 . 4 7 ]
M . A . A n g a d i , A . D .
C a p l i n , J . R . L a v e r t y
a n d Z . X .
S h e n ,
P h y s i c a
C ,
1 7 7 .
4 7 9
( 1 9 9 1 ) .
8 3
Chapter 2 : Experimental Techniques
[2.48] R.B. Goldfarb, M. Lelental and C.A. Thompson in Proceedings of Magnetic
Susceptibility of Superconductors and Other Spin Systems, pp 49, Coolfont,
West Virginia, U.S.A., 1991 (Plenum Press, New York)
[2.49] V. Calzona, M.R. Cimberle, C. Ferdeghini, M. Putti, A.S. Ski and R.
Vaccarone, Physica C, 162-164, 369 (1989).
[2.50] V. Calzona, M.R. Cimberle, C. Ferdeghini, M. Putti and A.S. Siri, Physica C,
157, 425 (1989).
[2.51] A.M. Campbell, J. Phys. C (Solid St. Phys.), 2, 1492 (1969).
[2.52] A.M. Campbell, J. Phys. C, 4, 3186 (1971).
[2.53] J.H. Claassen, IEEE Trans. Magn., 25, 2233 (1989).
[2.54] R.W. Rollins, H. Kiipfer and W. Gey, J. Appl. Phys., 45, 5392 (1974).
84
C h a p t e r
3
:
J c
H y s t e r e s i s
i n
Y B C O
C H A P T E R 3 : M E A S U R E M E N T S O F
H Y S T E R E S I S O F
J C
I N
S I N T E R E D
Y B C O .
3 . 1 I N T R O D U C T I O N
I n a s u p e r c o n d u c t o r
w h i c h
i s i n h o m o g e n o u s ,
a n i s o t r o p i c , o r
b o t h ,
s u c h a s a l l
k n o w n
H T S C s ,
a s i m p l e s i n g l e v a l u e o f
J c
c a n n o t
b e d e f i n e d
b e c a u s e o f t h e
v a r i a t i o n
o f
p r o p e r t i e s
t h r o u g h o u t t h e
s a m p l e
[ 3 . 1 ] .
I n
a d d i t i o n ,
i t h a s b e e n
k n o w n
s i n c e
s o o n a f t e r
t h e
d i s c o v e r y
o f H T S C s t h a t
t h e
i n t e r g r a n u l a r
c o n t a c t s i n s i n t e r e d
H T S C s a r e
w e a k
l i n k s
( s e e ,
f o r e x a m p l e
[ 3 . 2 ] ) .
T h i s s e v e r e l y
i m p e d e s
s u p e r c u r r e n t f l o w i n t h e s e
m a t e r i a l s ,
m a k i n g t h e
J c
o f
a
p o l y c r y s t a l l i n e
H T S C
b o t h n o n - s i n g l e v a l u e d a n d l i m i t e d b y
t h e
w e a k e s t
l i n k s
i n
t h e
c u r r e n t
p a t h .
I n r a n d o m l y o r i e n t e d g r a n u l a r a n i s o t r o p i c s u p e r c o n d u c t o r s
t h e
c u r r e n t
t a k e s
a
m e a n d e r i n g
r o u t e
t h r o u g h t h e
s a m p l e d u e t o t h e r a n d o m
o r i e n t a t i o n s
o f
t h e g r a i n s
a n d t h e
r a n d o m
d i s t r i b u t i o n o f
t h e w e a k
a n d
s t r o n g
l i n k s b e t w e e n
t h e m .
T h i s
m e a n s t h a t t h e
a n i s o t r o p y o f
J c
w i l l t e n d t o b e a v e r a g e d o u t
a s
t h e r e a r e
a l w a y s
s o m e g r a i n s
w h e r e
t h e
f i e l d i s a l i g n e d w i t h t h e i n t e r g r a n u l a r
j u n c t i o n s .
M e a s u r e m e n t s
o f t r a n s p o r t
J c
i n s i n t e r e d
Y B a 2 C u 3 C > 7 _ 5
( Y B C O )
a s
a f u n c t i o n o f
i n c r e a s i n g
a n d d e c r e a s i n g a p p l i e d m a g n e t i c f i e l d
s h o w c l e a r h y s t e r e t i c
b e h a v i o u r
[ 3 . 3 ] .
T h i s o n l y
o c c u r s i f
t h e f i e l d
r i s e s a b o v e a c e r t a i n v a l u e a n d
i s s e e n
a s
a n
i n c r e a s e i n t h e
t r a n s p o r t
J c
o n
t h e d e c r e a s i n g f i e l d c y c l e
a b o v e
t h a t
f o r i n c r e a s i n g f i e l d
u p
t o a
m a x i m u m
a t
a f i e l d
B p e
a k
>
0 ,
f o l l o w e d b y a
d e c r e a s e i n
J c
a s t h e f i e l d
c o n t i n u e s t o f a l l .
r i s e s
w h i l e
t h e h e i g h t o f t h e
p e a k f a l l s
a s
t h e m a x i m u m a p p l i e d f i e l d
r i s e s
[ 3 . 4 ] ,
S i m i l a r
h y s t e r e t i c
b e h a v i o u r
i s s e e n t o o c c u r i n m o s t
H T S C s ,
f r o m
s i n t e r e d b u l k m a t e r i a l
t o
s i n g l e
g r a i n
b o u n d a r y j u n c t i o n s
i n t h i n f i l m Y B C O
[ 3 . 5 ] ,
a n d i n f i e l d s a s h i g h
a s 7 T
( s e e ,
f o r
e x a m p l e , c h a p t e r
4 o f t h i s
t h e s i s ) .
S u c h h y s t e r e t i c
b e h a v i o u r i s
o n l y
l i k e l y t o o c c u r i n i n h o m o g e n e o u s
o r g r a n u l a r
s u p e r c o n d u c t o r s w h e r e t h e r e a r e
v e r y d i f f e r e n t
v a l u e s
o f
J c
i n t h e g r a i n s a n d
t h e g r a i n
b o u n d a r i e s ,
l e a d i n g
t o
f l u x m o t i o n b e t w e e n t h e g r a i n s w h i l e f l u x w i t h i n
t h e
g r a i n s
r e m a i n s
p i n n e d .
T h i s c o n t r a s t s
w i t h
t h e
b e h a v i o u r i n
h o m o g e n e o u s
m a t e r i a l s w h e r e
a s s o o n a s
t h e
c r i t i c a l c u r r e n t i s e x c e e d e d
c o n t i n u o u s
f l u x
m o v e m e n t e r a s e s m o s t f l u x
t r a p p i n g e f f e c t s
[ 3 . 6 ] ,
8 5
Chapter 3 : Jc Hysteresis in YBCO
Understanding this behaviour is necessary to fully comprehend the Jc-B
characteristics of HTSCs, a requirement for them to find large-scale applications. The
model of Evetts and Glowacki (the EG model) [3.3] attributes the hysteresis to the fact that
in a granular superconductor with intragranular flux pinning, hysteresis of Jc as a function
of field should appeal' if it has been exposed to fields high enough to allow flux to penetrate
the grains. This arises because flux will be trapped in the grains as the field increases and
the back flux from this when the field decreases will partially cancel the applied field in
some of the intergranular regions (though it will increase the field in other intergranular
regions [3.7]). This leads to an increased intergranular, and therefore overall, transport Jc
on the decreasing field leg of a magnetic field cycle. Jc on the decreasing field leg will not
rise to the virgin zero-field value as the trapped flux will not exactly cancel the applied field
in all the intergrain regions due to the spread in, for example, junction size and
misalignment, so the average internal field will not reach zero, but will pass through a
minimum. As the maximum applied field increases more flux is trapped in the grains, so
Bpeak moves a higher field, but the statistical distribution of field strengths within the
sample becomes broader, suppressing the height of the decreasing-field peak [3.8]. The
effects of flux trapping are shown schematically in figure 3.1.
->
7D ->-E
<D .
X3 ->-
CX
CX<
->
Figure 3.
flux trapping can both add to and cancel the applied field. The shaded areas
represent grains of superconductor. The trapped field is shown in only one
grain for clarity. From. Askew et al. [3.7],
To account for the observed behaviour, Evetts and Glowacki find it necessary to
include the effects of persistent current loops on a scale larger than the grains. This is the
subject of some controversy (see, for example [3.9]).
Region Where
Trapped Field
Cancels Applied
Field
Region Where
.Trapped Field
Adds to Applied
Field
1 : Schematic diagram of grains in a superconductor showing how
86
C h a p t e r
3 :
J c
H y s t e r e s i s
i n
Y B C O
F i g u r e 3 . 1 s h o w s t h a t t h e o r i e n t a t i o n o f
t h e
t r a n s p o r t
c u r r e n t w i t h
r e s p e c t t o t h e
a p p l i e d
f i e l d
w i l l
a f f e c t
t h e
a m o u n t o f h y s t e r e s i s .
I f
t h e
a p p l i e d c u r r e n t a l w a y s
f l o w s
p a r a l l e l t o
t h e a p p l i e d f i e l d t h e i n t e r g r a n u l a r
j u n c t i o n s i n
t h e
c u r r e n t p a t h w i l l
b e
r e g i o n s
w h e r e t h e t r a p p e d f i e l d
a d d s
t o t h e
a p p l i e d
f i e l d ,
f o r c i n g
t h e c u r r e n t
t o
t a k e
a m e a n d e r i n g
p a t h t h r o u g h
h i g h e r -
J c
i n t e r g r a i n s w h e r e t h e t r a p p e d f i e l d c a n c e l s t h e
a p p l i e d f i e l d .
W h e n
t h e a p p l i e d
c u r r e n t
i s
p e r p e n d i c u l a r
t o
t h e
a p p l i e d
f i e l d ,
o n
t h e o t h e r
h a n d ,
m o s t i n t e r g r a i n s
i n
t h e c u r r e n t p a t h w i l l b e o n e s w h e r e t h e
t r a p p e d
f i e l d
c a n c e l s
t h e
a p p l i e d
f i e l d ,
e n h a n c i n g
t h e i n t e r g r a n u l a r
J c
f o r
d e c r e a s i n g f i e l d .
T h i s
i m p l i e s
t h a t i n t h e / / / / l e n g t h / / c u r r e n t
c a s e t h e
c u r r e n t w i l l t a k e
a m o r e m e a n d e r i n g
p a t h
t h o u g h t h e
h i g h
J c
i n t e r g r a i n s
t h a n i n t h e
/ / T w i d t h J x u r r e n t o r
/ / / / w i d t h T c u i r e n t c a s e s .
T h e f l u x
i n
t h e g r a i n s
m a n i f e s t s i t s e l f
a s a
m a g n e t i s a t i o n .
I t w a s s h o w n [ 3 . 1 0 ]
t h a t
t h e
e f f e c t
o f
s a m p l e s h a p e
o n
J c
c o u l d b e t a k e n i n t o a c c o u n t b y p l o t t i n g
J c
a s
a
f u n c t i o n o f
t h e
i n t e r n a l
f i e l d g i v e n b y
H
= H 0 - n M
( 3 . 1 )
w h e r e
H 0
i s t h e e x t e r n a l
f i e l d ,
M t h e
m a g n e t i s a t i o n
a n d n t h e
d e m a g n e t i s i n g f a c t o r .
M i s h r a e t a l . f i n d
a
s i m i l a r
r e s u l t ,
b u t
t h e
d e m a g n e t i s i n g
f a c t o r i s r e p l a c e d
b y a
c o n s t a n t
w h i c h a l s o i n c l u d e s
d e p e n d e n c i e s o n g r a i n
s i z e ,
s h a p e a n d p a c k i n g
f r a c t i o n
[ 3 . 1 1 ] .
T h i s
s u g g e s t s
t h a t i t
s h o u l d
b e p o s s i b l e
t o f i n d
a
q u a n t i t a t i v e r e l a t i o n b e t w e e n
t h e h y s t e r e s i s
o f
J c
a n d t h e
m a g n e t i s a t i o n .
I t
w a s
f o u n d
b y K w a s n i t z a
[ 3 . 1 2 ]
t h a t
h y s t e r e s i s o f t r a n s p o r t
J c
o c c u r s a t
v e r y h i g h
f i e l d s
w h e r e
t h e s a m p l e m a g n e t i s a t i o n i s n e g l i g i b l e , i n d i c a t i n g t h a t
t h e
e x p l a n a t i o n f o r t h e
h y s t e r e s i s o f
J c
i s
m o r e c o m p l i c a t e d t h a n s u g g e s t e d a b o v e . F l u x
t r a p p i n g a t h i g h
f i e l d s
r e q u i r e s
v e r y
h i g h
p i n n i n g e n e r g i e s
( s e e b e l o w ) .
T h i s
o b s e r v a t i o n o f v e r y h i g h
f i e l d
h y s t e r e s i s
i s ,
h o w e v e r ,
i n
a g r e e m e n t
w i t h t r a n s p o r t m e a s u r e m e n t s o n
Y B C O t h i c k
f i l m s
a n d
s i l v e r - c l a d
T l :
1
2 2 3 t a p e s , d e s c r i b e d i n
c h a p t e r s
4
a n d 5 o f t h i s
t h e s i s r e s p e c t i v e l y .
T h e f o l l o w i n g c a l c u l a t i o n w a s u s e d t o e s t i m a t e t h e c u r r e n t d e n s i t y n e c e s s a r y
t o
e x p l a i n
t h e
h y s t e r e s i s
o f
J c
a t h i g h f i e l d s b y f l u x t r a p p i n g , s u c h a s t h a t
s h o w n i n
f i g u r e 3 . 2
f o r
a
s i l v e r - c l a d
T l : 1 2 2 3
t a p e
( s e e
c h a p t e r
5 ) .
T h e f i e l d g e n e r a t e d a t a
p o i n t a l o n g t h e a x i s o f
a c u r r e n t
l o o p o f r a d i u s
r ,
c a r r y i n g
a
c u r r e n t /
=
J
■
d r
■
d t a
d i s t a n c e
t . f r o m t h e l o o p i s g i v e n
b y
\ l 0 J d r d t r
2
2
( r + r 2 f
( 3 . 2 )
T h e
g e o m e t r y
o f t i n s
c o n f i g u r a t i o n
i s s h o w n
s c h e m a t i c a l l y i n f i g u r e 3 . 3 .
8 7
Chapter 3 : Jc Hysteresis in YBCO
Figure 3.2 : Jc versus B of a silver-clad Tl:1223 tape at 77K infields of up
to 8T for B perpendicular to the width of the tape. Solid symbols indicate
increasing field, open symbols indicate decreasing field.
Figure 3.3 : Schematic diagram showing the geometry of the current
carrying loop described in equation 3.2.
Assuming each grain is a cylinder with height = diameter = 2a, and its axis
parallel to the applied field, then the above equation can be integrated over the radius
(0 to a) and height (0 to 2a) of the cylinder to give the field generated by the same current
density circulating throughout the whole cylinder. Rearrangement and integration of
equation 3.2 gives
J = 2B
IM
a + J(a2 +4a2
2a
4B
\l0a
(3.3)
88
C h a p t e r
3
:
J c
H y s t e r e s i s
i n
Y B C O
T y p i c a l l y ,
a s
s h o w n
i n f i g u r e
3 . 2 ,
t h e f i e l d
A B
w h i c h
n e e d s
t o
b e c a n c e l l e d
i n
o r d e r t o a c c o u n t
f o r
t h e
v a l u e
o f
J C ( B
d e c r e a s i n g )
a t
J c
~
2 0 0
A c n r 2
i s A B
~
4 T . T h e
T l : l 2 2 3
s a m p l e m e a s u r e d
i n f i g u r e 3 . 2 h a s a
-
5 ( i m ,
s o f o r
A B
~
4 T ,
J
~
2 . 5 x 1 0 1 2 A m ' 2
=
2 . 5
x 1 0 8 A c n r 2 .
T h e m a x i m u m
J c
m e a s u r e d f o r T l : 1 2 2 3 a t 4 . 2 K
a n d
z e r o f i e l d
i s
l e s s
t h a n
1
x 1 0 7 A c m - 2 .
T h i s i n d i c a t e s t h a t a
m e c h a n i s m
w h i c h
i n c l u d e s m o r e
t h a n
s i m p l e f l u x
t r a p p i n g i s n e c e s s a r y t o
a c c o u n t f o r
t h e l a r g e
v a l u e o f A B ( J C )
u n l e s s
t h e r e a r e
s t r o n g
c u r r e n t - c a r r y i n g
l o o p s
w i t h
s i z e o n
t h e
o r d e r
o f
t h e w h o l e
s a m p l e .
I f t h i s w a s t h e
c a s e
t h e n
a
~
5
x
1 0 _ 3 m
g i v i n g J
~
2 . 5 x
1 0 5 A c n r 2 . W h i l e
t h i s i s
a
r e a s o n a b l e
v a l u e
f o r
J c
i t
i s
v e r y h i g h f o r a
n o n - t h i n
f i l m
s a m p l e a t 7 7 K . A s
f i g u r e
3 . 2
s h o w s
h y s t e r e s i s
a t h i g h
f i e l d
a n d
7 7 K t h i s i s u n l i k e l y
t o
b e
t h e
c a s e ,
i n a g r e e m e n t w i t h t h e
r e s u l t o f
W a t a n a b e e t a l .
[ 3 . 1 3 ] ,
I t i s
u n l i k e l y t h a t s u c h a p a t h
c o u l d e x i s t w i t h o u t i t s
b e i n g
d e t e c t e d
i n
t r a n s p o r t ,
o r
e s p e c i a l l y m a g n e t i c
m e a s u r e m e n t s ,
w h i c h
d o e s n o t o c c u r . S i m i l a r
l a r g e h y s t e r e s i s
o f
J c
i s
s e e n i n
t h e
m e l t - p r o c e s s e d t h i c k
f i l m s o f Y B C O d e s c r i b e d
i n
c h a p t e r
4
o f
t h i s
t h e s i s . T h i s
a r g u e s
a g a i n s t
t h e
a p p l i c a b i l i t y
o f
t h e E G
m o d e l ,
a t l e a s t a t h i g h
f i e l d s .
M c H e n r y
e t
a l .
[ 3 . 8 ]
f o u n d
t h a t
i n t r a g r a n u l a r
c u r r e n t s
d o m i n a t e
t h e
e f f e c t s o f
i n t e r g r a n u l a r
f i e l d s
o n t h e
t r a n s p o r t
J c
o f p o l y c r y s t a l l i n e
Y B C O
a t l o w
t e m p e r a t u r e s ,
i n
d i s a g r e e m e n t
w i t h t h e E G
m o d e l . T h e y a t t r i b u t e t h e h y s t e r e s i s
o f
J c
t o t h e
e f f e c t
o f
g r a d i e n t s
i n
t h e
p i n n e d f l u x
t r a p p e d
i n i n d i v i d u a l
g r a i n s ,
e a c h
o f w h i c h
o b e y s t h e
B e a n
m o d e l
[ 3 . 1 4 ] ,
t h o u g h t h e
s a m p l e a s
a w h o l e
d o e s n o t .
C h e n
a n d
Q i a n
[ 3 . 1 5 ]
f i n d h y s t e r e s i s
i n
J c
a n d
a l s o i n m a g n e t o r e s i s t a n c e
i n s i n t e r e d
Y B C O . T h e y
e x p l a i n t h i s u s i n g a
m o d e l w h e r e c u r r e n t
f l o w s
i n a s i n g l e
l o o p o v e r t h e
w h o l e
s a m p l e
w i t h f l u x
e n t r y c o n t r o l l e d b y
w e a k l i n k s a t t h e
s u r f a c e a n d
J c
d e p e n d a n t o n
t h e
l o c a l r a t h e r t h a n t h e
a p p l i e d f i e l d . T h e y
g e n e r a t e i n c r e a s i n g a n d
d e c r e a s i n g f i e l d
J c - B
c h a r a c t e r i s t i c s
s h o w i n g
a
p e a k
i n
t h e d e c r e a s i n g
f i e l d l e g .
H o w e v e r ,
t h e i r
s i m u l a t e d d a t a
d o e s n o t
c o m p a r e w e l l w i t h t h e i r
a c t u a l r e s u l t s a n d s h o w s c o n s i d e r a b l y
m o r e h y s t e r e s i s i n
J c
t h a n t h e
r e s u l t s
s h o w n i n t h i s c h a p t e r .
E k i n
e t
a l .
[ 3 . 9 ]
i n v e s t i g a t e d a l i g n e d
p o l y c r y s t a l l i n e Y B C O .
T h e y f o u n d t h a t
a l i g n m e n t
s i g n i f i c a n t l y
i m p r o v e d s a m p l e q u a l i t y a n d t h a t t h e r e i s e v i d e n c e
f o r t w o
p a r a l l e l
c o m p o n e n t s
t o t h e
i n t e r g r a n u l a r
c u r r e n t s .
O n e o f
t h e s e a r i s e s f r o m
w e a k - l i n k e d
i n t e r g r a n u l a r
m a t e r i a l a n d t h e o t h e r
f r o m
s t r o n g l y
l i n k e d r e g i o n s
b e h a v i n g
l i k e i n t r a g r a n u l a r
m a t e r i a l .
H o w e v e r ,
t h e s e
s t r o n g l y
l i n k e d r e g i o n s a r e f o u n d t o b e o n l y - 0 . 0 5 %
o f
t h e g r a i n
b o u n d a r y a r e a
e v e n
i n a l i g n e d Y B C O .
A l t s h u l e r e t a l .
[ 3 . 1 6 ]
f o u n d t h a t t h e
g r a i n s i n
a s i n t e r e d
s a m p l e w e r e t h e
m a i n f l u x
t r a p p i n g
e l e m e n t s .
T h e y f o u n d
t h a t t h e f l u x t r a p p e d
b y
p e r s i s t e n t l o o p s i n t h e
w e a k
l i n k
8 9
Chapter 3 : Jc Hysteresis in YBCO
network had much less influence on the Jc-B characteristics, only producing asymmetry in
the decreasing field curves, in disagreement with the EG model but agreeing with that of
Ekin. They later found [3.4] that the low-field results could be explained by a simple
grain-junction ensemble model where the grains are regarded as simple magnetic dipoles.
However, their model is invalid for high fields (i.e. H » 200mT) as the magnetisation of
the grains does not follow the Bean model in this regime.
Navarro and Campbell [3.17] use the ideas of effective medium theory to model a
sample consisting of identical superconducting grains randomly dispersed in a
non-magnetic matrix. They were able to model Jc (H ) but were unable to derive the
correct relative positions of the Jc (H) and J (H) curves. They interpret their work as
evidence against the EG model.
Kugel and Rakhmanov [3.18] attempted to model the behaviour of Jc with B taking
into account flux expulsion, the Bean-Livingstone surface barrier (BLSB), intergranular
pinning and the resulting non-uniform flux distribution. Although they state that their
model is too simple to account for all the features of the of real JC{B) curves, they do find
that a non-uniform magnetic flux distribution affects the dissipative processes within
superconductors and that the BLSB may significantly affect properties such as A.C. losses.
Increasing Field Decreasing Field
Figure 3.4 : Schematic diagram, showing the surface screening current
density which depends on the Meissner effect and surface flux pinning
(a) reducing the Jc of the intergrain in increasing field, and (b) increasing
the Jc of the intergrain in decreasing field. From D'yachenko [3.19].
D'yachenko [3.19] explains the hysteresis of Jc in terms of the dipole field of a
grain or current loop with an additional contribution if the irreversible field dependence of
90
C h a p t e r
3 :
J c
H y s t e r e s i s
i n
Y B C O
t h e
g r a i n
s u r f a c e
c u r r e n t
a l t e r s
t h e
i n t e r g r a n u l a r f i e l d .
H e p o i n t s
o u t t h a t
t h e
J o s e p h s o n
r e l a t i o n f o r t h e
c u r r e n t
t h r o u g h a j u n c t i o n
i s o n l y v a l i d
b e l o w
H w i t h
t h e
g r a i n s
i n
t h e
M e i s s n e r s t a t e .
T h e p h a s e d i f f e r e n c e a c r o s s t h e j u n c t i o n
d e p e n d s
o n
a n y
s u r f a c e
c u r r e n t a s
w e l l
a s
t h e d i p o l e f i e l d .
I n a n i n c r e a s i n g
f i e l d
t h e s e c u r r e n t s f l o w
i n o n e
d i r e c t i o n a n d
i n
d e c r e a s i n g f i e l d i n
t h e o p p o s i t e d i r e c t i o n s o t h a t t h e y r e d u c e
J c
i n i n c r e a s i n g
f i e l d s a n d
i n c r e a s e i t
i n d e c r e a s i n g f i e l d s . T h i s i s s h o w n i n
f i g u r e
3 . 4 . T h i s
t h e o r y
h a s t h e
a d v a n t a g e
t h a t ,
r a t h e r t h a n
s h i f t i n g t h e e f f e c t i v e i n c r e a s i n g a n d
d e c r e a s i n g f i e l d i t
s h i f t s t h e
c u r r e n t
d e n s i t y , w h i c h
s e e m s
t o a g r e e m o r e w i t h t h e o b s e r v e d
e f f e c t s .
R i e s
e t a l .
[ 3 . 2 0 ]
e x p l a i n t h e h y s t e r e s i s
o f
J c
u s i n g a n
e x t e n s i o n o f D ' y a c h e n k o s
t h e o r y .
T h e y a t t r i b u t e t h e p e r s i s t e n c e o f
J c
t o h i g h
f i e l d s t o t h e
J o s e p h s o n
c o u p l i n g o f
g r a i n s i n
t h e
m i x e d s t a t e a n d
t h e h i g h - f i e l d
h y s t e r e s i s o f
J c
a s a r i s i n g f r o m
t h e
i r r e v e r s i b l e
e n t r y ,
e x i t a n d
p i n n i n g
o f f l u x l i n e s
i n
t h e g r a i n s .
T h e i r t h e o r y
h a s a n a d v a n t a g e
o v e r t h e
o d i e r
t h e o r i e s i n t h a t
i t
c l a i m s
t o
a c c o u n t f o r t h e h y s t e r e s i s o f
J c
s e e n a t h i g h
f i e l d s .
B e c a u s e t h e
h y s t e r e s i s
o f
J c
i s
a n
i m p o r t a n t
f a c t o r
i n
t h e
b e h a v i o u r
o f H T S C s
a n
i n v e s t i g a t i o n
o f i t w a s c a r r i e d
o u t
a s p a r t o f t h e o v e r a l l i n v e s t i g a t i o n
i n t o t h e
d i s c r e p a n c i e s
b e t w e e n
t r a n s p o r t
a n d
m a g n e t i c
m e a s u r e m e n t s i n H T S C s .
T h i s
c h a p t e r
d e t a i l s
m e a s u r e m e n t s
o f
t h e h y s t e r e s i s o f
t r a n s p o r t
J c ,
a n d
a l s o
d i s c u s s e s
t h e
m a g n e t i s a t i o n
o f
s l a b s o f s i n t e r e d Y B C O
i n
d i f f e r e n t
o r i e n t a t i o n s w i t h r e s p e c t t o t h e
a p p l i e d m a g n e t i c
f i e l d .
T h i s p a r t i c u l a r f o r m o f Y B C O w a s c h o s e n
a s
i t
i s a
s y s t e m
m a d e
u p
o f
r a n d o m l y o r i e n t e d
' w e a k ' w e a k
l i n k s . A t t e m p t s t o e x p l a i n t h e r e s u l t s o b t a i n e d
w e r e m a d e
i n t e r m s
o f
t h e
s a m p l e d e m a g n e t i s i n g
f a c t o r
a n d a l s o
i n t e r m s o f a
c o n s t a n t
w h i c h
t a k e s i n t o a c c o u n t
g e o m e t r i c a l
e f f e c t s
w h i c h
i n c r e a s e
t h e f i e l d
i n
t h e i n t e r g r a n u l a r
w e a k
l i n k s .
T h i s w o r k w a s
p r e v i o u s l y p u b l i s h e d
i n
[ 3 . 2 1 ] ,
3 .
2
E X P E R I M E N T A L T E
C H N I Q
U E
3 . 2 . 1 S A M P L E
P R E P A R A T I O N
S i n t e r e d
p e l l e t s o f Y B C O w e r e p r e p a r e d f r o m c a l c i n e d p o w d e r s u s i n g a
s t a n d a r d
m e t h o d s i m i l a r
t o
t h a t d e s c r i b e d
b y
M u r a k a m i
i n
[ 3 . 2 2 ] ,
T h e s e w e r e c u t
i n t o r e c t a n g u l a r
b a r s w i t h
d i m e n s i o n s
o f
1 2
x 4 x
1 m m
u s i n g
a
d i a m o n d - c o a t e d
c u t t i n g
w h e e l . D u e t o
t h e i r
f r a g i l i t y t h e s a m p l e s w e r e n o t n e c k e d t o
i n c r e a s e t h e
c u r r e n t d e n s i t y
i n
t h e
c e n t r a l
r e g i o n .
T h e l o w
J c
s o f
t h e s e
s a m p l e s a l l o w e d
m e a s u r e m e n t s
t o
b e m a d e
w i t h o u t h e a t i n g
a t
t h e c u r r e n t
c o n t a c t s a f f e c t i n g t h e m e a s u r e d
J c .
E x a m i n a t i o n u s i n g
e l e c t r o n m i c r o s c o p y
9 1
Chapter 3 : Jc Hysteresis in YBCO
allowed the average grain size in the samples, 1.8 x 1.3|im, to be determined. Current
and voltage contacts to the samples were made using the following procedure :
(a) Four silver pads approximately 0.5|im thick were deposited over the whole width
of one wide face of the sample using an Edwards E306A thermal evaporation coating
system.
(b) Current leads of 0.71mm diameter tinned copper wire, the ends of which were
flattened to increase the contact area with the sample, were attached to the pads at each end
of the sample using indium solder.
(c) Voltage leads of 25|im diameter gold wire were attached to the central contact pads
using indium solder.
Once current and voltage leads were applied the samples were mounted on a critical
current measuring probe. Because the current leads were of large diameter, and thus fairly
robust, they were also used to support the sample on the probe head.
3.2.2 TRANSPORT MEASUREMENTS
Jc was measured at 77K in liquid nitrogen using a lp.V/cm criterion and the basic
D.C. system described in section 2.3.3. Measurements in magnetic field were carried out
by placing the probe and sample between the poles of an iron-cored electromagnet in three
orientations of applied field :
(a) Field parallel to the broad face of the slab and perpendicular to current
(demagnetising factor = 0).
(b) Field perpendicular to the broad face of the slab and perpendicular to current
(demagnetising factor =1).
(c) Field parallel to the current and length of the slab (demagnetising factor = 0).
Figure 3.5 shows these diree orientations schematically.
Zero-field cooled (ZFC) and field-cooled (FC) transport measurements were carried
out in applied fields of up to 20mT, where Jc became too low to be determined with the
92
C h a p t e r
3
:
J c
H y s t e r e s i s
i n
Y B C O
i n s t r u m e n t a t i o n
u s e d .
Z F C
m e a s u r e m e n t s
w e r e c a r r i e d
o u t
i n
a l l
t h r e e
o r i e n t a t i o n s w h i l e
F C m e a s u r e m e n t s
w e r e
o n l y
c a r r i e d o u t f o r t h e
/ / A w i d t h _ L c u r r e n t
o r i e n t a t i o n f o r t h e
I
f o l l o w i n g r e a s o n s .
I n
t h e Z F C
c a s e
t h e M e i s s n e r e f f e c t
i n t h e g r a i n s
c a u s e s f l u x
c o m p r e s s i o n
i n
t h e
i n t e r g r a i n s a s t h e f i e l d
i s
a p p l i e d , s u p p r e s s i n g
t h e m
f a s t e r t h a n
i n t h e
F C
c a s e .
T h i s a g r e e s w i t h t h e
w o r k o f
M i s h r a e t a l . [ 3 . 1 1 ] .
T h e
a m o u n t
o f
f l u x
c o m p r e s s i o n d e p e n d s
o n t h e r e l a t i v e
s i z e s
o f t h e g r a i n s a n d t h e
s u p e r c o n d u c t i n g
p e n e t r a t i o n
d e p t h
[ 3 . 1 9 ] .
T h e F C c a s e
w i t h
t r a p p e d
f l u x
i s
t h u s
i n t e r m e d i a t e
b e t w e e n t h e
M e i s s n e r
s t a t e
e x c l u s i o n o f
f l u x o n t h e i n c r e a s i n g Z F C c u r v e a n d t h e
s t a t e w h e r e
t h e
s a m p l e
h a s b e e n
p e n e t r a t e d
a n d
h a s
t r a p p e d
f l u x
o n t h e d e c r e a s i n g Z F C c u r v e [ 3 . 2 3 ] ,
B
F i g u r e
3 . 5 : T h e t h r e e
o r i e n t a t i o n s u s e d i n t h e m e a s u r e m
e n t
o f
t r a n s p o r t
J c .
(
i
)
f i e l d - L w i d t h ± c u r r e n t ,
( i i )
f i
e l d / / w
i
d t h - L c u r r e n t ,
(
H i
)
f i e l d / A e n g t h / / c u r r e n t .
3 . 2 . 3 M A G N E T I C M E A S U R E M E N T S
F o l l o w i n g t h e
t r a n s p o r t
m e a s u r e m e n t s ,
t h e Z F C
s a m p l e m a g n e t i s a t i o n
w a s
m e a s u r e d w i t h
t h e
f i e l d p a r a l l e l t o t h e l o n g
a x i s
o f t h e
s l a b
( o r i e n t a t i o n
( i i i )
i n f i g u r e
3 . 5 )
f o r i n c r e a s i n g a n d d e c r e a s i n g f i e l d s
u p t o 2 2 m T
u s i n g a
Q u a n t u m
D e s i g n
M P M S - 1 S Q U I D
m a g n e t o m e t e r .
T h i s m a x i m u m f i e l d w a s
u s e d a s
t h e S Q U I D
b o r e
p r e v e n t s l o n g
s a m p l e s
b e i n g i n s e r t e d
t r a n s v e r s e t o t h e
f i e l d
a n d
i t
w a s
c a l c u l a t e d t h a t a t
t h i s
f i e l d
t h e
i n t e r n a l
f i e l d
o f
t h e s a m p l e w a s t h e s a m e
i n
t h e
l o n g i t u d i n a l f i e l d
c a s e
a s f o r
t h e
t r a n s v e r s e f i e l d
c a s e
i n
a
f i e l d o f
2 0 m T ,
a s s u m i n g t h a t a r e c t a n g u l a r
s l a b i s e q u i v a l e n t t o a n
e l l i p s o i d
w i t h
t h e
s a m e
v o l u m e a n d
a s p e c t
r a t i o
f o r
c a l c u l a t i n g
t h e s a m p l e d e m a g n e t i s i n g
f a c t o r .
A l l m a g n e t i c
m e a s u r e m e n t s w e r e c a r r i e d o u t b y D r . J . D .
J o h n s o n .
T h e m e a s u r e d
M - H
c u r v e w a s u s e d t o d e t e r m i n e t h e
Z F C
m a g n e t i s a t i o n
f o r
t h e
s a m p l e i n
t h e t r a n s v e r s e f i e l d
e x p e r i m e n t s . A s
w i t h t h e
t r a n s p o r t m e a s u r e m e n t s ,
F C
m e a s u r e m e n t s o f
t h e
s a m p l e m a g n e t i s a t i o n w e r e a l s o m a d e .
T h e s e w e r e c a r r i e d
o u t i n
a
s e r i e s o f f i e l d s u p
t o
2 0 m T
i n t h e
l o n g i t u d i n a l
o r i e n t a t i o n . T h i s
l o w e r m a x i m u m
f i e l d w a s
u s e d a s t h e d e m a g n e t i s i n g f a c t o r i s f a r
l e s s
s i g n i f i c a n t f o r t h e F C
c a s e
b e c a u s e t h e s a m p l e i s
a l r e a d y f u l l y
p e n e t r a t e d
b y
t h e a p p l i e d
f i e l d
w h e n i t
b e c o m e s
s u p e r c o n d u c t i n g
( s e e
s e c t i o n
3 . 2 . 2 ) .
9 3
Chapter 3 : Jc Hysteresis in YBCO
3.3 RESULTS
3.3.1 TRANSPORT MEASUREMENTS
Figures 3.6(a) to 3.6(d), show Jc versus B for the samples in the increasing field,
decreasing field, and FC situations for the three geometries shown in figure 3.5.
Applied Field (mT)
Figure 3.6 : Transport Jcfor different orientations with respect to field, (a),
(b) and (c) show ZFC data, (d) shows FC data with ZFC data in the same
orientation for comparison. Note the different y-axis scales.
The transport Jcs are purposefully low, due to oxygen underdoping, giving the
sample very weak intergranular weak links. For these experiments this was advantageous,
as it reduced the effect of the intergrain currents, which in a sample with a higher Jc could
have significant effects on the results obtained, and made the measurements much more
sensitive to applied field.
Note that the FC results in figure 3.6(d) lie between the increasing and decreasing
ZFC data. This arises from the more homogenous distribution of flux inside the sample in
the FC case, due to the even trapping of flux in the grains as they are cooled in field (see
section 3.2.2).
94
C h a p t e r
3
:
J c
H y s t e r e s i s
i n
Y B C O
3 . 3 . 2
M A G N E T I C
M E A S U R E M E N T S
T h e Z F C a n d F C m a g n e t i s a t i o n c u r v e s o f
t h e
s a m p l e
a r e
s h o w n
i n f i g u r e
3 . 7 .
F i g u r e
3 . 7 :
M a g n e t i s a t i o n
c u r v e s
o f
Y B C O s a m p l e
u s e d .
S o l i d
s y m b o l s
i n d i c a t e Z F C d a t a .
O p e n s y r n b o l s
i n d i c a t e F C d a t a .
N o t e t h a t t h e F C d a t a l i e s b e t w e e n t h e i n c r e a s i n g a n d
d e c r e a s i n g
Z F C
d a t a ,
s i m i l a r
t o t h e
t r a n s p o r t r e s u l t s .
A l s o ,
t h e i n c r e a s i n g f i e l d Z F C
c u r v e i s b e g i n n i n g t o
d r o p
a t
t h e h i g h e s t
f i e l d s ,
i m p l y i n g
t h a t
H C i
h a s b e e n e x c e e d e d . F r o m t h e t r a n s p o r t
J c - B
b e h a v i o u r
t h i s H
i s
a s s u m e d
t o b e t h a t
o f
t h e g r a i n s , w i t h t h e f i e l d
f o r p e n e t r a t i o n o f t h e i n t e r g r a i n s
b e i n g
t o o
l o w t o
d i s c e r n
o n t h e s c a l e
u s e d
h e r e .
S i n c e
H c
o f t h e g r a i n s
i s
o n l y
j u s t e x c e e d e d
a t t h e
h i g h e s t a p p l i e d
f i e l d s ,
t h i s w i l l s i g n i f i c a n t l y a f f e c t
t h e
r e s u l t s o f a n y a n a l y s i s .
I t
i m p l i e s t h a t
t h e
m e a s u r e d
m a g n e t i s a t i o n w i l l
b e
c l o s e
t o t h a t o f
a n
a r r a y o f
d e c o u p l e d g r a i n s
r a t h e r t h a n
o f a w e l l i n t e r c o n n e c t e d
s a m p l e .
F i g u r e
3 . 7 a l s o s h o w s
t h a t t h e m i n i m u m v a l u e o f
t r a p p e d f i e l d f o r
H
=
0
i s
~ 2 m T ,
c o r r e s p o n d i n g t o t h e f i e l d w h e r e
J c
r e a c h e s a m a x i m u m
i n t h e
d e c r e a s i n g f i e l d
J c - B
c u r v e f o r
7 / T c u r r e n t J . w i d t h . T h i s c o n f i r m s
t h e
a s s u m p t i o n
t h a t t h e l o n g i t u d i n a l
m a g n e t i s a t i o n u s i n g
a m a x i m u m f i e l d o f 2 2 m T
i s
e q u i v a l e n t t o t h e
t r a n s v e r s e m a g n e t i s a t i o n
i n
a m a x i m u m f i e l d
o f 2 0 m T
( s e e
s e c t i o n
3 . 2 . 3 ) .
9 5
Chapter 3 : Jc Hysteresis in YBCO
3.4 DISCUSSION
3.4.1 SELF-FIELD EFFECTS
If the hysteresis of transport Jc arises from flux trapping it is to be expected that the
decreasing field Jc-B curves will show some indication of the point where the external field
balances the average trapped field of the sample. Figure 3.6 indicates that the maximum
cancellation of the applied field, assumed to be the peak of the decreasing Jc versus field
curve, is ~2mT for HlJclw for this sample.
It was considered that the self-field of the sample current might be responsible for
this peak. The self field of a sample carrying a current I can be calculated from Amperes
law. This gives j>H -d£ = I where dl is along the path of integration. For a sample of width
w and thickness f, this equation becomes H ■ (2w + 2t) = 7, or, rearranging,
B=-U*L-2(w + t) (3.4)
For the sample measured here w = 4mm, t= 1mm and I ~ 1A, giving a
self-field of -O.lmT at die surface, decreasing into the body of the sample.
This is considerably less than the field of the peak of the decreasing Jc versus field
curve, indicating that the maximum self-field has only a small effect on the results obtained.
This low self-field indicates that the use of the transverse magnetisation measurements in
section 3.3.2 is a valid approximation, particularly since the connection to the self-field is
not very large.
3.4.2 AMOUNT OF HYSTERESIS
Figure 3.8 shows the hysteresis in Jc as a function of field, given by
AJC(B) = Jc(Binc) - Jc(Bdec), extracted from figures 3.6(a) to (c), normalised to their
respective values of AJC at zero field.
The form of the AJC versus B curve arises from the peak in the decreasing field Jc-B
curve, which gives the minima in the AJC-B curve, and the crossover point where Jc(Bdec)
drops below Jc(Binc) at which AJC changes sign. The 5//length//current orientation shows
the least hysteresis, as expected from geometrical considerations (see section 3.1). That Jc
for decreasing field rises above that for increasing field even in this orientation implies that
current is taking a meandering route through regions where the applied field is partially
96
C h a p t e r
3
:
J c
H y s t e r e s i s
i n Y B C O
c a n c e l l e d
b y t r a p p e d
f i e l d s
a n d n o t p a r a l l e l t o
t h e
a p p l i e d
f i e l d t h r o u g h r e g i o n s
w h e r e
t r a p p e d
f i e l d s e n h a n c e t h e a p p l i e d f i e l d .
F i g u r e
3 . 8 : A m o u n t
o f h y s t e r e s i s
i n
J c
a s a
f u n c t i o n
o f f i e l d
f o r
t h e
t h r e e
o r i e n t a t i o n s
m e a s u r e d , n o r m a l i s e d t o t h e v a l u e
o f
A J C
a t
z e r o
f i e l d .
T h e
i n s e r t s h o w s t h e
d a t a
o v e r
t h e e n t i r e
r a n g e o f
n o r m a l i s e d
A J C
3 . 4 . 3
D E M A G N E T I S I N G F A C T O R
F o l l o w i n g t h e
c o n j e c t u r e o f C a m p b e l l
i n
[ 3 . 1 0 ] ,
i t
w a s s u p p o s e d t h a t
p l o t t i n g
J c
a s
a f u n c t i o n o f
H = H 0 - n M
( e q u a t i o n
3 . 1 ) ,
w h e r e n i s
t h e
d e m a g n e t i s i n g
f a c t o r ,
w o u l d a l l o w
t h e
i n c r e a s i n g a n d d e c r e a s i n g f i e l d
c u r v e s t o
b e m o v e d
s o
a s t o c o i n c i d e .
Q u a l i t a t i v e l y t h i s
a p p e a r s
a t t r a c t i v e f o r t h e f o l l o w i n g r e a s o n s . T h e F C
J c s
a n d t h e F C m a g n e t i s a t i o n l i e
b e t w e e n t h o s e f o r i n c r e a s i n g a n d d e c r e a s i n g
f i e l d s ,
a s i s e x p e c t e d f r o m a g r a n u l a r
s a m p l e
( s e e
s e c t i o n
3 . 2 . 2 ) .
A l s o
t h e h y s t e r e s i s
i s
c o n s i d e r a b l y
l e s s
w h e n
n
i s
a
m i n i m u m , i . e .
w i t h
H p a r a l l e l t o t h e w i d e f a c e o f t h e s l a b .
A p p r o x i m a t e v a l u e s
o f
t h e d e m a g n e t i s i n g f a c t o r
f o r
t h e
s a m p l e u s e d
a r e n ~
0 . 7 4
f o r
/ A L c u r r e n t l w i d t h ,
n ~
0 . 1 6
f o r
7 7 _ L c u r r e n t / / w i d t h
a n d
n
=
0 . 1 f o r
7 / / / c u r r e n t / / l e n g t h
[ 3 . 2 4 ] .
A n a l y s i s
o f
f i g u r e
3 . 7 a l l o w s a n e s t i m a t i o n o f t h e
t r a p p e d f i e l d f o r e a c h
v a l u e o f
9 7
Chapter 3 : Jc Hysteresis in YBCO
decreasing field to be made. For each value of M it is assumed that the internal field of the
sample is the same, so the difference between the increasing and decreasing applied fields
for that M is the value of trapped field, Htrapped- The values of Htrapped corresponding to
the values of M for decreasing field were subtracted from Hdecreasing in an attempt to
overlay the increasing and decreasing field cuives, as shown in figure 3.9.
0.25 " —i—i—i—i—n—i—r«p—ff—1—i—i—i—i—1—i—i—i—i—1—i—i—i—i—1—i—i—i—i--1 \ \ B Increasing ’
l \ \ \ —♦— B // Length // current-
0.2- -Vs \ \ t —•— B _L width _L current --
V\ \ \\ —■— B // width _L current
- \V \ \ \ B Decreasing
§0.15" V\ \ \\ — — B // Length // current
O \ \ V — B _L width ± current -
\\ \ \\ —B— B // width _L current -
PQ
w 0 1'
; \\ \\; V\ :
0.05-
0"
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
]
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
1
_
Q
_ I — —- I I — — I -J— —ÿ—1— ■ i-l. I j —I......I I Ml. I I I _
0 1 2 3 4 5 6
Field (mT)
Figure 3.9 : Attempts to overlay the decreasing field Jc-B curves onto the
increasing field curves for all three orientations using equation 3.1. Note
that the decreasing field curve does not overlay on the increasing field curve
for all orientations.
For the //_Lwidth_Lcurrent orientation the Hdecreasing curve is overlaid on the
increasing field curve for higher fields while deviating from it at lower fields. For the other
two orientations the Hdecreasing curve does not overlay the increasing field curve at any
value of field, even when the decreasing field Jc is normalised to the peak in the decreasing
field Jc-B curve rather then the virgin zero-field Jc (not shown). This suggests that either
the trapped field is less than that indicated by the M-H loop (so that the Hdecreasing 3C-B
curves are moved too far towards zero) or that the hysteresis seen does not behave as this
model would predict.
98
C h a p t e r
3 :
J c
H y s t e r e s i s
i n Y B C O
3 . 4 . 4
F U R T H E R I N V E S T I G A T I O N
I t
i s
l i k e l y
t h a t
g e o m e t r i c a l e f f e c t s
i n c r e a s e
t h e f i e l d
i n t h e w e a k
l i n k s
a b o v e t h e
a v e r a g e
g i v e n b y
t h e
d e m a g n e t i s i n g f a c t o r .
I t
w a s t h e r e f o r e a s s u m e d
t h a t
J c
w a s g i v e n
b y
J c
=
f ( H 0 - k M )
( 3 . 5 )
T h e c o n s t a n t k i s a s s u m e d
t o b e a p u r e l y g e o m e t r i c a l
r e l a t i o n s h i p , a n d
i s
d e t e r m i n e d
a s f o l l o w s .
F o r
e a c h
v a l u e
o f
J c
o n a
g r a p h s u c h
a s F i g u r e
3 . 6 ( a )
t h e
t w o
v a l u e s o f
H 0
g i v i n g t h i s
J c
w e r e
d e t e r m i n e d ,
o n e
f o r
i n c r e a s i n g f i e l d a n d o n e
f o r
d e c r e a s i n g
f i e l d .
T h e i r
d i f f e r e n c e i s
A H 0 .
T h i s i s s h o w n
i n
f i g u r e
3 . 1 0 ( a ) .
T h e
t w o
v a l u e s o f
m a g n e t i s a t i o n
c o r r e s p o n d i n g
t o t h e s e t w o f i e l d s w e r e d e t e r m i n e d f r o m
f i g u r e
3 . 7 . T h e i r
d i f f e r e n c e i s
A M
a s
s h o w n i n
f i g u r e
3 . 1 0 ( b ) .
S i n c e
J c
i s t h e s a m e
t h e
t w o
v a l u e s
o f
H 0 - k M
s h o u l d b e
t h e
s a m e
a n d t h e v a l u e
o f
k
g i v e n b y
A H 0
/ A M . T h i s p r o c e d u r e
w a s a l s o
p e r f o r m e d
f o r
J c
s
f r o m t h e
i n c r e a s i n g
f i e l d
a n d
F C e x p e r i m e n t s ,
a n d t h e
d e c r e a s i n g
f i e l d
a n d
F C
e x p e r i m e n t s .
I f
t h i s
h y p o t h e s i s
i s
c o r r e c t ,
k s h o u l d b e a c o n s t a n t f o r a l l
f i e l d s
a n d
c o n f i g u r a t i o n s .
I f
i t
i s t h e d e m a g n e t i s i n g f a c t o r
i t
m u s t a l s o b e l e s s
t h a n o n e .
F i g u r e
3 . 1 0 ( a )
: A n
e x a m p l e o f
t h e d e t e r m i n a t i o n
o f
A H Q (
J c ) f r o m
J c
v e r s u s
H
d a t a f o r i n c r e a s i n g
a n d
d e c r e a s i n g f i e l d
c u r v e s .
9 9
Chapter 3 : Jc Hysteresis in YBCO
Figure 3.10(b) : An example of the determination of AM(JC) from M versus
H data for increasing and decreasing applied field.
The data extracted from figures 3.6(a) to (c) using the above techniques is shown
below. Figure 3.11(a) shows AH as a function of transportÿ while figure 3.11(b) shows
the equivalent AM versus transport Jc data. All results shown are from applied fields greater
than or equal to the peak in the decreasing Jc-B curve for each orientation.
For all values of Jc, AH increases with the demagnetising factor of the sample, in
agreement with the results shown in figure 3.7, while AM. decreases with increasing
demagnetising factor. For //_Lcurrent_Lwidth AH and AM are both smooth functions of /c,
but for the other two orientations this is not the case. AM plotted against AH shows that for
//Xcurrent//width and ////current//length there is a range of AM where AH is approximately
constant. All these observations imply that lc may be more than a simple constant.
100
C h a p t e r
3
:
J c
H y s t e r e s i s
i n
Y B C O
F i g u r e
3 . 1 1
:
P a r a m e t e r s e x t r a c t e d
f r o m t h e d a t a i n
f i g u r e
3 . 6
f o r
u s e i n
a n a l y s i s
( w
r e p r e s e n t s
w i d t h ,
L L e n g t h
a n d
I
c u r r e n t
i n t h e l e g e n d s ) ,
( a )
A H
a s a
f u n c t i o n
o f
J c ;
t h e i n s e t s h o w s t h e s a m e d a t a
w i t h t h e
a x e s
s w a p p e d f o r
c o m p a r i s o n w i t h
f i g u r e
3 . 6 .
T h e
B J - w J J d a t a d o e s n o t
e x t e n d
t o
a s l o w
f i e l d s
a s t h e
o t h e r
t w o o r i e n t a t i o n s d u e t o t h e
h i g h e r p e a k
i n t h e
d e c r e a s i n g
J c - B
c u r v e ,
( b )
T h e
e q u i v a l e n t
A M
v e r s u s
J c
d a t a ; t h e
i n s e r t
s h o w s
A M
p l o t t e d
a s
a
f u n c t i o n o f
A H f o r
a l l t h r e e o r i e n t a t i o n s . N o t e t h a t
A M
f o r
B A . W - L 1
p a s s e s
t h r o u g h
z e r o
a t
J c
~
0 . 8 .
1 0 1
Chapter 3 : Jc Hysteresis in YBCO
It should be noted that, depending on Hinc and Hgec and where this places them on
the M-H loop, AM does not necessarily increase with AH as shown in figure 3.12.
Figure 3.12 : Schematic diagram of an M-H loop showing the variation of
AM with different values of Hinc and Hgec, assuming Hgec is always greater
than H[nc. With AH between A and B, AM is zero. AH between C and D is
approximately the same as that between E and F but AM(E—>F) is
considerably less than AM(C—>D)
Figure 3.13(a) shows k for the situation in figure 3.6(a), i.e. iALwidthTcurrent
and hysteresis between increasing and decreasing fields. Figure 3.13(b) shows of k for
/7//width_Lcurrent and ////lengtliZ/current from figures 3.6(b) and 3.6(c). Figures 3.13(c)
and 3.13(d) show the results for the three geometries comparing the increasing field with
FC data and figure 3.13(e) compares FC with decreasing field for all geometries. All
results are shown since there seems to be no consistent model for k.
All of these graphs show that k is nowhere constant. For figure 3.13(a),
//-Lwidthixurrent in increasing and decreasing fields, at low Jcs (high fields) k starts at
-15, passes through a singularity, and at high Jcs (low fields) is of similar magnitude but
positive. This implies that at high fields one of AHQ or AM increases while the other
decreases, while above the singularity they both change in the same sense (see
figure 3.11). This arises from the flattening of the M-H curve at high fields and the fall of
Minc as the applied field rises from 20mT to 22mT (see figures 3.7 and 3.12). In both
cases in figure 3.13(b) the demagnetising factor is approximately zero but an effect is still
observed, and is similar in both cases with a peak in k at7c = 0.5Acnr2 followed by a
102
C h a p t e r
3
:
J c
H y s t e r e s i s
i n
Y B C O
s t e a d y
f a l l
i n k
t o b e l o w z e r o . T h i s
a g r e e s w i t h f i g u r e
3 . 1 1
a s i t
s h o w s
m a x i m a a n d
m i n i m a i n
b o t h
A H o
a n d
A M ,
a n d
s h o w s
b o t h
A H Q
a n d
A M
p a s s i n g
t h r o u g h
z e r o .
T h i s
w i d e v a r i a t i o n o f
k
i s c o n s i s t e n t
w i t h t h e
s u g g e s t i o n
t h a t t h e c u r r e n t
t a k e s
a
m e a n d e r i n g
p a t h
a n d
r e d i s t r i b u t e s
i t s e l f t h r o u g h t h e s a m p l e s o t h e r e
a r e
a l w a y s
s e c t i o n s
p e r p e n d i c u l a r
t o
t h e
a p p l i e d
f i e l d ,
r e d u c i n g a n y
o r i e n t a t i o n
d e p e n d e n c e .
F i g u r e
3 . 1 3 : k
v e r s u s
J c
p l o t s
( a )
J c
i n
i n c r e a s i n g
v e r s u s
d e c r e a s i n g f i e l d ,
H A c u r r e n t A w i d t h .
( Z F C )
( b )
J c
i n
i n c r e a s i n g
v e r s u s
d e c r e a s i n g f i e l d ,
H A c u r r e n t / Z w i d t h
( Z F C )
a n d
H / / c u r r e n t / / l e n g t h
( Z F C ) ( c )
J c
i n
i n c r e a s i n g
f i e l d
v e r s u s
F C ,
H A c u r r e n t A w i d t h
( Z F C ) ( d )
J c
i n i n c r e a s i n g f i e l d
v e r s u s
F C , f o r
b o t h H A c u r r e n t Z Z w i d t h
( Z F C )
a n d
H / / c u r r e n t / / 1 . e n g t h .
( Z F C )
( e )
J c
i n d e c r e a s i n g f i e l d
v e r s u s F C s i t u a t i o n , f o r
a l l
o r i e n t a t i o n s . N o t e
t h e
d i f f e r e n t
x a n d y a x i s r a n g e s .
1 0 3
Chapter 3 : Jc Hysteresis in YBCO
Both figures 3.13(c) and 3.13(d) show much smaller values of k, but again the
transverse field shows a larger effect while the two parallel field configurations give similar
results. The singularity in k in figure 3.13(c) is hard to explain as
Jc(FC) > Jc( increasing, ZFC) and M(increasing, ZFC) > M(FC) for all fields, k is still
larger than one, but less than in the transverse field case, so it appears that whatever
determines the hysteresis in this configuration, it is enhanced by the demagnetising field in
the transverse case. This qualitatively agrees with the results of Yang et al. [3.25] who also
observe an increase in the local field of sintered YBCO which is faster than the increase in
applied field. However, they were also unable to explain this behaviour.
Figure 3.13(e) shows k for the decreasing versus FC situation. All orientations
show similar behaviour implying either a minimum in AHo or a maxima in AM. In fact AHo
should, in all cases (including those shown in figures 3.13(a) to (d)) change sign as
JC(B decreasing) goes through a peak. In this case the size of the changes in k increase
with the sample demagnetising factor from the ////length//current configuration to the
//-Lwidth-Lcurrent configuration. As the FC data is the same for all three curves it implies
the controlling factor in this case is JC(B decreasing). Note that although the singularities in
k are significant, they are not the main result of this analysis. The most significant result of
this analysis is that there is such wide variation in k, implying that no model which adjusts
the external field by a constant factor dependent on the magnetisation of the grains will fit
the results obtained. Some effect of this type is not unexpected since a zero magnetisation,
for example, would produce different local fields depending on whether the grain is in the
virgin Meissner state or is trapping equal amounts of positive and negative field. However,
the flux distribution should be a secondary correction to the effect of the average
magnetisation and this appears not to be the case.
Although direcdy plotting k is a sensitive test of the relationship between hysteresis
in Jc and the applied field, the singularities in k shown in figure 3.13, and the behaviour of
Add and AM with Jc shown in figure 3.11 indicate the qualitative nature of the problem.
For example, at a critical current density of ~0.85Acnr2 in the increasing versus decreasing
transverse field case (figure 3.6(a)) there are two different external fields which give this
value of Jc. However, it may be seen from figure 3.7 that the magnetisation at these two
fields is also the same. Another anomaly is the size of k. As well as being very variable its
magnitude is very much larger than any possible demagnetising coefficient and in some
cases also changes sign. All these factors imply that k in equation 3.6 is not a simple
geometrical constant and that other factors must be considered.
104
C h a p t e r
3 :
J c
H y s t e r e s i s
i n
Y B C O
3 . 4 . 5
F I T T I N G R E S U L T S T O
T H E O R Y
T o d e t e r m i n e
w h e t h e r l o c a l f i e l d s b e t w e e n g r a i n s
a r e m u c h
l a r g e r
t h a n
f i e l d s
c a l c u l a t e d f r o m t h e
d e m a g n e t i s i n g
f a c t o r
a
t h e o r e t i c a l
c a l c u l a t i o n
w a s m a d e
b y
D r A . M . C a m p b e l l
o f t h e f i e l d b e t w e e n
t w o
g r a i n s
u s i n g t h e
d i p o l e
a p p r o x i m a t i o n ,
i . e .
a s s u m i n g t h a t e a c h g r a i n i n
t h e s u p e r c o n d u c t o r
i s
a
p e r f e c t s p h e r i c a l m a g n e t i c
d i p o l e .
A
h e x a g o n a l
c l o s e
p a c k e d
a r r a y o f
d i p o l e s
w a s
a s s u m e d a n d t h e f i e l d
c o n t r i b u t i o n
f r o m
e a c h
d i p o l e c a l c u l a t e d
a t
t h e m i d p o i n t
b e t w e e n
e a c h p a i r o f
d i p o l e s .
F o r a n
a r r a y
o f
3 0 0
x
3 0 0
x
5 0
d i p o l e s t h e
i n t e r d i p o l e
f i e l d
w a s f o u n d t o b e - 0 . 5 6 M
f o r
f i e l d s p a r a l l e l
t o
t h e b r o a d f a c e
o f
t h e
a r r a y
( d e m a g n e t i s i n g f a c t o r
~ 0 . 1 ) ,
a n d
- 1 . 3 3 M
f o r f i e l d s
p e r p e n d i c u l a r t o t h e b r o a d f a c e ( d e m a g n e t i s i n g
f a c t o r
~ 0 . 8 ) .
T h i s
c o n f i r m s t h e
c o n n e c t i o n
b e t w e e n t h e d e m a g n e t i s i n g
f a c t o r a n d t h e
i n t e r d i p o l e
f i e l d d u e
t o t h e m a g n e t i s a t i o n ,
b u t
g i v e s
v a l u e s
v e r y
s i m i l a r t o t h o s e o b t a i n e d f r o m t h e s t a n d a r d
d e m a g n e t i s i n g
f a c t o r .
A l t h o u g h t h e s e r e s u l t s w o u l d
e x p l a i n
a v a l u e
o f
k
s l i g h t l y l a r g e r t h a n
u n i t y
t h e y c a n n o t
e x p l a i n t h e v e r y l a r g e v a l u e s o f
k
f o u n d a b o v e . I t
s e e m s u n l i k e l y t h a t a f u l l
f i n i t e
e l e m e n t
c a l c u l a t i o n
w o u l d s i g n i f i c a n t l y a l t e r t h i s
c o n c l u s i o n .
T h e r e
i s
n o
m o d e l q u a n t i t a t i v e l y c o n s i s t e n t w i t h t h e s e
e x p e r i m e n t a l
r e s u l t s b u t a
n u m b e r o f r e a s o n s
f o r d e v i a t i o n s
f r o m t h e
s i m p l e
m o d e l
c a n b e
p o s t u l a t e d
[ 3 . 2 1 ] .
T h e e f f e c t s g i v i n g
r i s e
t o t h e
o b s e r v e d
h y s t e r e s i s
a r e m u c h
m o r e l o c a l t h a n
t h o s e
p r e d i c t e d b y
a n y
f o r m u l a
i n v o l v i n g
t h e a v e r a g e m a g n e t i s a t i o n ,
p r o b a b l y d u e
t o t h e
d i f f e r e n t
e f f e c t s
t h e l o c a t i o n
o f t r a p p e d
f l u x w i l l h a v e
o n
J c
o n t h e B
d e c r e a s i n g
l e g
o f t h e
m e a s u r e m e n t
c y c l e . A s s u m i n g t h e
a p p l i e d
f i e l d i s
p e r p e n d i c u l a r t o t h e a p p l i e d c u r r e n t
t h e n f l u x
t r a p p e d
n e a r t h e g r a i n
s u r f a c e s
( f o r
e x a m p l e
b y
a s u r f a c e
b a r r i e r )
w i l l r e t u r n
i n t h e i n t e r g r a i n s
a n d
s o
h a v e a l a r g e e f f e c t o n
J c .
H o w e v e r ,
f l u x t r a p p e d
i n
t h e g r a i n
c e n t r e s w i l l c r o s s
i n t e r g r a i n s p a r a l l e l t o t h e c u r r e n t p a t h a n d s o h a v e m u c h l e s s e f f e c t a s i t w i l l
o n l y a f f e c t t h e
m u c h h i g h e r i n t r a g r a n u l a r
J c .
T h i s a g r e e s w i t h t h e
r e s u l t s s h o w n i n
f i g u r e
3 . 8 . F i g u r e 3 . 1 4
s h o w s t h e s e
p r o c e s s e s s c h e m a t i c a l l y .
A l s o ,
t h e q u a l i t y
o f
t h e i n t e r g r a n u l a r j u n c t i o n s
v a r i e s c o n s i d e r a b l y . T h e w e a k e s t
j u n c t i o n s m a y o n l y c a r r y
a
s u p e r c u r r e n t
i n
t h e v i r g i n
s t a t e ,
w h e n t h e r e
a r e n o i n t e r n a l
f i e l d s . A f t e r a f i e l d c y c l e z e r o m a g n e t i s a t i o n
o c c u r s
o n l y b y
t h e c a n c e l l a t i o n
o f l o c a l i n t e r n a l
f i e l d s
w h i c h w i l l
c o n t i n u e t o h o l d s o m e w e a k e r j u n c t i o n s
i n
t h e
n o r m a l s t a t e
( t h i s
e x p l a i n s
t h e
d e c r e a s e i n s i z e o f
t h e
p e a k
o n t h e
B
d e c r e a s i n g
l e g
o f
t h e f i e l d
c y c l e ) .
1 0 5
Chapter 3 : Jc Hysteresis in YBCO
Applied
Current -Grain
Figure 3.14 : Schematic diagram showing the differences in the effects of
flux trapped near (a) the centre or (b) the edge of sintered grains on the
intergranular regions.
Comparison with the theory of D'yachenko [3.19] indicates that it may account for
most of the observed behaviour. However, a quantitative comparison of the results
obtained here and the predictions of this theory has not been done for two reasons. First, in
order to make a true comparison with D'yachenko's theory, measurements would have to
be extended to higher applied magnetic fields. Secondly, the wide variation of granular
properties within the samples used here makes the application of this theory considerably
harder, as it assumes uniform grain properties across the sample, though an average over
all grains could conceivably be used.
Also, the theory of Mune et al. [3.26] should be taken into consideration when
formulating an explanation for the observed hysteresis of Jc.
3.4 CONCLUSIONS
The hysteresis in the Jc of sintered superconducting ceramics follows qualitatively
the effect of the magnetisation of the grains on the internal field as suggested by the EG
model. However, analysis shows that the effects seen are much larger and more variable
than can be explained by any model which only uses the average magnetisation of the
sample. It appears that the hysteresis must be determined by the local field distribution on a
scale comparable with the grain size although it appears the results obtained cannot be
explained in terms of a constant which takes into account any geometrical effects which
increase the field in the intergranular weak links.
106
C h a p t e r 3
:
J c
H y s t e r e s i s
i n
Y B C O
F u r t h e r w o r k
i s
n e e d e d t o c l a r i f y
t h e s e p o i n t s .
3 . 5 R E F E R E N C E S
[ 3 . 1 ]
J . E .
E v e t t s ,
I E E E
T r a n s .
M a g n . ,
M A G - 1 3 ,
1
1 0 9
( 1 9 8 3 ) .
[ 3 . 2 ]
R . L . P e t e r s o n
a n d
J . W .
E k i n ,
P h y s . R e v . B ,
3 7 ,
9 8 4 8
( 1 9 8 8 ) .
[ 3 . 3 ]
J . E .
E v e t t s a n d B . A .
G l o w a c k i ,
C r y o g e n i c s ,
2 8 ,
6 4 1
( 1 9 8 8 ) .
[ 3 . 4 ]
E .
A l t s h u l e r ,
J .
M u s a ,
J .
B a r r o s o ,
A . R . R . P a p a a n d
V . V e n e g a s ,
C r y o g e n i c s ,
3 3 ,
3 0 8
( 1 9 9 3 ) .
[ 3 . 5 ]
M . D a u m l i n g , E .
S a r n e l l i ,
P .
C h a u d h a r i ,
A . G u p t a
a n d J .
L a c e y ,
A p p l .
P h y s .
L e t t ,
6 1 ,
1 3 5 5
( 1 9 9 2 ) .
[ 3 . 6 ]
J . E . E v e t t s i n C o n c i s e E n c y c l o p a e d i a
o f M a g n e t i c
a n d
S u p e r c o n d u c t i n g
M a t e r i a l s ,
p p
4 7 8 ,
e d i t e d b y J . E .
E v e t t s
( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 3 . 7 ]
T . R .
A s k e w ,
R . B .
F l i p p e n , K . J . L e a r y a n d M . N . K u n c h u r ,
J .
M a t e r .
R e s . ,
6 ,
1 1 3 5
( 1 9 9 1 ) .
[ 3 . 8 ]
M . E . M c H e n r y ,
M . P . M a l e y a n d J . O .
W i l l i s ,
P h y s i c a l
R e v i e w
B ,
4 0 ,
2 6 6 6
( 1 9 8 9 ) .
[ 3 . 9 ]
J . W .
E k i n ,
H . R .
H a r t
J r . a n d A . R .
G a d d i p a t i , J .
A p p l .
P h y s . ,
6 8 ,
2 2 8 5
( 1 9 9 0 ) .
[ 3 . 1 0 ]
A . M . C a m p b e l l a n d F . J .
B l u n t ,
S u p e r c o n d .
S c i .
T e c h n o l . ,
3 ,
4 5 0
( 1 9 9 0 ) .
[ 3 . 1 1 ]
P . K .
M i s h r a ,
G .
R a v i k u m a r ,
P .
C h a d d a h ,
S . K u m a r a n d
B . A .
D a s a n n a c h a r y a ,
J p n . J . A p p l .
P h y s . ,
2 9 ,
L 1 6 1 2
( 1 9 9 0 ) .
[ 3 . 1 2 ]
K .
K w a s n i t z a ,
B . J a k o b a n d G .
V e c s e y
i n
P r o c e e d i n g s o f
H i g h T
W o r k s h o p ,
p p
3 8 4 ,
G e n o a ,
I t a l y , 1 9 8 7
( B r u s s e l s ,
B e l g i u m
:
C o m m E u r
C o m m u n i t i e s )
[ 3 . 1 3 ]
K .
W a t a n a b e ,
K .
N o t o ,
H .
M o r i t a ,
H .
F u j i m o r i , K .
M i z u n o ,
T .
A o m i n e ,
B .
N i ,
T .
M a t s u s h i t a ,
K . Y a m a f u j i a n d Y .
M u t o , C r y o g e n i c s ,
2 9 ,
2 6 3
( 1 9 8 9 ) .
[ 3 . 1 4 ]
C . P .
B e a n ,
R e v . M o d .
P h y s . ,
3 6 ,
3 1
( 1 9 6 4 ) .
[ 3 . 1 5 ]
K . Y .
C h e n
a n d Y . J . Q i a n ,
P h y s i c a
C ,
1 5 9 ,
1 3 1
( 1 9 8 9 ) .
[ 3 . 1 6 ]
E . A l t s h u l e r ,
S . G a r c i a
a n d J .
B a r r o s o ,
P h y s i c a
C ,
1 7 7 ,
6 1
( 1 9 9 1 ) .
1 0 7
Chapter 3 : Jc Hysteresis in YBCO
[3.17] R. Navarro and L.J. Campbell, Superconductor Science and Technology, 5, 100
(1992).
[3.18] K.I. Kugel and A.L. Rakhmanov, Cryogenics, 33, 281 (1993).
[3.19] A.I. D'yachenko, Physica C, 213, 167 (1993).
[3.20] G. Ries, H.-W. Neumiiller, W. Schmidt and C. Struller in Proceedings of 7th.
IWCC, pp 537, Alpbach, Austria, 1994 (World Scientific Publishing Co.)
[3.21] A.R. Jones, R.A. Doyle, F.J. Blunt and A.M. Campbell, Physica C, 196, 63
(1992).
[3.22] M. Murakami, Supercond. Sci. Technol., 5, 185 (1992).
[3.23] A.M. Campbell, F.J. Blunt, J.D. Johnson and P.A. Freeman, Cryogenics, 31,
732 (1991).
[3.24] J.A. Osborn, Phys. Rev., 67, 351 (1945).
[3.25] Y. Yang, C. Beduz and S.P. Ashworth, Cryogenics, 30, 618 (1990).
[3.26] P. Mune, E. Altshuler and J. Musa, Physica C, 246, 55 (1995)
108
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
C H A P T E R
4 :
C R I T I C A L
C U R R E N T S I N
M E L T
P R O C E S S E D
Y B C O
T H I C K
F I L M S
4 . 1 I N T R O D U C T I O N
T h e
a d v e n t o f m e l t - p r o c e s s i n g
t e c h n i q u e s f o r t h e
f a b r i c a t i o n
o f
b u l k
Y B a 2 C u 3 0 7 . 5
( Y B C O )
h a s e s t a b l i s h e d t h e p o t e n t i a l
o f t h i s
m e l t - p r o c e s s e d ( M P )
m a t e r i a l
f o r
b u l k
a p p l i c a t i o n s
[ 4 . 1 ,
2 ] .
T h e i r l a r g e c u r r e n t c a r r y i n g
c a p a c i t y ( t y p i c a l l y
3 0
0 0 0 A c m r 2 a t
I T
a n d
7 7 K ) , h o w e v e r ,
r e q u i r e s
t h e
u s e o f
s p e c i m e n s
o f
s m a l l
c r o s s - s e c t i o n a l
a r e a i f
t r a n s p o r t
J c
s a r e
t o
b e m e a s u r e d .
T h i s
h a s
p r o v e d
d i f f i c u l t g i v e n
t h e
b r i t t l e n a t u r e o f
Y B C O .
C o n s e q u e n t l y
m o s t
J c s
r e p o r t e d t o d a t e h a v e b e e n
d e r i v e d
f r o m m a g n e t i s a t i o n
m e a s u r e m e n t s
[ 4 . 1 ] .
T h e
a v a i l a b i l i t y
o f
t h i c k f i l m M P Y B C O
m a y
s i g n i f i c a n t l y a i d
i n
t h e
u n d e r s t a n d i n g
o f t h e p r o p e r t i e s o f b u l k
m a t e r i a l s ,
b a s e d o n s i m i l a r i t i e s b e t w e e n t h e
g r a i n
s t r u c t u r e
i n
t h e
t w o f o r m s
o f t h e m a t e r i a l . T h e
p r o d u c t i o n
o f t h i s f o r m
o f Y B C O w a s f i r s t
r e p o r t e d
b y
A s t r o v
a n d V a i n e r
i n 1 9 8 8
[ 4 . 3 ] , B u l k
M P
Y B C O
t y p i c a l l y c o n t a i n s g r a i n s
o f u p t o s e v e r a l
c e n t i m e t r e s
i n d i a m e t e r e a c h o f w h i c h
i s
u s u a l l y
c h a r a c t e r i s e d b y a
f o u r - f a c e t e d s u b - g r a i n
s t r u c t u r e r a d i a l
t o
a c e n t r a l n u c l e a t i o n p o i n t
( o r ' h u b ' ) -
T h i c k
f i l m s e x h i b i t a
s i m i l a r
h u b - t y p e m i c r o s t r u c t u r e a t
t h e i r p o i n t o f
n u c l e a t i o n ,
c o n n e c t e d t o a n
a r r a y o f
r a d i a l
s u b - g r a i n s . A n a l y s i s o f
M P
t h i c k
f i l m s t h e r e f o r e
m a y
p r o v i d e i n s i g h t
i n t o t h e
m e c h a n i s m s
o f c u r r e n t f l o w w i t h i n b u l k m a t e r i a l s .
A l s o ,
c o r r e l a t i o n s b e t w e e n
t r a n s p o r t
a n d
m a g n e t i s a t i o n
J c
s m a y b e m a d e u s i n g t h i c k f i l m s
a s
n o
m e c h a n i c a l t h i n n i n g
i s r e q u i r e d t o
f a b r i c a t e
s a m p l e s o f s u i t a b l e
g e o m e t r y .
L a s t l y ,
t h i c k
f i l m s
h a v e t h e i r
o w n p o t e n t i a l
a p p l i c a t i o n s , f o r e x a m p l e i n
d e v i c e s r e q u i r i n g c o n f o r m a l c o a t i n g s
s u c h
a s t u b e s a n d
l a r g e
a r e a p a s s i v e m i c r o w a v e d e v i c e s .
R e s u l t s f r o m
t h i c k f i l m s
s i m i l a r t o
t h o s e m e a s u r e d h e r e
h a v e b e e n
r e p o r t e d
b y D a y e t
a l .
i n ,
f o r e x a m p l e
[ 4 . 4 , 5 ] .
T h e m a i n a i m
o f t h i s
s t u d y
i s
t o
c o m p a r e
m a g n e t i s a t i o n
a n d
t r a n s p o r t r e s u l t s
t o a c c o u n t f o r t h e
d i f f e r e n c e s b e t w e e n
t h e m .
T o
a c h i e v e
t h i s ,
m e a s u r e m e n t s
w e r e c a r r i e d o u t o n t w o
s e p a r a t e
s t r u c t u r e s i n a
n u m b e r o f
t h i c k
f i l m s a m p l e s . T h e s e w e r e
w i t h i n
t h e H - S
g r a i n s a n d
a c r o s s t h e b o u n d a r i e s s e p a r a t i n g
i n d i v i d u a l
H - S
g r a i n s .
A s e c o n d a r y
a i m o f
t h e s e
m e a s u r e m e n t s
f o r t h e p u r p o s e s
o f
t h i s t h e s i s i s t h a t i t w a s
h o p e d t h e y
w o u l d p r o v i d e a n e x a m p l e o f a m a t e r i a l
w i t h ' s t r o n g '
w e a k
l i n k s .
1 0 9
Chapter 4 : YBCO Thick Films
4.1.1 SAMPLE PROCESSING AND PREPARATION
YBCO thick film samples 30mm x 30mm in size and 50|im thick were grown on
yttria-stabilised zirconia (YSZ) substrates by I.C.I. Superconductors. Although YBCO
thick films are also grown using other methods [4.6-8], MP YBCO thick films can be
grown using the following process :
1) Pre-calcined YBCO powder with a grain size of less than 5pm is mixed with a
suspendant such as polyethylene glycol (PEG) in a ratio of 1 gram YBCO to 1cm3 PEG.
The YBCO powder can have up to 5 weight % silver powder added to it [4.4, 5], though
the I.C.I. samples do not have these additions.
2) The YSZ substrate is placed on a photoresist spinner and the YBCO/PEG mixture
added from a pipette.
3) The substrate is spun at -2000 r.p.m., yielding a uniform YBCO/PEG coating.
4) The substrate is heated on a hot plate, burning off the PEG and leaving a uniform
layer of YBCO powder coating the substrate surface.
5) The sample is then melt-processed in a tube furnace under static air at -1070°C,
using a process analogous to that used in bulk melt processing. The film is heated to above
the peritectic for ten minutes or less, then cooled and oxygenated at 400°C.
Microstructural analysis reveals that a BaCuo.3Zro.7O3 interfacial layer less than
10pm thick forms on the surface of the substrate as the liquid YBCO phase reacts with the
YSZ substrate. This appears critical to the growth of high quality films. The longer the
sample is kept above the peritectic the thicker this layer becomes, making ten minutes the
maximum amount of time for which the sample can be kept above the peritectic.
4.1.2 THE HUB-AND-SPOKE GRAIN STRUCTURE
As mentioned above bulk MP YBCO and MP YBCO thick films exhibit similar
hub-type microstructures at their point of nucleation, connected to a circular or elliptical
array of radial sub-grains [4.4], This form of structure in the thick films is similar to that
observed for many complex ceramics, minerals and polymers [4.9] although it is two
dimensional rather than three dimensional. The physical reasons why the film should grow
in this manner are uncertain, although it is likely that they are related to growth rate
instabilities caused by compositional variations within the melt [4.10], The sizes and
110
C h a p t e r
4 :
Y B C O T h i c k
F i l m s
s h a p e s o f
i n d i v i d u a l H - S
g r a i n s
v a r y
c o n s i d e r a b l y
w i t h i n
a g i v e n
s a m p l e , a g a i n
p r e s u m a b l y d u e t o
l o c a l
c o m p o s i t i o n a l d i f f e r e n c e s . F i g u r e 4 .
1 s h o w s a
m i c r o g r a p h
o f
a
p e l l e t o f b u l k
M P
Y B C O w h i l e f i g u r e 4 . 2
s h o w s
a
m i c r o g r a p h o f a
t h i c k
f i l m
s a m p l e
s h o w i n g a n u m b e r
o f H - S g r a i n s t r u c t u r e s .
F i g u r e 4 . 1
:
M i c r o g r a p h
o f M P
Y B C O p e l l e t s h o w i n g f o u r - f a c e t e d
g r o w t h
s t r u c t u r e
(
o n e d i v i s i o n o n
s c a l e
=
1 m m ) .
F i g u r e 4 . 2 :
M i c r o g r a p h
o f
Y B C O
t h i c k f i l m s h o w i n g H - S
g r a i n
s t r u c t u r e .
E x a m i n a t i o n o f t h e
f i l m s r e v e a l s a n u m b e r o f
p e r t i n e n t
f e a t u r e s .
T h e ' h u b '
r e g i o n i s
s e e n t o
b e o f r o u g h l y
s q u a r e
g e o m e t r y
w i t h a s i z e o f ~ 5 0
x
5 0 j l m
a n d o f t e n
e x h i b i t s
1 1 1
Chapter 4 : YBCO Thick Films
growth facets at 90° to each other, roughly similar to the behaviour found in bulk MP
YBCO. The 'spokes' seem to nucleate at the hub and occasionally exhibit microcracks
perpendicular to their length (i.e. perpendicular to the growth direction), probably caused
by thermal contraction during processing [4.11],
An important feature is the change in sample microstructure with thickness (4.11],
In thin samples (below ~50|im) the H-S grains appear unconnected. As the sample
thickness increases the connectivity of the H-S grains increases. The inter-H-S grain region
is defined by low-angle grain boundaries in this regime. As the thickness continues to
increase the surface of the H-S grains begins to be covered with a small grained granular
layer which increases in thickness as the sample thickness increases, although the H-S
structure appears to be retained in the bulk of the sample. This behaviour indicates that
there is an optimum thickness for these films, although this varies with processing
conditions and the regime in which the film is expected to operate [4. 1 1].
The results of microscopic examinations of the thick films measured in this chapter
are discussed in section 4.3.3.
4.2 EXPERIMENTAL TECHNIQUE
Three large area 30mm x 30mm thick film specimens were supplied for this
investigation, identified by the sample codes TF799, TF390 and TF930. The third thick
film, TF930, was fabricated with a central 'neck' area 4x4 mm in size containing two
individual H-S grains to allow investigation of the variation of current flow within a
specimen.
4.2.1 TRANSPORT MEASUREMENTS
Bars nominally 2cm long and 1mm wide were cut from samples TF799 and TF390
using a diamond cutting wheel. A low cutting speed was used to minimise mechanical
damage to the film. No lubricant was used during the cutting process to avoid possible
contamination or degradation of the film surface. Despite this there is evidence that some
damage to the sample occurred during the cutting process, possibly from heating effects.
This is indicated by the different R-T curves before and after cutting shown in figure 4.6,
below.
112
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
F i g u r e
4 . 3
:
O p t i c a l
m i c r o g r a p h s o f
i n t r a - a n d
i n t e r
- H - S g r a i n s i n t h e
t h i c k
f i l m
s a m p l e s , w i t h
v o l t a g e
c o n t a c t s
a t t a c h e d ,
( a )
s h o w s a
H - S
i n t r a g r a i n
r e g i o n
w i t h
c o n t a c t s o n e i t h e r
s i d e
o f
t h e h u b ,
( b )
s h o w s a
H - S
i n t e r g r a i n
r e g i o n
w i t h
c o n t a c t s a p p l i e d
o n e i t h e r
s i d e
o f t h e g r a i n
b o u n d a r y .
T h e
b a r s w e r e
e x a m i n e d
u n d e r
a n
o p t i c a l m i c r o s c o p e
t o
l o c a t e
a r e a s s u i t a b l e
f o r
m e a s u r i n g
t r a n s p o r t
c r i t i c a l c u r r e n t s .
R e g i o n s w h e r e e i t h e r a
c o m p l e t e H - S g r a i n
o r
a
1 1 3
Chapter 4 : YBCO Thick Films
well-defined intergrain boundary was continuous across the entire width of the bar were
selected as candidate specimens, eventually yielding four candidate bar samples from
TF799 and two from TF390 containing a total of eight intra-H-S grain regions and eleven
inter-H-S grain regions. To facilitate ease of handling each bar sample was attached to an
alumina plate using du Pont 6838 silver paint. Contacts were then attached to the sample,
again with the aid of an optical microscope, using du Pont 6838 silver paint. Two types of
contact were applied to each sample :
1) Current contacts, made on each end of the sample using 0.25mm diameter silver
wire with large 1 x 2 mm contact pads to reduce heating effects.
2) Voltage contacts, made using 25pm diameter gold wire with small 0.3mm diameter
contact pads to maximise voltage resolution.
All contacts were cured onto the mounted samples by baking in oxygen for ten
minutes at 500°C. Figure 4.3 shows optical micrographs of contacts attached to measure
intra- and intergrain Jcs.
Figure 4.4: Photograph of the entire 25 x25mm thick film sample.
To investigate the distribution of current flow over a specimen, sample TF930 was
used. This was a 25 x 25mm thick film which had been fabricated with a central 'neck'
area 4x4 mm in size containing two individual H-S grains. Four pairs of voltage
contacts were placed around the 'neck' area to determine which path, if any, was the most
favourable for current flow through the 'neck'. Pair 1 was placed across a 'clean' intergrain
to probe how much current flow across it was inhibited. Pair 2 was placed within a H-S
grain while pair 3 was placed along a 'clean' intergrain to determine whether the grain or
the intergrain was the dominant current path through the 'neck'. Pair 4 was placed so as to
114
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
m e a s u r e t h e
p r o p e r t i e s o f t h e
' n e c k ' a s a
w h o l e . L a r g e c u r r e n t
c o n t a c t s w e r e
u s e d
t o
r e d u c e
r e s i s t i v e
h e a t i n g i n t h e
s a m p l e a n d
e n s u r e
a n
e v e n i n i t i a l
c u r r e n t
d i s t r i b u t i o n .
F i g u r e
4 . 4
s h o w s a p h o t o g r a p h
o f t h e e n t i r e
s a m p l e s h o w i n g a l l
c o n n e c t i o n s t o i t
w h i l e
f i g u r e
4 . 5
i s
a
s c h e m a t i c d i a g r a m
o f t h e
' n e c k ' a r e a s h o w i n g
t h e
p o s i t i o n i n g o f
t h e
v o l t a g e
c o n t a c t s
r e l a t i v e t o t h e H - S
g r a i n s .
4 m m
D i r e c t i o n o f
O v e r a l l
_
C u r r e n t
F l o w
F i g u r e 4 . 5
: S c h e m a t i c
d i a g r a m o f
' n e c k '
a r e a
o f
s a m p l e
T F 9 3 0
s h o w i n g
p o s i t i o n i n g
o f
v o l t a g e
c o n t a c t s .
A , B
a n d C a r e t h e t h r e e
H - S
g r a i n s
m e a s u r e d . 1 , 2 , 3 a n d
4
a r e t h e
p a i r s o f v o l t a g e
c o n t a c t s u s e d .
T h e
r e s i s t a n c e v e r s u s t e m p e r a t u r e
( R - T )
c h a r a c t e r i s t i c o f e a c h
s a m p l e w a s m e a s u r e d
a t z e r o
m a g n e t i c f i e l d u s i n g a n A . C .
t e c h n i q u e a s d e s c r i b e d
i n s e c t i o n 2 . 2 . 1 .
T r a n s p o r t c u r r e n t -
v o l t a g e
( / - V )
c u r v e s
w e r e
i n i t i a l l y
m e a s u r e d
f o r
o n e s a m p l e a s a
f u n c t i o n
o f
t e m p e r a t u r e i n
z e r o m a g n e t i c f i e l d f o r a n
i n t e r g r a i n a n d
a n i n t e r g r a i n .
T h i s w a s
d o n e i n
a n O x f o r d
I n s t r u m e n t s
c o n t i n u o u s f l o w c r y o s t a t .
D a t a w e r e
t a k e n
f r o m 8 K t o 9 0 K
a n d
J c
a s
a
f u n c t i o n o f t e m p e r a t u r e
w a s t h e n e x t r a c t e d f o r t h e
t w o
r e g i o n s
m e a s u r e d .
F o r m o s t s a m p l e s I - V
c u r v e s
w e r e m e a s u r e d a t
4 . 2 K .
S o m e
m e a s u r e m e n t s w e r e
a l s o c a r r i e d o u t a t 7 7 K f o r
c o m p a r i s o n
w i t h t h e m a g n e t i s a t i o n
m e a s u r e m e n t s
( s e e
b e l o w ) .
1 1 5
Chapter 4 : YBCO Thick Films
All bar-shaped samples were measured in magnetic fields of up to 70mT using a
water-cooled electromagnet, with the applied field perpendicular to both the current and the
plane of the film. All the inter-H-S and intra-H-S regions of samples TF799 and TF390
were measured in this regime to provide a statistically significant range of data. One
bar-shaped sample was also measured at 4.2K in magnetic fields of up to 8T in an Oxford
Instruments superconducting solenoid with the applied field perpendicular to the current
and both parallel and perpendicular to the plane of the sample. The large sample TF930 was
also measured in the 8T solenoid at fields of up to IT at 4.2K and 77K. For this sample the
applied field was perpendicular to the current flow and the plane of the film. All
measurements used the computerised D.C. current measurement system described in
section 2.3.2.
The I-V characteristic for each sample and magnetic field was analysed to extract a
value of Ic from which Jc was calculated, assuming a film thickness of 50p.m. No electric
field criterion was used, rather Ic was taken to have been reached when the sample voltage
rose approximately 50nV (the resolution of the experimental instruments) above the
background voltage signal caused by the temperature gradient along the voltage leads (see
section 2.3.1). This method was used due to the great difficulty of defining any meaningful
electric field criterion for /-Vs measured across the very narrow boundaries between H-S
grains. Fortunately the I-V curves for the thick films generally showed sufficiently sharp
transitions at Jc for this method to give unambiguous results.
4.2.2 MAGNETIC MEASUREMENTS
Magnetisation measurements were performed by Dr. D.A. Cardwell using an
Oxford Instruments vibrating sample magnetometer (VSM). Further details of this
technique are given in section 2.4. Measurements were carried out on four square samples
cut from the same thick films as the samples used for transport measurements, again using
a diamond cutting wheel. These had dimensions of 1 x 1mm, 1.7 x 1.7mm, 3 x 3mm
and 4 x 4mm. Hysteresis loops were measured at 4.2K and 77K using fields of up to 12T
with the applied field perpendicular to the plane of the sample. The average Jc in the
measurement geometry used is directly proportional to the width of the observed hysteresis
loop if current flows on the length scale of the sample, which earlier measurements by
Cardwell et al. [4.12] have shown that it does at fields greater than ~1T. Below this field
there is not a full critical state and the distribution of induced currents is complex [4.13] so
that meaningful Jcs cannot easily be calculated. Using these assumptions Jc for square
116
C h a p t e r 4
:
Y B C O T h i c k
F i l m s
p l a n a r
s a m p l e s
w a s
c a l c u l a t e d
f r o m
t h e
B e a n
m o d e l
[ 4 . 1 4 ]
f o r
f i e l d s
g r e a t e r
t h a n I T
u s i n g
e q u a t i o n 1 . 1 2 .
F o l l o w i n g
t h e V S M
m e a s u r e m e n t s A C S
m e a s u r e m e n t s
a s
d e s c r i b e d i n
s e c t i o n 2 . 5 . 1 w e r e c a r r i e d o u t
o n
t h e 4 x
4 m m
s a m p l e t o
o b t a i n a
c o m p a r i s o n w i t h t h e
R - T m e a s u r e m e n t s .
T h e
s a m p l e w a s p l a c e d i n s i d e a g e l a t i n
c a p s u l e
a n d
h e l d
s t a t i o n a r y
w i t h
a p a c k i n g o f
P T F E
t a p e . M e a s u r e m e n t s
w e r e
c a r r i e d o u t
u s i n g 0 . 1
m T ,
0 . 2 5 m T
a n d
1 . 3 4 m T A . C .
d r i v e
f i e l d s
a t a
f r e q u e n c y o f 3 3 3 H z w i t h
z e r o D . C .
f i e l d a n d
t h e
A . C . f i e l d
p a r a l l e l
t o t h e
p l a n e
o f t h e
s a m p l e .
T h e
s a m p l e
w a s
m e a s u r e d f r o m 5 K
t o
1
1 O K
u s i n g a ! K
p e r
m i n u t e h e a t i n g
r a t e . A
r u n u n d e r i d e n t i c a l
c o n d i t i o n s u s i n g a
g e l a t i n
c a p s u l e
p a c k e d
w i t h P T F E t a p e
b u t n o
s a m p l e
w a s a l s o e a r n e d o u t
t o
o b t a i n t h e
b a c k g r o u n d
s i g n a l
o f
t h e
A C S
s y s t e m
w h i c h w a s
s u b t r a c t e d
f r o m t h e m e a s u r e d A C S s i g n a l t o
p r o v i d e
t h e t r u e
A C S
s i g n a l
o f t h e
s a m p l e .
4 . 2 . 3 M I C R O S T R U C T U R A L O B S E R V A T I O N S
O p t i c a l m i c r o s c o p y o f
t h e t h i c k
f i l m
s a m p l e s i n d i c a t e s t h r e e
d i s t i n c t
r e g i o n s w i n
s e
m i c r o s t r u c t u r e i s
o f i n t e r e s t .
T h e s e
a r e t h e
h u b ,
t h e
s p o k e s
a n d
t h e i n t e r - H - S g r a m r e g i o n .
T h e s e
r e g i o n s
w e r e e x a m i n e d
b y M r .
P . D .
F l u n n y b a l l
a n d
M r . C . D . D e w h u r . -
1
o n
s e v e r a l
t h i c k
f i l m
s a m p l e s
u s i n g a s c a n n i n g
e l e c t r o n m i c r o s c o p e
t o c o r r e l a t e t h e
s t r u c t u r e s o f
t h e d i f f e r e n t
a r e a s
w i t h t h e
r e s u l t s o b t a i n e d f r o m m a g n e t i c a n d
t r a n s j
,
r t
m e a s u r e m e n t s .
4 . 3 R E S U L T S A N D
D I S C U S S I O N
4 . 3 . 1 T R A N S P O R T
M E A S U R E M E N T S
R e s i s t a n c e
v e r s u s T e m p e r a t u r e M e a s u r e m e n t
A t y p i c a l R - T p l o t f o r a t h i c k f i l m s a m p l e
i s i l l u s t r a t e d
i n
f i g u r e 4 . 0 . w i t h t h e i n s e r t
s h o w i n g t h e R - T
c h a r a c t e r i s t i c
o f
a s a m p l e b e f o r e h e a t t r e a t m e n t .
T h e r e a r e s i g n i f i c a n t
d i f f e r e n c e s b e t w e e n t h e R - T
c u r v e s w i t h a n d w i t h o u t h e a t
t r e a t m e n t . T h e
p r e s e n c e
o f
a r e s i s t i v e
t a i l
t o q u i t e l o w
t e m p e r a t u r e s
( w h i c h
e x t e n d
-
b e l o w
7 7 K i n s o m e
s p e c i m e n s )
a n d t h e p e a k
i n
r e s i s t a n c e j u s t
a b o v e
T c
i n t h e
h e a t
t r e a t e d
s a m p l e
s u g g e s t t h a t t h e
h e a t
t r e a t m e n t a s s o c i a t e d
w i t h
t h e
a p p l i c a t i o n o f t h e
c u r r e n t
a n d
w b : : a
t
1 1 7
Chapter 4 : YBCO Thick Films
contacts has resulted in some de-oxygenation of the specimen. Possible explanations of the
peak just above Tc are discussed in section 2.2.
Figure 4.6 : A resistance versus temperature curve for a melt-processed
thick film after heat-treatment of contacts. The inset shows a resistance
versus temperature curve for a thick film before heat treatment for
comparison.
Measurement of Jr as a Function of T
Figure 4.7(a) shows the I-V curves for the intragrain region measured as a function
of temperature while figure 4.7(b) shows the I-V curves for the intergrain region.
The good agreement observed between increasing and decreasing current curves in
both figure 4.7 indicates that these measurements are insensitive to the thermal effects
which are often inherent to transport Jc measurements. Note the gradually increasing
gradient for all the TV curves from the lowest temperatures to approximately 80K,
implying that the flux flow resistivity of the sample is increasing with temperature, in
agreement with the theory of Stmad et al. [4.15, 16].
118
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
F i g u r e
4 . 7 ( a )
: I n c r e a s i n g a n d d e c r e a s i n g I - V
c u r v e s
f o r
t h e
i n t r a g r a i n
r e g i o n
m e a s u r e d a s
a
f u n c t i o n o f t e m p e r a t u r e .
I n
a s c e n d i n g
o r d e r
t h e
t e m p e r a t u r e s a t
w h i c h
t h e I - V
c u r v e s
w e r e m e a s u r e d
a r e 8 . 6 K
,
2 2 . I K .
3 0 . 5 K ,
4 0 .
5 K ,
5 0 . 4 K , 6 0 .
3 K ,
6 5 .
6 K ,
7 0 . 0 K , 7 5 . 1 K ,
8 0 . 1
K .
8 2 . 2
K ,
8 5 .
I K ,
8 7 . 4 K
a n d 9 0 . O K . T h e s i m i l a r i t i e s
o f
t h e
i n c r e a s i n g
a n d
d e c r e a s i n g
c u r r e n t c u r v e s i n d i c a t e s
t h a t
n o
s i g n i f i c a n t s a m p l e h e a t i n g i s
t a k i n g
p l a c e .
F i g u r e
4 . 7 ( b )
: I n c r e a s i n g a n d d e c r e a s i n g I - V
c u r v e s
f o r
t h e
i n t e r g r a i n
r e g i o n
m e a s u r e d a s a
f u n c t i o n
o f
t e m p e r a t u r e .
M e a s u r e m e n t
t c m p e r a t u r ,
s
a r e t h e s a m e a s
f o r f i g u r e
4 . 7 ( a ) .
1 1 9
Chapter 4 : YBCO Thick Films
Figure 4.8 shows a plot of Jc versus T in zero field for the intragrain and intergrain
extracted from the I-V curves shown in figure 4.7.
Figure 4.8 : Transport Jc versus temperature in zero field for a thick film
sample. Note that in this case the intragranular Jc is lower than the
intergranular Jc
Note that for this sample the intragranular Jc is lower than the intergranular Jc.
Although this result is the reverse of what was expected in that it was assumed that the
intergrain Jc would be lower, it formed the basis of much of the explanation of the
mechanism of current flow in these thick films, as will be explained below.
Measurements on Large Necked Sample
Figure 4.9 shows the Jc versus B characteristics for the four sets of voltage contacts
applied to the large sample TF930 at 4.2K and 77K.
All contact pairs show Jc versus B characteristics which are essentially identical at
4.2K, and very similar at 77K. This indicates that the current is flowing along the best
current path through the 'neck' rather than through the neck as a whole, and that this path is
120
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
e i t h e r
s u f f i c i e n t l y
m e a n d e r i n g
o r s u f f i c i e n t l y
f a r
f r o m a l l t h e
v o l t a g e
c o n t a c t s
i n p a i r s
1 t o
3
t h a t t h e y
a l l d e t e c t t h e
s a m e v o l t a g e d r o p r e g a r d l e s s
o f
p o s i t i o n .
F i g u r e
4 . 9 :
J c
v e r s u s B c h a r a c t e r i s t i c s
f o r
a l l c o n t a c t
p a i r s
o n s a m p l e
T F 9 3 0
a t 4 . 2 K a n d 7 7 K . N o t e t h e
s i m i l a r i t y
b e t w e e n t h e
f o u r
s e t s
o f
m e a s u r e m e n t s a t e a c h
t e m p e r a t u r e . T h e i n c r e a s e d
n o i s e i n t h e
7 7 K
m e a s u r e m e n t s i s
d u e t o t h e m u c h l o w e r
s a m p l e
c u r r e n t s u s e d a t t h i s
t e m p e r a t u r e .
M e a s u r e m e n t s o n B a r - S h a p e d S a m p l e s
F i g u r e 4 . 1 0 s h o w s t h e
r a n g e
o f t r a n s p o r t
J c
v e r s u s B
c h a r a c t e r i s t i c s a t 4 . 2 K i n
t h e
l o w
f i e l d r e g i m e f o r a l l t h e s a m p l e s
m e a s u r e d ,
a s s u m i n g t h a t c u r r e n t
f l o w s u n i f o r m l y o v e r
t h e e n t i r e w i d t h o f
t h e
s p e c i m e n
( s e e b e l o w ) .
A l t h o u g h b o t h i n t r a -
a n d i n t e r - g r a i n
s a m p l e s s h o w a s i m i l a r g e n e r a l
f o r m
i n
t h e
v a r i a t i o n o f
J c
w i t h B , t h e r e
i s w i d e v a r i a t i o n i n
t h e a c t u a l v a l u e o f
J c
f o r
b o t h
t y p e s
o f
g r a i n
f e a t u r e m e a s u r e d . I n
g e n e r a l
t h e i n t r a - H - S
g r a i n
J c
e x c e e d s t h a t
o f
t h e
i n t e r - H - S
g r a i n
v a l u e b y a
f a c t o r o f a t l e a s t f o u r . N o t e
t h a t t h i s
c o n t r a d i c t s t h e
r e s u l t s s h o w n i n
f i g u r e
4 . 8 .
1 2 1
0 10 20 30 40 50 60 70
B(mT)
Figure 4.10 : A plot showing the range of intra- and inter-H-S grain
transport Jcs measured for applied magnetic fields of up to 70mT at 4.2K.
The insert shows the orientation of the applied field with respect to the
transport current. Note the logarithmic y-axis.
Figure 4.11 shows the variation of intra- and inter-H-S Jc with B for one sample at
4.2K in fields of up to 8T in fields both perpendicular and parallel to the plane of the
sample.
As in the low-field measurements these data show a relatively rapid fall-off of Jc
with field in the low-field regime ( B < lOmT) for both inter- and intra-H-S grain
measurements. Also, there is hysteresis of Jc at fields as high as 4T for both orientations,
considerably larger than is expected from flux trapping (see section 3.1)., These
measurements are similar to those of Daumling et al. on Josephson grain boundary
junctions in high fields [4.17] which also show significant hysteresis at high fields. The
perpendicular orientation shows a larger hysteresis of Jc for both the intra- and intergrain
measurements, in agreement with the low field results and measurements on sintered
YBCO (see chapter 3).
Significantly, these samples show a small but finite inter H-S grain transport Jc
measured from the I-V characteristic in applied fields as high as 8T. Figure 4.12 shows
122
S a m p l e
V o l t a g e
( i i V )
J c
( A c m
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
i n t r a - a n d
i n t e r g r a n u l a r
I - V
c u r v e s
a t 4 . 2 K
a n d
8 T w i t h t h e
f i e l d
p e r p e n d i c u l a r
t o t h e
p l a n e
o f
t h e
s a m p l e .
B o t h c l e a r l y
s h o w
s u p e r c o n d u c t i n g
t r a n s i t i o n s .
F i g u r e
4 . 1 1
:
J c - B
c u r v e s
f o r a p p l i e d
f i e l d s o f u p
t o
8 T
a t
4 . 2 K .
( a )
d a t a
o v e r t h e e n t i r e
f i e l d r a n g e
f o r
i n c r e a s i n g
a n d
d e c r e a s i n g f i e l d ,
w i t h
B - L c u r r e n t - L p l a n e
o f
s a m p l e ,
( b )
a
m a g n i f i e d
v i e w
o f
t h e
l o w - f i e l d
r e g i o n
f o r
B
i n c r e a s i n g
o n l y ,
( c )
s h o w s
a s i t u a t i o n a s i n
( a ) ,
b u t
w i t h
B l . c u r r e n t / / p l a n e o f
s a m p l e .
S o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g
f i e l d ,
o p e n
s y m b o l s
i n d i c a t e
d e c r e a s i n g
f i e l d .
F i g u r e
4 . 1 2 : I - V c u r v e s
f o r
Y B C O t h i c k
f i l m
a t
4 . 2 K
a n d
8 T
w i t h
B ± c u r r e n t - L p l a n e
o f s a m p l e f o r
( a )
i n t r a g r a i n
a n d
( b )
i n t e r g r a i n .
T h e l i n e s
a r e
g u i d e s
f o r
t h e
e y e .
N o t e t h e c l e a r
s u p e r c o n d u c t i n g
t r a n s i t i o n s .
1 2 3
Chapter 4 : YBCO Thick Films
The fact that there is still a measurable supercurrent at such high fields indicates that
there are still a small number of strong superconducting pathways in this regime. From this
it can be deduced that the only factor limiting the carrying of high currents at high fields in
these films is the need to optimise the processing conditions so that the whole sample is as
strongly linked as the pathways producing the above /-Vcurves.
4.3.2 MAGNETIC MEASUREMENTS
Magnetisation Jr
Figure 4.13 shows the magnetisation Jc as a function of B for the four samples of
different sizes which were measured.
Figure 4.13 : Magnetisation Jc as a function of applied field,and sample size
for square thick film samples.
It can be seen that Jc does not scale linearly with sample size. There is a distinct
jump in Jc between that for the 1.7 x 1.7mm sample and that for the 3 x 3mm sample.
This is assumed to arise from the observed signal being dominated by the intergrains in the
large samples and by the intragrains in the small samples. This is discussed by Cardwell
et al. in [4.12],
124
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
F i g u r e 4 . 1 4
s h o w s t h e
v a r i a t i o n
o f
t h e
a s s u m e d
i n t r a -
a n d
i n t e r - H - S
J c
w i t h
B
u s i n g t h e
a b o v e a s s u m p t i o n
[ 4 . 1
1 ,
1 2 ] .
F i g u r e 4 . 1 4
: P l o t
o f
m a g n e t i s a t i o n
J c
v e r s u s
B
c u r v e s
f o r
i n t r a -
a n d
i n t e r - H - S
g r a i n s
a t 4 . 2 K .
A . C . S u s c e p t i b i l i t y
F i g u r e 4 . 1 5 s h o w s t h e
i n - p h a s e
a n d
o u t - o f - p h a s e
A C S s i g n a l s
u n d e r t h e
c o n d i t i o n s
d e s c r i b e d i n s e c t i o n
4 . 2 . 4 , a b o v e ,
f o r t h e
O . l m T ,
0 . 2 5 m T a n d 1 . 3 4 m T
d r i v e
f i e l d s
r e s p e c t i v e l y .
T h e s i g n a l
s i z e i n c r e a s e s w i t h
i n c r e a s i n g
a p p l i e d A . C .
f i e l d ,
a s
e x p e c t e d ,
a n d t h e
t r a n s i t i o n b r o a d e n s
w i t h i n c r e a s i n g
A . C . f i e l d s .
I t c a n b e s e e n f r o m f i g u r e
4 . 1 5 ( a )
t h a t t h e
s a m p l e s h o w s
a
t r a n s i t i o n
w i d t h o f
a p p r o x i m a t e l y
8 K
i n
a
O . l m T
A . C .
f i e l d . E x a m i n a t i o n
o f t h e A C S
r e s u l t s
s h o u l d a l l o w t h e e x t r a c t i o n o f t h e r e s i s t i v e
T c
a s t h e
t e m p e r a t u r e a t
w h i c h t h e i n - p h a s e s i g n a l
i s
- 1 7 %
o f
i t s l o w - t e m p e r a t u r e
v a l u e ,
i . e . w h e n 1 7 %
o f t h e
s a m p l e i s s u p e r c o n d u c t i n g . T h i s
c o r r e s p o n d s
t o t h e f o r m a t i o n o f t h e
f i r s t c o n t i n u o u s
s u p e r c o n d u c t i n g
p a t h
t h r o u g h t h e
s a m p l e
[ 4 . 1 8 ] .
T h i s c a n
o n l y
b e d o n e
f o r t h e O . l m T
r e s u l t s
a s t h e
0 . 2 5 m T
a n d
1 . 3 4 m T
r e s u l t s
o n l y e x t e n d d o w n t o 5 0 K .
F r o m f i g u r e
4 . 1 4 ( a )
t h e
t e m p e r a t u r e a t w h i c h t h e
s i g n a l
i s 1 7 %
o f i t s l o w t e m p e r a t u r e
v a l u e
i s 8 9 . 7 K .
T h i s
1 2 5
Chapter 4 : YBCO Thick Films
compares to the value of Tc(R-0) extracted from the inset of figure 4.6 of 86.4K. This
implies that in this case somewhat more than 17% of the sample had to become
superconducting before a continuous superconducting path through the sample was
established. The data from the inset of figure 4.6 is used as this is from a sample which has
not had contacts annealed on it and is thus a closer match to the sample measured by ACS.
Figure 4.15 : ACS measurement on YBCO thick film using a frequency of
333Hz with the A.C. field, parallel to the plane of the sample, aD.C. applied
field of zero, and a IK per minute heating rate at an A.C. drive field of
(a) O.lmT, (b) 0.25mT and (c) 1.34mT. Solid symbols indicate the
in-phase signal while open symbols indicate the out-of-phase signal.
4.3.3 ELECTRON MICROSCOPY
Figure 4.16 shows four micrographs. Figure 4.16(a) shows a hub region with
spokes radiating out from it. Figure 4.16(b) shows several radial spokes away from a hub.
Examination of the films revealed that inter-H-S grain region could actually be subdivided
into two sub-types, shown in figures 4.16(c) and 4.16(d). Figure 4.16(c) shows a 'clean'
boundary between two H-S grains while figure 4.16(d) shows an 'amorphous' boundary
between two H-S grains.
126
C h a p t e r 4 :
Y B C O T h i c k
F i l m s
F i g u r e
4 . 1 6 ( a )
:
E l e c t r o n
m i c r o g r a p h o f
a
h u b
r e g i o n
( o n
t h e l e f t
o f t h e
m i c r o g r a p h
)
w i t h s p o k e s r a d i a t i n g o u t
f r o m i t .
F i g u r e
4 . 1 6 ( b )
:
E l e c t r o n m i c r o g r a p h o f
s e v e r a l r a d i a l
s p o k e s
a w a y
f r o m
a
h u b d i s p l a y i n g
t h e a l t e r n a t i n g
c - a x i s
o r i e n t a t i o n b e t w e e n a d j a c e n t s p o k e s .
1 2 7
Chapter 4 : YBCO Thick Films
601]: 26KU m) i[00Hm IJD26
Figure 4.16(c) : Electron micrograph of a 'clean' boundary between two
H-S grains.
Figure 4.16(d) : Electron micrograph of an ’amorphous' inter-H-S grain
boundary.
128
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
F i g u r e s
4 . 1 6 ( a )
a n d
4 . 1 6 ( b )
s h o w t h a t e a c h
' s p o k e '
i s
a c t u a l l y
m a d e u p
o f a
l a r g e
n u m b e r o f s m a l l g r a i n s
o r p l a t e l e t s , w h i c h
i n e a c h s p o k e
a p p e a r
t o b e
a l i g n e d
w i t h
t h e
c - a x i s
a l t e r n a t e l y
p a r a l l e l
a n d p e r p e n d i c u l a r t o
t h e p l a n e o f t h e
s u b s t r a t e .
F i g u r e
4 . 1 6 ( d )
s h o w t h a t t h e
' a m o r p h o u s ' i n t e r - H - S g r a i n
r e g i o n
a p p e a r s
t o
b e
m a d e
u p
o f a
m a s s o f s m a l l
( <
l O j a m l e n g t h )
c r y s t a l s . T h e s e a r e
f o r m e d o f
Y 2 B a C u C > 5
a n d
h a v e b e e n s e e n b e f o r e
i n
f i l m s
o f t h i s
k i n d
b y D a y
e t
a l .
[ 4 . 4 ] ,
T h e s m a l l
s i z e o f
t h e s e
c r y s t a l s i m p l i e s r a p i d c r y s t a l l i s a t i o n
i n
t h i s r e g i o n , p o s s i b l y c a u s e d
b y
t h e
g r o w i n g
Y B C O
g r a i n s
p u s h i n g
e x c e s s
m a t e r i a l
( a b o v e
t h a t n e e d e d
f o r s t o i c h i o m e t r i c
g r o w t h )
a h e a d o f t h e
g r o w t h f r o n t
u n t i l t h e t w o g r a i n s m e e t . T h e g r a i n o n t h e l e f t
a l s o s h o w s
d i s t i n c t
s t e p s o n
i t s
s u r f a c e .
T h e
r e a s o n s
w h y
s o m e
i n t e r - H - S g r a i n
r e g i o n s
s h o w
t h i s ' a m o r p h o u s '
s t r u c t u r e
w h i l e o t h e r s
a r e
' c l e a n ' ,
a s s h o w n
i n f i g u r e
4 . 1 6 ( c ) ,
i s
u n c l e a r ,
b u t m a y
i n v o l v e
v a r i a t i o n s
i n
t h e
s t a r t i n g
c o m p o s i t i o n
o f t h e
f i l m i n
d i f f e r e n t
a r e a s a c r o s s i t s
s u r f a c e s i m i l a r
t o t h o s e
w h i c h m a y c a u s e t h e i n i t i a l s p h e r u l i t i c
g r a i n g r o w t h .
4 . 3 . 4 C O M P A R I S O N
O F T R A N S P O R T A N D
M A G N E T I C
M E A S U R E M E N T S
C o m p a r i n g t h e t r a n s p o r t
m e a s u r e m e n t s
( f i g u r e
4 . 1 0 )
w i t h c o r r e s p o n d i n g
m a g n e t i c
m e a s u r e m e n t s ( f i g u r e
4 . 1 4 )
i t c a n b e s e e n
t h a t i n a l l c a s e s
t h e
i n t r a - a n d
i n t e r - H - S g r a i n
m a g n e t i s a t i o n
J c
s a r e
a t
l e a s t a n
o r d e r o f m a g n i t u d e h i g h e r t h a n t h e
c o r r e s p o n d i n g
t r a n s p o r t
J c s .
F i g u r e
4 . 1 0 s h o w s
t h a t
t h e r e
i s a
s i g n i f i c a n t
s p r e a d
i n t h e r a n g e
o f i n t r a - H - S g r a i n
c r i t i c a l c u r r e n t s o b s e r v e d . A
v e r y s m a l l n u m b e r
o f
i n t r a g r a i n
s a m p l e s , s u c h a s
t h o s e s h o w n
i n
f i g u r e
4 . 8 ,
a c t u a l l y e x h i b i t l o w e r
J c s
t h a n
t h e i r
i n t e r - g r a i n
c o u n t e r p a r t s . U p o n
e x a m i n a t i o n
o f t h e s e s a m p l e s
i t
w a s o b s e r v e d
t h a t t h e c e n t r e
o f t h e H - S g r a i n h a d
b e e n
r e m o v e d f r o m t h e
s a m p l e
d u r i n g t h e c u t t i n g p r o c e s s ,
l e a v i n g o n l y
a n
a r r a y
o f r a d i a l g r a i n s
( s p o k e s )
a c r o s s t h e w i d t h o f t h e
s a m p l e . T h i s
s u g g e s t s
t h a t
t h e
t r a n s p o r t c u r r e n t m u s t f l o w
a l o n g
r a d i a l
p a t h s t h r o u g h t h e c e n t r a l h u b o f e a c h g r a i n f o r a H - S g r a i n
t o
d i s p l a y a
h i g h
t r a n s p o r t
J c .
4 . 3 . 5 C O R R E L A T I O N O F R E S U L T S A N D
M I C R O S T R U C T U R E
-
H U B
A N D
S P O K E
M O D E L
T h e s u g g e s t i o n g i v e n
a b o v e i s
s u p p o r t e d
b y t h e
e l e c t r o n
m i c r o g r a p h s s h o w n i n
f i g u r e s
4 . 1 6 ( a )
a n d
4 . 1 6 ( b ) .
T h e s e i m p l y
t h a t f o r c u r r e n t t o
f l o w b e t w e e n
s p o k e s i t
m u s t
c r o s s f r o m
r e g i o n s
w i t h t h e
c - a x i s p a r a l l e l
t o t h e
f i l m s u r f a c e i n t o r e g i o n s
w h e r e i t i s
p e r p e n d i c u l a r
t o t h e
f i l m s u r f a c e .
C u r r e n t f l o w
a l o n g
t h e s p o k e s ,
h o w e v e r ,
a l w a y s
o c c u r s
1 2 9
Chapter 4 : YBCO Thick Films
parallel to the a-b plane, and so will be the preferred route. These observations together
form the basis of the Hub and Spoke (H-S) model. The basic premise of this model is that
current flow in these thick films is not distributed evenly over the entire cross-section of the
film, but instead occurs via a meandering route along the spokes and through the hubs of
the H-S grains as shown schematically in figure 4.17.
Figure 4.17 : Schematic diagram, of a thick film sample showing current
being 'focused' through H-S grain hubs.
The size of the grain centre (or hub) was measured for all intra-H-S grain samples
using optical microscopy and found to be ~47fim. This was then used as the definitive
dimension in deriving the intra-grain transport Jc, rather than the width of the sample as a
whole, enhancing Jc by a factor of ~21 for a 1mm wide sample. This gives values of
intra-grain transport Jc of ~105Acnr2 at OmT and 2 X 104 Acm'2 at 70mT. At low applied
fields these values agree much more closely with the values of Jc obtained from magnetic
measurements, indicating that at these fields the dimensions of the hub determine critically
the local value of Jc. However, at high applied fields, the measured values of transport Jc
remain much lower than those of the magnetisation Jc.
4.3.6 TESTING THE HUB AND SPOKE MODEL
An experiment was devised to test the hypothesis that the presence of the hub is
necessary in order for there to be a high Jc current path through the grain. If this is so then
its removal should depress Jc severely. If not then there should be no significant change in
Jc after the change in film cross-section is considered.
130
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
S e v e r a l m e t h o d s o f
r e m o v i n g
t h e h u b s o f
g r a i n s
w e r e i n v e s t i g a t e d ,
i n c l u d i n g
m e c h a n i c a l d r i l l i n g w i t h
s e v e r a l
t y p e s
o f b i t a n d
s c r a p i n g w i t h a
s c a l p e l
b l a d e . F i n a l l y ,
u l t r a s o n i c
d r i l l i n g
w i t h a
w a t e r - b a s e d p a s t e a b r a s i v e
p r o v e d
t h e
m o s t
p r a c t i c a l a n d
e f f i c i e n t
t e c h n i q u e . T w o
s a m p l e s
h a d t h e i r
h u b s r e m o v e d
c o m p l e t e l y b y
t h i s
m e t h o d .
A c o n t r o l
s a m p l e w a s
p r e p a r e d f o r t h e
d r i l l i n g
p r o c e s s
i n e x a c t l y t h e s a m e
w a y a s
t h e s e
s p e c i m e n s
a l t h o u g h t h e h u b o f t h e g r a i n t o
b e m e a s u r e d w a s n o t a c t u a l l y
r e m o v e d . T h i s
s p e c i m e n
a l l o w e d p r o c e s s - d e p e n d e n t
e f f e c t s ,
s u c h a s
a n y
r e a c t i o n b e t w e e n
t h e
w a t e r - b a s e d
a b r a s i v e
p a s t e
a n d t h e s a m p l e
s u r f a c e ,
t o b e t a k e n i n t o a c c o u n t w h e n
i n t e r p r e t i n g t h e
c r i t i c a l
c u r r e n t
m e a s u r e m e n t s .
T h e t h r e e
s a m p l e s
w e r e m e a s u r e d b e f o r e
a n d a f t e r t h e
d r i l l i n g
p r o c e s s a t
4 . 2 K
i n
f i e l d s
o f
u p
t o 7 0 m T .
F i g u r e
4 . 1 8 s h o w s
t h e r e s u l t s o n t h e
s a m p l e s
i n
w h i c h
t h e
h u b s w e r e
r e m o v e d ,
w h i l e
f i g u r e 4 .
1 9 s h o w s
t h e r e s u l t s f r o m t h e c o n t r o l s a m p l e .
F i g u r e
4 . 1 8 : T r a n s p o r t .
J c
v e r s u s
B
c h a r a c t e r i s t i c s
a t 4 . 2 K
f o r
t w o
i n t r a - H - S
g r a i n s
b e f o r e a n d
a f t e r d r i l l i n g
o u t
o f
t h e
h u b
r e g i o n .
T h t
o p
,
a n d
f i l l e d
d a t a p o i n t s r e p r e s e n t m e a s u r e m e n t s o n
t h e
t w o
d i f f e r e n t
s a m p l e s .
T h e l i n e s a r e
g u i d e s f o r
t h e
e y e ;
t h e s t e p s
i n
t h e m
a r e a r t e f a c t s
o f t h e f i t t i n g
p r o g r a m u s e d .
1 3 1
Chapter 4 : YBCO Thick Films
Figure 4.19 : Transport Jc versus B characteristic at 4.2K for undrilled
control sample before and after preparation for the drilling process.
It can be seen that all three samples show some reduction in Jc. For the control
sample this reduction is by approximately one order of magnitude. In the case of the two
samples which had their hubs removed, however, the Jc is reduced by approximately three
orders of magnitude. The data from both drilled samples are in excellent agreement with no
statistically significant difference between them (note that the Jc data presented in
figures 4.18 and 4.19 were calculated assuming the hub size as the critical dimension).
Also, the variation of Jc with B between the drilled and undrilled samples is different. In
the undrilled sample the zero-field Jc is almost the same before and after the treatment, but
falls to a lower value as the applied field is increased as shown in figure 4.19. In the drilled
samples, however, the Jc versus B curve has a similar form before and after the drilling
process, but in the latter has been depressed by approximately three orders of magnitude
for all values of field. These measurements support the earlier hypothesis that the centre of
the H-S grain determines critically the Jc of these specimens.
4.3.7 IMPLICATIONS OF THE HUB AND SPOKE MODEL
The apparent constraint of the current flow through the H-S grain hub has
implications for the measured magnitude of the intergrain critical current. It can be seen
from figure 4.17 that the passage of current between H-S grains will not be uniform across
132
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
t h e e n t i r e H - S g r a i n b o u n d a r y .
F o r
e x a m p l e ,
t h e
c u r r e n t
c a r r y i n g
s p o k e s
o n t h e
h u b t o
h u b
a x i s b e t w e e n a d j a c e n t
g r a i n s
w i l l
d e f i n e a l o w e r - a n g l e g r a i n
b o u n d a r y t h a n
t h o s e
o f f t h i s
a x i s
a n d ,
t h e r e f o r e ,
a r e l i k e l y
t o e x h i b i t
a
g r e a t e r
J c
[ 4 . 1 9 ] .
H e n c e t h e
a c t u a l
i n t e r g r a i n
J c
i s
l i k e l y
t o b e c o n s i d e r a b l y
g r e a t e r t h a n t h a t
c a l c u l a t e d h e r e
u s i n g
t h e e n t i r e
w i d t h o f t h e
s a m p l e a s t h e c r i t i c a l
d i m e n s i o n .
H o w e v e r ,
u n l i k e t h e
s i z e o f t h e
h u b ,
t h e
s i z e o f t h e
i n t e r g r a i n c u r r e n t - c a r r y i n g r e g i o n
i s v e r y d i f f i c u l t
t o q u a n t i f y
a n d h a s
n o t b e e n
i n c l u d e d
i n
t h i s s t u d y .
T h e
r e p o r t e d
i n t e r
H - S g r a i n
J c s ,
t h e r e f o r e ,
r e p r e s e n t l o w e r
e s t i m a t e s o f
t h i s
p a r a m e t e r .
T h i s d i s t r i b u t i o n o f c u r r e n t i n a
s a m p l e i s
i n a g r e e m e n t w i t h
t h e
w o r k
o f
A s k e w
e t a l .
o n
p o l y c r y s t a l l i n e
Y B C O
[ 4 . 2 0 ]
w h o
a l s o
c o n c l u d e
t h a t c u r r e n t
f l o w
t h r o u g h
t h e i r
s a m p l e s
f o r m s a d i s t r i b u t i o n g o v e r n e d b y t h e a r r a n g e m e n t
a n d
t y p e o f
c u r r e n t p a t h s
t h r o u g h t h e s a m p l e .
E x a m i n a t i o n
o f I - V
C u r v e s
F u r t h e r i n s p e c t i o n
o f t h e I - V
c h a r a c t e r i s t i c s
f o r b o t h
i n t e r - H - S a n d
i n t r a - H - S
g r a i n
r e g i o n s r e v e a l s t h e
p r e s e n c e
o f
u p
t o t h r e e d i s t i n c t l i n e a r
r e g i o n s
a s s h o w n i n f i g u r e
4 . 2 0 .
T h i s f i g u r e
a l s o
s h o w s
l i n e a r f i t s t o t h e t h r e e r e g i o n s
a l l o w i n g
e x t r a c t i o n o f t h e
d i f f e r e n t
J c s
f r o m
t h e d i s c o n t i n u i t i e s
o f t h e
I - V c u r v e .
0 . 1 0 . 3
0 . 4
C u r r e n t
( A )
F i g u r e
4 . 2 0
:
T h i c k
f i l m I - V
c h a r a c t e r i s t i c
s h o w i n g
f i t s
t o t h e t h r e e l i n e a r
r e g i o n s i n d i c a t i n g t h e p r e s e n c e o f
t h r e e d i s t i n c t
v a l u e s
o f
t r a n s p o r t
J
c .
1 3 3
Chapter 4 : YBCO Thick Films
This has been observed previously in both transport measurements [4.21] and
results derived from magnetic measurements [4.11], They may be interpreted as indicating
the presence of three distinct Jcs for the H-S grain structures measured. Each linear region
appears to indicate a separate regime of ideal flux flow with a different value of flux
pinning [4.16]. This initially caused problems of interpretation, since at first sight no pair
of contacts should see more than two distinct Jcs corresponding to the inter- and intra-H-S
grain Jcs. However, magnetisation measurements suggest that some samples exhibit a
granular layer above the main bulk of the film [4.11]. This third Jc is therefore interpreted
as deriving from this layer, although it is also possible that it derives from the Jc of the
spokes themselves, indicating that they are entirely separate structures from the hubs and
the intergrains [4.22],
As the magnetic field applied to the sample increases it is found that the discrete
changes in gradient remain visible, but move to lower currents, implying that all three
components are being suppressed in the applied field by approximately the same amount.
This is supported by the similar structure which can be seen in the high-field I-V curve
shown in figure 4.12(b).
Although taking the size of the grain centre into account improves the agreement
between magnetic and transport Jcs significantly, only a qualitative comparison can be
made here due to fundamental differences in the nature of each measurement and the
degradation of the transport Jc during the sample preparation process. For example, despite
the good low-field agreement between magnetisation and transport Jcs, the decay of the
former with respect to the latter at higher fields as shown in figures 4.11 and 4.14 may be
accounted for by errors in calculating the magnetic Jc, which corresponds to an average
over the whole sample. This, by definition, puts the same current through all parts of the
sample, eliminating any sensitivity to local variations in Jc from the data. Hence the
magnetisation Jc tends to be insensitive to areas with a lower Jc since they will be
short-circuited by the induced current. The transport Jc, on the other hand, is dominated by
weak links in the current path. Hence any suppression of the weak link Jc in a transport
measurement significantly reduces the Jc of the whole sample. In addition, the transport Jc
of the samples measured is almost certainly degraded by the formation of microcracks
during the mechanical cutting process and in the heat treatment used to attach the current
and voltage leads. Although samples used for both transport and magnetisation
measurements were cut in the same way, any damage caused is likely to have more effect
on the transport measurements, as indicated above.
134
C h a p t e r 4
: Y B C O
T h i c k
F i l m s
F i n a l l y , t r u e
q u a n t i t a t i v e
c o m p a r i s o n s
c a n
o n l y
b e
m a d e
b e t w e e n
t r a n s p o r t
a n d
m a g n e t i s a t i o n
J c s
i f a
s u f f i c i e n t
n u m b e r
o f
t r a n s p o r t
m e a s u r e m e n t s
a r e
p e r f o r m e d
o n
i n d i v i d u a l g r a i n s
t o y i e l d a
s t a t i s t i c a l
s i g n i f i c a n c e
c o m p a r a b l e
w i t h t h e
u n c e r t a i n t i e s
i n t h e
m a g n e t i c
d a t a .
T h e r e f o r e ,
f o r
e x a m p l e ,
a n
e r r o r o f
1 %
w o u l d
r e q u i r e a t
l e a s t 1 0
0 0 0
t r a n s p o r t
J c s
t o b e
d e t e r m i n e d ,
a
p r o h i b i t i v e l y
t i m e - c o n s u m i n g
t a s k .
4 . 4 C O N C L U S I O N S
T h e s e e x p e r i m e n t s s h o w t h a t c u r r e n t f l o w w i t h i n
m e l t - p r o c e s s e d
Y B C O
t h i c k
f i l m s
i s n o t
a
s i m p l e
p r o c e s s . A w a y
f r o m t h e
c u r r e n t c o n t a c t s o n l y
a s m a l l
f r a c t i o n
o f t h e
f i l m
c a r r i e s t h e
e n t i r e
c u r r e n t ,
t h i s f r a c t i o n
b e i n g
d e t e r m i n e d b y t h e
a r r a n g e m e n t o f
h i g h - / c
p a t h s
t h r o u g h i t . W h e n t h e c u r r e n t
e n t e r s
t h e
s a m p l e ,
a l t h o u g h
i n i t i a l l y
d i s t r i b u t e d
a c r o s s
i t s
w h o l e
w i d t h ,
i t
b e c o m e s
' f o c u s e d ' t h r o u g h t h e
f i r s t
g r a i n
' h u b ' i t
e n c o u n t e r s ,
a n d f r o m
t h e r e c o n t i n u e s
o n l y a l o n g h i g h
J c
' s p o k e s '
t h r o u g h o t h e r
' h u b s ' u n t i l
i t
r e a c h e s t h e o t h e r
c u r r e n t
c o n t a c t .
B e c a u s e
o f t h i s t h e
t r a n s p o r t
c r i t i c a l c u r r e n t
i s
v e r y
s e n s i t i v e
t o
a n y w e a k
l i n k s
i n
t h e c u r r e n t p a t h , a n d s o d r o p s o f f f a r m o r e q u i c k l y w i t h
m a g n e t i c f i e l d
t h a n
m a g n e t i c
m e a s u r e m e n t s
o f
J c
w o u l d i n d i c a t e . T h i s c o n f i r m s t h e
o b s e r v a t i o n
t h a t t h e
w e a k e s t l i n k s
i n t h e c u r r e n t
p a t h
t h r o u g h t h e s a m p l e g o v e r n t h e
m e a s u r e d
t r a n s p o r t
J c .
T h i s
c o m p l e x
c u r r e n t f l o w m a y
a l s o e x p l a i n
w h y t h e m a g n e t i s a t i o n
d o e s
n o t
s c a l e d i r e c t l y w i t h
s a m p l e s i z e .
T h i s s t u d y h a s s h o w n t h a t a m e a s u r a b l e i n t e r - g r a i n
t r a n s p o r t c u r r e n t
f l o w s w i t h i n
t h e s a m p l e s
m e a s u r e d i n
m a g n e t i c f i e l d s
o f
8 T a t 4 . 2 K .
T h i s i s
p a r t i c u l a r l y s i g n i f i c a n t
g i v e n t h e
p o l y c r y s t a l l i n e n a t u r e o f t h e s p e c i m e n s a n d e m p h a s i s e s
t h e i r
p o t e n t i a l
f o r
o p e r a t i o n
a t
h i g h e r
t e m p e r a t u r e s
( e . g . i n
s c r e e n i n g a n d
R . F . a p p l i c a t i o n s )
i f t h e i r p r o p e r t i e s
c a n
b e o p t i m i s e d .
T h e
a s p e c t s o f t h e
f i l m m i c r o s t r u c t u r e w h i c h r e q u i r e o p t i m i s i n g
b e f o r e i n c r e a s e d
J c
s a m p l e s c a n b e
e n g i n e e r e d
h a v e b e e n i d e n t i f i e d . T h e
d i m e n s i o n o f t h e h u b h a s b e e n f o u n d
t o c r i t i c a l l y
d e t e r m i n e
t h e
o b s e r v e d
m a g n i t u d e
o f t h e t r a n s p o r t
J c
i n t h e s e m e l t - t e x t u r e d
Y B C O t h i c k
f i l m s ,
a n d i t
i s
l i k e l y t h a t c o n t r o l o v e r t h e
g r o w t h
o r i e n t a t i o n
o f t h e c r y s t a l l i t e s
w i t h i n e a c h
s p o k e
w o u l d a l s o a f f e c t
J c .
4 . 5
R E F E R E N C E S
[ 4 . 1 ]
M .
M u r a k a m i ,
S u p e r c o n d . S c i .
T e c h n o l . ,
5 ,
1 8 5
( 1 9 9 2 ) .
1 3 5
Chapter 4 : YBCO Thick Films
[4.2] K. Salama, Processing and Properties ofHigh-Tc Superconductors, Vol 1 : Bulk
Materials, 155, edited by S. Jin (World Scientific Singapore 1993)
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[4.8] W. Neuhaus, M. Damaske, A.I. Usoskin and H.C. Freyhardt in Proceedings of
7th IWCC, 647, Alpbach, Austria, 1994 (World Scientific Publishing Co.)
[4.9] G. Lofgren, J. Geophys. Res., 76, 5635 (1971).
[4.10] H.D. Keith and F.J. Padden Jr., Journal of Applied Physics, 34, 2409 (1963).
[4.11] N.J.C. Ingle, D.A. Cardwell, A.R. Jones, F. Wellhofer and T.W. Button,
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[4.12] D.A. Cardwell, A.R. Jones, N.J.C. Ingle, A.M. Campbell, T.W. Button, N.M.
Alford, F. Wellhofer and J.S. Abell, Cryogenics, 34, 671 (1994).
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(1993).
[4.14] C.P. Bean, Rev. Mod. Phys., 36, 31 (1964).
[4.15] A.R. Strnad, C.F. Hempstead and Y.B. Kim, Phys. Rev. Lett., 13, 794 (1964).
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[4.17] M. Daumling, E. Sarnelli, P. Chaudhari, A. Gupta and J. Lacey, Appl. Phys.
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136
C h a p t e r
4
:
Y B C O
T h i c k
F i l m s
[ 4 . 1 9 ]
M . B .
F i e l d ,
X . Y .
C a i ,
S . E . B a b c o c k a n d
D . C .
L a r b a l e s t i e r ,
I E E E
T r a n s a c t i o n s
o n A p p l i e d
S u p e r c o n d u c t i v i t y ,
3 ,
1 4 7 9
( 1 9 9 3 ) .
; j
[ 4 . 2 0 ]
T . R .
A s k e w ,
R . B . F l i p p e n , K . J . L e a r y
a n d M . N . K u n c h u r ,
J .
M a t e r .
R e s . ,
6 ,
1 1 3 5
( 1 9 9 1 ) .
[ 4 . 2 1 ]
J .
R i c k e t t s ,
W . F .
V i n e n ,
J . S . A b e l l a n d T . C .
S h i e l d s ,
P h y s i c a
C ,
1 8 5 - 1 8 9 ,
2 5 2 1
( 1 9 9 1 ) .
[ 4 . 2 2 ]
C . D . D e w h u r s t
( 1 9 9 4 ) ,
P e r s o n a l
C o m m u n i c a t i o n
1 3 7
C h a p t e r
5
:
T h a l l i u m
T a p e s
C H A P T E R 5
:
M E A S U R E M E N T S
O N
T H A L L I U M - B A S E D
S U P E R C O N D U C T I N G
T A P E S
5 . 7
I N T R O D U C T I O N
S i n c e t h e i r d i s c o v e r y b y
S h e n g
a n d H e r m a n
i n 1 9 8 8
[ 5 . 1 ] ,
a
n u m b e r
o f
t h a l l i u m - b a s e d h i g h
t e m p e r a t u r e
s u p e r c o n d u c t o r s h a v e
b e e n
d i s c o v e r e d [ 5 . 2 - 5 ] ,
A
n u m b e r
o f t h e i r p r o p e r t i e s g i v e
t h e s e c o m p o u n d s a w i d e
r a n g e o f
p o t e n t i a l
a p p l i c a t i o n s
a t
7 7 K . T h e
f i r s t
o f
t h e s e i s t h e i r h i g h
T c s
( 1 1 0 K
i n ( T l , P b ) S r 2 C a 2 C u 3 0 9 ( T l : 1 2 2 3 )
a n d
1 2 5 K
i n
T l 2 B a 2 C a 2 C u 3 0 i o
( T l : 2 2 2 3 ) ) ,
a m o n g t h e h i g h e s t
k n o w n . S e c o n d l y ,
t h e
T l : 1 2 2 3
c o m p o u n d
h a s
a
h i g h
i r r e v e r s i b i l i t y
l i n e
[ 5 . 6 ] ,
c o n s i d e r a b l y
a b o v e t h a t f o r
Y B C O a n d
T l : 2 2 2 3 .
T h i s
a r i s e s f r o m t h e h i g h e r
T c
o f T l : 1 2 2 3 s o t h a t
i f p l o t t e d a g a i n s t
T /
T c
t h e
i r r e v e r s i b i l i t y l i n e o f T l : 1 2 2 3 f a l l s
b e l o w
t h a t
o f
Y B C O
[ 5 . 7 ] ,
t h o u g h
a b o v e
t h a t o f
T l : 2 2 2 3
[ 5 . 6 ] .
T l : 1 2 2 3
a l s o h a s
t h e s t r o n g e s t f l u x p i n n i n g o f t h e
t h a l l i u m - b a s e d
h i g h - T c
s u p e r c o n d u c t o r s
[ 5 . 8 ] ,
w h i l e t h a t o f
T l : 2 2 2 3 i s l o w
a t
h i g h
t e m p e r a t u r e s
[ 5 . 9 ] .
T h e s e
f a c t o r s
m e a n t h a t t h e r e
i s
a s i g n i f i c a n t h i g h f i e l d a n d t e m p e r a t u r e r e g i m e
i n w h i c h T l : 1 2 2 3
c a n c o m p e t e w i t h
Y B C O a n d
s u r p a s s
T l : 2 2 2 3
[ 5 . 1 0 ] .
A l s o ,
T l : 1 2 2 3
i s c o n s i d e r a b l y
m o r e
t h r e e
d i m e n s i o n a l t h a n
m a n y o f
t h e o t h e r h i g h - T c c o m p o u n d s d u e t o
i t s s i n g l e C u O
l a y e r
( s e e
s e c t i o n 1 . 8 . 4 a n d
f i g u r e
1 . 1 1 ) .
T h i s g i v e s
r i s e
t o r e l a t i v e l y
s t r o n g
c o u p l i n g b e t w e e n
t h e C u O l a y e r s
[ 5 . 8 ,
1 1 ] ,
r e d u c i n g a n i s o t r o p y a n d g i v i n g
c o n s i d e r a b l y
b e t t e r
c - a x i s
t r a n s p o r t b e h a v i o u r c o m p a r e d
t o
t h e B S C C O
c o m p o u n d s a n d o t h e r
t h a l l i u m -
b a s e d
c o m p o u n d s
[ 5 . 1 2 ] ,
T h i s
a l s o
g i v e s
T l : 1 2 2 3
g r a i n s w i t h a
s p h e r o i d a l
m o r p h o l o g y r a t h e r
t h a n t h e p l a t e - l i k e
m o r p h o l o g y
o f
m a n y
o f t h e o t h e r
H T S C s ,
i m p l y i n g
t h a t
t h e r e m a y b e
p r o b l e m s w i t h a l i g n m e n t a n d g r a n u l a r i t y .
S e v e r a l g r o u p s h a v e p u b l i s h e d
r e s u l t s
o n t h e
t h a l l i u m - b a s e d
s y s t e m ,
i n c l u d i n g b o t h
t r a n s p o r t
a n d m a g n e t i c
m e a s u r e m e n t s o f
J c
i n
T l : 1 2 2 3 . T h e s e
g i v e
t r a n s p o r t
J c
v a l u e s
o f
u p
t o ~ 1 0 5 A c r c r 2 a t
4 . 2 K a n d 8 T [ 5 . 1 1 , 1 3 ,
1 4 ]
a n d o f u p t o
~ 3 0 0 0 A c n r 2 a t
7 7 K
a n d
I T
[ 5 . 1 5 ]
i n
e p i t a x i a l t h i n f i l m s o f
T l : 1 2 2 3 .
M a g n e t i s a t i o n
J c s
a r e
c o n s i d e r a b l y h i g h e r ,
~ 1 0 6 A c n r 2 a t 4 . 2 K a n d 1 0 T
[ 5 . 1 2 ,
1 6 ]
a n d ~ 3 0 0 A c n r 2 a t
7 7 K
a n d
1 0 T
[ 5 . 1 2 ]
i n b u l k
T l : 1 2 2 3 . X - r a y
m e a s u r e m e n t s o n T l : 1 2 2 3
h a v e f o u n d t h a t t h e h i g h - c u r r e n t
c o n d u c t i o n
p a t h s t h r o u g h i t
m a y n o t b e v i a
w e l l - a l i g n e d
g r a i n
b o u n d a r i e s ,
b u t
i n s t e a d o c c u r
t h r o u g h
t h e m o r e c o m m o n l o w - a n g l e g r a i n
b o u n d a r i e s
[ 5 . 1 7 ] ,
i m p l y i n g
t h a t p e r f e c t g r a i n a l i g n m e n t
i s n o t
n e c e s s a r y f o r a h i g h
J c
i n t h i s m a t e r i a l .
T h i s ,
c o m b i n e d w i t h t h e
s h o r t e r p r o c e s s i n g
t i m e s
f o r
T l : 1 2 2 3
c o m p a r e d t o Y B C O o r B S C C O
[ 5 . 1 8 ]
m a k e s
T l : 1 2 2 3
a t t r a c t i v e f r o m a
p r o c e s s i n g
p o i n t o f v i e w .
A l l
t h e s e f e a t u r e s
m a k e
T l : 1 2 2 3 w e l l s u i t e d
f o r p r a c t i c a l
a p p l i c a t i o n s [ 5 . 8 ] ,
H o w e v e r ,
t e c h n i q u e s a l l o w i n g
t h e s e
c o m p o u n d s t o b e
p r o c e s s e d
o n a
1 3 8
Chapter 5 : Thallium Tapes
large scale into forms which can carry high currents in high magnetic fields must be
developed before they can find wide-scale use. Also, the toxicity of the thallium
compounds requires that methods to process them safely must be developed, and has
undoubtedly deterred many researchers from working on them and industrial concerns
from funding such research.
This chapter describes experiments carried out on silver- and gold-palladium-clad
tapes of Tl:1223 and Tl:2223 as part of a collaboration with the Hitachi corporation. For the
purpose of this thesis these tapes were measured because they provide examples of a
granular material whose properties have been improved by processing.
Several tapes from three separate batches were measured during these experiments,
in a variety of magnetic field and temperature regimes. In addition to measuring transport Jc
as a function of orientation, temperature and magnetic field, the samples were sufficiently
long that a number of voltage contacts could be placed along their length in a controlled
manner. This allowed the variation of Jc with position along the tape to be quantitatively
measured and thus allows an estimate of sample homogeneity to be made. Measurements of
Jc spaced over a period of 800 hours were carried out to determine any possible
degradation of Jc with time.
Once the transport measurements were completed the tapes were cut into sections
and magnetic measurements carried out. The transport and magnetic measurements were
then combined in an attempt to produce a coherent picture of the behaviour of these tapes.
5.1.1 TAPE FABRICATION
All tapes used in these experiments were fabricated by the Hitachi corporation using
the method of Aihara et al. described in [5.19], This used a powder in tube (PIT) technique
where superconducting powder was placed inside a metal tube which was then drawn into
thin wires, cold-rolled into 3mm wide x 0.3mm thick tapes, then annealed in order to sinter
the grains together and heal microcracks caused by the tape processing.
Two types of tapes were made. The first, on which most measurements were
carried out, were sheathed in 99.99% purity silver. The second type of tape had a sheath of
95(atomic)% gold and 5(atomic)% palladium.
139
C h a p t e r
5 :
T h a l l i u m T a p e s
5 . 2
E X P E R I M E N T A L T E C H N I Q U E
5 . 2 . 1
T R A N S P O R T M E A S U R E M E N T S
A l l t r a n s p o r t
J c
m e a s u r e m e n t s
w e r e c a r r i e d o u t
w i t h
t h e
t a p e
i m m e r s e d
i n
a
l i q u i d
c r y o g e n ,
e i t h e r n i t r o g e n
o r h e l i u m .
T o m a x i m i s e t h e h e a t
t r a n s f e r t o
t h e
c r y o g e n
t h e
t a p e s
w e r e m o u n t e d w i t h a s m u c h
o f t h e i r
s u r f a c e a s p o s s i b l e
i n
c o n t a c t
w i t h i t
( s e e
s e c t i o n
2 . 3 . 1 ) .
T h i s i s e s p e c i a l l y
a d v a n t a g e o u s f o r
t r a n s p o r t
J c
m e a s u r e m e n t s b e c a u s e
o f
p o s s i b l e
h e a t i n g w h i c h
c a n o c c u r a t t h e
s a m p l e c u r r e n t
c o n t a c t s .
T h e
t a p e
s a m p l e s w e r e
s u p p o r t e d
a w a y f r o m t h e
s a m p l e
h o l d e r
b y t h e i r
c u r r e n t
l e a d s ,
e a c h o f w h i c h w a s
a
l o o p
o f w i r e
w i t h t h e e n d f l a t t e n e d a n d
b e n t
i n t o a T J '
s h a p e , a s
s h o w n i n
f i g u r e
2 . 6 .
V o l t a g e
c o n t a c t s t o
t h e
s a m p l e s u s e d
2 5 | i m
g o l d
w i r e s w r a p p e d
a r o u n d t h e
t a p e
a n d a t t a c h e d w i t h
r o o m - t e m p e r a t u r e d r y i n g s i l v e r
p a i n t ,
f o r m i n g
c o n t a c t s
~ 0 . 5 m m w i d e . F o r
t h e l o n g
s a m p l e s m u l t i p l e v o l t a g e
l e a d s
w e r e u s e d ,
s p a c e d
1 0 m m
a p a r t .
T h e s i z e o f t h e s e s a m p l e s , 1 0 0 m m
x
3 m m
x
0 . 1 m m ,
a l l o w e d
e i g h t
v o l t a g e
l e a d s t o
b e
a t t a c h e d ,
g i v i n g t h e
c a p a b i l i t y t o
i n d e p e n d e n t l y
m e a s u r e s e v e n
s e c t i o n s o f t h e
t a p e
( s e e
f i g u r e
2 . 6 ) .
A l l
e x p e r i m e n t s
a t
7 7 K w e r e c a r r i e d o u t i n a l i q u i d n i t r o g e n
b a t h .
T h e f i r s t s e t o f
m e a s u r e m e n t s u s e d
a c o p p e r
c o i l ,
a l s o
i m m e r s e d i n l i q u i d n i t r o g e n ,
t o
g e n e r a t e
l o w
m a g n e t i c f i e l d s .
B e c a u s e
o f t h e
s m a l l s i z e o f t h i s c o i l a n d
l i m i t a t i o n s
o f
f i e l d
h o m o g e n e i t y
e x p e r i m e n t s c o u l d
o n l y
b e
p e r f o r m e d
i n
t w o
o r i e n t a t i o n s
( f i e l d ± w i d t h _ L c u r r e n t ,
f i e l d / / w i d t h J _ c u r r e n t ) .
T h r e e
s e t s o f m e a s u r e m e n t s w e r e c a r r i e d
o u t : z e r o
f i e l d c o o l e d
( Z F C )
i n i n c r e a s i n g a n d d e c r e a s i n g f i e l d ,
a n d
f i e l d - c o o l e d
( F C ) .
S u b s e q u e n t m o d i f i c a t i o n
o f t h e a p p a r a t u s a l l o w e d
t h e
t a p e s t o b e
m e a s u r e d a t 7 7 K
b e t w e e n t h e p o l e s o f a
w a t e r - c o o l e d
e l e c t r o m a g n e t i n
a n y
o n e
o f
t h r e e
o r i e n t a t i o n s
( f i e l d _ L w i d t h _ L c u r r e n t ,
f i e l d / / w i d t h _ L c u r r e n t
a n d
f i e l d / / l e n g t h / / c u r r e n t ) .
F i g u r e
5 . 2
s h o w s
s c h e m a t i c d i a g r a m s
o f
t h e
t h r e e
o r i e n t a t i o n s i n
w h i c h m e a s u r e m e n t s w e r e
c a r r i e d o u t .
B
F i g u r e
5 . 2 : T h e t h r e e
o r i e n t a t i o n s
u s e d i n t h e
m e a s u r e m e n t
o f
t r a n s p o r t
J c .
(
i
)
f i e l d h w i d t h d - c u r r e n t ,
(
i i )
f i e l d / A v i d t h - L c u r r e n t ,
(
i i i
)
f i
e I d / A e n g
t h / / c u
r r e n
t .
1 4 0
Chapter 5 : Thallium Tapes
High-field measurements at 77K were earned out in the variable-temperature insert
(VTI) of an Oxford Instruments 8T superconducting magnet system, using a second insert
which was filled with liquid nitrogen. This limited the possible sample orientations to
fieldTwidthJLcurrent and field//width_Lcurrent.
High field measurements at 4.2K were made in the same VTI filled with liquid
helium pumped from the main magnet bath. It was critical to have the sample immersed
when measuring at this temperature due to the lower thermal capacity of liquid helium (see
section 2.3.1). Again, the available sample orientations were limited to
fieldTwidth_Lcurrent and field//widthJxurrent.
Measurements of zero-field Jc spaced over a period of approximately 800 hours
were carried out on one tape to determine whether any degradation was occurring with
time. These were carried out concurrently with the experiments mentioned above, so that
the sample was warmed and cooled a number of times between measurements, and also
stored at room temperature.
Initial measurements were carried out using the manual D.C. system described in
the first part of section 2.3.3. Later measurements used the computer controlled D.C.
system described in the later parts of section 2.3.3. All measurements used a voltage
criterion of l|i,V/cm and all Jcs are calculated assuming that the current flows only in the
superconducting core of the tape. This is assumed to be a 3 x 0.08mm rectangle, giving
an area of 2.4 x 10'3cm2.
5.2.2 MAGNETIC MEASUREMENTS
Upon completion of the transport measurements, the Tl:1223 and Tl:2223 tapes
were cut into 3 x 3mm squares for magnetic- measurements. All magnetic measurements
were carried out by Dr. D.N. Zheng and Dr. J.D. Johnson. Several sections were cut
from the same tape to further determine any variation of tape properties with length.
Magnetic hysteresis loops for these sections were measured using a vibrating sample
magnetometer (VSM) in applied fields of up to 12T at fixed temperatures of 4.2K, 30K and
77K. Section 2.4 describes this in more detail. In all cases the field was applied
perpendicular to the plane of the tape. Care was taken in using the VSM to ensure
temperature stabilisation.
141
C h a p t e r
5 :
T h a l l i u m
T a p e s
5 . 3 R E S U L T S
A N D
D I S C U S S I O N
5 . 3 . 1
L o w
F I E L D T R A N S P O R T M E A S U R E M E N T S
F i g u r e
5 . 3
s h o w s
t h e
t r a n s p o r t
J c
v e r s u s B
c h a r a c t e r i s t i c s f o r t h e
f i r s t
s e t
o f
t a p e s .
M e a s u r e m e n t s
f o r
b o t h T l : 1 2 2 3 a n d
T l : 2 2 2 3 t a p e s a r e
s h o w n .
F i e l d ( m T )
F i e l d
( m T )
F i g u r e
5 . 3 :
L o w - f i e l d t r a n s p o r t
J
c
v e r s u s
B
c h a r a c t e r i s t i c s a t 7 7 K f o r
t h e
f i r s t
s e t
o f
T l : 1 2 2 3 a n d T l : 2 2 2 3
t a p e s .
O n t h e
z e r o - f i e l d
c o o l e d d a t a
s o l i d
a n d
o p e n s y m b o l s
i n d i c a t e
i n c r e a s i n g
a n d d e c r e a s i n g
f i e l d
r e s p e c t i v e l y .
I t c a n b e
s e e n
f r o m f i g u r e s
5 . 3 ( a )
a n d
( c )
t h a t
f o r b o t h
t h e
T l : 1 2 2 3 a n d T l : 2 2 2 3
t a p e s
J c
f a l l s o f f m o r e r a p i d l y w i t h f i e l d
i n
t h e B p e r p e n d i c u l a r t o w i d t h
o r i e n t a t i o n ,
a s i s
t o
b e
e x p e c t e d f r o m t h e
l o w e r
d e m a g n e t i s i n g
f a c t o r i n
t h i s o r i e n t a t i o n
( ~ 0
f o r 5 ± w i d t h a n d ~ 1
f o r
5 / / w i d t h ) .
H o w e v e r ,
t h e f a c t t h a t t h e f i e l d h a s a
s i g n i f i c a n t
e f f e c t
i n
t h e B l l w i d t h c a s e
i n d i c a t e s i m p e r f e c t a l i g n m e n t o f t h e
a p p l i e d
f i e l d w i t h t h e s a m p l e , o r a s i g n i f i c a n t s p r e a d
i n
t h e a l i g n m e n t
o f t h e g r a i n s w i t h i n t h e s a m p l e .
I n
a d d i t i o n ,
w h i l e t h e T l : 2 2 2 3
t a p e
h a s
a
l o w e r
J c
t h a n t h e T l : 1 2 2 3
t a p e ,
f o r b o t h o r i e n t a t i o n s
i t s c r i t i c a l c u r r e n t
d e n s i t y
f a l l s
o f f m o r e
s l o w l y
w i t h
a p p l i e d f i e l d .
T h i s
a g r e e s w i t h m e a s u r e m e n t s c a r r i e d
o u t o n t h i n f i l m s o f
T l : 1 2 2 3
a n d T l : 2 2 2 3
b y
N a b a t a m e
e t .
a l .
[ 5 . 1 3 ] ,
a n d
m e a s u r e m e n t s
o n A u - P d
c l a d
t a p e s o f
T l : 2 2 2 3 b y
O k a d a e t a l .
[ 5 . 2 0 ]
w h i c h
a l s o s h o w
a
s l o w e r
f a l l
o f
J c
w i t h
B f o r
T l : 2 2 2 3
i n
1 4 2
Chapter 5 : Thallium Tapes
low fields for the B±ab-plane field orientation (although Nabatame does find that Tl:1223
maintains a higher Jc at high fields). The small amount of hysteresis of Jc seen in these
measurements arises from the maximum applied field being less than that required for full
penetration of the grains within the samples [5.21],
Also, the field cooled (FC) Jc is always higher than the zero field cooled (ZFC) Jc.
This indicates that flux compression is occurring in the ZFC measurements. This arises
from the granular nature of these superconductors [5.21J. In the ZFC case the applied field
penetrates the sample via the intergranular regions but is excluded from the grains. This
leads to compression of flux in the intergrain regions [5.22], the weak links in the current
carrying path, causing a greater reduction in Jc. In the FC case the applied field is evenly
trapped on cooling and therefore evenly distributed through the sample so flux compression
does not occur, giving a lower field in the intergrains and thus a higher Jc.
5.3.2 MEASUREMENTS ON LONG TAPES IN ZERO FIELD
Figure 5.4 shows the 1-V curves for all sections of the first long tape measured at
77K and zero field, incrementally offset along the y-axis for clarity.
Figure 5.4 : 1-V curves of the seven sections of long tape 1 at 77K and zero
field. All curves are shown with an incremental offset to clarify the
differences between them. The inset shows the TV characteristic along the
whole tape.
143
C h a p t e r
5 :
T h a l l i u m
T a p e s
I t
i s
c l e a r t h a t t h e c u r v e s
v a r y
s i g n i f i c a n t l y .
S o m e ,
f o r
e x a m p l e
t h o s e f o r
s e c t i o n s
2 ,
3 a n d
7 ,
s h o w a t w o - s t a g e
t r a n s i t i o n ,
a c h a r a c t e r i s t i c f e a t u r e
o f
g r a n u l a r i t y
( s e e
s e c t i o n
1 . 1 2 ) .
T h e
s h a p e
o f
t h e
I - V c u r v e s
i n d i c a t e s t h a t t h e y a r e
s h o w i n g
f l u x - f l o w
t y p e
b e h a v i o u r
[ 5 . 2 3 ] .
T h e o n s e t o f
r e s i s t i v i t y
a l s o v a r i e s w i t h s e c t i o n ,
f r o m
- 6 . 5 A
f o r
s e c t i o n
7 ,
t o ~ 1 1 A
f o r
s e c t i o n s
1 ,
5 a n d
6 .
T h e s e
d i f f e r e n c e s
c o u l d a r i s e
f r o m a
n u m b e r
o f
s o u r c e s ,
i n c l u d i n g
p o s i t i o n a l v a r i a t i o n s
o f
c r o s s - s e c t i o n a l a r e a
( s u c h
a s
t h a t
s h o w n b y
P e t e r s o n e t a l .
i n
[ 5 . 1 8 ] ) ,
c o m p o s i t i o n , a l i g n m e n t
o f
t h e
t a p e
o r
i n t e r g r a n u l a r
c o n n e c t i v i t y
( i n c l u d i n g t h e
e f f e c t s
o f m i c r o c r a c k i n g ) . N o t e t h a t t h e I - V
c u r v e f o r t h e
w h o l e
t a p e s h o w s
t h a t t h e
w e a k e s t
s e c t i o n
l i m i t s t h e
J c
o f t h e e n t i r e
s a m p l e .
F i g u r e 5 . 5
s h o w s
t h e
v a r i a t i o n
o f t h e 7 7 K
z e r o - f i e l d
J c
w i t h
p o s i t i o n
a l o n g
t a p e s
1
a n d 2
e x t r a c t e d f r o m
t h e
m e a s u r e d
I - V
c u r v e s .
u
l “ 9
3 0 0 C n
-1-
*
-
'
-
'
-
*
-1-1-
012345678
S e c t i o n
F i g u r e
5 . 5
:
V a r i a t i o n
o f
J c
a t 7 7 K a n d
z e r o
f i e l d
w i t h
p o s i t i o n
f o r
T l : 1 2 2 3
t a p e s
1
( f i l l e d
c i r c l e s
)
a n d
2
( o p e n s q u a r e s ) . N o t e t h e
d i f f e r e n c e s
b e t w e e n
b o t h
s e c t i o n s
o f
t h e s a m e t a p e a n d b e t w e e n
t a p e s . T h e
J c
o f
t h e
t a p e
a s a
w h o l e w i l l
b e
g o v e r n e d b y
t h e w o r s t s e c t i o n s
o f
t h e
t a p e ,
i n b o t h c a s e s
s e c t i o n
7 .
T h e l i n e s a r e
g u i d e s
f o r
t h e
e y e .
I t c a n b e s e e n t h a t b o t h t a p e s
e x h i b i t
s i g n i f i c a n t
l o c a l
v a r i a t i o n s i n
J c
,
b u t w i t h
t h a t
o f
t a p e
1
r e m a i n i n g a p p r o x i m a t e l y
c o n s t a n t
a l o n g t h e
l e n g t h
o f
t h e
t a p e , a n d t h a t o f t a p e
2
d e c r e a s i n g
f r o m s e c t i o n 1
t o 7 . I t s h o u l d b e r e m e m b e r e d t h a t t h e
J c
o f
t h e
w e a k e s t s e c t i o n s
w i l l
l i m i t t h e t r a n s p o r t
J c
o f t h e
t a p e
a s
a
w h o l e
a s s h o w n
i n
f i g u r e 5 . 4 .
1 4 4
Chapter 5 : Thallium Tapes
Measurements of zero-field Jc as a function of time over -800 hours for tape 2 are
shown in figure 5.6.
Figure 5.6 : Jc at 77K and zero field as a function of time for the seven
sections of tape 2. The number on each line indicates which section of tape
the data is from.
Although sections 1, 3 and 6 show a slight initial fall in Jc, others, such as section
7, appear to show a slight increase with time. Given the relatively small changes of Jc in
each section with time these variations are explained by experimental error introduced by
variation of the experimental conditions between measurements.
5.3.3 MEASUREMENTS ON LONG TAPES IN MAGNETIC FIELDS.
Figures 5.7(a) to (c) show the Jc-B characteristics for a representative section of a
long silver-clad TF1223 tape measured in liquid nitrogen in three different orientations of
applied field. Figure 5.8 shows the result of similar Jc-B measurements carried out on the
95% gold- 5% palladium clad TF1223 tapes.
145
C h a p t e r
5 :
T h a l l i u m
T a p e s
B
( m T )
B
( m T )
F i g u r e
5 . 7
:
J c - B
c h a r a c t e r i s t i c s
f o r
s i l v e r - c l a d
t a p e
a t 7 7 K .
I n a l l
c a s e s
s o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g f i e l d ,
o p e n
s y m b o l s
i n d i c a t e d e c r e a s i n g
f i e l d .
F i g u r e
5 . 8
:
J c - B
m e a s u r e m e n t
o n
g o l d - p a l l a d i u m ,
c l a d
t a p e .
I n a l l
c a s e s
s o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g
f i e l d , o p e n
s y m b o l s
i n d i c a t e
d e c r e a s i n g
f i e l d .
T h e
s i m i l a r i t i e s b e t w e e n t h e d i f f e r e n t o r i e n t a t i o n s s h o w n
i n f i g u r e 5 . 7
i m p l i e s
t h a t
t h e r e i s l i t t l e c r y s t a l l o g r a p h i c a l i g n m e n t o f
t h e s u p e r c o n d u c t i n g g r a i n s w i t h i n
t h e
t a p e .
N o t e
t h a t t h e
h y s t e r e s i s
i s
m o s t p r o n o u n c e d f o r
( a ) ,
w h e r e t h e d e m a g n e t i s i n g
f a c t o r i s
~ 0 ,
a n d
l e a s t p r o n o u n c e d f o r
( c )
w i t h
c u r r e n t .
I f
t h e a ÿ - p l a n e s
i n t h e
s u p e r c o n d u c t o r i n
t h e
t a p e
w e r e
p e r f e c t l y a l i g n e d i t
w o u l d b e e x p e c t e d t h a t
( b )
m i g h t
s h o w o n l y
a
s m a l l
f a l l - o f f
o f
J c
d u e
t o i t s l o w
d e m a g n e t i s i n g
f a c t o r a n d t h e
l a r g e
H
f o r
B / / a b .
a n d
( c )
w o u l d
1 4 6
Chapter 5 : Thallium Tapes
show no fall-off of Jc with B, and no hysteresis of Jc, due to the lack of any Lorentz force
in the Bllcurrent configuration. This, and the pronounced hysteresis seen, indicates the lack
of strong alignment of the Tl:1223 in the tape.
It is apparent that the variation of Jc with B in figure 5.8 again shows greater
hysteresis in the 5J_widthJ_current orientation. Also, on the field decreasing part of the
Jc-B curve, the hysteresis rises to a higher percentage of the virgin zero-field Jc than for the
silver-clad tapes. If hysteresis is caused by trapped flux cancelling the applied field on the
decreasing field leg [5.21], this indicates that these tapes trap field more homogeneously
than the silver-clad tapes. Also, Jc falls off more slowly for increasing field in the 5//width
orientation than for the i?±width case, indicating that the gold-palladium clad TI:1223 tapes
have significantly better alignment and homogeneity than the silver-clad tapes although their
overall Jcs are somewhat lower.
This contradicts the results of Miller et al. on PIT T1.T223 wires [5.24], They find
that silver lowers the melting point of Tl:1223 and enhances the fonnation of Tl:1223 over
the other possible phases, whereas a gold-clad tape forms a material with a smaller
percentage of Tl:1223. Presland et al. [5.6] also find that silver is important in obtaining a
textured Tl:1212 tape. In this case the larger the ratio of surface area of the silver to
superconductor volume, the higher the Jc. The reasons for this difference are unclear, but
may relate to differences in the initial composition and processing routes of the tapes, or
simply to the presence of palladium in the cladding of these tapes.
5.3.4 HIGH FIELD TRANSPORT MEASUREMENTS
Figures 5.9 and 5.10 show the 4.2K results for 5Twidth and 5//width
respectively; figures 5.11 and 5.12 show the equivalent results at 77K.
0 -o.s -0.25 0.25 0.S 0.75
B (T) B (T)
Figure 5.9 : Jc versus B at 4.2K infields of up to 8T for BTwidth.
(a) shows the whole field range, (b) shows a magnified view of the low
field region. Solid symbols indicate increasing field, open symbols indicate
decreasing field.
147
(Acm2
)
J c
(Acm'2
)
J c
(Acm'3
C h a p t e r
5
:
T h a l l i u m
T a p e s
B
( T )
n
< T )
F i g u r e
5 . 1 0
:
J c
v e r s u s B a t
4 . 2 K
i n f i e l d s
o f
u p
t o S T
f o r
B / A v i d t h .
( a )
s h o w s
t h e
w h o l e
f i e l d r a n g e ,
( b )
s h o w s
a m a g n i f i e d
v i e w
o f
t h e l o w
f i e l d r e g i o n .
S o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g f i e l d ,
o p e n
s y m b o l s
i n d i c a t e
d e c r e a s i n g f i e l d .
B
( T )
B
( T )
F i g u r e
5 . 1 1 :
J c
v e r s u s
B
a t 7 7 K i n
f i e l d s
o f
u p
t o 8 T
f o r
B ± w i d t h .
( a )
s h o w s
t h e w h o l e
f i e l d
r a n g e ,
( b )
s h o w s a
m a g n i f i e d
v i e w o f
t h e i o n -
f i e l d
r e g i o n .
S o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g f i e l d , o p e n
s y m b o l s
i n d i c t e e
d e c r e a s i n g
f i e l d .
B
( T )
B
( T )
F i g u r e 5 . 1 2 :
J c
v e r s u s
B
a t
7 7 K i n
f i e l d s o f u p
t o
S T
f o r
B / / w i d t h .
( a )
s h o w s
d a t a
f o r
t h e
w h o l e
f i e l d
r a n g e ,
( b )
s h o w s a
m a g n i f i e d
v i e w
o f
t i n
l o w
f i e l d
r e g i o n .
S o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g
f i e l d , o p e n s y m b o l s
i n d i c a t e d e c r e a s i n g f i e l d .
1 4 8
Chapter 5 : Thallium Tapes
These results show that Jc persists at a finite value up to 8T at temperatures as high
as 77K. This is highly significant from an applications point of view. Further, the Jc at
77K and 8T is only about 50% lower than the Jc for 4.2K and 8T, indicating that with
proper processing this material may be useful for applications in high fields at liquid
nitrogen temperatures. A finite Jc in fields of 8T in Ba and Pb substituted Tl:1223 has also
been reported by Doi et al. [5.25], although they do not report at what temperature their
measurements were made. Peterson et al. also see a transport Jc of greater than lOOAcmr2
at 64K in fields of 6T [5.18], while Matsuda et al. and Kamo et al. find a Jc of
-lOOAcnr2 at 77K and 8T [5.26, 27],
It can be seen that Jc appears to increase with increasing B on the increasing B leg
of the Jc versus B curve in figure 5.11. This behaviour is confirmed by examination of the
measured I-V curves and has also been seen in bulk Tl:2223 by Martin and Gruehn [5.28],
although they do not attempt to explain it. A possible explanation is that each time the field
is ramped to a new value it overshoots the set field slightly before settling to the desired
value. This would move the Jc from the increasing field curve to the decreasing field curve,
which has a higher Jc. This effect will not be cumulative with each B step as, unless the
step is very small (which it is not) each increase in B will return to the same increasing field
curve.
There are two possible implications of the hysteresis in Jc at fields as high as 7T.
First, and more simply, the sample has an enormous flux trapping capability, which is
extremely promising from an applications point of view. However, this is unlikely given
the huge current densities necessary to trap fields of this magnitude (see section 3.1) and
would be obvious from magnetisation measurements where currents of this magnitude are
not seen (see section 5.3.3). This indicates that the flux trapping model of the hysteresis of
Jc [5.21] cannot explain this high-field hysteresis. Another explanation is needed, for
example by the theory of Ries et al. [5.29] who explain the hysteresis of Jc with field in
terms of a Josephson current in the grain boundaries when the grains are in the mixed state,
i.e. with the vortices altering the phase of the superconducting composite. Also, the
asymmetry seen in the decreasing field Jc-B characteristics implies that there may be flux
trapped by persistent loops- in the sample weak link network, as suggested by Altshuler
et al. [5.30].
To confirm that the samples are showing a true superconducting critical current at
high field and temperature the I-V curves taken in this regime were examined. Figure 5.13
shows two I-V curves at 77K and 8T, with the field parallel and perpendicular to the width
of the tape. These I-V curves clearly show superconducting behaviour, though with very
149
C h a p t e r
5
:
T h a l l i u m
T a p e s
l o w
I c
s .
T h i s
i s
c o n f i r m e d
b y
p l o t t i n g t h e d a t a
w i t h a l o g a r i t h m i c
y - a x i s ,
w h i c h
s h o w s ,
f o r
d a t a
a b o v e t h e d i g i t i s a t i o n l e v e l
o f
t h e
v o l t m e t e r
u s e d ,
t h e
v o l t a g e
e x t r a p o l a t i n g t o
z e r o
[ 5 . 3 1 ] ,
F i g u r e
5 . 1 3 : I - V c u r v e s a t 7 7 K a n d
8 T
w i t h
a p p l i e d f i e l d
p a r a l l e l
a n d
p e r p e n d i c u l a r
t o t h e
w i d t h o f t h e t a p e . T h e
i n s e t s h o w s t h e s a m e d a t a p l o t t e d
w i t h a l o g a r i t h m i c
y - a x i s .
T h e
l e v e l l i n g o f f o f
t h e I - V
c u r v e s a n d t h e s t e p s
i n t h e m a t l o w c u r r e n t s a r e
d u e
t o
t h e
v o l t a g e
s i g n a l
g o i n g
b e l o w t h e
d i g i t i s a t i o n
l e v e l
o f
t h e v o l t m e t e r u s e d . N o t e
t h a t
a b o v e
t h i s
l e v e l b o t h I - V
c u r v e s a p p e a r
t o
e x t r a p o l a t i n g
t o z e r o ,
i n d i c a t i n g
t h a t t h e s a m p l e
i s i n
a t r u e
s u p e r c o n d u c t i n g s t a t e i n b o t h c a s e s .
T o g a i n
f u r t h e r i n f o n n a t i o n o n t h e s a m p l e s
m e a s u r e d ,
a
c o m p a r i s o n w a s m a d e
o f
t h e s i z e o f t h e p e a k i n
t h e d e c r e a s i n g f i e l d
l e g
o f t h e
J c - B
m e a s u r e m e n t c y c l e
c o m p a r e d
t o
t h e i n i t i a l z e r o f i e l d
J c .
T h i s i s s h o w n i n
t a b l e 5 . 1 .
T h e 4 . 2 K
m e a s u r e m e n t s u p t o 8 T s h o w s m a l l r a t i o s w h i c h a r e r o u g h l y
t h e s a m e
a s
e a c h o t h e r .
T h e
l o w v a l u e o f t h i s
r a t i o
i m p l i e s
a
l a r g e d i s t r i b u t i o n i n t h e
s t r e n g t h
o f t h e
i n t e r g r a n u l a r
r e g i o n s g i v i n g a w i d e r a n g e o f
l o c a l
i n t e r n a l
f i e l d s ,
w i t h
o n l y t h e s t r o n g e s t
s t i l l
c a r r y i n g a
s u p e r c u r r e n t
o n t h e r e t u r n l e g .
T h e 7 7 K
m e a s u r e m e n t s
s h o w a
l a r g e
d i f f e r e n c e b e t w e e n t h e
B J L w J - L
a n d t h e
B / A v l L r a t i o s
a n d
i m p l i e s
a
m o r e e v e n
d i s t r i b u t i o n
o f w e a k
l i n k
s t r e n g t h s i n
t h e B ± w ± L
c a s e .
T h i s
i s
n o t
u n e x p e c t e d
a s t h e r e
i s
a m u c h
1 5 0
Chapter 5 : Thallium Tapes
smaller thickness of superconductor parallel to the applied field in this case. The ratios for
the data in figures 5.7 and 5.8 show similar results, that the weak link strengths and
homogeneity are similar regardless of orientation. This arises at least partly because fewer
weak links will have been completely suppressed by the applied field and is another
indication of the lack of alignment in these materials.
Type of Tape From
Figure
Orientation T (K) Maximum
Field
Peak Field
(mT)
Jc(peak)
Jc(zero)
Ag-Clad 5.9 BlwlL 4.2 8T 124 0.23
Ag-Clad 5.10 BZZwlL 4.2 8T 52 0.28
Ag-Clad 5.11 BlwlL 77 8T 52 0.72
Ag-Clad 5.12 BZ/wlL 77 8T 13 0.43
Ag-Clad 5.7 BlwlL 77 150mT 8.3 0.66
Ag-Clad 5.7 BZ/wlL 77 150mT 6.8 0.66
Ag-Clad 5.7 BZ/w/ZL 77 150mT 6.2 0.59
Au-Pd Clad 5.8 BlwlL 77 160mT 9.7 0.84
Au-Pd Clad 5.8 BZZwlL 77 160mT 5.7 0.87
Table 5.1 : Comparison of the ratio of Jc at the peak of the decreasing field
leg of the Jc-B measurement with the initial zero field Jcfor all the tapes
measured. In the orientation column, w represents the width of the tape and
L represents its length. Peak field is the value of decreasing field at which
the peak in Jc occurs.
5.3.5 MAGNETIC MEASUREMENTS
The hysteresis loops for the Tl:1223 and Tl:2223 tapes at 4.2K are shown in
figure 5.14 and at 77K in figure 5.15. Also shown is Jc(magnetic) extracted from the
hysteresis loop data using the Bean Model [5.32] (see section 2.4).
Jc(m.agnetic) for the Tl:1223 and Tl:2223 tapes is approximately the same at 4.2K
and shows roughly the same Jc-B behaviour. Both show Jcs considerably lower than that
of YBCO. The 77K data indicates that the Tl:2223 is non-superconducting in fields above
-0.6T while the Tl:1223 and YBCO show similar Jc-B behaviour. Other reports have
indicated that Tl:2223 shows worse Jc-B behaviour than Tl:1223 at 77K [5.10, 12, 33,
34], though this disagrees with the transport results shown in figure 5.3. The reason for
this discrepancy between transport and magnetic measurements is unknown, but may arise
from differences in the properties of the different tapes due to, for example, different
151
C h a p t e r
5
: T h a l l i u m T a p e s
p r o c e s s i n g
c o n d i t i o n s ,
o r
f r o m t h e m u c h
l o w e r e f f e c t i v e v o l t a g e
c r i t e r i o n
i n v o l v e d
i n t h e
m a g n e t i c
m e a s u r e m e n t s
[ 5 . 3 5 ] .
T h e
T l : 2 2 2 3
t a p e w h i c h w a s m e a s u r e d
m a g n e t i c a l l y
h e r e
m a y
s i m p l y b e
o f i n f e r i o r
q u a l i t y
a n d
s o
n o n - s u p e r c o n d u c t i n g
a t
7 7 K ,
a l t h o u g h
i t
i s
m o r e
l i k e l y
t h a t t h e
r e s u l t s s h o w n a r i s e f r o m
t h e v e r y l o w
i r r e v e r s i b i l i t y
f i e l d
( l e s s
t h a n
I T )
o f
T l : 2 2 2 3 a t h i g h
t e m p e r a t u r e s
[ 5 . 7 , 9 ] .
F i g u r e
5 . 1 4
:
( a )
M - H l o o p s
a n d
( b )
J c ( m a g n e t i c )
e x t r a c t e d
f r o m
t h e
M - H
l o o p s ,
a s
a f u n c t i o n o f a p p l i e d
f i e l d
a t
4 . 2 K
f o r
t h e T l :
1 2 2 3
a n d T l : 2 2 2 3
s a m p l e s .
S i m i l a r
d a t a
f o r
Y B C O a r e a l s o i n c l u d e d
f o r c o m p a r i s o n .
F i g u r e
5 . 1 5 :
( a )
M - H
l o o p s a n d
( b )
J c (
m a g n e t i c )
e x t r a c t e d
f r o m
t h e
M - H
l o o p s ,
a s a
f u n c t i o n
o f
a p p l i e d f i e l d
a t
7 7 K
f o r
t h e T l : 1 2 2 3
a n d T l : 2 2 2 3
s a m p l e s . S i m i l a r d a t a
f o r
Y B C O a r e a l s o
i n c l u d e d
f o r c o m p a r i s o n .
F i g u r e
5 . 1 6 s h o w s
h y s t e r e s i s
l o o p
w i d t h A m
a s
a f u n c t i o n o f
a p p l i e d f i e l d
a t
4 . 2 K ,
3 0 K a n d 7 7 K . A l t h o u g h b o t h m a t e r i a l s
s h o w
s i m i l a r b e h a v i o u r a t
4 . 2 K ,
a t
h i g h e r
t e m p e r a t u r e s
( T
>
3 0 K )
t h e
p e r f o r m a n c e
o f t h e T l : 2 2 2 3
f a l l s i n c r e a s i n g l y b e l o w t h a t o f t h e
T l :
1
2 2 3 . T h i s a g r e e s w i t h t h e
m e a s u r e m e n t s
c a r r i e d o u t
o n t h i n
f i l m s
o f
T l : 1 2 2 3 a n d
T l : 2 2 2 3 b y N a b a t a m e
e t
a l .
[ 5 . 1 3 ] .
A s
a
p o t e n t i a l l y
i m p o r t a n t
p o i n t o n t h e
e f f e c t s
o f
p r o c e s s i n g ,
P e t e r s o n e t a l .
[ 5 . 1 8 ]
f i n d t h a t t h e h y s t e r e s i s
l o o p
w i d t h f o r
p r o c e s s e d
T l :
1 2 2 3
1 5 2
Chapter 5 : Thallium Tapes
tapes is less than that for the ground precursor powders, implying that there is very little
intergranular connectivity or overall grain alignment in their tapes.
Figure 5.16 : Hysteresis loop width as a function of field at 4.2K, 30K and
77Kfor Tl:1223 and Tl:2223. Note that despite their similar behaviour at
4.2K, Tl:2223 shows significantly worse performance at the two higher
temperatures shown.
Figure 5.17 shows the normalised hysteresis loop widths from a number of
sections of Tl:1223 tape, as (a) a function of field at constant temperature and (b) as a
function of temperature at constant field.
H
¥
<1
I
■ ' ■ ' ■ 1 ■ ' ' 1 ■ ■ ■ 1 ■ 1 .—o— Section 1 (HXtape) (a) 1 ' ‘ ' ■ 1 ‘ ' ' 1 ' ■ ' 1 1 ' ' ' 1 ' ' 'B = IT (b) --
0.9 Jk - -A- - Section 2 (Hi.tape)
0.8 Ea —o - Section 3 (HItape)
0.7 —ffl- - Section 4 (HItape) o 0.1 f
0.6 —A— Section 2 (H//tape)
0.5 Section 3 (H//tape) 2
- —o— Section 1 (Hitape) tfek
< 0.01 f - -A - •Section 2 (HXtape)
0.4
g ■ —o ■ Section 3 (HXtape) N.
0.3
<
0.001
_ —EB- - Section 4 (HXtape) s,
: —2i— Section 2 (H//tape) 3ÿ
0.2
T = 4.2K—1—1—*—1—1—1—1—1—1—1—'—1—1—*—1—1—1—1—1—1—*—‘—*— 0.0001 - - - Section 3 (H//tape), , . \. . .. , 4-.- * ■ | ■ ■■ . | ■ ■ ■0 2 A 6 8 10 12 o 20 AO 60 80 100 120
B (T) T (K)
Figure 5.17 : M-H loop widths Am for a number of sections of Tl:1223
tape, normalised to those at (a) 4.2K in varying field and (b) IT at varying
temperatures. Note the almost, identical responses between the different
sections and orientations.
153
C h a p t e r
5
:
T h a l l i u m
T a p e s
T h e s e r e s u l t s i n d i c a t e
t h a t t h e r e
i s ,
w i t h i n
e x p e r i m e n t a l
e r r o r ,
n o d i f f e r e n c e
b e t w e e n
t h e
d i f f e r e n t
s e c t i o n s
o r b e t w e e n
t h e t w o
d i f f e r e n t o r i e n t a t i o n s
m e a s u r e d . T h i s
i m p l i e s
t h a t
t h e r e
i s n o d i f f e r e n c e i n t h e
m a g n e t i c
p r o p e r t i e s o f
t h e
t a p e s f r o m
s e c t i o n t o
s e c t i o n a n d
i n d i c a t e s
t h a t t h e s e
m e a s u r e m e n t s
a r e
o f t h e i n t r a g r a n u l a r
p r o p e r t i e s o f
t h e
t a p e . T h e
s i m i l a r i t y b e t w e e n t h e d i f f e r e n t
s e c t i o n s
a n d
o r i e n t a t i o n s o f t h e
t a p e s a l s o
s u g g e s t s
t h a t
t h e r e i s n o o v e r a l l o r i e n t a t i o n w i t h i n t h e
t a p e s
m e a s u r e d .
5 . 3 . 6 C O M P A R I S O N O F T R A N S P O R T
A N D
M A G N E T I C R E S U L T S
F i g u r e
5 . 1 5 ,
a b o v e ,
i n d i c a t e s v e r y l i t t l e
v a r i a t i o n
o f
p r o p e r t i e s
b e t w e e n t h e
s e c t i o n s
o f
t a p e ,
i n d i s a g r e e m e n t
w i t h t h e
r e s u l t s o f
t h e
t r a n s p o r t
m e a s u r e m e n t s . F o r
e x a m p l e ,
f i g u r e
5 . 5 s h o w s c o n s i d e r a b l e
d i f f e r e n c e s
i n t r a n s p o r t
J c
b e t w e e n
s e c t i o n s o f
t w o d i f f e r e n t
t a p e s .
T h i s i n d i c a t e s t h a t t h e
m a g n e t i c
m e a s u r e m e n t s
a r e
d o m i n a t e d b y
c o n t r i b u t i o n s
f r o m
t h e g r a i n s
w i t h i n e a c h
s a m p l e , w h o s e p r o p e r t i e s
a p p e a l -
t o b e h o m o g e n o u s
t h r o u g h o u t t h e
t a p e ,
w i t h o n l y
a
m i n o r i t y o f t h e d e t e c t e d s i g n a l
a r i s i n g
f r o m
c u r r e n t s
f l o w i n g
o n
t h e
l e n g t h
s c a l e o f t h e
w h o l e
s a m p l e . T r a n s p o r t
m e a s u r e m e n t s ,
o n t h e o t h e r
h a n d ,
a r e
d o m i n a t e d b y
t h e i n t e r g r a n u l a r
l i n k s ,
t h e
n u m b e r a n d q u a l i t y
o f w h i c h
a p p e a r
t o v a r y
c o n s i d e r a b l y
a l o n g
t h e
t a p e . T h i s
a g r e e s
w i t h t h e h i g h - f i e l d t r a n s p o r t r e s u l t s w h i c h
s h o w
o n l y
a v e r y
s m a l l
t r a n s p o r t
( i . e .
i n t e r g r a i n )
J c
c o m p a r e d
t o t h e m a g n e t i s a t i o n
J c
a t
f i e l d s
h i g h e r
t h a n
~ 1 T .
I n a g r e e m e n t
w i t h t h e
t r a n s p o r t
r e s u l t s ,
t h e m a g n e t i c
m e a s u r e m e n t s s h o w l i t t l e
v a r i a t i o n
w i t h f i e l d
o r i e n t a t i o n ,
c o n f i r m i n g
t h a t t h e s e s a m p l e s
h a v e n o t
b e e n w e l l
a l i g n e d
b y
p r o c e s s i n g .
H o w e v e r ,
g r a i n
a l i g n m e n t o f T l : 1 2 2 3 h a s b e e n
a c h i e v e d ,
f o r
e x a m p l e
b y
D e L u c a e t a l .
[ 5 . 3 6 ]
s o t h i s i s
n o t a n
i n s o l u b l e p r o b l e m
f o r
a p p l i c a t i o n s
o f t h e s e
m a t e r i a l s .
T h e
f a c t
t h a t a t
h i g h
f i e l d s
t h e
t r a n s p o r t
J c
b e h a v e s
s i m i l a r l y
t o t h e m a g n e t i c
r e s u l t s
a l s o s h o w s
t h a t
a l t h o u g h t h e r e m a y o n l y
b e
a
s m a l l
n u m b e r o f
s u p e r c o n d u c t i n g
p a t h s
l e f t
t h o r o u g h t h e
s a m p l e
a t t h e s e
f i e l d s ,
t h e y
b e h a v e i n
a v e r y
w e l l - c o u p l e d
f a s h i o n .
T h i s
b e h a v i o u r i s
s i m i l a r
t o t h a t
e x h i b i t e d b y t h e Y B C O
t h i c k
f i h n s m e a s u r e d a t h i g h
f i e l d s
a n d
s h o w n i n
f i g u r e
4 . 9 ,
a n d
a l s o
t h e
m e a s u r e m e n t s
o f D a u m l i n g
e t a l . o n l o w - a n g l e
J o s e p h s o n j u n c t i o n g r a i n
b o u n d a r i e s
i n
Y B C O t h i n f i l m s
[ 5 . 3 7 ] .
H o w e v e r ,
t h i s b e h a v i o u r
o n l y
o c c u r s a t 4 . 2 K i n
Y B C O w h i l e
i t o c c u r s
u p
t o 7 7 K i n
T F 1 2 2 3 .
T h i s i s
a
v e r y
i m p o r t a n t f e a t u r e o f
t h e s e
m e a s u r e m e n t s ,
i n d i c a t i n g t h a t t h e h i g h
f i e l d a n d
t e m p e r a t u r e
J c
o f
T l : 1 2 2 3 i s l i m i t e d
b y
t h e p r o c e s s i n g
o f t h e
t a p e s
r a t h e r t h a n b y a n y
i n t r i n s i c
p r o p e r t i e s
o f
t h e
s u p e r c o n d u c t o r , i n a g r e e m e n t w i t h
t h e
r e s u l t s
o f P e t e r s o n e t
a l .
[ 5 . 1 8 ] ,
1 5 4
Chapter 5 : Thallium Tapes
5.4 CONCLUSIONS
Although the Tl:1223 tape has a fairly high zero-field transport Jc at 4.2K, it drops
rapidly to approximately 5% of this in applied magnetic fields as low as IT. Both the large
hysteresis of transport Jc and its rapid fall with B imply that these tapes are very granular,
and that the grains within them are very poorly aligned. This is probably related to the
spheroidal rather than plate-like morphology of Tl:1223 which arises from the
single-layered crystal structure of this material and makes it far more difficult to align by
pressing than a material with a plate-like morphology. However, the transport
measurements indicate that above fields of approximately IT the Jc does not drop
appreciably with applied field and that even at temperatures as high as 77K the sample
exhibits a clear critical current density in a field of 8T. Also, the results show that the Jc at
77K and 8T is only about 50% lower than Jc for 4.2K and 8T, indicating that this material
may be very useful for applications at liquid nitrogen temperatures. The presence of
hysteresis in the Jc-B characteristic even at 77K and 7T also implies that Tl:1223 can be
useful in this regime. All of this behaviour indicates that there is no fundamental barrier to
this material carrying very high currents at high fields and temperatures, but that its
processing needs to be optimised before this can be achieved. This contrasts with Tl:2223,
which, although it shows better behaviour than Tl:1223 at very low fields shows worse
behaviour at high fields and temperatures where applications are most likely to be found.
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:
T h a l l i u m
T a p e s
[ 5 . 7 ]
D . N . Z h e n g , P h . D .
T h e s i s
( C h r i s t ' s
C o l l e g e ,
C a m b r i d g e ,
1 9 9 4 )
[ 5 . 8 ]
D . H .
K i m ,
K . E .
G r a y , R . T .
K a m p w i r t h , J . C .
S m i t h ,
D . S . R i c h e s o n ,
T . J .
M a r k s ,
J . H . K a n g , J .
T a l v a c c h i o a n d M . E d d y , P h y s i c a
C ,
1 7 7 ,
4 3 1
( 1 9 9 1 ) .
[ 5 . 9 ]
K . T e n y a , H . M i y a j i m a ,
S . H a s e y a m a , Y .
I s h i k a w a a n d S .
Y o s h i z a w a ,
J o u r n a l
o f
t h e
P h y s i c a l
S o c i e t y
o f J a p a n ,
6 0 ,
2 3 2 4
( 1 9 9 1 ) .
[ 5 . 1 0 ]
T .
S a s o a k a ,
A .
N o m o t o ,
M .
S e i d o ,
T .
D o i a n d T . K a m o ,
J p n .
J . A p p l . P h y s . ,
3 0 ,
L 1 8 6 8
( 1 9 9 1 ) .
[ 5 . 1 1 ]
D . J .
M i l l e r ,
J . G .
H u ,
J . D . H e t t i n g e r ,
K . E . G r a y ,
J . E . T k a c z y k ,
J .
D e L u c a ,
P . L .
K a r a s ,
J . A .
S u t l i f f
a n d M . F .
G a r b a u s k a s ,
A p p l .
P h y s .
L e t t . ,
6 3 ,
5 5 6
( 1 9 9 3 ) .
[ 5 . 1 2 ] R . S . L i u , D . N . Z h e n g , J . W .
L o r a m ,
K . A .
M i r z a ,
A . M .
C a m p b e l l
a n d P . P .
E d w a r d s ,
A p p l . P h y s .
L e t t . ,
6 0 ,
1 0 1 9
( 1 9 9 2 ) .
[ 5 . 1 3 ]
T .
N a b a t a m e ,
Y .
S a i t o ,
K .
A i h a r a ,
T . K a m o a n d
S . - P .
M a t s u d a ,
J p n .
J . A p p l .
P h y s . ,
3 2 ,
L 4 8 4
( 1 9 9 3 ) .
[ 5 . 1 4 ]
J . E . T k a c z y k , J . A .
D e L u c a ,
P . L .
K a r a s ,
P . J . B e d n a r c z y k ,
M . F . G a r b a u s k a s ,
R . H .
A r e n d t ,
K . W . L a y
a n d J . S .
M o o d e r a ,
A p p l . P h y s .
L e t t . ,
6 1 ,
6 1 0
( 1 9 9 2 ) .
[ 5 . 1 5 ]
A .
P i e h l e r ,
J . P .
S t r o b e l ,
N .
R e s c h a u e r ,
R .
L o w ,
R .
S c h o n b e r g e r , K . F .
R e n k ,
M .
K r a u s ,
J . D a n i e l a n d
G .
S a e m a n n - I s c h e n k o ,
P h y s i c a C , 2 2 3 ,
3 9 1
( 1 9 9 4 ) .
[ 5 . 1 6 ]
M .
P a r a n t h a m a n ,
M .
F o l d e a k i ,
R . T e l l o a n d A . M .
H e r m a n n ,
P h y s i c a
C ,
2 1 9 ,
4 1 3
( 1 9 9 4 ) .
[ 5 . 1 7 ]
D . M . K r o e g e r , A . G o y a l , E . D . S p e c h t ,
Z . L .
W a n g , J . E . T k a c z y k ,
J . A . S u t l i f f
a n d J . A .
D e L u c a ,
A p p l . P h y s . L e t t . ,
6 4 ,
1 0 6
( 1 9 9 4 ) .
[ 5 . 1 8 ]
D . E .
P e t e r s o n ,
P . G .
W a h l b e c k ,
M . P . M a l e y , J . O .
W i l l i s ,
P . J . K u n g , J . Y .
C o u l t e r ,
K . V .
S a l a z a r ,
D . S .
P h i l l i p s ,
J . F . B i n g e r t , E . J . P e t e r s o n a n d
W . L .
H u l l s ,
P h y s i c a
C ,
1 9 9 ,
1 6 1
( 1 9 9 2 ) .
[ 5 . 1 9 ]
K .
A i h a r a ,
T .
D o i ,
A .
S o e t a ,
S .
T a k e u c h i ,
T .
Y u a s a ,
M .
S e i d o ,
T .
K a m o a n d S .
M a t s u d a ,
C r y o g e n i c s ,
3 2 ,
9 3 6
( 1 9 9 2 ) .
[ 5 . 2 0 ]
M .
O k a d a ,
K .
T a n a k a a n d T .
K a m o ,
J p n .
J . A p p l .
P h y s . ,
3 2 ,
2 6 3 4
( 1 9 9 3 ) .
[ 5 . 2 1 ]
J . E .
E v e t t s
a n d B . A .
G l o w a c k i ,
C r y o g e n i c s ,
2 8 ,
6 4 1
( 1 9 8 8 ) .
[ 5 . 2 2 ]
A . I .
D ' y a c h e n k o , P h y s i c a
C ,
2 1 3 ,
1 6 7
( 1 9 9 3 ) .
1 5 6
Chapter 5 : Thallium Tapes
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157
C h a p t e r
6
:
B S C C O
T h i c k
F i l m s
C H A P T E R
6 :
M E A S U R E M E N T S
O N
B S C C O
T H I C K
F I L M S
6 . 1
I N T R O D U C T I O N
O n e o f t h e
m o s t
p r o m i s i n g o f t h e h i g h -
T c
s u p e r c o n d u c t o r s ,
f r o m t h e
p o i n t
o f
v i e w
o f t e c h n o l o g i c a l a p p l i c a t i o n s ,
i s
t h e
B i - S r - C a - C u - O
( B S C C O )
s y s t e m .
T w o
c o m p o u n d s
i n
t h i s s y s t e m a r e s u p e r c o n d u c t i n g a t h i g h
t e m p e r a t u r e s : B i : 2 2 2 3
( B i 2 S r 2 C a 2 C u 3 0 i o )
a n d
B i : 2 2 1 2 ( B i 2 S r 2 C a C u 2 0 g ) .
A t h i r d
c o m p o u n d , B i : 2 2 0 1
( B ÿ S ÿ C u O g )
i s
s u p e r c o n d u c t i n g
a t l o w e r t e m p e r a t u r e s
[ 6 . 1 ] .
T a b l e
6 . 1 s u m m a r i s e s
t h e
T c S
o f t h e
B S S C O c o m p o u n d s .
C o m p o u n d
F o r m u l a
M a x i m u m
T c
( K )
B i : 2 2 0 1
B i 2 S r 2 C u C > 6
~ 2 5
B i : 2 2 1 2
B ÿ S ÿ C a C ÿ O g
9 0
B i : 2 2 2 3
B i 2 S r 2 C a 2 C u 3 0 i o
1 1 0
T a b l e
6 . 1
:
T c s
o f
t h e
c o m p o u n d s o f
t h e
B i - S r - C a - C u - 0
s y s t e m .
A l t h o u g h
B i : 2 2 2 3 i s o b v i o u s l y
b e t t e r f o r a p p l i c a t i o n s a t h i g h
t e m p e r a t u r e s ,
a n d
b o t h
i t a n d B i : 2 2 1 2
s h o w a
v e r y
h i g h
J c
a n d
a t
4 . 2
K ,
B i : 2 2 1 2
i s e a s i e r t o p r o c e s s
i n t o
u s e f u l
f o r m s
[ 6 . 2 ] .
T h i s m a k e s i t
p o t e n t i a l l y s u i t a b l e
f o r
u s e
i n a p p l i c a t i o n s
s u c h a s f i e l d
e n h a n c i n g
i n s e r t s
i n
c o n v e n t i o n a l L T S C m a g n e t s .
H o w e v e r ,
i n o r d e r f o r t h i s
m a t e r i a l
t o b e
u s e f u l
i n t h e s e a p p l i c a t i o n s ,
i t
m u s t
c a r r y
h i g h c u r r e n t s a n d
t e c h n o l o g i e s
t o
s h a p e
i t
i n t o
u s e f u l f o r m s m u s t b e
d e v e l o p e d .
S i n c e t h e i r
d i s c o v e r y t h e s e c o m p o u n d s
h a v e b e e n
m a d e
i n
a n u m b e r o f f o r m s i n c l u d i n g
p o l y c r y s t a l l i n e
c e r a m i c s ,
t h i n a n d t h i c k
f i l m s ,
m e l t - c a s t
c y l i n d e r s , s i l v e r - c l a d
t a p e s a n d
s i n g l e
c r y s t a l s
[ 6 . 3 - 6 ]
o f w h i c h
t a p e s a n d
t h i c k
f i l m s h a v e
t h e
b e s t p o t e n t i a l f o r
a p p l i c a t i o n s .
T h i s
c h a p t e r d e s c r i b e s t r a n s p o r t a n d
m a g n e t i c
m e a s u r e m e n t s c a r r i e d o u t o n
m e l t - p r o c e s s e d t h i c k
f i l m s
o f B i : 2 2 1 2
o n s i l v e r
s u b s t r a t e s ,
o v e r a r a n g e
o f
t e m p e r a t u r e s
f r o m 4 . 2 K
t o 8 0 K
i n a p p l i e d
m a g n e t i c
f i e l d s o f
u p
t o
0 . 5 T f o r
t r a n s p o r t
m e a s u r e m e n t s a n d
1 2 T
f o r
m a g n e t i c
m e a s u r e m e n t s . T h e
r e s u l t s
a r e
a n a l y s e d
i n a n
a t t e m p t
t o c o r r e l a t e t h e
t r a n s p o r t
a n d m a g n e t i c
m e a s u r e m e n t s . T h e s e s a m p l e s w e r e
c h o s e n
a s
t h e y
f o r m a n
e x a m p l e
o f a t e x t u r e d
s y s t e m w i t h
' s t r o n g ' w e a k
l i n k s .
1 5 8
Chapter 6 : BSCCO Thick Films
6.1.1 SAMPLE PREPARATION AND PROCESSING
All samples were prepared in the I.R.C. by A.P. Baker following the method
described by Baker et al. in [6.7]. Commercial Merck Bi:2212 powder was ball milled for
60 minutes in Analar grade acetone. This powder was then mixed with a solvent, ethyl
methyl ketone, and a dispersant, ICI Hypermer KD1, in a ratio of 1 : 0.61. Using the
blower system shown schematically in figure 6.1 this suspension of BSCCO was sprayed
onto a 1cm wide, 125(lm thick silver substrate, first on one side then the other. After each
spraying the sample was weighed to determine the ratio of masses of superconductor on
each side of the thick film (a ratio is used as the mass of deposited material changes when
the dispersant and suspendant burn off during heat treatment). The thick films were then
heated to remove the suspendant and dispersant before being partial-melt-processed.
Air Gun spraying Bi-2212
in dispersant/solvent. H|
Ag Foil
ESI Substrate
Template for
4 mm strip
Bi-2212
I Coating
Figure 6.1 : A schematic of the powder spraying system; (a) is a front view
and (b) a side view, showing suspended BSCCO being sprayed on both
sides of the silver substrate.
Both sides of the substrate were coated with BSCCO to increase mechanical
stability by avoiding bending of the sample upon cooling after heat treatment arising from
differential thermal contraction of the silver and superconductor.
6.2 EXPERIMENTAL METHOD
6.2.1 TRANSPORT MEASUREMENTS
Initial sample characterisation was carried out using X-ray diffraction (XRD),
texture goniometry, and low-field transport Jc measurements at 77K. Following this
samples were mounted on a probe used in an Oxford Instruments continuous gas flow
cryostat (CFC) where the cooling of the probe head is maximised by forced convection of
159
C h a p t e r
6
:
B S C C O
T h i c k
F i l m s
h e l i u m
p a s t
t h e
s a m p l e .
T e m p e r a t u r e s t a b i l i t y w a s
a c h i e v e d
b y
u s i n g
c u r r e n t
l e a d s
o f
1 3 0 p m
t h i c k
c o p p e r
f o i l
w h i c h ,
a l o n g
w i t h t h e s a m p l e t o
b e
m e a s u r e d ,
w e r e
t h e r m a l l y
a n c h o r e d t o a c o o l e d
c o p p e r b a s e p l a t e u s i n g e l e c t r i c a l
i n s u l a t i n g
d o u b l e
s i d e d
a d h e s i v e
t a p e . T h i s
g a v e e n h a n c e d
c o o l i n g o f
t h e c u r r e n t
l e a d s
b y
m a x i m i s i n g
t h e i r
s u r f a c e
a r e a
t o
v o l u m e
r a t i o ,
a n d c o n s e q u e n t l y t h e i r
h e a t t r a n s f e r t o t h e
p r o b e ,
e n s u r i n g
t h a t
t h e
p r o b e
t e m p e r a t u r e
s e n s o r
m e a s u r e d t h e a c t u a l
s a m p l e
t e m p e r a t u r e .
T h i s w a s
n e c e s s a r y
b o t h
b e c a u s e
o f
t h e
h i g h
c u r r e n t s r e q u i r e d t o m e a s u r e
t h e
s a m p l e s a t
l o w
t e m p e r a t u r e s
a n d
b e c a u s e
o f t h e
l i m i t s o f
t h e c o o l i n g p o w e r
o f t h e C F C s y s t e m .
V o l t a g e
l e a d s
c o n s i s t e d o f
t w i s t e d p a i r s o f e n a m e l l e d
c o p p e r
w i r e f i x e d t o t h e s a m p l e
u s i n g
s i l v e r
p a i n t .
F i g u r e 6 . 2
s h o w s t h e s a m p l e m o u n t i n g
t e c h n i q u e s c h e m a t i c a l l y .
E l e c t r i c a l
I n s u l a t i n g L a y e r
S u p e r c o n d u c t o r
S i l v e r
S u b s t r a t e
C o n t i n u o u s F l o w
C r y o s t a t
P r o b e
H e a d
C o p p e r F o i l
C u r r e n t
L e a d s
S i l v e r
P a i n t
V o l t a g e
P a d s
F i g u r e
6 . 2 :
S c h e m a t i c
d i a g r a m o f
B S C C O T h i c k
f i l m
s a m p l e
m o u n t i n g
a r r a n g e m e n t o n
t h e h e a d
o f
c o n t i n u o u s
f l o w c r y o s t a t
p r o b e .
C a l c u l a t i o n s o f t h e r e s i s t a n c e
o f t h e s i l v e r s u b s t r a t e
a t
7 7 K a n d
4 . 2 K
w e r e c a r r i e d
o u t t o
d e t e r m i n e
i f
t h e c u r r e n t
w o u l d f l o w o n b o t h s i d e s o f t h e
f i l m
a t t h e s e
t e m p e r a t u r e s
( a n d
s o a t
i n t e r m e d i a t e t e m p e r a t u r e s ) .
T h i s w a s
d o n e a s
f o l l o w s .
T h e r e s i s t i v i t y
o f s i l v e r a t 7 7 K
a n d 4 . 2 K i s :
f W
7 7 / 0
=
l ( r 9 C m
p s i l v e r ( 4 . 2 K )
=
1 0 - I O Q m
F o r a
s u b s t r a t e
1 2 5 p m
t h i c k o v e r a
~ 4 x
5 m m
a r e a
( t h e
s i z e o f
e a c h
c u r r e n t
c o n t a c t ) ,
t h e
r e s i s t a n c e
t h r o u g h
t h e
s u b s t r a t e i s :
R
—
P s i h e r
'
l
A
p s i l v e r -
1 2 5 x 1 0 ÿ
4 x K r 3 - 5 x l O - 3
P s i W e r
( 6 . 1 )
1 6 0
Chapter 6 : BSCCO Thick Films
For a voltage of l|lV across the thickness of the silver at 77K, a current of
lO'6 / 6 x 10‘9 = 170A is needed. At 4.2K this current would be -1700A. These values
are considerably higher than the Ics of the samples at these temperatures, indicating that
current will flow through the silver and be conducted via both layers of superconductor
across the entire range of temperatures measured. Thus the total thickness of
superconductor (50|im) is used when calculating Jc. The magnetisation measurements (see
below) also assume that current is induced in both layers of superconductor and again its
total thickness is used when calculating the magnetic Jc.
The transport properties of three separate thick film samples were measured. R-T
measurements were carried out on all samples at zero applied magnetic field using an A.C.
technique and a measuring current of 30mA (see section 2.2). Such a high measurement
current was used due to the very low resistance of the thick films (typically ~70|iX2 at
300K).
To obtain as much information as possible measurements were carried out over a
wide range of field and temperature. This involved measurements of Jc versus B at constant
T from OmT to approximately 500mT at 5K, 25K and 5IK. Measurements in decreasing
field were carried out to determine the hysteresis of Jc with B at these temperatures. Also,
Jc versus T at constant B was measured from 5K to 80K in applied fields of OmT, 32mT,
105mT and 305mT. In all cases measurements were performed with B perpendicular to the
face of the thick film, i.e. with B parallel to the c-axis. All Jc measurements used an electric
field criterion of l|J,V/cm. Initial measurements on sample 1 used a D.C. technique, while
later measurements on sample 1 and all those on samples 2 and 3 used a pulsed current
system. These techniques are described in section 2.3.3.
R-T measurements were carried out on the last sample in the same fields at which
transport Jcs were measured to determine TC(B), the variation of sample Tc with applied
magnetic field. These used the same measuring current as the zero field R-T measurements
described above.
6.2.2 MAGNETIC MEASUREMENTS
After completion of the transport measurements magnetic measurements were
carried out on discs of 4mm diameter punched from three areas of thick film 3: the central
region between the voltage contacts, and the two ends. Three areas were measured to gain
information on any variation in properties along the length of the sample. Two types of
161
C h a p t e r
6
:
B S C C O T h i c k
F i l m s
m a g n e t i c
m e a s u r e m e n t s
w e r e c a r r i e d o u t : A C S
m e a s u r e m e n t s
a n d V S M
m e a s u r e m e n t s
( s e e
s e c t i o n s
2 . 5 . 1 a n d
2 . 4 . 1
r e s p e c t i v e l y ) .
S c a n n i n g
e l e c t r o n
m i c r o s c o p y
( S E M )
w a s
p e r f o r m e d
o n
t h e r e m a i n d e r o f
t h e
f i l m
f o l l o w i n g r e m o v a l o f
t h e
d i s c s t o
d e t e r m i n e t h e
e x t e n t o f a n y d a m a g e
a s s o c i a t e d
w i t h
t h e p u n c h i n g
p r o c e s s . A s
w i t h t h e
t r a n s p o r t
m e a s u r e m e n t s ,
a l l m a g n e t i c
m e a s u r e m e n t s w e r e p e r f o r m e d
w i t h t h e
a p p l i e d
f i e l d
p e r p e n d i c u l a r t o
t h e p l a n e
o f
t h e
s a m p l e .
T h e
f i r s t s e t
o f
m e a s u r e m e n t s
u s e d
A C S t o d e t e r m i n e t h e
s h a p e a n d
s h a r p n e s s o f
t h e
s u p e r c o n d u c t i n g
t r a n s i t i o n
f o r
c o m p a r i s o n w i t h t h e
m e a s u r e d
R - T
c u r v e s . T h e
t h r e e
d i s c s a m p l e s w e r e e a c h p l a c e d i n s i d e
a
g e l a t i n e
c a p s u l e a n d h e l d
i n
p l a c e w i t h a
p a c k i n g
o f
P T F E
t a p e
t o
p r e v e n t
a n y m o t i o n o f t h e
s a m p l e .
M e a s u r e m e n t s
w e r e
e a r n e d
o u t
f r o m 5 K
t o
1 1 0 K a t a
h e a t i n g
r a t e o f
I K
p e r m i n u t e u s i n g
a n
A . C .
a p p l i e d f i e l d o f
O . l m T
i n
D . C .
f i e l d s
o f O m T a n d 1 . 3 4 m T
( t h e
m a x i m u m t h e A C S
c o u l d p r o d u c e ) .
A l l
a p p l i e d
f i e l d s
w e r e
p e r p e n d i c u l a r
t o
t h e p l a n e o f t h e s a m p l e .
I d e n t i c a l
r u n s
w e r e c a r r i e d
o u t
u s i n g a
g e l a t i n e
c a p s u l e p a c k e d
w i t h
P T F E
t a p e a l o n e t o
p r o v i d e
a m e a s u r e m e n t
o f a n y
b a c k g r o u n d
s i g n a l .
T h i s w a s s u b t r a c t e d
f r o m
a l l t h e
s a m p l e m e a s u r e m e n t s .
F o r t h e V S M
m e a s u r e m e n t s
e a c h
o f t h e t h r e e d i s c
s a m p l e s w a s
m o u n t e d o n
t h e e n d
o f a p e r s p e x
h o l d e r r o d
u s i n g
P T F E
t a p e . M e a s u r e m e n t s w e r e
c a r r i e d
o u t
i n O T
t o
1 2 T
a p p l i e d
D . C . f i e l d w i t h a n i n c r e a s i n g
a n d d e c r e a s i n g
s w e e p
r a t e
o f l O m T
p e r
s e c o n d
a t
t e m p e r a t u r e s
o f
5 K ,
1 0 K , 1 5 K , 2 0 K ,
2 5 K ,
3 0 K ,
4 0 K
a n d
5 0 K .
A g a i n ,
a l l
a p p l i e d
f i e l d s
w e r e p e r p e n d i c u l a r
t o
t h e
p l a n e
o f t h e
s a m p l e . B e t w e e n e a c h r u n
t h e
s a m p l e
w a s h e a t e d t o
w e l l a b o v e
T c
a n d
c o o l e d a g a i n t o
e l i m i n a t e
a n y
h i s t o r y - d e p e n d a n t
e f f e c t s .
S o f t w a r e w a s
u s e d
t o e x t r a c t t h e h y s t e r e s i s
l o o p
w i d t h ,
A m ,
a s a f u n c t i o n o f f i e l d
f o r e a c h
t e m p e r a t u r e .
F u r t h e r a n a l y s i s
o f
t h e
V S M d a t a
p r o d u c e d p l o t s o f
A m
v e r s u s T a t
c o n s t a n t
B .
6 . 3 R E S U L T S
6 . 3 . 1
I N I T I A L S A M P L E
C H A R A C T E R I S A T I O N
F o l l o w i n g
p r o c e s s i n g t h e
s a m p l e s
w e r e
c h a r a c t e r i s e d
b y
a
n u m b e r
o f m e t h o d s .
X R D
w a s u s e d t o d e t e r m i n e
t h e p h a s e s p r e s e n t .
F i g u r e 6 . 3
s h o w s a t y p i c a l
X R D
p a t t e r n
f o r o n e
o f
t h e t h i c k
f i l m s .
1 6 2
Chapter 6 : BSCCO Thick Films
Figure 6.3 : A typical X-ray diffraction pattern for one of the Bi:2212 thick
films measured.
Analysis of this XRD pattern indicates the presence of approximately 8% of
Bi:2201. This is a sufficient concentration to affect pinning within the specimen if
distributed as, for example, a random array of intergrowths and would especially affect
transport measurements if it accumulated at the grain boundaries. Examination of the
BSCCO samples by optical microscopy indicates that the Bi:2201 occurs as intergrowths of
size 10-100p.m within Bi:2212 crystallites, which will certainly affect the measured
properties. The presence of Bi:2201 is confirmed using ACS, where a transition is detected
at ~25K, the Tc of Bi:2201 (see section 6.3.3).
Texture goniometry was used to determine how well aligned the superconducting
grains were relative to the silver substrate as done previously by, for example, Shamray
et al. [6.8]. This data (not shown) gives a large, sharp, peak at the centre of the scan
pattern. Analysis of this indicates that 99% of the sample aÿ-planes are aligned to within
±5° of the substrate surface.
Following the X-ray measurements, measurements of Jc were carried out in liquid
nitrogen in magnetic fields of up to 12mT. Figure 6.4 shows a typical low-field Jc versus B
plot for increasing and decreasing magnetic fields.
163
C h a p t e r
6
:
B S C C O
T h i c k
F i l m s
F i g u r e
6 . 4 : P l o t
o f
i n i t i a l
l o w - f i e l d
J c
v e r s u s
B
v a l u e s
f o r
t h i c k
f i l m
3
a t
7 7 K . S o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g
f i e l d ,
o p e n s y m b o l s
i n d i c a t e
d e c r e a s i n g f i e l d .
C a l c u l a t i o n s o f t h e s a m p l e s e l f f i e l d w e r e c a r r i e d o u t
t o h e l p
d e t e r m i n e t h e
f a c t o r s
c o n t r o l l i n g
J c
a t l o w
f i e l d s .
T h e s e l f f i e l d o f a
s a m p l e c a r r y i n g a
u n i f o r m l y
d i s t r i b u t e d
c u r r e n t
I
c a n b e c a l c u l a t e d
f r o m A m p e r e s l a w . T h i s
g i v e s
j > H
■
d l
=
7
w h e r e d l
i s
a l o n g
t h e p a t h o f i n t e g r a t i o n
( 6 . 2 )
F o r
a s a m p l e o f w i d t h w a n d
t h i c k n e s s
t ,
t h i s e q u a t i o n
b e c o m e s H
■
( 2
w
+
2 t )
-
I .
F o r t h e s a m p l e s m e a s u r e d
h e r e
w
»
t
s o H
=
7 7 2
w ,
o r
2 w
( 6 . 3 )
I n t h i s c a s e w
=
4 m m ,
a n d
I
~
1 A ,
g i v i n g a
s e l f - f i e l d
o f
~ 0 . 2 m T .
B e l o w t h i s f i e l d
t h e
s a m p l e
c u r r e n t w i l l b e l i m i t e d b y t h e
s e l f - f i e l d
r a t h e r t h a n t h e
a p p l i e d f i e l d a n d o n l y
a b o v e t h i s v a l u e w i l l t h e
J c
s t a r t t o d e c r e a s e
w i t h i n c r e a s i n g
a p p l i e d f i e l d [ 6 . 9 ] .
A t
l o w
t e m p e r a t u r e s ,
w i t h
a p p l i e d c u r r e n t s o f - 1 0 0
A ,
t h e
s e l f
f i e l d
i n c r e a s e s t o
a s
m u c h
a s ~ 2 0 m T .
H o w e v e r ,
t h i s i s l o w
c o m p a r e d t o t h e f i e l d s a p p l i e d t o t h e s a m p l e s .
T h i s
c a l c u l a t i o n i g n o r e s
f i e l d
e n h a n c e m e n t d u e t o
e d g e
e f f e c t s .
H o w e v e r ,
t h i s i s u n l i k e l y
t o
s i g n i f i c a n t l y
a f f e c t t h e
c a l c u l a t e d
r e s u l t .
1 6 4
Chapter 6 : BSCCO Thick Films
6.3.2 TRANSPORT MEASUREMENTS
Sample 1
Figure 6.6 shows the R-T characteristic for thick film 1. The voltage contacts on
this film were 5.2mm apart. It can be seen that the resistance does not fall to exactly zero.
This is due to incorrect phasing of the lock-in amplifier used arising from the low sample
resistance.
Figure 6.6 : The resistance versus temperature characteristic for thick film 1.
The inset shows a magnified view of the R-T characteristic near Tc. The line
is a guide for the eye.
Initial Jc versus T measurements on thick film 1 were carried out using a D.C.
system. The very high Ics of these samples at low temperatures made the use of this system
impracticable and it was replaced by a pulsed current system. Figure 6.7 shows the D.C.
I-V curves for thick film 1 as a function of temperature. Figure 6.8 shows Jc versus T data
taken using the D.C. and pulsed current techniques, plotted on the same axes, for
comparison.
165
Voltage
( J L L V )
C h a p t e r
6 :
B S C C O
T h i c k F i l m s
F i g u r e
6 . 7
:
D . C .
I - V
c u r v e s
f o r s a m p l e
1
a t a
r a n g e o f
t e m p e r a t u r e s .
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0
8 0
T
( K )
F i g u r e
6 . 8
:
J c
v e r s u s T d a t a
f o r
t h i c k
f i l m 1
t a k e n
u s i n g D . C .
a n d p u l s e d
c u r r e n t
t e c h n i q u e s .
N o t e t h a t a t t h e
l o w e s t
t e m p e r a t u r e s
m e a s u r e d
t h e
I c
o f
t h i s
f i l m ,
w a s m o r e t h a n 1 0 0 A .
1 6 6
Chapter 6 : BSCCO Thick Films
It can be seen that there are discrepancies between Jc taken by the D.C. technique
and that taken used pulsed current, especially at low temperatures. There are several
possible reasons for these differences :
(a) Degradation of the tape between measurements by exposure to water vapour or CO2
in the atmosphere.
(b) A systematic error in one set of equipment. Both this explanation and (a) are
unlikely due to the similarities in the high temperature measurements.
(c) Degradation due to heating by the high D.C. currents applied to the sample. This is
unlikely to have occurred as most heating will occur near the top, room-temperature, end of
the probe rather than the lower, cooled end.
(d) Differences in the I-V characteristics caused by flux creep during the D.C. current
measurements which does not have time to occur in the pulsed measurements. This would
arise because the D.C. measurement has significantly more time to equilibrate than the
pulsed measurement (on the order of minutes rather than less than a second). However,
there are several problems with this idea. First, it will tend to increase the I-V curve
measured by the pulsed technique above the D.C. case [6.10], Secondly, flux pinning is
higher, and hence creep lower at low temperatures, which implies that this effect should be
larger at high temperatures, the reverse of what is seen. Lastly, calculations of the time
constant of the system from the skin depth [6.11] indicate that the self-field of the current
should penetrate to the centre in ~5ms, much less than the width of the current pulse used
(~0.5s). These factors imply that this is not the cause of the observed effect.
(e) Voltages induced in the sample by the rapid rise of the current pulse (ringing).
These induced voltages would become larger at lower temperatures due to the current pulse
becoming larger but staying the same length and would contribute to the measured sample
voltage. This could easily raise it above the voltage criterion before the sample Jc has
actually been reached, and also cause problems by saturating the voltage amplifier (see
section 2.3.3). Measurements on a 150m coil of silver-clad Bi:2212 tape by Hase et al.
show a loss voltage of ~0.5(i.V over a 1cm length at 0.1Hz, 20K and 40A A.C. [6.12],
easily enough to significantly lower the apparent Jc. Upon consideration of the results this
is the most likely explanation of the observed discrepancy.
167
C h a p t e r
6
:
B S C C O
T h i c k
F i l m s
S a m p l e
2
F i g u r e
6 . 9 s h o w s
t h e
R - T c h a r a c t e r i s t i c
o f t h i c k
f i l m 2 n e a r
t o
T c .
F o r t h i s
s a m p l e
t h e v o l t a g e
c o n t a c t s
w e r e s p a c e d 5 . 9 m m
a p a r t .
F i g u r e
6 . 9
:
T h e r e s i s t a n c e v e r s u s t e m p e r a t u r e
c h a r a c t e r i s t i c
f o r
t h i c k
f i l m
2
n e a r t o
T c .
T h e l i n e
i s a g u i d e f o r
t h e
e y e .
F i g u r e s
6 . 1 0 a n d 6 . 1 1
s h o w
J c
v e r s u s
T
a t
c o n s t a n t B a n d
J c
v e r s u s
B
a t c o n s t a n t T
r e s p e c t i v e l y f o r t h i s t h i c k f i l m . N o t e
t h e c h a n g e i n
g r a d i e n t
a t T
~
2 5 K
f o r
a l l
t h r e e
c u r v e s
i n
f i g u r e
6 . 1 0
w h i c h
s h i f t s t o l o w e r
t e m p e r a t u r e s
w i t h i n c r e a s i n g B .
T h e r e a r e
a n u m b e r o f
p o s s i b l e
e x p l a n a t i o n s
f o r
t h i s
b e h a v i o u r ,
i n c l u d i n g
a
2 D t o 3 D
t r a n s i t i o n
i n
t h e
b e h a v i o u r f
t h e f l u x
l i n e s
( s e e
s e c t i o n
1 . 1 0 ) ,
o r a
t r a n s i t i o n
t o
s u p e r c o n d u c t i v i t y
i n t h e B i . 2 2 0 1
i n t e r g r o w t h s
i n
t h e
s a m p l e
( s e e
s e c t i o n
6 . 3 . 1 ) .
F i g u r e
6 . 1 1 s h o w s
t h a t i n
t h e
3 0 . 5 K
m e a s u r e m e n t
t h e i n c r e a s i n g
f i e l d
. / ,
r i v
■
a b o v e
t h e
d e c r e a s i n g
f i e l d
J c
b e t w e e n
~ 1 0 0 m T a n d ~ 4 0 0 m T . T h i s
i s i n d i s a g r e e m e n t w i t h
o t h e r r e s u l t s s e e n i n
H T S C s ,
w h e r e t h e
d e c r e a s i n g
f i e l d
m e a s u r e m e n t
r i s e s a b o v e
t i n -
i n c r e a s i n g
f i e l d
J c ,
a s
s h o w n ,
f o r
e x a m p l e ,
i n f i g u r e 6 . 1 3 . N o i m m e d i a t e
e x p l a n a t i o n : « •
t h i s r e s u l t i s f o r t h c o m i n g
b u t
i t
i s i n c l u d e d h e r e f o r
c o m p l e t e n e s s .
1 6 8
Chapter 6 : BSCCO Thick Films
Figure 6.10 : Plot of Jc versus T at constant B for thick film 2.
Figure 6.11 : Plot of Jc versus B at constant T for thick film 2. Solid
symbols indicate increasing field, open symbols indicate decreasing field.
Only increasing field data was taken in the 15.2K measurement.
169
C h a p t e r
6
:
B S C C O T h i c k
F i l m s
S a m p l e 3
F i g u r e
6 . 1 2 s h o w s
t h e
R - T
c h a r a c t e r i s t i c
f o r
s a m p l e 3 . F o r t h i s
s a m p l e
t h e v o l t a g e
c o n t a c t s
w e r e s p a c e d
5 . 6 m m
a p a r t . F i g u r e 6 . 1 3 s h o w s
J c
v e r s u s B a t
c o n s t a n t T ,
w h i l e
f i g u r e
6 . 1 4 s h o w s
J c
v e r s u s T a t
c o n s t a n t B .
T h e s e
c u r v e s s h o w t h e
c h a r a c t e r i s t i c
d e c r e a s e
o f
J c
w i t h b o t h B a n d
T
w h i c h i s
e x p e c t e d
i n t h i s
m a t e r i a l
[ 6 . 6 ] .
F i g u r e 6 . 1 2 : R - T
c h a r a c t e r i s t i c
f o r
t h i c k
f i l m
3 . T h e
i n s e t
s h o w s a
m a g n i f i e d v i e w
o f
t h e
R - T
c h a r a c t e r i s t i c n e a r
T c .
F i g u r e
6 . 1 3
:
P l o t
o f
J c
v e r s u s
B
a t c o n s t a n t
T
f o r
t h i c k
f i l m
3 . S o l i d
s y m b o l s
i n d i c a t e
i n c r e a s i n g
f i e l d ;
o p e n
s y m b o l s
i n d i c a t e d e c r e a s i n g f i e l d .
1 7 0
Chapter 6 : BSCCO Thick Films
Figure 6.14 : Plot of Jc versus T at constant B for thick film 3. Note the
similarities between the curves measured at different applied fields. The
insert shows the same data plotted with a linear y-axis. i
There were initial concerns that the data in figure 6.14 could be distorted by their
being field-cooled in the higher field measurements as they started above the value of Tc for
the sample at that field. However, comparison of this data with figure 6.13 showed no
significant difference between the Jcs for corresponding values of B and T, leading to the
conclusion that the Jc versus T at constant B measurements were not significantly affected
by their being initially field-cooled. This could arise because flux creep or low flux pinning
at higher temperatures allows flux to move freely between pinning centres regardless of
whether the sample was initially in the zero field cooled or field cooled state [6.13].
Figure 6.15 shows a series of R-T curves for thick film 3 measured in a number of
applied magnetic fields. These R-T curves apparently show Tc(onset) shifting with applied
field, a result which is not normally seen in high-Tc superconductors [6.14], This is
actually an effect of the silver substrate short-circuiting the superconductor when the
voltage along it rises above that required to pass the same current through the silver. For
example, the resistivity of silver at 77K is ~10'9Om. For a silver substrate 1cm long with a
cross-sectional area of 1cm x 125(im = 1.25 x 10‘6m2, this gives a resistance, at 77K,
of ~8 x l()-6f2, which agrees with the value needed to cause the effect seen in
figure 6.15.
171
Resistance
( | i £ 0
C h a p t e r
6 :
B S C C O
T h i c k
F i l m s
F i g u r e
6 . 1 5 :
P l o t
o f
r e s i s t i v e
t r a n s i t i o n s
o f
t h i c k
f i l m
3
a s a
f u n c t i o n
o f
a p p l i e d m a g n e t i c
f i e l d ,
n e a r t o
T c .
F i g u r e
6 . 1 6
:
P l o t
o f T c ( R = 0 )
v e r s u s B
f o r
t h i c k
f i l m
3 . T h e
l i n e i s a
g u i d e
f o r
t h e
e y e .
1 7 2
Chapter 6 : BSCCO Thick Films
Figure 6.16 shows the variation of Tc(R=0) with B for thick film 3 as extracted
from these curves. The rapid fall in Tc with such low applied fields indicates that the
variation is due to the suppression of weak links in the current path.
6.3.3 MAGNETIC MEASUREMENTS
Figures 6.17(a) to 6.17(c) show the results of the ACS measurements, plotting
and x” against T for the three samples measured, with the background signal subtracted,
for both D.C. applied fields.
Figure 6.17 : Plots of ACS measurements for samples cut from thick film 3.
(a) central section, (b) end 1, (c) end 2. Not all data points are shown, for
clarity.
Note the significant changes in %' and x" for all three samples in an applied field as
low as 1.34mT. Also, there is considerable variation between the three sections, with the
central section being the best and end section 2 being the worst, in terms of signal size, the
sharpness of the superconducting transition, and the sensitivity to applied field. This is
discussed in more detail in section 2.4.2.
173
C h a p t e r
6 :
B S C C O T h i c k F i l m s
A l l
t h r e e s e t s
o f m e a s u r e m e n t s
s h o w
a n
a p p a r e n t s e c o n d t r a n s i t i o n a t
~ 2 5 K ,
a l t h o u g h
t h i s
i s l e s s
c l e a r i n
f i g u r e
6 . 1 7 ( a ) .
T h i s
c o u l d b e e i t h e r a
s e c o n d p h a s e
( e . g .
B i : 2 2 0 1 )
b e c o m i n g
s u p e r c o n d u c t i n g ,
o r a
2 D t o
3 D t r a n s i t i o n
i n
t h e f l u x
l i n e s p e n e t r a t i n g
t h e s a m p l e .
A l t h o u g h t h i s t e m p e r a t u r e
a g r e e s w i t h t h a t f o u n d f o r a 2 D
t o 3 D
t r a n s i t i o n
[ 6 . 1 5 ] ,
t h e
f i e l d s u s e d
i n
t h e A C S
a r e
l o w
e n o u g h t h a t t h e
s a m p l e s
w i l l
n o t
b e
f u l l y
p e n e t r a t e d
b y
t h e
a p p l i e d
f i e l d ,
s o
t h e r e w i l l b e n o
f l u x l i n e l a t t i c e a n d
a n y
e f f e c t s
c a u s e d
b y
t h e d e c o u p l i n g o f
f l u x l i n e s i n t o
f l u x p a n c a k e s
w i l l b e
v e r y
s m a l l .
I t m i g h t
b e
e x p e c t e d t h a t
t h e
s u p e r c o n d u c t i n g
B i : 2 2 1 2
w o u l d
s c r e e n
a n y
B i : 2 2 0 1
i n t e r g r o w t h s
f r o m
t h e a p p l i e d
f i e l d ,
m a k i n g
t h e A C S i n s e n s i t i v e
t o c h a n g e s
c a u s e d
b y t h e m .
H o w e v e r ,
t h e
g r a n u l a r
s t r u c t u r e o f t h e f i l m s
a l l o w s
t h e
a p p l i e d
f i e l d t o
p e n e t r a t e
t h e m ,
a n d s o
d e t e c t
t h e c h a n g e i n
r e s p o n s e
c a u s e d b y t h e
B i : 2 2 0 1
b e c o m i n g
s u p e r c o n d u c t i n g .
B i : 2 2 0 1 h a s b e e n d e t e c t e d
i n
t h e s e s a m p l e s b y
X R D
( s e e
s e c t i o n
6 . 3 . 1 )
a n d i t s
T c
m e a s u r e d a s
~ 2 5 K
[ 6 . 1 ] ,
s o t h i s
s e c o n d t r a n s i t i o n i s i n t e r p r e t e d
a s
a r i s i n g f r o m i t .
I f a
v a l u e o f
% '
w h i c h i s
- 1 7 %
o f i t s l o w t e m p e r a t u r e
v a l u e
c o r r e s p o n d s t o t h e
f o r m a t i o n
o f t h e f i r s t c o n t i n u o u s
p e r c o l a t i v e p a t h
t h r o u g h t h e
s a m p l e
[ 6 . 1 6 ] ,
i . e . z e r o
r e s i s t a n c e ,
t h e n
c o m p a r i s o n s
c a n b e m a d e b e t w e e n
t h e t w o
m e a s u r e m e n t s . T a b l e 6 . 2
s h o w s t h i s c o m p a r i s o n
f o r t h e d i s c
f r o m t h e c e n t r a l
r e g i o n o f t h i c k
f i l m
3 u s i n g
d a t a f r o m
f i g u r e s 6 . 1 2 a n d 6 . 1 6 .
A p p l i e d D . C . F i e l d
( m T )
T
f o r x ' ( 1 7 %
s i g n a l )
( K )
T c
( R
=
0 ) ( K )
0
8 7 . 5
8 7 . 3
1 . 3 4
8 5 . 0
8 5 . 1
T a b l e 6 . 2 :
C o m p a r i s o n
o f
r e s i s t i v e
a n d
m a g n e t i c
d e t e r m i n a t i o n s
o f T c f o r
s a m p l e 3 .
T h e
v a l u e s o f
T c
f r o m t h e
t w o m e t h o d s a r e
v e r y
c l o s e ,
a l t h o u g h
t h e r e s i s t i v e
T c
i s
s l i g h t l y l o w e r
i n
t h e z e r o
f i e l d
c a s e ,
i m p l y i n g
t h a t s l i g h t l y m o r e
t h a n
1 7 %
o f
t h e s a m p l e h a d
t o b e c o m e s u p e r c o n d u c t i n g
b e f o r e
a c o n t i n u o u s p a t h
w a s e s t a b l i s h e d .
F i g u r e
6 . 1 8 s h o w s
t w o t y p i c a l
h y s t e r e s i s
l o o p s f r o m
t h e c e n t r a l
d i s c
m e a s u r e d
b y
t h e
V S M
a t 5 K a n d 2 0 K .
H y s t e r e s i s l o o p s
a t h i g h e r t e m p e r a t u r e s
a r e n o t s h o w n a s
t h e y
r a p i d l y b e c o m e
t o o
s m a l l
t o b e
d i s t i n g u i s h e d o n
t h e s c a l e u s e d
h e r e .
N o t e t h a t
t h e
s i z e
o f
t h e h y s t e r e s i s
l o o p d e c r e a s e s r a p i d l y
w i t h
t e m p e r a t u r e
a n d
t h e
2 0 K l o o p s h o w s
t h e
i r r e v e r s i b i l i t y
l i n e
a t
- 7 T .
F i g u r e 6 . 1 9 s h o w s
A m v e r s u s
T
a t c o n s t a n t
B f o r
t h e
d i s c f r o m
t h e c e n t r a l s e c t i o n
o f t h i c k f i l m
3 .
1 7 4
(EMU)
Chapter 6 : BSCCO Thick Films
1; \
Figure 6.18: two typical hysteresis loops from the central disc from thick
film 3 measured at 5K and 20K. Note that the 20K loop shows the
beginning of reversibility at ~7T.
Figure 6.19 : Plot of hysteresis loop width versus temperature for a number
of fixed applied fields for the central section of thick film 3. In ascending
order the applied fields are 0.125T, 0.25T. 0.5T, 0.75T, LOT, 1.5T, 2T,
3T, 4T, 5T, 6T, 7T, 8T, 9T, 10T and 11T.
175
C h a p t e r 6
: B S C C O
T h i c k
F i l m s
N o t e
t h e q u a l i t a t i v e
s i m i l a r i t y
b e t w e e n
t h i s b e h a v i o u r a n d
t h a t
s h o w n
i n
f i g u r e
6 . 1 4 ,
i n d i c a t i n g t h a t t h e s a m e
m e c h a n i s m m a y b e
c o n t r o l l i n g
J c
i n
b o t h
m e a s u r e m e n t s .
T h e r e s u l t s
f r o m t h e
V S M
o n t h e e n d
s e c t i o n s o f s a m p l e 3
( n o t s h o w n )
s h o w
s i m i l a r b e h a v i o u r t o
t h e c e n t r a l s e c t i o n
b u t
h a v e
s m a l l e r h y s t e r e s i s
w i d t h s ,
a n d
t h e r e f o r e
s m a l l e r
m a g n e t i s a t i o n
J c s .
T h i s
c o n f i r m s t h e A C S
r e s u l t s i n
t h a t t h e
e n d
s e c t i o n s a r e
o f
l o w e r q u a l i t y t h a n
t h e c e n t r e .
A d d i t i o n a l a n a l y s i s u s i n g
t h e B e a n
m o d e l w a s
u s e d
t o c a l c u l a t e J c ( m a g n e t i c )
v e r s u s
B f o r t h e
s a m p l e
[ 6 . 1 7 ]
f r o m
t h e h y s t e r e s i s
l o o p w i d t h
( s e e
s e c t i o n
1 . 6 . 1 )
u s i n g
t h e
f o l l o w i n g e q u a t i o n :
3 A m
I n r ' b
( 6 . 4 )
w h e r e r i s t h e
r a d i u s o f t h e
d i s c s a m p l e
( 2 m m
i n
t h i s
c a s e )
a n d
b t h e
t h i c k n e s s o f
s u p e r c o n d u c t o r ( 5 0 | _ t m
f o r
t h e s e s a m p l e s ) .
T h i s
a s s u m e s t h a t t h e
s a m p l e
i s f u l l y
p e n e t r a t e d b y t h e
a p p l i e d
f i e l d
a n d
t h a t
t h e
i n d u c e d
c u r r e n t s f l o w
h o m o g e n e o u s l y o v e r t h e
e n t i r e
d i s c ,
i . e . t h a t a l t h o u g h
t h e
J c
o f
t h e
i n t e r g r a i n s
i s
s u p p r e s s e d b y f i e l d t h e y
r e m a i n
s u p e r c o n d u c t i n g . C a l c u l a t i o n s o f
J c
a s s u m i n g
t h e s a m p l e
i s
a n
a r r a y
o f
i n d e p e n d e n t g r a i n s
w e r e
a l s o
m a d e .
T h i s a s s u m p t i o n m o d i f i e s t h e
a b o v e
e q u a t i o n t o :
3
A
m
J c
=
-
j
—
w h e r e a i s
t h e g r a i n
r a d i u s .
( 6 . 5 )
2 % r a b
H o w e v e r ,
t h e
J c s
d e r i v e d
f r o m
t h i s
w e r e
a p p r o x i m a t e l y t w o o r d e r s o f
m a g n i t u d e
h i g h e r
t h a n
t h o s e o b t a i n e d b y a s s u m i n g
c u r r e n t
f l o w s
h o m o g e n e o u s l y
o v e r
t h e w h o l e
s a m p l e .
B e c a u s e
o f
t h e m u c h
c l o s e r a g r e e m e n t b e t w e e n t h e
t r a n s p o r t
J c s
a n d t h e
m a g n e t i s a t i o n
J c s
f r o m
e q u a t i o n
6 . 4 i t
w a s d e c i d e d t o
u s e
t h i s a s s u m p t i o n i n t h e
c a l c u l a t i o n
o f t h e
r e s u l t s u s e d i n
t h i s c h a p t e r .
F i g u r e
6 . 2 0
s h o w s t w o
t y p i c a l p l o t s o f
J c ( m . a g n e t i c )
v e r s u s
B
,
a s s u m i n g c u r r e n t
f l o w s
h o m o g e n e o u s l y
o v e r t h e
w h o l e
s a m p l e .
1 7 6
Chapter 6 : BSCCO Thick Films
Figure 6.20 : Plot of Jc( magnetic) versus B at 5K and lOKfor thick film. 3.
Note the similarities of the Jc-B characteristics for the two temperatures.
SEM examination of the sample showed that the disc removal process appeared to
cause little damage (see section 6.2.3). Although it is possible that there may be
microcracks below the resolution of the magnification used (x 300) the fact that, for
example, the magnetisation Jcs are comparable with the transport Jcs indicates that the
punching process caused little deterioration of the sample magnetisation (compare
figure 6.20 with figures 6.11 and 6.13).
6.4 DISCUSSION
6.4.1 TRANSPORT MEASUREMENTS
Figure 6.14 shows that the Jc versus T at constant B measurements all have a very
similar form. This similarity suggests that there may be some kind of scaling behaviour
taking place. To explain these results it is necessary to know the factors which influence the
change in Jc. Among the possible candidates are :
(a) The breakdown of intergranular weak links within the sample with increasing field
(possible Bi:2201 intergrowths).
177
C h a p t e r
6
: B S C C O
T h i c k
F i l m s
( b ) R e d u c e d
c o u p l i n g
b e t w e e n C u O l a y e r s g i v i n g a 3 D
t o 2 D
t r a n s i t i o n .
( c )
A v a r i a t i o n o f
t h e
p i n n i n g
f o r c e
w i t h a p p l i e d
m a g n e t i c
f i e l d .
I t
i s p o s s i b l e
t h a t t h e s e e f f e c t s
a r i s e f r o m
t h e s e l f - f i e l d
o f t h e
t r a n s p o r t
c u r r e n t
i n t h e
s a m p l e ,
o r g e o m e t r i c a l e f f e c t s c a u s i n g
c o n c e n t r a t i o n s o f f i e l d i n
s o m e
p a r t s o f i t .
C a l c u l a t i o n
o f t h e s e l f - f i e l d o f a
s a m p l e
c a n b e
p e r f o r m e d u s i n g
A m p e r e s L a w ( s e e
s e c t i o n
6 . 3 . 2 ) .
I n
a n a p p l i e d
m a g n e t i c
f i e l d m u c h g r e a t e r t h a n t h e
s e l f - f i e l d ,
o r a t
t e m p e r a t u r e s
m u c h l e s s
t h a n
T c
,
t h e
s e l f - f i e l d w i l l h a v e l i t t l e e f f e c t o n
c u r r e n t f l o w
w i t h i n
t h e
s a m p l e
a s
J c
w i l l n o t b e s i g n i f i c a n t l y a f f e c t e d b y t h e
a d d i t i o n o f a r e l a t i v e l y
s m a l l
a d d i t i o n a l
f i e l d . A t
a p p l i e d f i e l d s c o m p a r a b l e t o t h e
s e l f - f i e l d
o r
t e m p e r a t u r e s n e a r t o
T c
t h e
s e l f - f i e l d w i l l
c o n c e n t r a t e t h e
t r a n s p o r t
c u r r e n t
t o w a r d s t h e c e n t r e o f t h e t h i c k
f i l m a s t h e
e d g e s
w i l l
b e
d r i v e n
t o
t h e i r l o c a l
J c
b e f o r e t h e c e n t r e .
T h i s w o u l d c a u s e
a
s h i f t
o f t h e
J c - t
c u r v e s i n t h e
o p p o s i t e s e n s e
t o t h a t
s e e n ,
w i t h
t h e l o w a p p l i e d f i e l d c u r v e s b e i n g
a f f e c t e d
m o s t a n d
t h e
h i g h f i e l d c u r v e s t h e l e a s t .
T o e l u c i d a t e t h e m e c h a n i s m
g o v e r n i n g t h i s
b e h a v i o u r ,
i t
w a s d e c i d e d
t o i n v e s t i g a t e
t h i s a p p a r e n t
s c a l i n g
o f
J c .
P l o t s w e r e m a d e o f
J c
v e r s u s
t
w h e r e
t
=
T / T C ( B )
f o r t h i c k
f i l m s 2 a n d
3 u s i n g T C ( B )
d a t a f r o m f i g u r e
6 . 1 6 .
F i g u r e s
6 . 2 1 a n d
6 . 2 2 s h o w
t h e s e
p l o t s
f o r
t h i c k f i l m s 2 a n d 3
r e s p e c t i v e l y .
0 0 . 2 0 . 4 0 . 6
0 . 8
1
T /
T
( B )
c
F i g u r e
6 . 2 1
: A p l o t , o f
J c
v e r s u s
t f o r
t h i c k
f i l m
2 s h o w i n g i m p e r f e c t
s c a l i n g
b e h a v i o u r .
1 7 8
Chapter 6 : BSCCO Thick Films
Figure 6.22 : Plot of Jc versus tfor thick film 3 showing scaling behaviour
above t greater than approximately 0.4 and three distinct regimes of
behaviour ( labelled 1, 2 and 3). The inset shows a magnified view of the
low t region with the Jc in regime 3 rising above that expected by
extrapolation from regime 2 (indicated by the solid line).
Thick film 3 shows strong evidence of scaling behaviour over a wide range of
temperature, while thick film 2 shows considerably less evidence for this, although this
may merely be due to its having a different Tc-B relationship than thick film 3. This is
likely given the high degree of variation shown by these materials [6.18].
On the Jc-t curve for thick film 3 there are three distinct regimes :
(1) t > 0.7. In this regime J(.(transport) appears to depend on t only, with no other
dependence on B. An empirical fit to this data gives
a TJc(transport ) = Jc exp kB T (6.6)
In this regime a = 8.9 x 10’23 JK'1 and Jco = 227 000 Acrn"2.
a has no variation with either Tc or B in this regime.
(2) 0.7 > t > 0.3. As in regime (1) Jc(transport) depends only on t and again follows
an exponential relationship. However, the values of a and Jco are different in this regime,
with a = 4.2 x 10-23 JK-1 and Jco » 17 300 Acur2.
179
C h a p t e r
6 :
B S C C O
T h i c k F i l m s
( 3 )
t
<
0 . 3 . I n
t h i s
r e g i m e
J c
i s
n o
l o n g e r
d o m i n a t e d b y
T c ,
a s i s
t o
b e e x p e c t e d
f o r
T
«
T c ,
a n d t h e d e p e n d e n c e
o f
J c
o n
B b e c o m e s m u c h m o r e
i m p o r t a n t , w i t h
J c
r i s i n g
a b o v e t h a t
e x p e c t e d
f r o m
a n e x t r a p o l a t i o n
f r o m
r e g i m e
( 2 )
a t
l o w e r a p p l i e d f i e l d s
a n d
f a l l i n g b e l o w
t h a t e x p e c t e d
f r o m
a n e x t r a p o l a t i o n f r o m
r e g i m e
( 2 )
a t
h i g h e r
f i e l d s .
I f
t h e b e h a v i o u r o f
t h e
J c ( t r a n s p o r t ) v e r s u s
t
c u r v e s w a s c a u s e d
b y
t h e
b r e a k d o w n
o f w e a k
l i n k s
c o n t a i n i n g , f o r
e x a m p l e ,
B i : 2 2 0 1 ,
i t w o u l d b e e x p e c t e d t h a t t h e
z e r o - f i e l d
c u r v e
a t
l e a s t w o u l d s h o w
a c h a n g e
i n
J c
w h e r e t h e w e a k l i n k s b e c o m e
s u p e r c o n d u c t i n g . I t
w o u l d
a l s o b e e x p e c t e d
t h a t t h e r e
w o u l d
b e a c h a n g e i n
t h e f o r m o f t h e
J c - t
d e p e n d e n c e
a s
t h e s a m p l e t r a n s f o r m e d
f r o m a n
a r r a y
o f S - N - S J o s e p h s o n
j u n c t i o n s
( i . e .
c o n s i s t i n g
o f
B i : 2 2 1 2 - B i : 2 2 0 1 - B i : 2 2 1 2 )
t o
a n
a r r a y
o f S - S ' - S
j u n c t i o n s . I t
c a n
b e s e e n f r o m
f i g u r e 6 . 2 2
t h a t
t h e O m T a n d
3 2 m T
J c - t
c u r v e s d o
i n d e e d s h o w
a n
i n c r e a s e a b o v e
t h a t
e x p e c t e d b y
e x t r a p o l a t i o n
f r o m r e g i m e
( 2 ) ,
i n d i c a t i n g t h a t t h e f o r m
o f t h e
J c - t
c u r v e s i n
r e g i m e ( 3 )
m a y
b e d u e
t o t h i s m e c h a n i s m .
H o w e v e r ,
t h e r e s u l t s i n
r e g i m e
( 3 )
c o u l d a l s o
b e e x p l a i n e d
b y
a 3 D t o 2 D c r o s s o v e r
i n t h i s
r e g i o n . T h i s
h a s b e e n
d e t e c t e d i n B S C C O
b y C u b i t t e t a l .
[ 6 . 1 9 ]
u s i n g
n e u t r o n
d i f f r a c t i o n .
T h e i r r e s u l t s
i n d i c a t e
t h a t ,
o v e r
t h e e n t i r e t e m p e r a t u r e
r a n g e
i n w h i c h B i : 2 2 1 2 i s
s u p e r c o n d u c t i n g ,
b e l o w B
~ 6 0 m T
t h e f l u x l i n e
l a t t i c e
i n
B i : 2 2 1 2
h a s
3 D c h a r a c t e r ,
w h i l e
a b o v e t h i s
f i e l d i t i s a
c o l l e c t i o n
o f 2 D p a n c a k e
v o r t i c e s .
A l s o ,
a
2 D t o 3 D t r a n s i t i o n a t
~ 2 5 K h a s b e e n
d e t e c t e d b y
Y a n g e t a l .
[ 6 . 1 5 ] .
T h i s 2 D t o
3 D
t r a n s i t i o n w o u l d e n h a n c e
t h e
J c
i n
t h e
3 D
s t a t e
a n d ,
l i k e
t h e e n h a n c e m e n t
b y B i : 2 2 0 1 p r e c i p i t a t e s , a g r e e s w i t h t h e d a t a
p r e s e n t e d i n
t h i s c h a p t e r
a n d e s p e c i a l l y
t h a t s h o w n
i n
f i g u r e
6 . 2 2 .
U n f o r t u n a t e l y n o
e x p e r i m e n t s
w e r e c a r r i e d
o u t w h i c h
w o u l d a l l o w t h e
d i s t i n g u i s h i n g
o f t h e
p r e c i s e
m e c h a n i s m
o f
J c
e n h a n c e m e n t i n
r e g i m e
( 3 ) .
C o m p a r i s o n
o f R e s u l t s t o
T h e o r y
A t t e m p t s
w e r e
m a d e t o
a n a l y s e t h e
J c
v e r s u s
B
a t
c o n s t a n t T
c u r v e s f r o m s a m p l e s
3
a n d
4
u s i n g
t h e
m o d e l
o f G u r e v i c h
e t a l .
[ 6 . 2 0 ] ,
T h e y m o d e l t h e
I - V c h a r a c t e r i s t i c s o f
s i l v e r - s h e a t h e d
B i : 2 2 1 2 a n d B i : 2 2 2 3 t a p e s
i n
t e r m s o f
s t r o n g
b u l k p i n n i n g m o d i f i e d
b y
t h e i m a l f l u c t u a t i o n s .
F r o m
t h e i r m o d e l
t h e
I C ( B ) o f a s i l v e r - c l a d
B i : 2 2 1 2
t a p e
w i l l f o l l o w
a
p o w e r
l a w
r e l a t i o n s h i p a t
4 . 2
K ,
d e c r e a s i n g
a s B ' a w i t h a
=
0 . 1 5 ,
a n d a t
7 7 K
i t
w i l l
d e c r e a s e
e x p o n e n t i a l l y
w i t h B . T h e r e s u l t s
o f
f i t t i n g
t h e d a t a t o
b o t h
t h e s e r e l a t i o n s h i p s
a r e
s h o w n i n
f i g u r e
6 . 2 3 .
1 8 0
Chapter 6 : BSCCO Thick Films
Figure 6.23 : Fits to Jc versus B using the theory of Gurevich et al. Solid
lines show power law fits, dashed lines exponential fits, (a) shows the fits
to the increasing field transport data, (b) shows the fits to the magnetisation
data over the same field range.
For the transport Jc measurements, neither sample 2 or sample 3 shows clear power
law or exponential behaviour at any temperature from 5K to 50K. Fits of to
Jfimagnetic) versus B at constant T gave better, but still unsatisfactory results, especially at
5K, implying that Gurevich's theory fits the intragranular behaviour better than the
intergranular behaviour, in agreement with their assumptions described above.
Attempts were also made to model the variation of Jc with t using the model of
Savvides [6.21] for a granular superconductor consisting of an array of identical
181
C h a p t e r
6
: B S C C O
T h i c k
F i l m s
J o s e p h s o n - c o u p l e d
s u p e r c o n d u c t i n g
j u n c t i o n s a r r a n g e d
o n
a
c u b i c
l a t t i c e w i t h
a l a t t i c e
c o n s t a n t
a 0 .
T h e
f o r m o f
t h e
v a r i a t i o n
o f
J c
w i t h t v a r i e s d e p e n d i n g
o n w h e t h e r
t h e
t y p e
o f
j u n c t i o n .
F o r S - I - S
j u n c t i o n s
7 C A ( T )
2 e K
• t a n h 
U
k B T
( 6 . 7 )
w h e r e
A ( 7 )
i s
t h e B C S g a p
p a r a m e t e r ,
e i s t h e
c h a r g e
o n t h e
e l e c t r o n
a n d
R n
i s
t h e
j u n c t i o n s n o r m a l s t a t e
t u n n e l l i n g
r e s i s t a n c e
( a s s u m e d
t o b e
t e m p e r a t u r e
i n d e p e n d e n t )
a n d
J c
=
I Q / C L ] . C l o s e t o
T c ,
I o
i s
p r o p o r t i o n a l t o
A 2 ( 0 )
s o t h a t
/ . < * = (
1
-
1 ) .
E x p e r i m e n t a l l y ,
A m b e g a o k a r a n d B a r a t o f f
f o u n d t h a t J
c
( 1 -
t f / 2
[ 6 . 1 0 ] ,
w h i c h
i s a s e x p e c t e d
f r o m
G - L
t h e o r y
[ 6 . 2 2 ] .
F o r
S - N - S
j u n c t i o n s
:
/ „
(
t
)
« =
( 1
-
1 ) 2
e x p
a N 4 t -
( 6 . 8 )
w h e r e a
i s
t h e t h i c k n e s s o f t h e n o r m a l
m e t a l
b a r r i e r ,
t i s t h e r e d u c e d
t e m p e r a t u r e
T / T C ( B )
a n d
i s
t h e d i s t a n c e e l e c t r o n
p a i r s
p e n e t r a t e
t h e
b a r r i e r . N e a r
T c
t h i s
e q u a t i o n
g i v e s J c ° c ( l - t . ) 2 .
T h i s e q u a t i o n i s
s t r i c t l y o n l y v a l i d n e a r t o
T c
,
b u t
d o e s
h o l d
a p p r o x i m a t e l y
f u r t h e r f r o m
T c .
T h e g e n e r a l
f o r m o f t h e
J c - B
c u r v e
i n d i c a t e d t h a t t h e
S - N - S
m o d e l
w o u l d b e t t e r
f i t t h e r e s u l t s o b t a i n e d . T h e s e f i t s a r e s h o w n i n
f i g u r e
6 . 2 4 .
F i g u r e
6 . 2 4 : F i t s t o
J c
v e r s u s t
u s i n g t h e
t h e o r y o f
S a w
i d e s
a s s u m i n g a
S - N - S
t y p e
m o d e l
f o r
i n t e r g r a n u l a r
c o n d u c t i o n . P o i n t s a r e
e x p e r i m e n t a l
d a t a . L i n e s a r e
S - N - S
f i t s
t o t h e
d a t a .
1 8 2
Chapter 6 : BSCCO Thick Films
Unfortunately, fitting this relationship to the Jc(transport) versus t data gives a bad
fit near to Tc and a good one at low T, in contradiction to the above. This may arise from
inhomogeneity giving the sample a distribution of Tcs so that the high t fits do not include
contributions from the entire sample.
6.4.2 VSM MEASUREMENTS
Because of the similarities between the Jc versus T at constant B data (figure 6.14)
and the Am versus T at constant B data (figure 6.19) scaling Am with t for the three fields
which lie within the field range of the Tc versus B measurements was carried out and is
shown in figure 6.25.
Figure 6.25 : Am versus t at constant B from magnetisation measurements
for thick film 3, showing scaling behaviour similar to' that for transport Jc
versus t at constant B.
Am versus t shows apparent scaling behaviour, in agreement with the transport
measurements shown in figure 6.22. Again three regimes are seen, although the lower t
regimes are shifted to lower temperatures than those in figure 6.22. This implies that the
same mechanism may be controlling the field and temperature behaviour in both cases.
183
C h a p t e r 6 :
B S C C O T h i c k F i l m s
6 . 4 . 3
C O M P A R I S O N
O F
M A G N E T I C
A N D T R A N S P O R T M E A S U R E M E N T S
T o c o m b i n e
t h e
m a g n e t i c a n d t r a n s p o r t
m e a s u r e m e n t s i n t o a c o h e r e n t p i c t u r e
s e v e r a l
a n a l y s e s w e r e p e r f o r m e d .
C a l c u l a t i o n
o f
A m
F i r s t
t h e m e a s u r e d
t r a n s p o r t
J c
a n d t h e d i m e n s i o n s o f
t h e
p u n c h e d o u t
d i s c s w e r e
u s e d t o
c a l c u l a t e
t h e A m w h i c h w o u l d
b e e x p e c t e d f r o m
t h a t v a l u e o f
J c
f l o w i n g o n t h e
s c a l e
o f
t h e w h o l e s a m p l e
i n
a
m a g n e t i s a t i o n
m e a s u r e m e n t .
T h i s i s d o n e u s i n g t h e
B e a n M o d e l
r e l a t i o n f o r
J c (
m a g n e t i c ) r e a r r a n g e d t o g i v e :
„
2
T t J r
( t r a n s p o r t ) h r '
A m
=
2 m
=
---
—
-
( 6 . 9 )
T h e c a l c u l a t e d
A m f r o m t h i s w a s c o m p a r e d
t o A m
t a k e n f r o m t h e V S M
m e a s u r e m e n t s .
T h i s s h o u l d
i n d i c a t e t h e p e r c e n t a g e
o f t h e
m a g n e t i c a l l y
m e a s u r e d
A m
a r i s i n g
f r o m c u r r e n t f l o w o n
t h e s c a l e o f
t h e w h o l e
s a m p l e . F i g u r e 6 . 2 6
s h o w s
a
p l o t o f
A m ( m a g n e t i c )
/
A m ( t r a n s p o r t ) v e r s u s
T f o r
t h i c k f i l m
3 . N o
c u r v e i s s h o w n
f o r
z e r o
a p p l i e d
f i e l d d u e
t o t h e d i f f i c u l t i e s o f
e x t r a c t i n g
m e a n i n g f u l d a t a f r o m a
M - H l o o p
a t l o w
f i e l d s .
F i g u r e 6 . 2 6
: A p l o t
o f
A m (
m a g n e t i c
) /
A m (
t r a n s p o r t )
v e r s u s T
f o r
t h i c k
f i l m 3 .
N o c u r v e i s s h o w n
f o r
z e r o
a p p l i e d
f i e l d
d u e
t o t h e
d i f f i c u l t i e s
o f
e x t r a c t i n g
m e a n i n g f u l
d a t a
f r o m
a
M - H
l o o p
a t
l o w
f i e l d s .
1 8 4
Chapter 6 : BSCCO Thick Films
At low fields for all T and at higher temperatures in high fields the Am calculated
from the transport Jc is higher than the Am. measured from magnetisation. Also for all fields
the ratio of Am( transport) to Am( magnetic) increases with temperature, implying that
transport currents dominate at high temperatures when the grains in the sample are
decoupled [6.23].
There is a problem with this result. It is difficult to see how Am(transport) can be
greater than Am(magnetic) as Am(magnetic) arises from
Am(magnetic) = Am( grains )+ Am( disc ) (6.10)
= intragrain), r( grains )\+ f\Jc(intergrain ), r( sample )\
grains sample
where /and/ are functions. But, Jc(intergrain) - Jc(transport) so, from the Bean
Model
Am(magnetic) ~ f[jc (intragram), r(grainsj\ + itranÿPorj)ÿ> (6.11)
so that the magnetic Am should always be larger than that calculated from transport
measurements alone.
Figure 6.27 : Schematic diagram showing variation of the form of the
sample I-V curves with tempei-ature, and how this could affect the ratio
between transport and magnetic results.
At least part of this discrepancy arises from the magnetisation measurements using
an effective voltage criterion approximately two orders of magnitude less than that of the
transport measurements [6.24]. This would only shift the magnetisation curves relative to
the transport ones if the form of the sample I-V curves remained constant with temperature,
185
C h a p t e r
6 :
B S C C O T h i c k F i l m s
i . e . t h e r a t i o
b e t w e e n
t h e m
w o u l d r e m a i n c o n s t a n t . I f
t h e f o r m
o f t h e I - V c u r v e s
c h a n g e s
w i t h
t e m p e r a t u r e
a s
s h o w n i n
f i g u r e 6 . 7
a n d
s c h e m a t i c a l l y
i n
f i g u r e
6 . 2 7
t h i s b e c o m e s
m o r e c o m p l e x a s
t h e r a t i o
b e t w e e n
t h e m a g n e t i c a n d t r a n s p o r t c u r v e s
w o u l d
t h e n
v a r y w i t h
t e m p e r a t u r e .
A n
a t t e m p t
w a s m a d e t o
c o m p a r e
t h e
m a g n e t i c
A m w i t h t h a t
c a l c u l a t e d b y
e x t r a p o l a t i n g
t h e I - V c u r v e s
s h o w n i n f i g u r e
6 . 7
d o w n
t o t h e
e f f e c t i v e
v o l t a g e
c r i t e r i o n o f
t h e m a g n e t i c m e a s u r e m e n t s
( l O n V / c m ) .
H o w e v e r ,
t h i s
c a n o n l y
b e a n
a p p r o x i m a t e
c a l c u l a t i o n a s
t h e
r e s u l t s s h o w n
i n f i g u r e 6 . 7
a r e
i n
z e r o
f i e l d ,
f o r
w h i c h
t h e r e
i s
n o
v a l i d
m a g n e t i s a t i o n
d a t a ,
a n d
f o r a d i f f e r e n t t a p e
w h i c h
i s
l i k e l y t o
h a v e
a
s o m e w h a t d i f f e r e n t
J c - T
r e l a t i o n s h i p .
F i g u r e 6 . 2 8 s h o w s
a
c o m p a r i s o n
b e t w e e n A m c a l c u l a t e d
f r o m t h e I - V
c u r v e s i n
f i g u r e
6 . 7 ,
a n d
A m (
t r a n s p o r t )
a n d
A m (
m a g n e t i c )
f o r
t a p e
3 .
F i g u r e
6 . 2 8
: C o m p a r i s o n b e t w e e n
( a )
A m f o r t a p e 1
c a l c u l a t e d
f r o m .
z e r o - f i e l d
J a t a l O n V / c m
c r i t e r i o n ,
( b )
A m f o r
t a p e
3
c a l c u l a t e d
f r o m
J
c (
t r a n s p o r t ) a t
3 2 m T
u s i n g
a l p V / c m
c r i t e r i o n , a n d
( c )
A m
f o r
t a p e 3
m e a s u r e d
a t 3 2 m T
u s i n g
a V S M .
F i g u r e 6 . 2 8
s h o w s
t h a t A m f r o m
t h e
e x t r a p o l a t e d
I - V c u r v e s i s c o n s i d e r a b l y
c l o s e r
t o
t h a t m e a s u r e d
a t
3 2 m T t h a n t h a t
c a l c u l a t e d
f r o m t h e 3 2 m T
t r a n s p o r t
J c
u s i n g a
1
p V / c m
c r i t e r i o n ,
e s p e c i a l l y a
h i g h
t e m p e r a t u r e s .
A l t h o u g h t h i s c o m p a r i s o n
c a n
o n l y
b e
a p p r o x i m a t e ,
i t i m p l i e s t h a t
a t l e a s t p a r t
o f t h e d i s c r e p a n c y b e t w e e n t r a n s p o r t
a n d m a g n e t i c
r e s u l t s
a r i s e s f r o m
t h e d i f f e r e n t e f f e c t i v e c r i t e r i a b e t w e e n
t h e m .
1 8 6
Chapter 6 : BSCCO Thick Films
Even taking the factors above into account, it is difficult to see how a cross-over
from Am( magnetic) being larger than Am(transport) to its being smaller could arise. This
implies that some of the assumptions used in the calculation of Am from Jc( transport) are
invalid. The most likely explanation is that the induced currents at high B and T are not
flowing on the scale of the entire sample in the magnetic measurements.
Calculation of Effective Sample Size
A second attempt to correlate the magnetic and transport measurements used the
following method. Jc(transport) and Am( magnetic ) were used to calculate r, the effective
radius of the sample and the length scale on which current flow occurs, assuming that
Jc(intergrain) remains constant with r. This dimension was then compared with the actual
sample dimensions.
From equation 6.4 r- 3Am( magnetic) Am( magnetic)
2 KJC ( transport )b ]] Jc( transport )
(6.12)
where Am. is the intergrain magnetisation from the VSM measurements and Jc is the
transport critical current from the transport measurements.
0 10 20 30 40 50 60
T (K)
Figure 6.29 : A plot of r( calculated) versus T for thick film 3 in three
different applied magnetic fields. The line at a normalised radius of 1
indicates the actual radius of the sample.
187
C h a p t e r
6
: B S C C O T h i c k
F i l m s
F i g u r e 6 . 2 9
s h o w s
r ( c a l c u l a t e d )
n o r m a l i s e d
t o
t h e a c t u a l
s a m p l e r a d i u s
v e r s u s T f o r
t h r e e d i f f e r e n t a p p l i e d
m a g n e t i c f i e l d s . N o z e r o - f i e l d
c u r v e
i s
s h o w n f o r t h e
s a m e
r e a s o n s
a s
m e n t i o n e d f o r f i g u r e 6 . 2 6 .
F i g u r e
6 . 2 9 s h o w s
t h a t
t h e
r a t e o f d e c r e a s e o f
r
w i t h
T i n c r e a s e s w i t h
i n c r e a s i n g
f i e l d .
H o w e v e r ,
t h e 3 2 m T d a t a a g r e e
q u i t e
w e l l w i t h
t h e a c t u a l
s a m p l e
r a d i u s
a n d
d e c r e a s e
o n l y s l i g h t l y w i t h T .
I n a l l
c a s e s t h i s d e c r e a s e i s
a p p r o x i m a t e l y l i n e a r
w i t h
T .
N o t e t h e
s i m i l a r i t y b e t w e e n t h e f o r m o f t h i s g r a p h a n d f i g u r e
6 . 2 6 ,
a l t h o u g h
t h i s p l o t
h a s a
l i n e a r
y - a x i s
a s c o m p a r e d
t o i t s l o g a r i t h m i c y - a x i s .
T h i s i s
e x p e c t e d
a s
f i g u r e
6 . 2 6
p l o t s
A m ( m a g n e t i c )
/
A m ( t r a n s p o r t )
( w h e r e A m (
t r a n s p o r t )
J c ( t r a n s p o r t )
a s
d e s c r i b e d i n
e q u a t i o n
6 . 9 )
a n d i t c a n b e s e e m f r o m
e q u a t i o n 6 . 1 2 t h a t f i g u r e
6 . 2 9
s h o u l d h a v e
a
s i m i l a r f o r m .
T h e s e r e s u l t s i m p l y
t h a t a t h i g h e r f i e l d s A m
i n c r e a s e s f a s t e r w i t h
d e c r e a s i n g
T
t h a n
J c ( t r a n s p o r t )
d o e s . T h i s
i s n o t
t h e
r e s u l t w h i c h
w o u l d
b e
e x p e c t e d , n a m e l y , r
c o n s t a n t w i t h
T
a s
A m
a n d
J c (
t r a n s p o r t . ) d e c r e a s e a t
t h e
s a m e
r a t e ,
t h e n
a
s u d d e n
c h a n g e
i n
r w h e n
t h e
g r a i n s w i t h i n t h e
s a m p l e
b e c o m e
d e c o u p l e d , e f f e c t i v e l y c a u s i n g a
s u d d e n
d r o p i n A m . T h e
c r i t e r i o n
u s e d f o r
d e t e r m i n i n g
J c
w o u l d t e n d t o o v e r e s t i m a t e
J a
s o
t h i s
c a n n o t
e x p l a i n t h e
r e s u l t s o b t a i n e d . I t i s p o s s i b l e
t h a t
J c
h a s b e e n r e d u c e d b y t h e
s e l f - f i e l d a t
l o w
t e m p e r a t u r e s
w h e r e t h e s e l f - f i e l d w i l l b e
h i g h e s t
d u e t o t h e h i g h e r
c u r r e n t s
i n v o l v e d .
H o w e v e r ,
t h e
h i g h e s t
s e l f - f i e l d a t l o w t e m p e r a t u r e s i s ~ 2 0 m T
( s e e
s e c t i o n
6 . 3 . 2 )
w h i c h w i l l
r e d u c e t h e
J c
b y - 2 0 %
( s e e ,
f o r e x a m p l e , f i g u r e
6 . 1 3 ) .
I t
i s a l s o p o s s i b l e t h a t A m
i s b e i n g
o v e r - e s t i m a t e d
b y t h e
a s s u m p t i o n
t h a t a l l t h e m e a s u r e d m a g n e t i s a t i o n
a r i s e s f r o m
c u r r e n t s c i r c u l a t i n g
o n
t h e s c a l e
o f t h e w h o l e s a m p l e .
I f
t h e r e
i s
a s i g n i f i c a n t
i n t r a g r a n u l a r
c o n t r i b u t i o n t o A m . t h e n
t h i s w i l l l e a d
t o
a
m e a s u r e d
A m l a r g e r t h a n t h e a c t u a l v a l u e .
A n a d d i t i o n a l f a c t o r
w h i c h m a y c o n t r i b u t e
t o t h i s b e h a v i o u r
i s
t h e
d e g r a d a t i o n
o f
t h e
e d g e s o f
t h e
d i s c
b y t h e
p u n c h i n g
o u t
p r o c e s s s o t h a t t h e s t r e n g t h
o f t h e i n t e r g r a i n s
i n c r e a s e s t o w a r d s
t h e c e n t r e . T h i s w o u l d m e a n t h e g r a i n s
d e c o u p l e g r a d u a l l y
i n w a r d s f r o m
t h e
e d g e
w i t h i n c r e a s i n g
T
o r
B ,
s o
g r a d u a l l y d e c r e a s i n g t h e
e f f e c t i v e
s a m p l e s i z e
i n
t h e
m a g n e t i c
m e a s u r e m e n t .
T h e
t r a n s p o r t
c u r r e n t ,
o n t h e o t h e r
h a n d ,
w a s
m e a s u r e d b e f o r e
t h e
d i s c s w e r e
p u n c h e d
o u t a n d
w i l l
a l w a y s
b e f l o w i n g o n t h e
l e n g t h
s c a l e
o f t h e
w h o l e
s a m p l e ,
e v e n
i f
o n l y
a s a
m i n o r i t y c o n t r i b u t i o n .
T h u s ,
i t w i l l
n o t s h o w t h i s e f f e c t .
T h e l a c k o f
a s t e p i n
r ( c a l c u l a t e d )
v e r s u s T c o u l d b e d u e t o
J c
g o i n g u p
f r o m
a
l o w
i n t e r g r a n u l a r
v a l u e t o a
h i g h e r
i n t r a g r a n u l a r
v a l u e a s r g o e s d o w n f r o m t h e
s i z e o f
t h e
w h o l e
s a m p l e
t o t h e a v e r a g e g r a i n
s i z e
i n s u c h
a w a y
a s t o c a n c e l o u t a n y e f f e c t t h e y
h a v e o n
o n e
1 8 8
Chapter 6 : BSCCO Thick Films
another. However, this would require a change of the same percentage for both parameters
and so can be considered unlikely.
Further Considerations
In fact the real situation will be more complex than that described above due to
separate contributions from the sample as a whole and individual grains within it.
Assuming individual grains can be described as discs, equation 6.10 becomes
Am( total ) =
2nrÿJ b+-2-
3
where 7C, band r are from the disc as a whole and Jc’, r’ and b’ are from the
individual grains. However, b and b‘ are almost certainly equal so
Am( total ) ■ 2 zb 14 + Jc rcinter (6.13)
This allows any differences in the B and T dependencies of Jc and Jc’ to be taken
into account.
Assuming a geometric average over all grains then n =
grains in the sample, so
Am( total ) ~ ( nr’ '+rJc )
nr
is the number of
(6.14)
where Jc is the measured transport Jc and r' is the grain size. Assuming r ~ 2mm
and r' ~ 100(lm then n - 400.
Rearranging this for Jc' gives
r J
- - (6.15)nr
3Amitotal)
2nr1b
Equation 6.15 was then used to calculate the intragranular Jc, as shown in
figure 6.30.
Comparing this with the measured magnetic Jcs shown in figure 6.20 indicates that
these calculated intragranular Jcs are higher than the magnetisation Jcs by a factor of about
189
Chapter 6 : BSCCO Thick Films
35. Also, at low temperatures the higher field curves show higher Jcs than the 32mT curve.
This is similar to the results obtained when calculating the effective sample radius which
also shows higher values for high fields (see figure 6.29). The form of this plot is also very
similar to that of figure 6.26. This is unsurprising as they show very similar data, with
figure 6.30 having a small correction for the transport Jc added.
su<
u
CS
3a
c3u
u
T3
a>
5
3
C3
V
Figure 6.30 : Intragranular Jc calculated from measured transport Jc and
magnetic hysteresis loop width Am.
Additional factors may be necessary to account for grain size and shape variations.
If the Bi:2212 in the sample is very well connected, but there are significant amounts of
Bi:2201 inclusions then Jc (and the other parameters) could be considered those of the
Bi:2212 while Jc' could be considered that of the Bi:2201.
Plotting Am( magnetisation) against Jc( transport) may help to elucidate the
mechanisms of the observed behaviour. Figure 6.31 shows this.
If Am and Jc increased with decreasing temperature at the same rate, this would
produce a straight line, implying that the intra- and intergrain critical currents vary with field
in the same way. This is certainly not the case for the 105mT and 305mT data. At these
higher fields Am. rises progressively higher above a straight line through the low-/c data,
implying that as the temperature decreases Jc(intragrain) rises faster than Jc( intergrain), i.e.
190
Chapter 6 : BSCCO Thick Films
that the intergranular regions are suppressed faster by field then the intragrains. This effect,
if it occurs at all, is far less pronounced in the 32mT data which is almost linear.
Figure 6.31 : Am(magnetisation) plotted against Jc(transport) for the four
applied fields at which measurements were carried out. The sample
temperature decreases from, left to right in 5K steps to a minimum of 5K.
6.4.4 COMPARISON OF RESULTS WITH SINGLE CRYSTAL DATA
The Am versus T data for thick film 3 was also compared with similar data from a
Bi:2212 single crystal with no Bi:2201 intergrowths and no weak links [6.25]. The single
crystal results are shown in figure 6.32.
The single crystal shows qualitatively similar behaviour to the data shown in figure
6.19. The differences in absolute magnitude of Am are due to the difference in the masses
of the thick film and single crystal. These results indicate that die magnetic behaviour seen
in the thick films is "intrinsic" to Bi:2212 and not caused by the partial melt processing of
the thick film.
191
C h a p t e r
6 :
B S C C O
T h i c k
F i l m s
F i g u r e
6 . 3 2
: A m
v e r s u s T m e a s u r e m e n t s
f o r
a
B i : 2 2 1 2 s i n g l e c r y s t a l ,
f o r
c o m p a r i s o n
w i t h t h e t h i c k
f i l m
r e s u l t s s h o w n i n
f i g u r e
6 . 1 9 .
6 . 5 C O N C L U S I O N S
I t a p p e a r s
t h a t
t h e
v a r i a t i o n
o f
t r a n s p o r t
J c
w i t h
a p p l i e d f i e l d
i n t h e
s a m p l e s
m e a s u r e d
i s
g o v e r n e d
o n l y b y t h e f i e l d
s u p p r e s s i o n o f c u r r e n t f l o w
i n
t h e
g r a i n
b o u n d a r i e s
d o w n
t o T / T C ( B )
=
0 . 3 . B e l o w t h i s
t e m p e r a t u r e ,
a n d
i n
l o w
f i e l d s ,
J c
r i s e s
a b o v e t h a t
e x p e c t e d b y e x t r a p o l a t i o n f r o m h i g h e r
t e m p e r a t u r e s , w h i l e
a t
h i g h e r
f i e l d s
i t
d r o p s
t o b e l o w
t h e e x t r a p o l a t e d v a l u e s . T w o
p o s s i b l e m e c h a n i s m s e x i s t w h i c h c o u l d
a c c o u n t f o r t h i s
b e h a v i o u r .
F i r s t ,
a 2 D t o
3 D
t r a n s i t i o n i n l o w f i e l d s a s t h e t e m p e r a t u r e
d r o p s b e l o w
a p p r o x i m a t e l y 2 5 K . S e c o n d l y , i t
c o u l d
a r i s e
f r o m
t h e
p r e s e n c e o f
B i : 2 2 0 1
i n t e r g r o w t h s
o r
w e a k
l i n k s
w h i c h b e c o m e
s u p e r c o n d u c t i n g
a t
~ 2 5 K ,
a n d
w h i c h ,
b e l o w t h e i r
T c
a n d a t
l o w
f i e l d s e n h a n c e
J c
b u t
w h o s e
J c s
a r e
s u p p r e s s e d
m o r e
r a p i d l y
w i t h
i n c r e a s i n g f i e l d t h a n
t h o s e
o f t h e
b u l k o f
t h e B i : 2 2 1 2
m a t e r i a l .
T h e
X R D
a n d A C S
o b s e r v a t i o n o f B i : 2 2 0 1
i n
t h e
s a m p l e s
m e a s u r e d ,
a n d
t h e r e s u l t s s h o w n
a b o v e ,
s u p p o r t
t h e
s e c o n d o f
t h e s e
a l t e r n a t i v e s .
T h i s
i s b e c a u s e l o w f i e l d e f f e c t s a r e o b s e r v e d
w h i c h
c a n n o t
b e
e x p l a i n e d b y a 2 D t o
3 D
t r a n s i t i o n ,
a l t h o u g h
t h i s c a n n o t b e
e n t i r e l y
d i s c o u n t e d
f r o m t h e h i g h e r f i e l d
r e s u l t s . F u r t h e r
w o r k i s
n e e d e d
t o
f u l l y
e l u c i d a t e t h i s m e c h a n i s m .
F r o m t h e
r e s u l t s
o b t a i n e d a m e t h o d
f o r
t h e
d e p o s i t i o n a n d
p a r t i a l
m e l t - p r o c e s s i n g o f
B i : 2 2 1 2
t h i c k
f i l m s
o n s i l v e r s u b s t r a t e s h a s b e e n
d e v e l o p e d .
H o w e v e r ,
a l t h o u g h
t h e s e
t h i c k
1 9 2
Chapter 6 : BSCCO Thick Films
films are well connected in that they exhibit high Jcs and Ics over short lengths, there
remains room for improvement in their grain boundary properties before their production
can be extended to long lengths. It is possible to envisage that partial melt-processed
Bi:2212 thick films whose Jcs are limited only by the intrinsic properties of the Bi:2212
material itself rather than by microstructural defects could be developed for technological
applications.
6.6 REFERENCES
[6.1] R. Yoshizaki, H. Ikeda, L.-X. Chen and M. Akamatsu, Physica C, 224, 121 "1!
(1994).
[6.2] P. Haidar and L. Motowidlo, Journal of Materials, 10, 54 (1992).
[6.3] J. Bock and S. Elschner in Proceedings of ACS '94, pp Boston, U.S.A., 1994
[6.4] J. Bock and E. Preisler, Solid State Communications, 72, 453 (1989).
[6.5] K. Heine, T. Tenbrick and M. Thoner, Appl. Phys. Lett.., 55, 2441 (1989).
[6.6] H. Kumakura, K. Togano, J. Kase, T. Morimoto and H. Maeda, Cryogenics,
30, 919 (1990).
[6.7] A.P. Baker, B.A. Glowacki and R. Riddle, Advances in Cryogenic Engineering -
Materials, 40, 201 (1994).
[6.8] V.F. Shamray, A.A. Babarenko, Y.Y. Efimov, T.M. Frolova and E.A. : ■]
Myasnikova, Cryst. Res. Technol., 26, 623 (1991).
[6.9] M. Nakamura, G.D. Gu and N. Koshizuka, Physica C, 225, 65 (1994).
[6.10] B.A. Glowacki (1993), Personal Communication
[6.11] L. Solymar and D. Walsh , Lectures on the Electrical Properties of Materials,
Pages, Oxford University Press, Oxford (1990)
[6.12] T. Hase, T. Egi, K. Shibutani, S. Hayashi, R. Ogawa and Y. Kawate,
Cryogenics, 34, 603 (1994).
[6.13] S.P. Ashworth, Physica C, 229, 355 (1994).
193
C h a p t e r
6 : B S C C O T h i c k
F i l m s
[ 6 . 1 4 ] J . E . E v e t t s i n C o n c i s e
E n c y c l o p a e d i a o f
M a g n e t i c
a n d S u p e r c o n d u c t i n g
M a t e r i a l s
,
p p
4 7 8 ,
e d i t e d
b y
J . E .
E v e t t s
( P e r g a m m o n
P r e s s
1 9 9 2 )
[ 6 . 1 5 ]
G . Y a n g , P . S h a n g , S . D .
S u t t o n ,
I . P .
J o n e s ,
J . S .
A b e l l a n d
C . E .
G o u g h ,
P h y s .
R e v . B ,
4 8 ,
4 0 5 4
( 1 9 9 3 ) .
[ 6 . 1 6 ]
J . E .
E v e t t s ,
B . A .
G l o w a c k i ,
P . L .
S a m p s o n , M . G . B l a m i r e ,
N . M .
A l f o r d
a n d
M . A .
H a r m e r ,
I E E E
T r a n s a c t i o n s o n
M a g n e t i c s ,
2 5 ,
2 0 4 1
( 1 9 8 9 ) .
[ 6 . 1 7 ]
C . P .
B e a n ,
R e v . M o d .
P h y s . ,
3 6 ,
3 1
( 1 9 6 4 ) .
[ 6 . 1 8 ]
C . A l l g e i e r a n d J . S .
S c h i l l i n g ,
P h y s i c a
C ,
1 6 8 ,
4 9 9
( 1 9 9 0 ) .
[ 6 . 1 9 ]
R .
C u b i t t ,
E . M . F o r g a n ,
G .
Y a n g ,
S . L .
L e e ,
D . M .
P a u l ,
H . A . M o o k ,
M .
Y e t h i r a j ,
P . H .
K e s ,
T . W .
L i ,
A . A .
M e n o v s k y , Z .
T a r n a w s k i a n d K . M o r t e n s e n ,
N a t u r e ,
3 6 5 ,
4 0 7
( 1 9 9 3 ) .
[ 6 . 2 0 ]
A .
G u r e v i c h ,
A . E .
P a s h i t s k i ,
H . S . E d e l m a n a n d
D . C .
L a r b a l e s t i e r ,
A p p l . P h y s .
L e t t . ,
6 2 ,
1 6 8 8
( 1 9 9 3 ) .
[ 6 . 2 1 ]
N .
S a v v i d e s ,
P h y s i c a
C ,
1 6 5 ,
3 7 1
( 1 9 9 0 ) .
[ 6 . 2 2 ]
V . L . G i n z b u r g
a n d L . D .
L a n d a u ,
Z h . E k s p .
T e o r .
F i z . ,
2 0 ,
1 0 6 4
( 1 9 5 0 ) .
[ 6 . 2 3 ]
C . D .
D e w h u r s t
( 1 9 9 4 ) ,
P e r s o n a l C o m m u n i c a t i o n
[ 6 . 2 4 ]
A . D . C a p l i n , L . F .
C o h e n ,
G . K . P e r k i n s a n d
A . A .
Z h u k o v ,
S u p e r c o n d .
S c i .
T e c h n o l . ,
7 ,
4 1 2
( 1 9 9 4 ) .
[ 6 . 2 5 ]
C . D . D e w h u r s t
( 1 9 9 4 ) ,
U n p u b l i s h e d D a t a
1 9 4
C h a p t e r 7
:
C o n c l u s i o n s
C H A P T E R 7
: C O N C L U S I O N S
A N D F U T U R E
W O R K
7 . 1
C O N C L U S I O N S
T h e
c o n c l u s i o n s o f e a c h c h a p t e r
a r e
l i s t e d
a t t h e
e n d o f t h e
r e l e v a n t
c h a p t e r . T h i s
c h a p t e r
p r e s e n t s a n o v e r v i e w o f t h e c o n c l u s i o n s o f t h e
t h e s i s
a s
a w h o l e .
C h a p t e r 3
s h o w s
t h a t t h e h y s t e r e s i s
i n t h e c r i t i c a l
c u r r e n t
d e n s i t y
o f s i n t e r e d
s u p e r c o n d u c t i n g c e r a m i c s f o l l o w s q u a l i t a t i v e l y
t h e
e f f e c t o f t h e m a g n e t i s a t i o n
o f t h e
g r a i n s o n t h e
i n t e r n a l
f i e l d a s
s u g g e s t e d b y
t h e m o d e l o f E v e t t s a n d
G l o w a c k i ,
b u t t h a t t h e
h y s t e r e s i s m u s t
b e d e t e r m i n e d b y t h e
l o c a l
f i e l d
d i s t r i b u t i o n o n a s c a l e
c o m p a r a b l e w i t h
t h e g r a i n
s i z e .
H o w e v e r ,
t h e
r e s u l t s
o b t a i n e d c a n n o t b e
e x p l a i n e d i n
t e r m s o f
a
c o n s t a n t
w h i c h t a k e s i n t o a c c o u n t
a n y
g e o m e t r i c a l e f f e c t s w h i c h
i n c r e a s e t h e
f i e l d
i n t h e
i n t e r g r a n u l a r w e a k l i n k s . T h e t h e o r y
o f
D ' y a c h e n k o
a p p e a r s
t o p r o v i d e
a
b e t t e r
e x p l a n a t i o n f o r
t h e
r e s u l t s o b t a i n e d .
T h e
e x p e r i m e n t s
o n
m e l t - p r o c e s s e d
Y B C O t h i c k f i l m s
i n
c h a p t e r
4 s h o w
t h a t
c u r r e n t f l o w
w i t h i n
t h e m
i s
n o t
a s i m p l e
p r o c e s s . A w a y f r o m t h e c u r r e n t
c o n t a c t s o n l y a
f r a c t i o n o f t h e
f i l m c a r r i e s t h e e n t i r e
c u r r e n t ,
t h e d e t a i l s o f
t h i s b e i n g
d e t e r m i n e d b y
t h e
a r r a n g e m e n t
o f
h i g h - / c
p a t h s t h r o u g h t h e
f i l m .
W h e n t h e c u r r e n t
e n t e r s
t h e
s a m p l e ,
a l t h o u g h i n i t i a l l y
d i s t r i b u t e d
a c r o s s
t h e w h o l e w i d t h o f t h e s a m p l e , i t
b e c o m e s ' f o c u s e d '
t h r o u g h t h e
f i r s t
g r a i n
' h u b '
i t
e n c o u n t e r s ,
a n d
f r o m
t h e r e
c o n t i n u e s o n l y a l o n g h i g h
J c
' s p o k e s ' t h r o u g h o t h e r ' h u b s ' t o
t h e
o t h e r c u r r e n t c o n t a c t . T h e
d i m e n s i o n o f
t h e ' h u b '
c r i t i c a l l y
d e t e r m i n e s t h e
o b s e r v e d
m a g n i t u d e o f t h e t r a n s p o r t
J c
i n
t h e s e
s a m p l e s ,
a n d i t i s
l i k e l y
t h a t
c o n t r o l o v e r
t h e
g r o w t h o r i e n t a t i o n o f
t h e c r y s t a l l i t e s
w i t h i n e a c h
s p o k e
w o u l d
a l s o a f f e c t
J c .
T h u s
t h e
t r a n s p o r t
J c
i s
v e r y
s e n s i t i v e t o a n y w e a k l i n k s
i n
t h e
c u r r e n t p a t h ,
a n d d r o p s o f f f a r m o r e q u i c k l y
w i t h
f i e l d t h a n t h e m a g n e t i c
J c .
T h i s c o n f i r m s t h a t i t
i s t h e
w e a k e s t l i n k s i n
t h e c u r r e n t
p a t h
t h r o u g h t h e s a m p l e w h i c h g o v e r n
t h e m e a s u r e d
t r a n s p o r t
J c .
T h i s c o m p l e x c u r r e n t f l o w m a y a l s o e x p l a i n
w h y
t h e m a g n e t i s a t i o n
d o e s n o t s c a l e
d i r e c t l y w i t h s a m p l e s i z e .
I n
c h a p t e r
5 i t
i s
f o u n d
t h a t ,
a l t h o u g h t h e m e a s u r e d T l : 1 2 2 . 3
t a p e h a s a f a i r l y h i g h
J c
a t
4 . 2 K ,
t h i s d r o p s
r a p i d l y t o a p p r o x i m a t e l y
5 %
o f t h i s
i n
m a g n e t i c f i e l d s
a s l o w
a s
I T .
B o t h
t h e l a r g e h y s t e r e s i s
o f
J c ,
r a p i d f a l l o f
J c
w i t h
B a n d s i m i l a r i t y
b e t w e e n
m e a s u r e m e n t s i n d i f f e r e n t
o r i e n t a t i o n s i m p l y
t h a t t h e s e t a p e s
a r e v e r y
g r a n u l a r ,
w i t h t h e
g r a i n s b e i n g
v e r y p o o r l y
a l i g n e d . T h i s
i s p r o b a b l y r e l a t e d t o
t h e
s p h e r o i d a l
m o r p h o l o g y
o f T l : 1 2 2 3 a r i s i n g
f r o m
i t s
s i n g l e - l a y e r e d
c r y s t a l s t r u c t u r e
w h i c h
m a k e s i t f a r m o r e
1 9 5
Chapter 7 : Conclusions
difficult to align by pressing than a material with a plate-like morphology. In contrast,
Tl:2223 shows better behaviour than Tl:1223 at very low fields, but worse behaviour at
high fields and temperatures where applications are most likely to be found. This arises
from the different irreversibility lines of the two materials.
Chapters 4 and 5 both show that a measurable inter-grain transport current flows
at a magnetic field of 8T within silver-clad tapes of Tl:1223 at 4.2K and 77K and in
melt-processed thick films of YBCO at 4.2K. The transport measurements indicate that
above fields of ~1T the Jc does not drop appreciably with applied field and that even at
temperatures as high as 77K the Tl:1223 sample exhibits a clear Jc in a field of 8T. Also,
the results show that the Jc at 77K and 8T for the Tl:1223 tape is only about 50% lower
than that at 4.2K and 8T. This indicates that Tl:1223 may be very useful for applications
at high temperatures. The observed behaviour implies no fundamental barrier to these
materials carrying very high currents at high fields and temperatures. However, the
processing of this material must be optimised before this can be achieved. The results
seen are particularly significant given the polycrystalline nature of the specimens and
emphasises their potential for use in applications.
In the Bi:2212 thick film samples measured in chapter 6 it appears that above
TCTc(B) ~ 0.3 the variation of transport Jc with applied field is governed only by the field
suppression of current flow in the grain boundaries. Below this value of T/TC(B) and in
low fields, Jc rises above that expected by extrapolation from higher temperatures, while
at higher fields it drops below the extrapolated values. This seems to be explained by the
presence of Bi:2201 intergrowths or weak links which become superconducting at ~25K,
and which, below their Tc and at low fields enhance Jc but which are suppressed more
rapidly with increasing field than the bulk of the Bi:2212 material.
The method used for the deposition and partial melt-processing of Bi:2212 thick
films on silver substrates gives films which are well connected in that they exhibit high
Jcs and Ics over short lengths. However, there remains room for improvement in their
grain boundary properties before they can be produced in long lengths.
As an overall conclusion it can safely be said that the behaviour of Jc in HTSCs is
highly complex, varying with material, processing conditions, field, field orientation,
temperature and sample history. Although some conclusions have been drawn for
individual forms of HTSC, as yet there seems to be no overall model which explains the
behaviour of Jc in individual HTSCs, and certainly not in all HTSC materials under all
circumstances.
196
C h a p t e r 7
:
C o n c l u s i o n s
7 . 2
F U T U R E
W O R K
M o r e m e a s u r e m e n t s
s h o u l d
b e c a r r i e d o u t
o n
a
v a r i e t y
o f H T S C s
i n h i g h
f i e l d s ,
o v e r a r a n g e
o f t e m p e r a t u r e s
a n d
i n
d i f f e r e n t f i e l d o r i e n t a t i o n s .
T h i s w i l l g i v e
a
f u l l r a n g e
o f i n c r e a s i n g a n d d e c r e a s i n g f i e l d
J c - B
d a t a w h i c h i t i s
h o p e d w i l l
t h e n
a l l o w a
f u l l
e x p l a n a t i o n o f t h e b e h a v i o u r o f
J c
i n t h e s e m a t e r i a l s t o b e
d i s c o v e r e d .
M o r e m e a s u r e m e n t s s h o u l d b e c a r r i e d o u t o n t h e
Y B C O t h i c k
f i l m s t o
b e t t e r
d e t e r m i n e t h e
d e t a i l s o f t h e c u r r e n t p a t h t h r o u g h t h e i n t e r g r a i n
r e g i o n s ,
a n d
a l l o w
t h e
o p t i m i s a t i o n
o f t h e
p r o c e s s i n g r o u t e s o t h a t u n i f o r m h i g h
q u a l i t y
s a m p l e s
c a n
b e
p r o d u c e d .
F u r t h e r w o r k
i n
w h i c h t h e
p r o p e r t i e s
o f T l :
1
2 2 3 ,
T l : 2 2 2 3
a n d
Y B C O a r e
c o m p a r e d a t t h e s a m e
r e d u c e d t e m p e r a t u r e s w o u l d p r o v i d e
u s e f u l
i n f o r m a t i o n
o n
t h e
r e l a t i v e
p r o p e r t i e s o f t h e s e
m a t e r i a l s .
F u r t h e r
c o m p a r i s o n
o f
t h e
t r a n s p o r t
a n d m a g n e t i c
p r o p e r t i e s o f t h e t h a l l i u m
m a t e r i a l s w o u l d
t h e n a l l o w
t h e
e l u c i d a t i o n o f
t h e
f a c t o r s
c o n t r o l l i n g t h e i r
J c
a n d t h e
m e a n s t o
p r o d u c e
m a t e r i a l s w i t h h i g h
J c s
a t h i g h
f i e l d s a n d
t e m p e r a t u r e s
I n t h e B i : 2 2 1 2 t h i c k f i l m s f u r t h e r
w o r k n e e d s t o b e
c o n d u c t e d t o
e x t e n d t h e
r a n g e
o f
t h e
t r a n s p o r t
m e a s u r e m e n t s
t o h i g h e r
f i e l d s ,
p r o v i d i n g
g r e a t e r
c o r r e l a t i o n w i t h
t h e
m a g n e t i c
m e a s u r e m e n t s
a n d
h o p e f u l l y
a l l o w i n g
t h e l o w
t e m p e r a t u r e
b e h a v i o u r o f t h e s e
f i l m s
t o
b e
f u l l y a c c o u n t e d f o r . T h i s w o u l d a l s o a l l o w t h e
c o n c l u s i v e
d e t e r m i n a t i o n o f
w h e t h e r t h i s
b e h a v i o u r a r i s e s f r o m B i : 2 2 0 1 i n t e r g r o w t h s
o r a
2 D
t o
3 D
t r a n s i t i o n .
1 9 7
A p p e n d i x
:
P u b l i c a t i o n s
A P P E N D I X :
P U B L I S H E D P A P E R S
•
' T h e
R e l a t i o n s h i p
B e t w e e n
M a g n e t i s a t i o n
a n d
H y s t e r e s i s
o f
C r i t i c a l .
C u r r e n t
i n
S i n t e r e d Y B C O ' ; A . R .
J o n e s ,
R . A .
D o y l e , F . J .
B l u n t a n d
A . M .
C a m p b e l l ;
P h y s i c a
C ;
V o l u m e
1 9 6 ;
p p 6 3 - 6 7 ; 1 9 9 2 .
• ' M a g n e t i s a t i o n
a n d T r a n s p o r t
C r i t i c a l C u r r e n t
D e n s i t i e s i n
M e l t
P r o c e s s e d
Y B a 2 C u 3 0 y
5
T h i c k F i l m s '
;
D . A .
C a r d w e l l ,
A . R .
J o n e s ,
N . J . C . I n g l e ,
A . M .
C a m p b e l l ,
N . M c N .
A l f o r d ,
T . W .
B u t t o n ,
S . J .
P e n n ,
F .
W e l l h o f e r a n d J . S . A b e l l ;
P r o c e e d i n g s
o f
E u r o p e a n C o n f e r e n c e o n A p p l i e d S u p e r c o n d u c t i v i t y
( E . U . C . A . S . ) ;
G o t t i n g e n ;
G e r m a n y ;
1 9 9 3 .
•
' T r a n s p o r t
a n d
M a g n e t i c
C r i t i c a l C u r r e n t
D e n s i t i e s i n M e l t
P r o c e s s e d
Y B a 2 C u 3 0 y
5
T h i c k F i l m s '
;
A . R .
J o n e s ,
D . A .
C a r d w e l l ,
N . J . C . I n g l e , S . P . A s h w o r t h ,
A . M .
C a m p b e l l ,
N . M c N .
A l f o r d ,
T . W .
B u t t o n ,
F . W e l l h o f e r a n d J . S . A b e l l ;
P r o c e e d i n g s
o f 7 t h
I n t e r n a t i o n a l W o r k s h o p o n
C r i t i c a l C u r r e n t s
i n
S u p e r c o n d u c t o r s ;
W o r l d
S c i e n t i f i c
P u b l i s h i n g
C o . ;
A l p b a c h ;
A u s t r i a ;
p p l 0 9 - 1 1 2 ;
1 9 9 4 .
•
' I n v e s t i g a t i o n
o f
t h e C r i t i c a l S t a t e
i n M e l t P r o c e s s e d
Y B a 2 C u 3 0 y 5
T h i c k
F i l m s '
;
D . A .
C a r d w e l l ,
A . R .
J o n e s ,
N . J . C . I n g l e , A . M .
C a m p b e l l , T . W .
B u t t o n ,
N . M c N .
A l f o r d ,
F .
W e l l h o f e r a n d J . S .
A b e l l ;
C r y o g e n i c s ;
V o l u m e
3 4 ;
N u m b e r
8 ;
p p 6 7 1 - 6 7 7 ;
1 9 9 4 .
•
' C o r r e l a t i o n
o f
T r a n s p o r t a n d M a g n e t i c
C r i t i c a l
C u r r e n t s
i n
M e l t
P r o c e s s e d
Y B a 2 C u 3 0 y _ s
T h i c k F i l m s ' - , A . R .
J o n e s ,
D . A .
C a r d w e l l ,
N . J . C . I n g l e ,
S . P . A s h w o r t h ,
A . M .
C a m p b e l l , N . M c N . A l f o r d ,
T . W .
B u t t o n ,
F . W e l l h o f e r
a n d J . S . A b e l l ;
J o u r n a l o f
A p p l i e d P h y s i c s ; V o l u m e
7 6 ,
N u m b e r
3 ,
p p l 7 2 0 - 1 7 2 5 ; 1 9 9 4 .
•
' T h e
E f f e c t o f
T h i c k n e s s o n
t h e M a g n e t i c
P r o p e r t i e s o f
M e l t - P r o c e s s e d
Y B C O T h i c k
F i l m s ' - ,
N . J . C . I n g l e , D . A .
C a r d w e l l ,
A . R .
J o n e s ,
F .
W e l l h o f e r
a n d
T . W .
B u t t o n ;
S u p e r c o n d u c t o r S c i e n c e a n d
T e c h n o l o g y , V o l u m e
8 ,
p p 2 8 2 - 2 9 0 ; 1 9 9 5 .
•
' I n v e s t i g a t i o n
o f
C u r r e n t
F l o w i n
H i g h
T e m p e r a t u r e
S u p e r c o n d u c t i n g
T h i c k
F i l m s ' ;
A . R .
J o n e s ,
A . P . B a k e r ,
C . D .
D e w h u r s t ,
S . P .
A s h w o r t h ,
D . A .
C a r d w e l l a n d
A . M .
C a m p b e l l ;
P r o c e e d i n g s
o f 7 t h C o n f e r e n c e o n
S u p e r c o n d u c t i v i t y
a n d A p p l i c a t i o n s ,
B u f f a l o ;
U . S . A . ;
p u b l i s h e d i n
A p p l i e d
S u p e r c o n d u c t i v i t y ; V o l u m e
3 ,
N u m b e r
1 - 3 ,
p p 4 7 - 5 3 ; 1 9 9 5 .
1 9 8