Phonon Dispersion Relations in Chrystals
Authors
Peckham, Gordon Edward
Date
1964-07Awarding Institution
University of Cambridge
Qualification
Doctor of Philosophy (PhD)
Language
English
Type
Thesis
Metadata
Show full item recordCitation
Peckham, G. E. (1964). Phonon Dispersion Relations in Chrystals (Doctoral thesis). https://doi.org/10.17863/CAM.16571
Description
A note on this digital version of the thesis:
Optical character recognition was used to prepare digital text from a photocopy
of the original thesis. The document was typeset using LATEXwith the
American Mathematical Society’s package amsmath. Line drawings were rendered
into postscript using the package pstricks; other diagrams are from photocopies.
Pagination has changed – original page numbers are printed in the outside
margins. Because diagrams may be in a different location with respect to the
text some captions have been added to aid identification. The list of contents,
of course, now refers to the new page numbers.
A few typographic and spelling errors in the original have been corrected.
G. E. Peckham
2011
Abstract
Inelastic neutron scattering experiments can provide much information about
the thermal motions in solids and liquids. Neutrons which have been thermalised
by the moderator of a nuclear reactor have energies similar to those associated
with these thermal motions. It so happens that they also have wavelengths
similar to the interatomic spacing in solids and liquids. Quite large and easily
measured changes in energies and wave vectors are apparent when neutrons are
scattered from solids or liquids, and these may be related to properties of the
thermal motions.
The theory of the thermal motions in a crystalline solid is well-known, and
was first published as long ago as 1912 (Born, von Karman, 1912). The motion
is described in terms of plane waves or normal modes of vibration. At first, the
only experimental information came from specific heat measurements, and the
success of the very much simpler Debye theory did not encourage development of
the Born–von Karman crystal dynamics. However, discrepancies were apparent
and some more detailed calculations were made (e.g. Kellermann 1940).
Since the introduction of nuclear reactors, large fluxes of thermal neutrons
have been available for inelastic neutron scattering experiments. The scattering
from a single crystal enables us to deduce the phonon dispersion relation, that
is the frequency of the normal modes as a function of their wave vectors. These
experiments provide a far more direct test of theories of crystal dynamics than
do specific heat measurements.
The possibility of experimental measurements of the dispersion relation has
stimulated theoretical work on crystal dynamics. The theory of ionic crystals is
particularly well advanced. The Shell Model has been developed by Cochran and
others to give excellent agreement with the experimental dispersion relations for
the alkali halides (Cowley, Cochran, Brockhouse and Woods 1963).
This dissertation describes experiments to investigate the inelastic scattering
of neutrons from a magnesium oxide single crystal. The phonon dispersion
relation is deduced, and is discussed in terms of the Shell Model . The Shell
Model is shown to provide a good description of the crystal dynamics of magnesium
oxide. A less extensive experiment of the same type to deduce the phonon
dispersion relation for a lead single crystal is also described.
Identifiers
This record's DOI: https://doi.org/10.17863/CAM.16571