Domain wall dynamics and neuronic crackling noise

Abstract

Lattice parameter data from the literature have been used to provide a complete description of spontaneous strain variations across each of the six known phase transitions of WO3 in the temperature interval 5-1273 K. Analysis of strain/order parameter coupling reveals the character of each phase transition, a unified description of strain across the full temperature range, the relationship between strain and electronic effects, and new insights into the strain gradients likely to be present in each of the different domain walls that develop in four ferroelastic phases. Tetragonal and orthorhombic shear strains have values of 4-6% and 2-3% respectively, and are dominated by coupling with the order parameter for antiferroelectric-type displacements. Conversely, shear strains, $e_4$, $e_5$ and $e_6$ of up to 2% are controlled by octahedral tilting. Changes in electronic structure and properties have been related back to the susceptibility of W6+ to develop cooperative second-order-Jahn-Teller distortions. Proximity to tilt instabilities along with group-subgroup relationships in the $P4/nmm$ parent structure results in two overlapping sequences of structural phase transitions which differ in the form of their electronic structure. The possibility of a ground state structure in space group $P2_1/c$ can be rationalised in terms of the efficiency by which different combinations of shearing and tilting of the WO6 octahedra can reduce the unit cell volume and would imply that WO3 has a re-entrant phase transition. Gradients in up to three order parameters coupled with gradients in strain of up to 12% across ferroelastic domain walls indicate that the different ferroelastic phases of WO3 should have domain walls with varied and potentially exotic electronic properties for device applications such as in nanoelectronics and neuromorphic computing. Domain walls have distinct properties from the bulk and tailoring them to suit the needs of device applications is critical. Owing to the large amounts of strain stabilised across domain walls in WO3, it is a material of great interest for device applications that depend on domain wall properties. Domain wall motion and its contribution to the piezoelectric response have been investigated in WO3 from 300 K - 180 K using resonant ultrasound spectroscopy, and resonant piezoelectric spectroscopy which showed that the $P2_1/n$, $P\bar{1}$, and $P2_1/c$ phases give a piezoelectric response despite the bulk being nominally centrosymmetric. Second harmonic generation confirmed that polarity was strongest within the domain walls, and additional weak signals were found in the domains. Domain wall mobility was investigated in the $Pbcn$, $P2_1/n$, and $P2_1/c$ phases from 685 K to 5 K. Domain walls in the $P2_1/n$, and $P\bar{1}$ were more mobile than those in the $Pbcn$, and $P2_1/c$ structures and soon after the $P\bar{1}\rightarrow P2_1/c$ transition the walls become pinned at ~140 K. Domain walls in thin films of WO3 were shown to have alternating A and B domains which produce in-plane and out-of-plane piezoelectric responses. At the boundary between A and B domains "macro'' domain walls were found, and at the boundary between two A or two B domains "micro'' domain walls were found. In each case, domains and domain walls showed contrast in their piezoelectric responses, capacitance, and conductivity. The conductivity in the domains and domain walls was enhanced by He-ion irradiation, albeit over a narrow range of ion fluences. Systematic advances in the resolution and analytical interpretation of acoustic emission spectroscopy have, over the last decade, allowed for extensions into novel fields. The same dynamic failure patterns which have been identified in earthquakes, magnetism, and domain switching in ferroelastic and ferroelectric materials are shown to be equally important in medicine. In the first applications, we show that biological samples, i.e. kidney stones, can be analysed with acoustic emission and related to the progression of mechanical avalanches. Discrepancies between strong and weak acoustic emission signals are shown to have separate avalanche exponents for a urate kidney stone, with evidence of slight multi-branching. It is proposed that investigations of this nature can be adapted to the field of medicine, and in the case of kidney stones, provide a blueprint for selecting ideal combinations of energy and frequency to instigate their destruction. Kidney stones have a prevalence rate of > 10% in some countries. There has been a significant increase in surgery to treat kidney stones over the last 10 years, and it is crucial that such techniques are as effective as possible, while limiting complications. A selection of kidney stones with different chemical and structural properties were subjected to compression. Under compression, they emit acoustic signals called crackling noise. The variability of the crackling noise was surprisingly great comparing weddellite, cystine and uric acid stones. Two types of signals were found in all stones. At high energies of the emitted sound waves we found avalanche behaviour while all stones also showed signals of local, uncorrelated collapse. These two types of events are called ‘wild’ for avalanches and ‘mild’ for uncorrelated events. The key observation is that the crossover from mild to wild collapse events differs greatly between different stones. Weddellite showed brittle collapse, extremely low crossover energies (< 5 aJ), and wild avalanches over 6 orders of magnitude. In cystine and uric acid stones the collapse was more complicated with a dominance of local “mild” breakings, although they all contained some stress-induced collective avalanches. Cystine stones had high crossover energies typically ~750 aJ, and a narrow window over which they showed wild avalanches. Uric acid stones gave moderate values of crossover energies ~200 aJ, and wild avalanche behaviour for ~3 orders of magnitude. Further research extended to all stone types, and measurement of stone responses to different lithotripsy strategies, will assist in optimisation of settings of the laser and other lithotripsy devices to incite fragmentation by targeting the "wild" avalanche regime.