Evidence of the Monopolar-Dipolar Crossover Regime: A Multiscale Study of Ferroelastic Domains by In Situ Microscopy Techniques

The elastic interaction between kinks (and antikinks) within domain walls plays a pivotal role in shaping the domain structure, and their dynamics. In bulk materials, kinks interact as elastic monopoles, dependent on the distance between walls (d-1) and typically characterized by a rigid and straight domain configuration. In this work the evolution of the domain structure is investigated, as the sample size decreases, by the means of in situ heating microscopy techniques on free-standing samples. As the sample size decreases, a significant transformation is observed: domain walls exhibit pronounced curvature, accompanied by an increase in both domain wall and junction density. This transformation is attributed to the pronounced influence of kinks, inducing sample warping, where "dipole-dipole" interactions are dominant (d-2). Moreover, a critical thickness range that delineates a crossover between the monopolar and dipolar regimens is experimentally identified and corroborated by atomic simulations. These findings are relevant for in situ TEM studies and for the development of novel devices based on free-standing ferroic thin films and nanomaterials.

Acoustic emission of kidney stones: a medical adaptation of statistical breakdown mechanisms

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 [Formula: see text] 750 aJ, and a narrow window over which they showed wild avalanches. Uric acid stones gave moderate values of crossover energies, [Formula: see text] 200 aJ, and wild avalanche behaviour for [Formula: see text] 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 insight fragmentation by targeting the 'wild' avalanche regime.

Crackling noise microscopy

Crackling noise is a scale-invariant phenomenon found in various driven nonlinear dynamical material systems as a response to external stimuli such as force or external fields. Jerky material movements in the form of avalanches can span many orders of magnitude in size and follow universal scaling rules described by power laws. The concept was originally studied as Barkhausen noise in magnetic materials and now is used in diverse fields from earthquake research and building materials monitoring to fundamental research involving phase transitions and neural networks. Here, we demonstrate a method for nanoscale crackling noise measurements based on AFM nanoindentation, where the AFM probe can be used to study the crackling of individual nanoscale features, a technique we call crackling noise microscopy. The method is successfully applied to investigate the crackling of individual topological defects, i.e. ferroelectric domain walls. We show that critical exponents for avalanches are altered at these nanoscale features, leading to a suppression of mixed-criticality, which is otherwise present in domains. The presented concept opens the possibility of investigating the crackling of individual nanoscale features in a wide range of material systems.

Dynamic domain boundaries: chemical dopants carried by moving twin walls

Domain walls and specifically ferroelastic twin boundaries are depositaries and fast diffusion pathways for chemical dopants and intrinsic lattice defects. Ferroelastic domain patterns act as templates for chemical structures where the walls are the device and not the bulk. Several examples of such engineered domain boundaries are given. Moving twin boundaries are shown to carry with them the dopants, although the activation of this mechanism depends sensitively on the applied external force. If the force is too weak, the walls remain pinned while too strong forces break the walls free of the dopants and move them independently. Several experimental methods and approaches are discussed.

Avalanche criticality in LaAlO[Formula: see text] and the effect of aspect ratio

Ferroic domain dynamics, as a function of external stimuli, can be collectively described as scale-invariant avalanches characterised by a critical exponent that are sensitive to the complexity of the domain microstructure. The understanding and manipulation of these avalanches lies at the heart of developing novel applications such as neuromorphic computing. Here we combine in situ heating optical observations and mean-field analysis to investigate the collective domain behaviour in pure-ferroelastic lanthanum aluminate (LaAlO[Formula: see text]) as a function of aspect ratio, the ratio of sample length to width, where the movement of the domains is predominantly driven by thermal stresses via thermal expansion/contraction during heat cycling. Our observations demonstrate that the aspect ratio induces (1) distinctive domain microstructures at room temperature, (2) a deviation of dynamical behaviour at high temperatures and (3) critical exponent mixing in the higher aspect ratio samples that accompanies this behaviour. While the critical exponents of each aspect ratio fall within mean-field predicted values, we highlight the effect that the aspect ratio has in inducing exponent mixing. Hence, furthering our understanding towards tuning and controlling avalanches which is crucial for fundamental and applied research.

Energy exponents of avalanches and Hausdorff dimensions of collapse patterns

A simple numerical model to simulate athermal avalanches is presented. The model is inspired by the "porous collapse" process where the compression of porous materials generates collapse cascades, leading to power law distributed avalanches. The energy (E), amplitude (A_{max}), and size (S) exponents are derived by computer simulation in two approximations. Time-dependent "jerk" spectra are calculated in a single avalanche model where each avalanche is simulated separately from other avalanches. The average avalanche profile is parabolic, the scaling between energy and amplitude follows E∼A_{max}^{2}, and the energy exponent is ε = 1.33. Adding a general noise term in a continuous event model generates infinite avalanche sequences which allow the evaluation of waiting time distributions and pattern formation. We find the validity of the Omori law and the same exponents as in the single avalanche model. We then add spatial correlations by stipulating the ratio G/N between growth processes G (linked to a previous event location) and nucleation processes N (with new, randomly chosen nucleation sites). We found, in good approximation, a power law correlation between the energy exponent ε and the Hausdorff dimension H_{D} of the resulting collapse pattern H_{D}-1∼ɛ^{-3}. The evolving patterns depend strongly on G/N with the distribution of collapse sites equally power law distributed. Its exponent ɛ_{topo} would be linked to the dynamical exponent ε if each collapse carried an energy equivalent to the size of the collapse. A complex correlation between ɛ,ɛ_{topo}, and H_{D} emerges, depending strongly on the relative occupancy of the collapse sites in the simulation box.

Cracking of human teeth: An avalanche and acoustic emission study

Teeth are the hardest part of the human body. Cracking of human teeth under compression progresses by avalanches emitting acoustic noise. Acoustic emission (AE) spectroscopy reveals that tooth avalanches are statistically fully compatible with predictions of mean field (MF) theory. Avalanche energies collapse into a power law distributed which is stable over more than five decades with an energy exponent ε = 1.4. Acoustic amplitudes (exponent ~τ), durations (~α), correlations between amplitudes and energies (~x), and correlations between amplitude and duration (~χ) follow equally power laws with MF values of all exponents. The exponents correlation: τ-1 = x(ε-1) = (α-1)/χ is confirmed. Crack propagation bifurcates and shows the hallmarks of avalanches where main cracks nucleate secondary cracks.

The duration-energy-size enigma for acoustic emission

Acoustic emission (AE) measurements of avalanches in different systems, such as domain movements in ferroics or the collapse of voids in porous materials, cannot be compared with model predictions without a detailed analysis of the AE process. In particular, most AE experiments scale the avalanche energy E, maximum amplitude Amax and duration D as E ~ A_max^x and A_max ~ D^χ with x = 2 and a poorly defined power law distribution for the duration. In contrast, simple mean field theory (MFT) predicts that x = 3 and χ = 2. The disagreement is due to details of the AE measurements: the initial acoustic strain signal of an avalanche is modified by the propagation of the acoustic wave, which is then measured by the detector. We demonstrate, by simple model simulations, that typical avalanches follow the observed AE results with x = 2 and ‘half-moon’ shapes for the cross-correlation. Furthermore, the size S of an avalanche does not always scale as the square of the maximum AE avalanche amplitude A_max as predicted by MFT but scales linearly S ~ A_max. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.

Enhancement of polar nature of domain boundaries in ferroelastic Pb3(PO4)2 by doping divalent-metal ions

The effect of doping metal ions in ferroelastic Pb3(PO4)2 (PPO) on the polar nature of domain boundaries (DBs) was investigated using a second harmonic generation (SHG) microscope. It has been already reported that (DBs) of non-doped PPO is SH active and polar. The present study reveals that DBs of Ca-doped and Mg-doped PPO show greatly enhanced SH activity. This indicates that doping by metal ions enhances the polar nature of the DBs of PPO. This is important for future applications of DB nanotechnology. The enhancement of SH intensity is explained by a larger displacement of Ca2+ and Mg2+ ions in DBs due to smaller ionic radii. Analyses of the SH anisotropy experiments reveal that the symmetry-adapted W-wall belongs to monoclinic m and the non-adapted W'-wall to monoclinic 2. Both point groups are classified as the polar classes, which coincides with the case of pure PPO.

Domain Dynamics in Quantum-Paraelectric SrTiO_{3}

Twin dynamics forced by acoustic waves shows several linear and nonlinear response modes below T_{c}=106  K. In the quantum paraelectric state a "quantum domain glass" at 25  K<T<40  K shows intense relaxation and temperature hysteresis. Domains float collectively in a complex, smooth landscape with long relaxation times. In the "quantum domain solid" state below 25 K new phenomena occur. A temperature-dependent memory effect of the elastic response after anneal at 36 K depends on the lowest temperature reached in the quantum domain solid state below 25 K. The glassiness of twin boundary dynamics vanishes for temperatures approaching absolute zero.

Periodicity-Doubling Cascades: Direct Observation in Ferroelastic Materials

Very sensitive responses to external forces are found near phase transitions. However, transition dynamics and preequilibrium phenomena are difficult to detect and control. We have observed that the equilibrium domain structure following a phase transition in ferroelectric and ferroelastic BaTiO_{3} is attained by halving of the domain periodicity multiple times. The process is reversible, with periodicity doubling as temperature is increased. This observation is reminiscent of the period-doubling cascades generally observed during bifurcation phenomena, and, thus, it conforms to the "spatial chaos" regime earlier proposed by Jensen and Bak [Phys. Scr. T 9, 64 (1985)PHSTER0281-184710.1088/0031-8949/1985/T9/009] for systems with competing spatial modulations.

Rotatable precipitates change the scale-free to scale dependent statistics in compressed Ti nano-pillars

Compressed nano-pillars crackle from moving dislocations, which reduces plastic stability. Crackling noise is characterized by stress drops or strain bursts, which scale over a large region of sizes leading to power law statistics. Here we report that this “classic” behaviour is not valid in Ti-based nanopillars for a counterintuitive reason: we tailor precipitates inside the nano-pillar, which “regulate” the flux of dislocations. It is not because the nano-pillars become too small to sustain large dislocation movements, the effect is hence independent of size. Our precipitates act as “rotors”: local stress initiates the rotation of inclusions, which reduces the stress amplitudes dramatically. The size distribution of stress drops simultaneously changes from power law to exponential. Rotors act like revolving doors limiting the number of passing dislocations. Hence each collapse becomes weak. We present experimental evidence for Ti-based nano-pillars (diameters between 300 nm and 2 μm) with power law distributions of crackling noise P(s) ∼ s^−τ with τ ∼ 2 in the defect free or non-rotatable precipitate states. Rotors change the size distribution to P(s) ∼ exp(−s/s₀). Rotors are inclusions of ω-phase that aligns under stress along slip planes and limit dislocation glide to small distances with high nucleation rates. This opens new ways to make nano-pillars more stable.

Avalanche mixing and the simultaneous collapse of two media under uniaxial stress

Avalanches in coal and sandstone samples under common uniaxial stress serve as a model for mixing of avalanche exponents in ceramics, multiferroics, and alloys. The two media are sandwiched together and subjected to common uniaxial stress using high- and low-stress compression. Each medium collapses individually through avalanches that often coincide with secondary avalanches into the other medium. The total avalanche time sequence allows a detailed investigation of the mixing by superposition and delayed coincidence. Correlations can be described by an inter-media Båth's law.

Glasslike Dynamics of Polar Domain Walls in Cryogenic SrTiO_{3}

Polar and highly mobile domain walls in SrTiO_{3} move under electric and elastic fields. Two vastly different timescales dominate their dynamical behavior. The previously observed fast changes lead to anomalies near 40 K where the elastic moduli soften and the polarity of the walls becomes strong. Keeping the sample under isothermal conditions leads to a new and unexpected phenomenon: The softening vanishes over timescales of days while the piezoelectricity of the sample remains unchanged. The hardening follows glass dynamics below an onset at T^{*}≈40  K. The timescale of the hardening is strongly temperature dependent and can be followed experimentally down to 34 K when the relaxation is not completed within two days. The relaxation time of a stretched exponential decay increases exponentially with the decreasing temperature. This relaxation process follows similar dynamics after zero-field cooling and after applying or removing an electric field. The sluggish behavior is attributed to collective interactions of domain patterns following overdamped glass dynamics rather than ballistic dynamics.

Surface Proximity Effect, Imprint Memory of Ferroelectric Twins, and Tweed in the Paraelectric Phase of BaTiO3

We have used energy-filtered photoemission electron microscopy (PEEM) at the photoemission threshold to carry out a microscopic scale characterization of the surface charge and domain structure of the (001) surface in BaTiO₃. Signatures of ferroelectric and ferroelastic domains, and tweed, dominate the surface structure of BaTiO₃ at room temperature. The surface ferroic signatures are maintained on heating to temperature (~550 K), well above the transition temperature (393 K). This surface proximity effect provides the mechanism for memory of the bulk ferroelectric domain arrangement up to 150 K above T_C and thus can be considered as a robust fingerprint of the ferroelectric state near the surface. Self-reversal of polarization is observed for the tweed below T_C and for the surface domains above T_C. Annealing at higher temperature triggers the dynamic tweed which in turn allows a full reorganization of the ferroic domain configuration.

Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (SiO_{2}) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.

Locally preserved α → β phase transition in natural radiation-damaged titanite (CaTiSiO5): evidence from laser-induced photoluminescence and dielectric measurements

In situ temperature-dependent laser-induced photoluminescence and dielectric measurements provide new evidence for the local occurrence of the α  →  β phase transition near 500 K in the preserved crystalline parts of natural radiation-damaged titanite (sample E2335 with ~24% amorphous fraction, containing Fe and Al impurities). Photoluminescence spectroscopic measurements show an anomaly in the vicinity of 500 K. The temperature-dependent evolution of the real part of the electrical conductivity (σ) and the real (ε') and the imaginary (ε″) part of the complex dielectric permittivity (ε ^*) of titanite have been measured at various AC frequencies (~1.2-96.8 kHz). Despite the masking and smearing effect of impurities and defects, the temperature-dependent behaviour of ε' and ε″ around the transition temperature of the investigated natural titanite E2335 shows a remarkable similarity to that of the synthetic end-member material (see Zhang et al (1995 Phys. Chem. Miner. 22 41-9)). This study indicates the suitability of photoluminescence and impedance spectroscopy for the detection of phase transitions, even in heavily disordered systems.

Imaging and tuning polarity at SrTiO3 domain walls

Electrostatic fields tune the ground state of interfaces between complex oxide materials. Electronic properties, such as conductivity and superconductivity, can be tuned and then used to create and control circuit elements and gate-defined devices. Here we show that naturally occurring twin boundaries, with properties that are different from their surrounding bulk, can tune the LaAlO₃/SrTiO₃ interface 2DEG at the nanoscale. In particular, SrTiO₃ domain boundaries have the unusual distinction of remaining highly mobile down to low temperatures, and were recently suggested to be polar. Here we apply localized pressure to an individual SrTiO₃ twin boundary and detect a change in LaAlO₃/SrTiO₃ interface current distribution. Our data directly confirm the existence of polarity at the twin boundaries, and demonstrate that they can serve as effective tunable gates. As the location of SrTiO₃ domain walls can be controlled using external field stimuli, our findings suggest a novel approach to manipulate SrTiO₃-based devices on the nanoscale.

Analysis of crackling noise using the maximum-likelihood method: Power-law mixing and exponential damping

Crackling noise can be initiated by competing or coexisting mechanisms. These mechanisms can combine to generate an approximate scale invariant distribution that contains two or more contributions. The overall distribution function can be analyzed, to a good approximation, using maximum-likelihood methods and assuming that it follows a power law although with nonuniversal exponents depending on a varying lower cutoff. We propose that such distributions are rather common and originate from a simple superposition of crackling noise distributions or exponential damping.

Predicting mining collapse: Superjerks and the appearance of record-breaking events in coal as collapse precursors

The quest for predictive indicators for the collapse of coal mines has led to a robust criterion from scale-model tests in the laboratory. Mechanical collapse under uniaxial stress forms avalanches with a power-law probability distribution function of radiated energy P∼E^{-}^{ɛ}, with exponent ɛ=1.5. Impending major collapse is preceded by a reduction of the energy exponent to the mean-field value ɛ=1.32. Concurrently, the crackling noise increases in intensity and the waiting time between avalanches is reduced when the major collapse is approaching. These latter criteria were so-far deemed too unreliable for safety assessments in coal mines. We report a reassessment of previously collected extensive collapse data sets using "record-breaking analysis," based on the statistical appearance of "superjerks" within a smaller spectrum of collapse events. Superjerks are defined as avalanche signals with energies that surpass those of all previous events. The final major collapse is one such superjerk but other "near collapse" events equally qualify. In this way a very large data set of events is reduced to a sparse sequence of superjerks (21 in our coal sample). The main collapse can be anticipated from the sequence of energies and waiting times of superjerks, ignoring all weaker events. Superjerks are excellent indicators for the temporal evolution, and reveal clear nonstationarity of the crackling noise at constant loading rate, as well as self-similarity in the energy distribution of superjerks as a function of the number of events so far in the sequence E_{sj}∼n^{δ} with δ=1.79. They are less robust in identifying the precise time of the final collapse, however, than the shift of the energy exponents in the whole data set which occurs only over a short time interval just before the major event. Nevertheless, they provide additional diagnostics that may increase the reliability of such forecasts.

Strain intermittency due to avalanches in ferroelastic and porous materials

The avalanche statistics in porous materials and ferroelastic domain wall systems has been studied for slowly increasing compressive uniaxial stress with stress rates between 0.2 and 17 kPa s^-1. Velocity peaks [Formula: see text] are calculated from the measured strain drops and used to determine the corresponding Energy distributions [Formula: see text]. Power law distributions [Formula: see text] have been obtained over 4-6 decades. For most of the porous materials and domain wall systems an exponent [Formula: see text] was obtained in good agreement with mean-field theory of the interface pinning transition. For charcoal, shale and calcareous schist we found significant deviations of the exponents from mean-field values in agreement with recent acoustic emission experiments.

Direct observation of polar tweed in LaAlO3

Polar tweed was discovered in mechanically stressed LaAlO₃. Local patches of strained material (diameter ca. 5 μm) form interwoven patterns seen in birefringence images, Piezo-Force Microscopy (PFM) and Resonant Piezoelectric Spectroscopy (RPS). PFM and RPS observations prove unequivocally that electrical polarity exists inside the tweed patterns of LaAlO₃. The local piezoelectric effect varies greatly within the tweed patterns and reaches magnitudes similar to quartz. The patterns were mapped by the shift of the E_g soft-mode frequency by Raman spectroscopy.

Avalanche criticality during compression of porcine cortical bone of different ages

Crack events developed during uniaxial compression of cortical bones cut from femurs of developing pigs of several ages (4, 12, and 20 weeks) generate avalanches. These avalanches have been investigated by acoustic emission analysis techniques. The avalanche energies are power-law distributed over more than four decades. Such behavior indicates the absence of characteristic scales and suggests avalanche criticality. The statistical distributions of energies and waiting times depend on the pig age and indicate that bones become stronger, but less ductile, with increasing age. Crack propagation is equally age-dependent. Older pigs show, on average, larger cracks with a time distribution similar to those of aftershocks in earthquakes, while younger pigs show only statistically independent failure events.

Flexoelectricity, incommensurate phases and the Lifshitz point

The solutions for the minimizers of the energy density f (q, p)  =  Aq² + Bq⁴ + p² + gA,B + β(q'p - p'q)+ |q'|² +κ|p'|²] describe the flexoelectric effect with a flexoelectric coupling coefficient β. The order parameters q and p can be visualized as strain and polarisation, respectively. The parameter κ denotes the ratio of intrinsic length scales for q and p. We show that the structural ground-states include 3 phases, namely the paraelastic state q  =  p  =  0, the ferroelastic state where polarization exists inside and near twin boundaries, and the incommensurate (modulated) phases with a very rich array of structural modulations ranging from nearly pure sine waves to kink arrays and ripple states. The phases coincide in the multicritical Lifshitz point. Linear flexoelectricity p~q' is encountered only approximately inside the ferroelastic phase and near the phase boundary between the paraelastic phase and the incommensurate phase. The relationship between the polarisation and the strain gradient is highly non-linear in all other states. The spatial profiles and energy distributions are discussed in detail.

Influence of defects and domain walls on dielectric and mechanical resonances in LiNbO3

Monodomain and periodically poled LiNbO3 crystals (congruent composition) show dielectric and piezoelectric resonances between 100 K and 900 K. Dielectric measurements show resonances in some samples between 10-100 kHz. These resonances vanish under thermal anneal in monodomain crystals while they remain stable in periodically poled samples with high domain wall densities. The low activation energy of 0.18 eV suggests their electronic (bi-polaronic) origin. Resonant piezoelectric spectroscopy, RPS, shows two features in virgin samples: a relaxation peak at 420 K and a rapid hardening when the sample was slowly heated to ~500 K. The dynamic relaxation and the hardening are related to excitations and reorientations of Li defects. The relaxations and hardening are irreversibly suppressed by high temperature anneal. We do not observe domain wall related RPS resonances in annealed samples, which excludes the existence of highly charged walls. We suggest that domain walls stabilize polaronic states with (bi-)polarons located inside or near to the ferroelectric domain walls.

Breakdown of Shape Memory Effect in Bent Cu-Al-Ni Nanopillars: When Twin Boundaries Become Stacking Faults

Bent Cu-Al-Ni nanopillars (diameters 90-750 nm) show a shape memory effect, SME, for diameters D > 300 nm. The SME and the associated twinning are located in a small deformed section of the nanopillar. Thick nanopillars (D > 300 nm) transform to austenite under heating, including the deformed region. Thin nanopillars (D < 130 nm) do not twin but generate highly disordered sequences of stacking faults in the deformed region. No SME occurs and heating converts only the undeformed regions into austenite. The defect-rich, deformed region remains in the martensite phase even after prolonged heating in the stability field of austenite. A complex mixture of twins and stacking faults was found for diameters 130 nm < D < 300 nm. The size effect of the SME in Cu-Al-Ni nanopillars consists of an approximately linear reduction of the SME between 300 and 130 nm when the SME completely vanishes for smaller diameters.

Modulated minerals as potential ferroic materials

A list of potential (multi-) ferroic systems is derived based on the idea that structure gradients can generate ferroic distortions. Structure gradients are restricted here to structural modulations, which are commonly observed in natural minerals. These minerals contain transition metals and are prone to Jahn-Teller distortions and magnetic instabilities. The list contains mineral groups, which are often available in mineralogical collections.

Avalanches in compressed Ti-Ni shape-memory porous alloys: An acoustic emission study

Mechanical avalanches during compression of martensitic porous Ti-Ni have been characterized by high-frequency acoustic emission (AE). Two sequences of AE signals were found in the same sample. The first sequence is mainly generated by detwinning at the early stages of compression while fracture dominates the later stages. Fracture also determines the catastrophic failure (big crash). For high-porosity samples, the AE energies of both sequences display power-law distributions with exponents ɛ≃2 (twinning) and 1.7 (fracture). The two power laws confirm that twinning and fracture both lead to avalanche criticality during compression. As twinning precedes fracture, the observation of twinning allows us to predict incipient fracture of the porous shape memory material as an early warning sign (i.e., in bone implants) before the fracture collapse actually happens.

Strain-controlled thermal conductivity in ferroic twinned films

Large reversible changes of thermal conductivity are induced by mechanical stress, and the corresponding device is a key element for phononics applications. We show that the thermal conductivity κ of ferroic twinned thin films can be reversibly controlled by strain. Nonequilibrium molecular dynamics simulations reveal that thermal conductivity decreases linearly with the number of twin boundaries perpendicular to the direction of heat flow. Our demonstration of large and reversible changes in thermal conductivity driven by strain may inspire the design of controllable thermal switches for thermal logic gates and all-solid-state cooling devices.

Twin boundary profiles with linear-quadratic coupling between order parameters

A new type of twin boundary was found when two order parameters interact by linear-quadratic coupling QP(2). In this solution, we find that a domain wall consists of two layers in which in one layer both order parameters Q and P are active while in the second layer only Q is active. The adjacent domains are equally asymmetric (Q, P) and (Q, 0) so that one phase could be polar and/or magnetic and contain a ferroelastic strain while the second layer is ferroelastic only without polar or magnetic properties. The two layers represent a stepwise transition between the two domains.We analyze the full phase diagram depending on the coupling constant and anisotropy of the gradient term, and show that in a certain regime the order parameter Q becomes activated only in the interfacial region. A common solution contains kinks and breathers whereby the width of the interface can be very wide in agreement with the first order character of the transition.

Avalanches in compressed porous SiO(2)-based materials

The failure dynamics in SiO(2)-based porous materials under compression, namely the synthetic glass Gelsil and three natural sandstones, has been studied for slowly increasing compressive uniaxial stress with rates between 0.2 and 2.8 kPa/s. The measured collapsed dynamics is similar to Vycor, which is another synthetic porous SiO(2) glass similar to Gelsil but with a different porous mesostructure. Compression occurs by jerks of strain release and a major collapse at the failure point. The acoustic emission and shrinking of the samples during jerks are measured and analyzed. The energy of acoustic emission events, its duration, and waiting times between events show that the failure process follows avalanche criticality with power law statistics over ca. 4 decades with a power law exponent ɛ≃ 1.4 for the energy distribution. This exponent is consistent with the mean-field value for the collapse of granular media. Besides the absence of length, energy, and time scales, we demonstrate the existence of aftershock correlations during the failure process.

Predicting failure: acoustic emission of berlinite under compression

Acoustic emission has been measured and statistical characteristics analyzed during the stress-induced collapse of porous berlinite, AlPO4, containing up to 50 vol% porosity. Stress collapse occurs in a series of individual events (avalanches), and each avalanche leads to a jerk in sample compression with corresponding acoustic emission (AE) signals. The distribution of AE avalanche energies can be approximately described by a power law p(E)dE = E(-ε)dE (ε ~ 1.8) over a large stress interval. We observed several collapse mechanisms whereby less porous minerals show the superposition of independent jerks, which were not related to the major collapse at the failure stress. In highly porous berlinite (40% and 50%) an increase of energy emission occurred near the failure point. In contrast, the less porous samples did not show such an increase in energy emission. Instead, in the near vicinity of the main failure point they showed a reduction in the energy exponent to ~ 1.4, which is consistent with the value reported for compressed porous systems displaying critical behavior. This suggests that a critical avalanche regime with a lack of precursor events occurs. In this case, all preceding large events were 'false alarms' and unrelated to the main failure event. Our results identify a method to use pico-seismicity detection of foreshocks to warn of mine collapse before the main failure (the collapse) occurs, which can be applied to highly porous materials only.

Thermal and athermal crackling noise in ferroelastic nanostructures

The evolution of ferroelastic microstructures under external shear is determined by large-scale molecular dynamics simulations in two and three dimensions. Ferroelastic pattern formation was found to be almost identical in two and three dimensions, with only the ferroelastic transition temperature changing. The twin patterns generated by shear deformation depend strongly on temperature, with high wall densities nucleating under optimized temperature conditions. The dynamical tweed and mobile kink movement inside the twin walls is continuous and thermally activated at high temperatures, and becomes jerky and athermal at low temperatures. With decreasing temperature, the statistical distributions of dynamical tweed and kinks vary from a Vogel-Fulcher law P(E)~exp-(E/(T-TVF)) to an athermal power-law distribution P(E)~E-E. During the yield event, the nucleation of needles and kinks is always jerky, and the energy of the jerks is power-law distributed. Low-temperature yield proceeds via one large avalanche. With increasing temperature, the large avalanche is thermally broken up into a multitude of small segments. The power-law exponents reflect the changes in temperature, even in the athermal regime.

Avalanche correlations in the martensitic transition of a Cu-Zn-Al shape memory alloy: analysis of acoustic emission and calorimetry

The existence of temporal correlations during the intermittent dynamics of a thermally driven structural phase transition is studied in a Cu-Zn-Al alloy. The sequence of avalanches is observed by means of two techniques: acoustic emission and high sensitivity calorimetry. Both methods reveal the existence of event clustering in a way that is equivalent to the Omori correlations between aftershocks in earthquakes as are commonly used in seismology.

Thermal avalanches near a Mott transition

We probe the volume collapse transition (ΔV/Vo ∼ 15%) between the isostructural γ and α phases (T ∼ 100 K) of Ce0.9Th0.1 using the Hall effect, three-terminal capacitive dilatometry, and electrical resistivity measurements. Hall effect measurements confirm the itinerant ground state as the carrier concentration increases by a factor of 7 in the α phase, γ phase (nH = 5.28 × 10(26) m(-3)), and the α phase (nH = 3.76 × 10(27) m(-3)). We were able to detect a noise spectrum consisting of avalanches while slowly varying the temperature through the hysteretic region. We surmise that the avalanches originate from intergranular stresses at the interfaces between partially transformed high-volume and low-volume phases. The statistical distribution of avalanches obey power laws with energy exponent ϵ ≃ 1.5. Hall effect measurements, combined with universal critical exponents, point to short electron mean-free percolation pathways and carrier localization at phase interfaces. Carrier localization was predicted many years ago for elemental cerium by Johansson (1974 Phil. Mag. 30 469).

Domains within domains and walls within walls: evidence for polar domains in cryogenic SrTiO3

Resonant piezoelectric spectroscopy shows polar resonances in paraelectric SrTiO3 at temperatures below 80 K. These resonances become strong at T<40  K. The resonances are induced by weak electric fields and lead to standing mechanical waves in the sample. This piezoelectric response does not exist in paraelastic SrTiO3 nor at temperatures just below the ferroelastic phase transition. The interpretation of the resonances is related to ferroelastic twin walls which become polar at low temperatures in close analogy with the known behavior of CaTiO3. SrTiO3 is different from CaTiO3, however, because the wall polarity is thermally induced; i.e., there exists a small temperature range well below the ferroelastic transition point at 105 K where polarity appears on cooling. As the walls are atomistically thin, this transition has the hallmarks of a two-dimensional phase transition restrained to the twin boundaries rather than a classic bulk phase transition.

Resonant ultrasonic spectroscopy and resonant piezoelectric spectroscopy in ferroelastic lead phosphate, Pb3(PO4)2

Elastic properties of the ferroelastic compound Pb3(PO4)2 were investigated using resonant ultrasonic spectroscopy. Results show softening of the mechanical resonance frequencies at the D3m → C2/c ferroelastic transition temperature Ttrans = 453.6 K with no noticeable frequency dispersion. The reduction of resonance frequencies corresponds to 25% softening of the effective elastic constants at Ttrans relative to the value at 700 K. The data analysis indicates that the elastic precursor softening is driven by a displacive soft mode that is coupled to the order-disorder movements of Pb atoms around the rhombohedral threefold axis, which gives rise to local monoclinicity in the paraelastic phase. Finally, resonant piezoelectric spectroscopy (RPS) is used to determine if microstructures are polar in the cubic phase. RPS measurements find no evidence of piezoelectric signals in Pb3(PO4)2, confirming that the possible polar behavior detected using second harmonic generation is due to crystal imperfections.

Crackling noise during failure of alumina under compression: the effect of porosity

We study acoustic emission avalanches during the process of failure of porous alumina samples (Al2O3) under compression. Specimens with different porosities ranging from 30% to 59% have been synthesized from a mixture of fine-grained alumina and graphite. The compressive strength as well as the characteristics of the acoustic activity have been determined. The statistical analysis of the recorded acoustic emission pulses reveals, for all porosities, a broad distribution of energies with a fat tail, compatible with the existence of an underlying critical point. In the region of 35%-55% porosity, the energy distributions of the acoustic emission signals are compatible with a power-law behaviour over two decades in energy with an exponent ϵ = 1.8 ± 0.1.

Mechanical loss in multiferroic materials at high frequencies: friction and the evolution of ferroelastic microstructures

Energy absorption in multiferroic materials stems typically from strain relaxation which can be strong even when no extrinsic defects exist in the material. Computer simulations of a simple two-dimensional model on a generic, proper ferroelastic material identify the dissipative mechanisms associated with the dynamical motion as: a) advance and retraction of needle-shaped twin domains and, b) movement of kinks inside twin boundaries. Both movements involve friction losses.

Intermediate structures in radiation damaged titanite (CaTiSiO5): a Raman spectroscopic study

Effects of radiation damage and thermal annealing on the crystal structure of natural titanite (CaTiSiO(5)) were studied using Raman spectroscopy. The results show that well crystallized natural titanites generally have the P2(1)/a structure at the unit cell level, in contrast to the A2/a symmetry reported previously. Radiation caused by naturally incorporated impurities (such as U and Th) leads to structural damage and amorphization in titanite, as evidenced by a significant loss of band intensity, spectral broadening and frequency shifts. Additional bands (e.g. near 574 and 650 cm(-1)) occur in weakly or partially metamict titanite due to the formation of an intermediate phase (with the A2/a symmetry). Raman spectra of titanite thermal glasses showed features different from those of metamict titanite, especially in the Ti-O and Si-O stretching regions. The effect of thermal annealing is strongly affected by the initial degrees of damage that the sample experienced. Weakly damaged titanite samples showed that annealing leads to a structural recovery, and the spectral patterns of these recovered crystals are consistent with the P2(1)/a symmetry. Highly damaged titanite starts to recrystallize into an A2/a phase near 700-800 K, and additional structural modification occurs when annealed at 1300-1400 K, which involves significant change in broad Ti-O features. However, in terms of bandwidths, the metamict samples are far from fully recovered even on being annealed at 1300-1400 K.

Statistical similarity between the compression of a porous material and earthquakes

It has long been stated that there are profound analogies between fracture experiments and earthquakes; however, few works attempt a complete characterization of the parallels between these so separate phenomena. We study the acoustic emission events produced during the compression of Vycor (SiO(2)). The Gutenberg-Richter law, the modified Omori's law, and the law of aftershock productivity hold for a minimum of 5 decades, are independent of the compression rate, and keep stationary for all the duration of the experiments. The waiting-time distribution fulfills a unified scaling law with a power-law exponent close to 2.45 for long times, which is explained in terms of the temporal variations of the activity rate.

Domain wall damping and elastic softening in SrTiO3: evidence for polar twin walls

A marked change in anelastic properties, namely, elastic softening accompanied by increased damping, has been observed in a single crystal of SrTiO(3) below ~50 K by resonant ultrasound spectroscopy. This correlates with other subtle changes in structure and properties which have been explained in the past in terms of a novel quantum state and the formation of polar clusters in an incipient ferroelectric structure. Comparison of the new data, obtained at frequencies near 1 MHz, with mechanical spectroscopy data collected at a few Hz or a few kHz, reveals a distinct dispersion with frequency and is interpreted in terms of an acoustic loss mechanism which depends primarily on the mobility under stress of ferroelastic twin walls. In most ferroelastic materials, it is found that the twin walls become immobile below some low-temperature interval due to the pinning effects of defects. It is proposed instead for SrTiO(3) that associated with the local atomic displacements within the incipient ferroelectric clusters is a change in structure of the twin walls such that their mobility becomes enhanced. We propose that the structural change is not correlated with structural changes of the bulk material but relates to increasing polarity of the walls. This interpretation implies that ferroelastic domain walls in SrTiO(3) become ferroelectric at low temperatures.

High junction and twin boundary densities in driven dynamical systems

A novel mechanism for the generation of device materials with very high domain boundary densities is described: we shear the sample in a computer experiment and achieve higher twin densities than in rapid quench. These domain patterns are very stable. Elastically soft materials (image with 6.4$ \times $10(5) atoms) has greater twin densities than hard materials, even for nano-crystals.

Order-parameter coupling in the improper ferroelectric lawsonite

Low-temperature specific heat and thermal expansion measurements are used to study the hydrogen-based ferroelectric lawsonite over the temperature range 1.8 K ≤ T ≤ 300 K. The second-order phase transition near 125 K is detected in the experiments, and the low-temperature phase is determined to be improper ferroelectric and co-elastic. In the ferroelectric phase T ≤ 125 K, the spontaneous polarization P(s) is proportional to (1) the volume strain e(s), and (2) the excess entropy ΔS(e). These proportionalities confirm the improper character of the ferroelectric phase transition. We develop a structural model that allows the off-centering of hydrogen positions to generate the spontaneous polarization. In the low-temperature limit we detect a Schottky anomaly (two-level system) with an energy gap of Δ ∼ 0.5 meV.

Evidence for direct impact damage in metamict titanite CaTiSiO₅

We have measured the dose dependence of the degree of amorphization of titanite, CaTiSiO(5). Titanite is an often metamict mineral which has been considered as a matrix for the encapsulation of radiogenic waste, such as Pu. The amorphous fraction p of geologically irradiated samples (ages between 0.3 and 1 Ga) follows p = 1 - exp(-B(a)D) where D is the total dose and the characteristic amorphization mass is B(a) = 2.7(3) × 10(-19) g. Amorphization follows the direct impact mechanism where each α-decay leads to a recoil of the radiogenic atoms (mostly Th and U), which then, in turn, displaces some 5000 atoms of the titanite matrix. The amorphization behaviour is almost identical with that of zircon, ZrSiO(4), which has a similar molecular mass. While the recrystallization mechanism and elastic behaviour of the two minerals are very different, we do not find significant differences for the amorphization mechanism. Our samples have undergone little reheating over their geological history, since heating over 800 K would lead to rapid recrystallization for which we have found no evidence.

Direct observation of ferrielectricity at ferroelastic domain boundaries in CaTiO3 by electron microscopy

High-resolution aberration-corrected transmission electron microscopy aided by statistical parameter estimation theory is used to quantify localized displacements at a (110) twin boundary in orthorhombic CaTiO(3). The displacements are 3-6 pm for the Ti atoms and confined to a thin layer. This is the first direct observation of the generation of ferroelectricity by interfaces inside this material which opens the door for domain boundary engineering.

Pressure-induced phase transition(s) in KMnF3 and the importance of the excess volume for phase transitions in perovskite structures

We report a pressure-dependent investigation of KMnF(3) by x-ray diffraction up to 30 GPa. The results are discussed in the framework of Landau theory and in relation to the isostructural phase transition in SrTiO(3). The phase transition temperature near 186 K in KMnF(3) shifts to room temperature at a critical pressure of P(c) = 3.4 GPa; the pressure dependence of the transition point follows ΔP(c)/ΔT(c) = 0.0315 GPa K(-1). The transition becomes second order under high pressure, close to the tricritical point. The phase transition is determined by the rotation of MnF(6) octahedra with their simultaneous expansion along the rotation axis. The rotation angle was found to increase to 10.5° at 24 GPa. An additional anomaly was observed at higher pressure around 25 GPa, suggesting a further phase transition.

Linear–quadratic order parameter coupling and multiferroic phase transitions

The coupling between order parameters in systems with several instabilities has been analysed within Landau theory. The dominant term considered in this paper is linear in one order parameter and quadratic in the second order parameter ~QP²; other coupling terms have been treated previously. Typical examples for Q are proper or pseudo-proper ferroelastic instabilities, while P might be octahedral tilting in a perovskite, (anti-)ferromagnetic ordering or (anti-)ferroelectric soft modes. Coupling of this type is common in fluorites, Verwey transitions, Jahn-Teller systems, pnictide superconductors, etc. Analytical solutions and characteristic phase diagrams of the stable configurations are compiled. The coupling can lead to stepwise phase transitions even when the uncoupled systems would show continuous transitions. Mixed phases are common, so that many 'intermediate phases' described in the literature may be the result of this linear-quadratic coupling.

Unexpected controllable pair-structure in ferroelectric nanodomains

The imminent inability of silicon-based memory devices to satisfy Moore's Law is approaching rapidly. Controllable nanodomains of ferroic systems are anticipated to enable future high-density nonvolatile memory and novel electronic devices. We find via piezoresponse force microscopy (PFM) studies on lead zirconate titanate (PZT) films an unexpected nanostructuring of ferroelectric-ferroelastic domains. These consist of c-nanodomains within a-nanodomains in proximity to a-nanodomains within c-domains. These structures are created and annihilated as pairs, controllably. We treat these as a new kind of vertex-antivertex pair and consider them in terms of the Srolovitz-Scott 4-state Potts model, which results in pairwise domain vertex instabilities that resemble the vortex-antivortex mechanism in ferromagnetism, as well as dislocation pairs (or disclination pairs) that are well-known in nematic liquid crystals. Finally, we show that these nanopairs can be scaled up to form arrays that are engineered at will, paving the way toward facilitating them to real technologies.

Raman spectroscopy of CaSnO3 at high temperature: a highly quasi-harmonic perovskite

Calcium stannate perovskite (CaSnO(3)) has been studied by Raman spectroscopy at two excitation wavelengths (514.5 and 632.8 nm). No phase transition was observed. Rather, the thermal evolution of the Raman lines showed a high degree of harmonicity with small Grüneisen parameters and thermal line broadening following Γ=Acothθ/T, where the quantum temperature θ is determined by the phonon branch without further coupling with other degrees of freedom. The geometrical nature of phonon lines has been identified. High-temperature powder x-ray diffraction measurements provide thermal expansion coefficients of α(x)=13.9 × 10(-6) K(-1), α(y)=2.7 × 10(-6) K(-1), α(z)=14.3 × 10(-6) K(-1). The strongly quasi-harmonic behaviour observed and the lack of any indication of instability with respect to the post-perovskite structure points to the strongly first-order character of the reported perovskite to post-perovskite phase transition in this material, which appears to behave as a very good analogue to MgSiO(3) in the Earth's interior.