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.

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.

Twisting of a Pristine α-Fe Nanowire: From Wild Dislocation Avalanches to Mild Local Amorphization.

The torsion of pristine α-Fe nanowires was studied by molecular dynamics simulations. Torsion-induced plastic deformation in pristine nanowires is divided into two regimes. Under weak torsion, plastic deformation leads to dislocation nucleation and propagation. Twisting-induced dislocations are mainly 12<111> screw dislocations in a <112>-oriented nanowire. The nucleation and propagation of these dislocations were found to form avalanches which generate the emission of energy jerks. Their probability distribution function (PDF) showed power laws with mixing between different energy exponents. The mixing stemmed from simultaneous axial and radial dislocation movements. The power-law distribution indicated strongly correlated 'wild' dislocation dynamics. At the end of this regime, the dislocation pattern was frozen, and further twisting of the nanowire did not change the dislocation pattern. Instead, it induced local amorphization at the grip points at the ends of the sample. This "melting" generated highly dampened, mild avalanches. We compared the deformation mechanisms of twinned and pristine α-Fe nanowires under torsion.

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 ~ Amaxx and Amax ~ Dχ 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 Amax as predicted by MFT but scales linearly S ~ Amax. We propose that the AE rise time reflects the atomistic avalanche time profile better than the duration of the AE signal.

Avalanche criticality during ferroelectric/ferroelastic switching.

Field induced domain wall displacements define ferroelectric/ferroelastic hysteresis loops, which are at the core of piezoelectric, magnetoelectric and memristive devices. These collective displacements are scale invariant jumps with avalanche characteristics. Here, we analyse the spatial distribution of avalanches in ferroelectrics with different domain and transformation patterns: Pb(Mg1/3Nb2/3)O3-PbTiO3 contains complex domains with needles and junction patterns, while BaTiO3 has parallel straight domains. Nevertheless, their avalanche characteristics are indistinguishable. The energies, areas and perimeters of the switched regions are power law distributed with exponents close to predicted mean field values. At the coercive field, the area exponent decreases, while the fractal dimension increases. This fine structure of the switching process has not been detected before and suggests that switching occurs via criticality at the coercive field with fundamentally different switching geometries at and near this critical point. We conjecture that the domain switching process in ferroelectrics is universal at the coercive field.

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

Ferroelectric switching in ferroelastic materials with rough surfaces.

Electric switching of non-polar bulk crystals is shown to occur when domain walls are polar in ferroelastic materials and when rough surfaces with steps on an atomic scale promote domain switching. All domains emerging from surface nuclei possess polar domain walls. The progression of domains is then driven by the interaction of the electric field with the polarity of domain boundaries. In contrast, smooth surfaces with higher activation barriers prohibit effective domain nucleation. We demonstrate the existence of an electrically driven ferroelectric hysteresis loop in a non-ferroelectric, ferroelastic bulk material.

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.

Author Correction: Temperature Chaos, Memory Effect, and Domain Fluctuations in the Spiral Antiferromagnet Dy.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

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.

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.

Temperature Chaos, Memory Effect, and Domain Fluctuations in the Spiral Antiferromagnet Dy.

The spiral antiferromagnetic phase of polycrystalline dysprosium between 140 K and the Néel temperature at 178 K and its domain wall (DW) dynamics were investigated using high-resolution ultrasonic spectroscopy. Two kinetic processes of quasi-static DW motion occur under non-isothermal and isothermal conditions. A "fast" process is proportional to the rate of the temperature change and results in a new category of anelastic phenomena: magnetic transient ultrasonic internal friction (IF). This IF, related to fast moving magnetic DWs, decays rapidly after interruptions of cooling/heating cycles. A second, "slow" kinetic process is seen as logarithmic IF relaxation under isothermal conditions. This second process is glass-like and results in memory and temperature chaos effects. Low-frequency thermal fluctuations of DWs, previously detected by X-ray photon correlation spectroscopy, are related to critical fluctuations with Brownian motion-like dynamics of DWs.

Acoustic Emission from Porous Collapse and Moving Dislocations in Granular Mg-Ho Alloys under Compression and Tension.

We identified heterogeneous Mg-Ho alloys as an ideal material to measure the most extensive acoustic emission spectra available. Mg-Ho alloys are porous and show a high density of dislocations, which slide under external tension and compression. These dislocations nucleate near numerous heterogeneities. Two mechanisms compete under external forcing in the structural collapse, namely collapsing holes and the movements of dislocations. Their respective fingerprints in acoustic emission (AE) measurements are very different and relate to their individual signal strengths. Porous collapse generates very strong AE signals while dislocation movements create more but weaker AE signals. This allows the separation of the two processes even though they almost always coincide temporarily. The porous collapse follows approximately mean-field behavior (ε = 1.4, τ' = 1.82, α = 2.56, x = 1.93, χ = 1.95) with mean field scaling fulfilled. The exponents for dislocation movement are greater (ε = 1.92, τ' = 2.44, α = 3.0, x = 1.7, χ = 1.42) and follows approximately the force integrated mean-field predictions. The Omori scaling is similar for both mechanisms. The Bath's law is well fulfilled for the porous collapse but not for the dislocation movements. We suggest that such 'complex' mixing behavior is dominant in many other complex materials such as (multi-) ferroics, entropic alloys and porous ferroelastics, and, potentially, homogeneous materials with the simultaneous appearance of different collapse mechanisms.

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.

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 → ß 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 → ß 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.