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A ferroelectric phase transition under an external bias electric field after field cooling and zero field cooling in barium titanate single crystals shows scale invariant nucleation and growth of complex domain structures. The avalanche energy exponents vary with the external bias, depending on the cooling history of the sample under applied field or zero field cooling. After field cooling, resulting in a single domain sample, the energy exponent is near the integrated mean field value of 5/3, namely, 1.68 ± 0.022. The sample after field cooling shows the same exponent with an external bias electric field range of up to 4.5 kV/cm. The exponent of a multi-domain sample, after zero field cooling, decreases from ε = 1.85 to the fixed point of 1.66 under high fields. The different behavior is attributed to the greater complexity of domain patterns in the multi-domain sample, which reduces to a single domain state under strong applied fields. Compared with the single-domain state, the multi-domain state has more domain boundaries and the intersections formed by these domain boundaries. These domain boundaries and their intersections will hinder the movement of the phase boundary and act as a pinning effect on the front of the phase interface. The effect is to generate more small energy signals, making the critical exponent high. At the same time, the aftershock time distribution (Omori law) remains the same for all switching conditions with an Omori exponent near −1 and switching time correlations of −1 ± 0.05 for short times (<1 s) and −2 ± 0.10 for long times (>1 s). [ABSTRACT FROM AUTHOR]

Intermittent avalanches in a multitude of materials are characterized by acoustic emission, AE, where local events lead to strain relaxations and generate shock waves (so-called "jerks"), which are measured at the sample surface. The bane of this approach is that several avalanche mechanisms may contribute to the same AE spectrum so that a detailed analysis of each individual contribution becomes virtually impossible. It is, hence, essential to develop tools to separate signals from different dynamical processes, such as ferroic domain switching, collapse of porous inclusions, dislocation movements, entanglements, and so on. Particularly, difficult cases are dynamical microstructures in fcc alloys where the AE signal strength is weak. Nevertheless, using profile analysis of AE signals, we can distinguish between two mechanisms, namely, dislocation movements and dynamic entanglements in fcc 316L stainless steel. In this approach, we are able to measure the statistical AE durations of both subsets separately. The fingerprint for superposed avalanches with different durations is seen by the scaling between the energy E and the maximum amplitude A of each avalanche E ∼ Ax with x = 2. While the same exponent x applies for both mechanisms, the scaling relation shows two branches with different absolute energy values. The two mechanisms are then confirmed by separating the energy distributions P(E) ∼ E−ε for the two mechanisms with ε = 1.55 for dislocation movements and ε = 1.36 for entanglements. [ABSTRACT FROM AUTHOR]

A ferroelectric hysteresis depends on the orientation of the applied field with respect to the spontaneous polarization. The ferroelectric switching occurs through correlated domain movements forming avalanches. We tested whether avalanches in single crystals of the prototypic ferroelectric BaTiO3 and the relaxor ferroelectric 0.7Pb(Mg2/3Nb1/3)O3–0.3PbTiO3 show anisotropic field dependences. The anisotropy of the energy exponent of avalanches is very small in BaTiO3 with exponents between 1.53 and 1.6, which is remarkably close to the prediction of mean field theory 5/3. The anisotropy is much stronger in 0.7Pb(Mg2/3Nb1/3)O3–0.3PbTiO3 with one exponent slightly above the typical range of mean field values (4/3–5/3): 1.43 ± 0.02, 1.64 ± 0.03, and 1.79 ± 0.03 for fields along [100], [110], and [111], respectively. This anisotropy indicates a variation of the fractal dimensions of the transient domain patterns depending on the direction of the switching field. [ABSTRACT FROM AUTHOR]

The investigation of acoustic emission (AE) reveals mixing of avalanche processes in porous 316L stainless steel. One avalanche mechanism relates to the movement of dislocations, the other to crack propagation. Both mechanisms occur under different external tensions: small tension dislodges dislocations while crack propagation occurs at much higher tension close to the mechanical failure point. In an intermediate overlap regime, both effects occur simultaneously. The avalanche related power laws show a mixing behavior where the higher avalanche exponents form an upper limit for the mixing curve and the lower exponent is approached asymptotically for strong AE signals. The power law probability distribution functions, show a characteristic upwards bend near the crossover between the two mechanisms. The three regimes, namely, the dislocation movement, mixing, and crack propagation, are confirmed by other avalanche characteristics: the sparseness of the AE spectra, the avalanche exponents of energy, amplitude, and duration. Only the crack propagation follows mean field predictions, while the dislocation movements (in confined spaces) deviates significantly from mean field behavior with much greater exponents than those predicted in this approximation. We demonstrate that apparent deviations from scale invariance are, in reality, the result of two superimposed avalanche processes whereby each of them remains scale invariant. The seeming deviations from scale invariance are actually superposition effects. [ABSTRACT FROM AUTHOR]

The motion of phase fronts during a ferroelectric phase transition is intermittent and follows avalanche dynamics. In the present study, we show that an intermittent propagation mode generates spikes of depolarization currents at an extremely slow heating rate of 0.05 K/min in BaTiO3 (BTO) and 0.7Pb(Mg2∕3Nb1∕3)O3-0.3PbTiO3 (PMN-PT) single crystals. Such "jerks" are indicative of avalanche dynamics, and their energy exhibits a power law distribution with exponents of ε = 1.3 ± 0.10 and ε = 1.5 ± 0.10 for BTO and PMN-PT, respectively. The rate of aftershocks after big events decays as an Omori-like power-law and interevent times are characterized by a universal double power-law distribution, indicating the critical temporal correlations between the avalanche events. [ABSTRACT FROM AUTHOR]