Elastic relaxations associated with the Pm3m-R3c transition in LaAlO(3): III. Superattenuation of acoustic resonances

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.

Order-disorder, ferroelasticity and mobility of domain walls in multiferroic Cu-Cl boracite

Domain walls in Cu-Cl boracite develop as a consequence of an improper ferroelastic, improper ferroelectric transition, and have attracted close interest because some are conductive and all can be mechanically written and repositioned by application of an electric field. The phase transition and its associated dynamical properties have been analysed here from the perspective of strain and elasticity. Determination of spontaneous strains from published lattice parameter data has allowed the equilibrium long-range order parameter for F [Formula: see text]3c → Pca2₁ to be modelled simply as being close to the order-disorder limit. High acoustic loss in the cubic phase, revealed by resonant ultrasound spectroscopy, is consistent with the presence of dynamical microdomains of the orthorhombic structure with relaxation times in the vicinity of ∼10^-5-10^-6 s. Low acoustic loss in the stability field of the orthorhombic structure signifies, on the other hand, that ferroelastic twin walls which develop as a consequence of the order-disorder process are immobile on this time scale. A Debye loss peak accompanied by ∼1% elastic stiffening at ∼40 K is indicative of some freezing of defects which couple with strain or of some more intrinsic freezing process. The activation energy of ⩾∼0.01-0.02 eV implies a mechanism which could involve strain relaxation clouds around local ferroelectric dipoles or freezing of polarons that determine the conductivity of twin walls.

Elastic and anelastic relaxation behaviour of perovskite multiferroics II: PbZr0.53Ti0.47O3 (PZT)-PbFe0.5Ta0.5O3 (PFT)

Elastic and anelastic properties of ceramic samples of multiferroic perovskites with nominal compositions across the binary join PbZr_0.53Ti_0.47O₃-PbFe_0.5Ta_0.5O₃ (PZT-PFT) have been assembled to create a binary phase diagram and to address the role of strain relaxation associated with their phase transitions. Structural relationships are similar to those observed previously for PbZr_0.53Ti_0.47O₃-PbFe_0.5Nb_0.5O₃ (PZT-PFN), but the magnitude of the tetragonal shear strain associated with the ferroelectric order parameter appears to be much smaller. This leads to relaxor character for the development of ferroelectric properties in the end member PbFe_0.5Ta_0.5O₃. As for PZT-PFN, there appear to be two discrete instabilities rather than simply a reorientation of the electric dipole in the transition sequence cubic-tetragonal-monoclinic, and the second transition has characteristics typical of an improper ferroelastic. At intermediate compositions, the ferroelastic microstructure has strain heterogeneities on a mesoscopic length scale and, probably, also on a microscopic scale. This results in a wide anelastic freezing interval for strain-related defects rather than the freezing of discrete twin walls that would occur in a conventional ferroelastic material. In PFT, however, the acoustic loss behaviour more nearly resembles that due to freezing of conventional ferroelastic twin walls. Precursor softening of the shear modulus in both PFT and PFN does not fit with a Vogel-Fulcher description, but in PFT there is a temperature interval where the softening conforms to a power law suggestive of the role of fluctuations of the order parameter with dispersion along one branch of the Brillouin zone. Magnetic ordering appears to be coupled only weakly with a volume strain and not with shear strain but, as with multiferroic PZT-PFN perovskites, takes place within crystals which have significant strain heterogeneities on different length scales.

Elastic Properties and Enhanced Piezoelectric Response at Morphotropic Phase Boundaries

The search for improved piezoelectric materials is based on the morphotropic phase boundaries (MPB) between ferroelectric phases with different crystal symmetry and available directions for the spontaneous polarization. Such regions of the composition x - T phase diagrams provide the conditions for minimal anisotropy with respect to the direction of the polarization, so that the polarization can easily rotate maintaining a substantial magnitude, while the near verticality of the TMPB(x) boundary extends the temperature range of the resulting enhanced piezoelectricity. Another consequence of the quasi-isotropy of the free energy is a reduction of the domain walls energies, with consequent formation of domain structures down to nanoscale. Disentangling the extrinsic and intrinsic contributions to the piezoelectricity in such conditions requires a high level of sophistication from the techniques and analyses for studying the structural, ferroelectric and dielectric properties. The elastic characterization is extremely useful in clarifying the phenomenology and mechanisms related to ferroelectric MPBs. The relationship between dielectric, elastic and piezoelectric responses is introduced in terms of relaxation of defects with electric dipole and elastic quadrupole, and extended to the response near phase transitions in the framework of the Landau theory. An account is provided of the anelastic experiments, from torsional pendulum to Brillouin scattering, that provided new important information on ferroelectric MPBs, including PZT, PMN-PT, NBT-BT, BCTZ, and KNN-based systems.

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.

Strain coupling mechanisms and elastic relaxation associated with spin state transitions in LaCoO₃

Advantage is taken of the wealth of experimental data relating to the evolution with temperature of spin states of Co(3+) in LaCoO₃ in order to undertake a detailed investigation of the mechanisms by which changes in electronic structure can influence strain, and elastic and anelastic relaxations in perovskites. The macroscopic strain accompanying changes in the spin state in LaCoO₃ is predominantly a volume strain arising simply from the change in effective ionic radius of the Co(3+) ions. This acts to renormalize the octahedral tilting transition temperature in a manner that is easily understood in terms of coupling between the tilt and spin order parameters. Results from resonant ultrasound spectroscopy at high frequencies (0.1-1.5 MHz) reveal stiffening of the shear modulus which scales qualitatively with a spin order parameter defined in terms of changing Co-O bond lengths. From this finding, in combination with results from dynamic mechanical analysis at low frequencies (0.1-50 Hz) and data from the literature, four distinctive anelastic relaxation mechanisms are identified. The relaxation times of these are displayed on an anelasticity map and are tentatively related to spin-spin relaxation, spin-lattice relaxation, migration of twin walls and migration of magnetic polarons. The effective activation energy for the freezing of twin wall motion below ~590 K at low frequencies was found to be 182 ± 21 kJ mol(-1) (1.9 ± 0.2 eV) which is attributed to pinning by pairs of oxygen vacancies, though the local mechanisms appear to have a spread of relaxation times. It seems inevitable that twin walls due to octahedral tilting must have quite different characteristics from the matrix in terms of local spin configurations of Co(3+). A hysteresis in the elastic properties at high temperatures further emphasizes the importance of oxygen content in controlling the properties of LaCoO₃.

Anelastic loss behaviour of mobile microstructures in SrZr(1-x)Ti(x)O3 perovskites

Anelastic loss mechanisms associated with phase transitions in SrZr(1-x)Ti(x)O(3) perovskites (x = 0.375, 0.450, 0.550, 0.775) have been investigated by dynamic mechanical analysis between 128 and 723 K at frequencies of 0.1-50 Hz. Distinctive patterns of changes in the elastic moduli due to octahedral tilting transitions correlate closely with data for the shear modulus obtained previously by resonant ultrasound spectroscopy at high frequencies (∼0.5 MHz). The I4/mcm <--> Imma transition is first order and has a characteristic minimum in the shear modulus and Young's modulus. For x = 0.450 and 0.550, a dissipation peak occurs at the transition temperature, the maximum of which varies with frequency according to a power law relationship of the form tanδ = Af(n), with n≈ - 0.3. Debye-like dissipation peaks in the stability field of the Imma structure at x = 0.375 have a frequency and temperature dependence consistent with twin wall pinning by defects with an activation energy ∼ 184 kJ mol(-1). These results indicate that there is diversity of pinning and relaxation processes for transformation twin walls and interfaces in different perovskites with I4/mcm, Imma and Pnma structures.