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.

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.

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 TC 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 TC and for the surface domains above TC. Annealing at higher temperature triggers the dynamic tweed which in turn allows a full reorganization of the ferroic domain configuration.

Re-entrant spin glass transitions: new insights from acoustic absorption by domain walls.

Re-entrant spin glass (RSG) transitions in Ni-Mn and Au-Fe have been reassessed by acoustic measurements of the magneto-mechanical damping by domain walls. Stress-induced non-thermally activated domain wall dynamics is progressively replaced by an intense thermally activated relaxational response when the temperature approaches the RSG freezing point. A "frozen" state with negligible motion of domain walls on atomic and mesoscopic scales occurs in the RSG. We propose that RSG freezing has its origin in intrinsic properties of domain walls.

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.

Quantification by aberration corrected (S)TEM of boundaries formed by symmetry breaking phase transformations.

The present contribution gives a review of recent quantification work of atom displacements, atom site occupations and level of crystallinity in various systems and based on aberration corrected HR(S)TEM images. Depending on the case studied, picometer range precisions for individual distances can be obtained, boundary widths at the unit cell level determined or statistical evolutions of fractions of the ordered areas calculated. In all of these cases, these quantitative measures imply new routes for the applications of the respective materials.

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.

Thermal avalanches near a Mott transition.

We probe the volume collapse transition (ΔV/Vo âˆ¼ 15%) between the isostructural γ and α phases (T âˆ¼ 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).

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.

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.

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.

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 âˆ¼ 0.5 meV.

Linear­quadratic 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.

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.

High pressure ferroelastic phase transition in SrTiO3.

High pressure measurements of the ferroelastic phase transition of SrTiO3 (Guennou et al 2010 Phys. Rev. B 81 054115) showed a linear pressure dependence of the transition temperature between the cubic and tetragonal phase. Furthermore, the pressure induced transition becomes second order while the temperature dependent transition is near a tricritical point. The phase transition mechanism is characterized by the elongation and tilt of the TiO6 octahedra in the tetragonal phase, which leads to strongly nonlinear couplings between the structural order parameter, the volume strain and the applied pressure. The phase diagram is derived from the Clausius-Clapeyron relationship and is directly related to a pressure dependent Landau potential. The nonlinearities of the pressure dependent strains lead to an increase of the fourth order Landau coefficient with increasing pressure and, hence, to a tricritical-second order crossover. This behaviour is reminiscent of the doping related crossover in isostructural KMnF3.

Elastic and antiferromagnetic anomalies in Pr0.48Ca0.52MnO3 as determined by resonant ultrasonic spectroscopy.

The Pnma incommensurate phase transition in the perovskite Pr(0.48)Ca(0.52)MnO(3) at ∼ 235 K is accompanied by shear strains of up to ∼ 2.5% (from neutron diffraction) and changes in the shear modulus of up to ∼ 40% (from resonant ultrasound spectroscopy, RUS), indicating strong coupling between the structural order parameter and strain. In contrast, the antiferromagnetic (AFM) ordering transition at ∼ 180 K displays no detectable static strain, implying that there is either no coupling or only very weak coupling between the magnetic order parameter and strain. Conventional analysis of RUS data, based on measurements of resonance peak frequencies and peak widths, also failed to detect any anomaly in elastic or anelastic properties due to the AFM ordering. A new approach to the analysis the RUS data, based on autocorrelation and convolution of the entire spectra, however, has revealed that the AFM order does indeed affect the elastic behaviour in an unexpected manner. The new analysis shows, firstly, that dynamical fluctuations of the charge density ordering at T > T(c) = 237 K lead to an increase of the RUS amplitude and of the spectral convolution function. Secondly, fluctuations and convolution effects peak at the transition point and decrease with decreasing temperatures. Below 180 K the stripe structure is essentially static. Finally, AFM ordering leads to an increase in the damping of the elastic resonances.

Improper ferroelectricity in lawsonite CaAl2Si2O7(OH)2·H2O: hysteresis and hydrogen ordering.

Ferroelectric hysteresis measurements on ceramic lawsonite show a temperature dependence of the remanent polarization P(r) = P(o)Θ(s)(cothΘ(s)/T - cothΘ(s)/T(c)) ∼ Q(2), Θ(s) = 26 K, where Q is the thermodynamic order parameter of the phase transition Pmcn-P 2(1)cn. This almost linear temperature evolution of P(r) proves the improper nature of ferroelectricity in lawsonite. The Curie temperature is T(c) = 124 K. The phase transition is strictly continuous, with a weak conjugated field near the transition point, and hydrogen ordering is discussed as the primary driving mechanism.

Thermally activated proton hopping in lawsonite, the ferroelectric transition at 125 K, and the co-elastic phase transition at 270 K.

Lawsonite, CaAl(2)Si(2)O(7)(OH)(2)H(2)O, is a novel ferroelectric material which is dominated by ordering and disordering of protons. We report related elastic anomalies in lawsonite. A new approach to extracting acoustic data from resonant ultrasonic spectroscopy has been applied to investigate the ordering and disordering of protons. This approach is based on analysis of entire spectra, rather than the more conventional fitting of individual resonance peaks and captures three features of the transitions. Firstly, structural disorder of protons persists down to low temperatures. Secondly, the structural transition between two paraelectric phases near 270 K is mainly of the order/disorder type but is not directly coupled to the proton mobility. Thirdly, the ferroelectric transition at 125 K shows a direct link with the proton mobility with an activation energy of 0.03 eV. The latter transition occurs in the large class of ferroelectric crystals where the molecular groups are linked by hydrogen and its thermodynamic potential is almost identical to that of KDP (KH(2)PO(4)), albeit with a smaller isotope effect. While some damping is seen in small temperature intervals below the transition points, these anomalies are much smaller than those that occur at ferroelastic phase transitions.