Twin Walls Research Articles

Acoustic attenuation due to transformation twins in CaCl2: Analogue behaviour for stishovite

CaCl2 undergoes a tetragonal (P42/mnm) to orthorhombic (Pnnm) transition as a function of temperature which is essentially the same as occurs in stishovite at high pressures. It can therefore be used as a convenient analogue material for experimental studies. In order to investigate variations in elastic properties associated with the transition and possible anelastic loss behaviour related to the mobility of ferroelastic twin walls in the orthorhombic phase, the transition in polycrystalline CaCl2 has been examined using resonant ultrasound spectroscopy (RUS) at high frequencies (0.1–1.5MHz) in the temperature interval 7–626K, and dynamic mechanical analysis (DMA) at low frequencies (0.1–50Hz) in the temperature interval 378–771K. RUS data show steep softening of the shear modulus as the transition temperature is approached from above and substantial acoustic dissipation in the stability field of the orthorhombic structure. DMA data show softening of the storage modulus, which continues through to a minimum ∼20K below the transition point and is followed by stiffening with further lowering of temperature. There is no obvious acoustic dissipation associated with the transition, as measured by tanδ, however. The elastic softening and stiffening matches the pattern expected for a pseudoproper ferroelastic transition as predicted elsewhere. Acoustic loss behaviour at high frequencies fits with the pattern of behaviour expected for a twin wall loss mechanism but with relaxation times in the vicinity of ∼10−6s. With such short relaxation times, the shear modulus of CaCl2 at frequencies corresponding to seismic frequencies would include relaxations of the twin walls and is therefore likely to be significantly lower than the intrinsic shear modulus. If these characteristics apply also to twin wall mobility in stishovite, the seismic signature of the orthorhombic phase should be an unusually soft shear modulus but with no increase in attenuation.

Magnetoelastic coupling and multiferroic ferroelastic/magnetic phase transitions in the perovskite KMnF3

The magnetic, elastic, and anelastic behavior of single-crystal KMnF${}_{3}$ have been investigated by superconducting quantum interference device (SQUID) magnetometry and resonant ultrasound spectroscopy (RUS) through the sequence of phase transitions: phase I, $Pm$$\overline{3}$$m$ $\ensuremath{\rightarrow}\phantom{\rule{0.16em}{0ex}}({T}_{\mathrm{c}1}$ $=$ 185 K) \ensuremath{\rightarrow} phase II, $I$4/mcm $\ensuremath{\rightarrow}({T}_{\mathrm{c}2}$ $=\phantom{\rule{0.16em}{0ex}}{T}_{\mathrm{N}}$ $=$ 87 K) \ensuremath{\rightarrow} phase III, antiferromagnetic, Cmcm \ensuremath{\rightarrow} (${T}_{\mathrm{c}3}$ $=$ 82 K) \ensuremath{\rightarrow} phase IV, canted ferromagnet, Pnma. It is concluded that observed changes in the elastic properties can be explained simply in terms of strain/order parameter coupling for the octahedral tilting transitions. There appears to be no evidence in the present data or in data from the literature for coupling between the magnetic order parameter and shear strains. Any coupling between the magnetic and structural transitions is therefore weak, probably occurring only biquadratically through a small common volume strain. The combined data show unambiguously that, for the crystal used, the N\'eel point and the structural transition at 87 K are coincident. In other crystals, with slightly different stoichiometries and defect contents, this need not be the case, however, and the overlap of transition temperatures in KMnF${}_{3}$ is essentially accidental. Strong acoustic dissipation at \ensuremath{\sim}0.1--1 MHz in the stability field of phase II is attributed to the local mobility of transformation twin walls under externally applied stress. A Debye-like loss peak near 130 K is attributed to pinning of at least some twin walls by defects, but relatively high levels of acoustic dissipation below this freezing temperature imply that some of the twin walls remain mobile due to weak pinning or the absence of any pinning. Acoustic losses continue in the stability field of phase III (Cmcm) but diminish substantially in the stability field of phase IV (Pnma), implying quite different twin mobilities in the different structure types. Overlap of the structural and magnetic instabilities in KMnF${}_{3}$ opens up possibilities for manipulation of ferroelastic twinning by application of a magnetic field and for creation of materials in which the ferroelastic twin walls have quite different magnetic properties from the matrix in which they lie.

Elastic and anelastic anomalies associated with the antiferromagnetic ordering transition in wüstite, FexO

The elastic and anelastic properties of three different samples of FexO have been determined in the frequency range 0.1–2 MHz by resonant ultrasound spectroscopy and in the range 0.1–50 Hz by dynamic mechanical analysis in order to characterize ferroelastic aspects of the magnetic ordering transition at TN ∼ 195 K. No evidence was found of separate structural and magnetic transitions but softening of the shear modulus was consistent with the involvement of bilinear coupling, λe4q, between a symmetry-breaking strain, e4, and a structural order parameter, q. Unlike a purely ferroelastic transition, however, C44 does not go to zero at the critical temperature, , due to the intervention of the magnetic ordering at a higher temperature. The overall pattern of behaviour is nevertheless consistent with what would be expected for a system with separate structural and magnetic instabilities, linear–quadratic coupling between the structural (q) and magnetic (m) driving order parameters, λqm2, and . Comparison with data from the literature appears to confirm the same pattern in MnO and NiO, with a smaller difference between TN and in the former and a larger difference in the latter. Strong attenuation of acoustic resonances at high frequencies and a familiar pattern of attenuation at low frequencies suggest that twin walls in the rhombohedral phase have typical ferroelastic properties. Acoustic dissipation in the stability field of the cubic phase is tentatively attributed to anelastic relaxations of the defect ordered structure of non-stoichiometric wüstite or of the interface between local regions of wüstite and magnetite, with a rate controlling step determined by the diffusion of iron.

Implications of twinning kinetics on the frequency response in NiMnGa actuators

The explicit kinetic relation for twin wall motion in NiMnGa is used to correlate basic material properties to magneto-mechanical actuation rates in these crystals. In particular, we identify two parameters: the Peierls energy barrier and the twin wall mobility, which directly determine the dynamic response of NiMnGa actuators at frequencies above 10 Hz. Comparison between the kinetics of type I and type II twin walls reveals a correlation between the Peierls energy barrier and the commonly used twinning stress property. However, it is shown that twinning stress dictates twin wall dynamics only at very slow frequencies, typically below 1 Hz.

Interfacial polarization and pyroelectricity in antiferrodistortive structures induced by a flexoelectric effect and rotostriction

Theoretical analysis based on the Landau-Ginzburg-Devonshire (LGD) theory is used to show that the product effect of flexoelectricity and rotostriction can lead to a spontaneous polarization in the vicinity of antiphase boundaries, ferroelastic twin walls, surfaces and interfaces in the octahedrally tilted phase of otherwise non-ferroelectric perovskites such as CaTiO3, SrTiO3, and EuTiO3. As an example, we numerically demonstrate a large spontaneous polarization on the order of 1-5muC/cm2 at the SrTiO3 antidistortive phase boundaries at temperatures lower than the antiferrodistortive structural phase transition temperature of ~105 K

Impact of Free Charges on Polarization and Pyroelectricity in Antiferrodistortive Structures and Surfaces Induced by a Flexoelectric Effect

Landau-Ginzburg-Devonshire theory has been used to show that the combined effect of flexoelectricity and rotostriction can lead to a spontaneous polarization and pyroelectricity in the vicinity of antiphase boundaries, structural twin walls, surfaces, and interfaces in the octahedrally tilted phase of otherwise non-ferroelectric SrTiO3. In particular, the spontaneous polarization reaches the values ∼0.1–5μC/cm2 at the SrTiO3 antiphase boundaries and twins without free charges. In the current study we consider the contribution of free charges and show that the spontaneous polarization reaches the values ∼1–5μC/cm2 in the case. Pyroelectric coefficients also strongly increase allowing for the free charges.

X-ray nanodiffraction of tilted domains in a poled epitaxial BiFeO3 thin film

We present measurements of crystallographic domain tilts in a (001) BiFeO3 thin film using focused beam x-ray nanodiffraction. Films were ferroelectrically pre-poled with an electric field orthogonal and parallel to as-grown tilt domain stripes. The tilt domains, associated with higher energy (010) vertical twin walls, displayed different nanostructural responses based on the poling orientation. Specifically, an electric field applied perpendicular to the as-grown domain stripe allowed the domain tilts and associated vertical twin walls to persist. The result demonstrates that thin film ferroelectric devices can be designed to maintain unexpected domain morphologies in working poled environments.

Twin wall distortions through structural investigation of epitaxial BiFeO3 thin films

Abstract

Ferroic switching, avalanches, and the Larkin length: Needle domains in LaAlO3

Propagation of wedge-shaped needle domains in LaAlO3 is driven mechanically and the change of wall shapes is observed. Twin walls remain smooth, whereas the one-dimensional front line of the needle tip shows “wiggles” when propagating through defect fields. The front line becomes highly distorted during approach to, or retraction from, the sample surface. Singularities of the characteristic (∼Larkin) length occur when the front line breaks. Elastic forces produce planar twin walls with very large Larkin lengths, whereas the front line is not restrained by the compatibility energy and displays considerably shorter Larkin lengths.

Large kinetic asymmetry in the metal-insulator transition nucleated at localized and extended defects

Superheating and supercooling effects are characteristic kinetic processes in first-order phase transitions, and asymmetry between them is widely observed. In materials where electronic and structural degrees of freedom are coupled, a wide, asymmetric hysteresis may occur in the transition between electronic phases. Structural defects are known to seed heterogeneous nucleation of the phase transition, hence reduce the degree of superheating and supercooling. Here we show that in the metal-insulator transition of single-crystal VO${}_{2}$, a large kinetic asymmetry arises from the distinct spatial extension and distribution of two basic types of crystal defects: point defects and twin walls. Nanometer-thick twin walls are constantly consumed but regenerated during the transition to the metal phase, serving as dynamical heterogeneous nucleation seeds and eliminating superheating. On the other hand, the transition back to the insulator phase relies on nucleation at point defects because twinning is structurally forbidden in the metal phase, leading to a large supercooling. By controlling the formation, location, and extinction of these defects, the kinetics of the phase transition might be externally modulated, offering possible routes toward unique memory and logic device technologies.

Anelasticity maps for acoustic dissipation associated with phase transitions in minerals

Acoustic dissipation due to structural phase transitions in minerals could give rise to large seismic attenuation effects superimposed on the high temperature background contribution from dislocations and grain boundaries in the Earth. In addition to the possibility of a sharp peak actually at a transition point for both compressional and shear waves, significant attenuation might arise over wider temperature intervals due to the mobility of transformation twins or other defects associated with the transition. Attenuation due to structural phase transitions in quartz, pyroxenes, perovskites, stishovite and hollandite, or to spin state transitions of Fe2+ in magnesiowustite and perovskite and the hcp/bcc transition in iron–nickel (Fe–Ni) alloy, are reviewed from this perspective. To these can be added possible loss behaviour associated with reconstructive transitions which might occur by a ledge mechanism on topotactic interfaces (orthopyroxene/clinopyroxene, olivine/spinel and perovskite/postperovskite), with impurities (Snoek effect) or with mobility of protons. There are experimental difficulties associated with measuring dissipation effects in situ at simultaneous high pressures and temperatures, so reliance is currently placed on investigation of analogue phases such as LaCoO3 for spin-state behaviour and LaAlO3 for the dynamics of ferroelastic twin walls. Similarly, it is not possible to measure loss dynamics simultaneously at the low stresses and low frequencies that pertain in seismic waves, so reliance must be placed on combining different techniques, such as dynamic mechanical analysis (low frequency, relatively high stress) and resonant ultrasound spectroscopy (high frequency, low stress), to extrapolate acoustic loss behaviour over wide frequency, temperature and stress intervals. In this context ‘anelasticity maps’ provide a convenient means of representing different loss mechanisms. Contouring of the inverse mechanical quality factor, Q−1, can be achieved if the appropriate constitutive laws are known. The overall approach is illustrated using the examples of spin-state transitions of Co3+ in LaCoO3 and twin mobility in single crystals of the rhombohedral phase of LaAlO3. Anelasticity maps of this type should give seismologists a clearer view of the characteristic patterns of seismic velocity and attenuation that could be used to detect (or rule out) the presence of particular phase transitions or loss behaviour in the core and mantle.

Thermally activated avalanches: Jamming and the progression of needle domains

Large-scale computer simulations of a simple model with a square-lattice topology, a small shear deformation (${4}^{\ifmmode^\circ\else\textdegree\fi{}}$ shear angle), and open (free) boundary conditions show that domain boundary movements under adiabatic strain deformation lead to Vogel-Fulcher behavior at high temperatures. The activation energy is independent of temperature and details of the twin patterns. Below the Vogel-Fulcher temperature, no thermal activation was found and the time evolution of the domain pattern becomes athermal. The movement of domain boundaries is now dominated by the nucleation and growth of needle domains. Their movement occurs in fast jerks. The probability to observe jerks follows a power-law spectrum with energy exponents close to $\ensuremath{\alpha}\ensuremath{\approx}2$. At even lower temperatures, the boundary kinetics becomes erratic even in our large (${10}^{6}$atoms) system. The lateral movement of twin walls is found for our thin twin walls ($w=3$ layers) to operate by kinks which propagate along the twin wall. The needle domains nucleate either from the surface or from other existing twin walls. Intersections of twin walls constitute pinning centers which impede the free movement of the kinks in the walls. These intersection points then act as a pattern of intrinsic, self-induced defects which lead ultimately to the power-law distribution of the crackling noise of the domain walls.

Strain coupling mechanisms and elastic relaxation associated with spin state transitions inLaCoO3

Advantage is taken of the wealth of experimental data relating to the evolution with temperature of spinstates of Co3 + in LaCoO3 in order to undertake a detailed investigation of the mechanisms by which changes inelectronic structure can influence strain, and elastic and anelastic relaxations inperovskites. The macroscopic strain accompanying changes in the spin state inLaCoO3 is predominantly a volume strain arising simply from the change in effective ionic radius of theCo3 + ions. This acts to renormalize the octahedral tilting transition temperature in a mannerthat 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) revealstiffening of the shear modulus which scales qualitatively with a spin order parameterdefined in terms of changing Co–O bond lengths. From this finding, in combination withresults from dynamic mechanical analysis at low frequencies (0.1–50 Hz) and data from theliterature, four distinctive anelastic relaxation mechanisms are identified. The relaxationtimes of these are displayed on an anelasticity map and are tentatively related to spin-spinrelaxation, spin-lattice relaxation, migration of twin walls and migration of magneticpolarons. The effective activation energy for the freezing of twin wall motion below ∼ 590 K at low frequencieswas found to be 182 ± 21 kJ mol − 1 (1.9 ± 0.2 eV) which is attributed to pinning by pairs of oxygen vacancies, though thelocal mechanisms appear to have a spread of relaxation times. It seemsinevitable that twin walls due to octahedral tilting must have quite differentcharacteristics from the matrix in terms of local spin configurations ofCo3 + . A hysteresis in the elastic properties at high temperatures furtheremphasizes the importance of oxygen content in controlling the properties ofLaCoO3.

Domain Evolution in PbMg1/3Nb2/3O3-60at%PbTiO3 with Temperature and Electric Field

The domain structure of Pb(Mg1/3Nb2/3)O3–60%PbTiO3 (PMN–60%PT) was investigated by polarized light, piezo-force, and transmission electron microscopies. Two sets of stripe-like domain patterns were observed with 〈011〉-type twin walls, which were geometrically arranged within larger domain platelets. Upon application of an electric field E along a direction that was different than that of the spontaneous polarization, the domain platelets were destabilized, favoring one set of domain striations over another. Interestingly, on removal of E, the original domain structure was not recovered: revealing a history dependence.

The kinetic relation for twin wall motion in NiMnGa

A complete description of magnetically induced strains in ferromagnetic shape memory alloys (FSMAs) requires knowledge of the constitutive equation describing twin wall motion, commonly referred to as the kinetic relation. Here we present a unique experimental setup that allows for direct measurement of individual twin wall velocities as a function of a magnetically induced driving force in a NiMnGa FSMA, i.e., the kinetic relation. Our results demonstrate the validity of a general kinetic law that is typical of a viscous interface motion in a periodic potential. Values of basic material properties that govern twin wall motion, such as the Peierls energy barrier and the crystal viscosity, are extracted, and a simple model suggests that the viscosity measured in NiMnGa represents the magnitude of this property in other non-ferromagnetic shape memory alloys.

ACROSS MASS TRANSFER PHENOMENON IN A CHANNEL OF LOWER STRETCHING WALL

This study aims to investigate the effect of across mass transfer (AMT) phenomenon on a three-dimensional steady viscous flow in a channel of lower stretching wall. The phenomenon of AMT is established by imposing suction at one plate and injection at the other plate of the channel simultaneously. Both the walls are assumed to be porous so that suction/injection can take place. Interesting observations regarding viscous drag at the stretching plate have been recorded in the presence of AMT phenomenon at the twin walls. A highly accurate purely analytic solution has been obtained for the governing nonlinear equations. The issue of convergence and accuracy of the analytic solution has been discussed in detail. Results are discussed through graphs.

Ferroelastic phase transitions and anelastic dissipation in theLaAlO3-PrAlO3solid solution series

Resonant ultrasound spectroscopy has been used on single-crystal samples to observe pseudoproper ferroelastic softening across the $(\text{La},\text{Pr}){\text{AlO}}_{3}$ solid solution. It is suggested that softening is due to the presence of an intrinsic zone-center instability in addition to the small Jahn-Teller stabilization expected for ${\text{Pr}}^{3+}$. Softening increases as smaller ${\text{Pr}}^{3+}$ ions are substituted for larger ${\text{La}}^{3+}$ which is attributed to a simple size effect as well as the possibility of bilinear coupling of the intrinsic instability with the weak Jahn-Teller effect. Superattenuation is observed above 600 K for all samples, which is consistent with twin wall related dissipation behavior seen in other perovskites with octahedral tilting. Superattenuation is also observed in the low-temperature monoclinic phase, implying a high mobility also for the monoclinic twin walls.

Low amplitude, low frequency elastic measurements using Dynamic Mechanical Analyzer (DMA) spectroscopy

Abstract The applications of DMA methods for the investigation of the dynamical mechanical properties of materials are reviewed. Experimental details of this method are described including the combination of DMA with X-ray rocking curve measurements to investigate the details of the domain patterns. Emphasis is given to the effect of phase transitions, in particular in ferroelastic and co-elastic systems where the ‘easy’ movement of domain boundaries, twin walls and other interfaces lead to super-elastic softening of the material. Thermodynamic constraints, such as in the adiabatic-isothermal crossover are discussed. Smooth, ballistic propagation of domain walls are contrasted with the jerky behaviour of interfaces when phase transitions of first order are investigated. It is shown that for the ballistic behaviour, momentum driven wall movements are common and that their representation in Cole-Cole plots leads to depressed semi-circles, similar to methods used in dielectric spectroscopy. In jerky elastic responses the energy dissipation follows power law dependences. Domain wall pinning and domain wall freezing is discussed in some detail.

Pseudoproper ferroelastic softening behaviour and dynamic microstructure of monoclinic PrAlO3 perovskite

Elastic and anelastic properties of single crystal PrAlO3 have been investigated by resonant ultrasound spectroscopy at 0.2–1.2 MHz. Non-linear (pseudoproper) softening with falling temperature in the stability field below ∼690 K is related to the elastic stability limit . Before this instability point is reached, the first order Imma transition intervenes and is marked by a steep minimum in shear elastic constants. Further pseudoproper ferroelastic softening then occurs, consistent with at ∼151 K for the second-order Imma ↔ C2/m transition. Superattenuation of acoustic resonances within the stability field of the C2/m structure implies that the monoclinic twin walls are highly mobile, apart from in a narrow temperature interval near 100 K where the structure becomes metrically tetragonal. PrAlO3 appears to represent a general class of Jahn–Teller phase transitions in perovskites for which the predominant order parameter transforms according to symmetry and which displays an unusual anelastic dissipation.

Microstructure dynamics in orthorhombic perovskites

Anelastic loss mechanisms associated with phase transitions in ${\text{BaCeO}}_{3}$ have been investigated at relatively high frequency $\ensuremath{\sim}1\text{ }\text{MHz}$ and low stress by resonant ultrasound spectroscopy (RUS), and at relatively low frequency $\ensuremath{\sim}1\text{ }\text{Hz}$ and high stress by dynamic mechanical analysis (DMA). Changes in the elastic moduli and dissipation behavior clearly indicate phase transitions due to octahedral tilting: $Pnma\ensuremath{\leftrightarrow}Imma\ensuremath{\leftrightarrow}R\overline{3}c\ensuremath{\leftrightarrow}Pm\overline{3}m$ structures at 551 K, 670 K, and 1168 K, and strain analysis shows that they are tricritical, first-order, and second-order phase transitions, respectively. Structures with intermediate tilt states ($R\overline{3}c$ and $Imma$ structures) show substantial anelastic softening and dissipation associated with the mobility of twin walls under applied stress. The $Pnma$ structure shows elastic stiffening which may be due to the simultaneous operation of two discrete order parameters with different symmetries. In contrast with studies of other perovskites, ${\text{BaCeO}}_{3}$ shows strong dissipation at both DMA and RUS frequencies in the stability field of the $Pnma$ structure. This is evidence that ferroelastic twin walls might become mobile in $Pnma$ perovskites and suggests that shearing of the octahedra may be a significant factor.