Ferroelastic Twin Research Articles

Phase-field simulation of magnetoelastic couplings in ferromagnetic shape memory alloys

Ferromagnetic shape memory alloys (FSMAs) possess coupled ferroelastic and ferromagnetic orderings simultaneously, making it possible to manipulate ferroelastic twins of FSMAs via a magnetic field or magnetic domains via mechanical loading. In this paper, we develop a phase-field model to simulate the formation and evolution of magnetoelastic domains in FSMAs under combined mechanical and magnetic loadings, taking into account both variant rearrangement and magnetization rotation. It is found that the large magnetic field induced strain in FSMAs results from a variant rearrangement process, yet such variant rearrangement can be blocked by a relatively large compressive stress, substantially reducing the magnetic field induced strain. Furthermore, either pseudoelastic or quasiplastic behavior is exhibited in FSMAs subjected to varying compressive stress, depending on the strength of the constant magnetic field applied. These results agree well with experiments, and can be used to guide the design and optimization of FSMAs.

Symmetry and strain analysis of structural phase transitions inPr0.48Ca0.52MnO3

Structural evolution as a function of temperature through the $Pnma\ensuremath{\leftrightarrow}\text{incommensurate}$ (IC) phase transition in ${\text{Pr}}_{0.48}{\text{Ca}}_{0.52}{\text{MnO}}_{3}$ perovskite has been analyzed from the perspectives of symmetry and strain. The structure and stability of both phases are shown to depend on combinations of order parameters which have symmetries associated with irreducible representations ${\text{M}}_{3}^{+}$, ${\text{R}}_{4}^{+}$, ${\text{M}}_{2}^{+}$, ${\ensuremath{\Gamma}}_{3}^{+}$ and ${\ensuremath{\Sigma}}_{2}$ of space group $Pm\overline{3}m$. The physical origin of these can be understood in terms of octahedral tilting, cooperative Jahn-Teller distortions and charge order/Zener polaron ordering. The ${\text{M}}_{2}^{+}$ order parameter describes the Jahn-Teller ordering scheme which develops in ${\text{LaMnO}}_{3}$ while the ${\ensuremath{\Gamma}}_{3}^{+}$ order parameter relates to an ordering scheme in which the unique axes of the distorted octahedra are all aligned in the same direction. Irrep ${\ensuremath{\Sigma}}_{2}$ contains two components with gradient coupling and provides the symmetry-breaking mechanism by which the IC transition can occur. Each order parameter couples with macroscopic spontaneous strains in a manner that depends strictly on symmetry and this leads to specific interactions between the order parameters through their coupling with common strains. In order to establish the extent and importance of this coupling, symmetry-adapted strains have been extracted from a new set of lattice parameters obtained by high-resolution powder neutron diffraction in the temperature interval 10--1373 K. It is found that the predominant strain of the incommensurate structure (up to $\ensuremath{\sim}2.5\mathrm{%}$) is a tetragonal shear strain which arises by bilinear coupling with the ${\ensuremath{\Gamma}}_{3}^{+}$ order parameter. This combination is probably responsible for most of the energy reduction accompanying the $Pnma\ensuremath{\leftrightarrow}\text{IC}$ transition and also gives it some characteristics typical of a pseudoproper ferroelastic transition. Strain coupling promotes mean-field behavior and the evolution of the symmetry-breaking order parameter can be described by a standard Landau tricritical solution, ${q}^{4}\ensuremath{\propto}({T}_{\text{c}}\ensuremath{-}T)$ with ${T}_{\text{c}}=237\ifmmode\pm\else\textpm\fi{}2\text{ }\text{K}$. Octahedral tilting at high temperatures is closely similar to tilting in the $Pnma$ structure of other perovskites, such as ${\text{SrZrO}}_{3}$. This is accompanied by a degree of Jahn-Teller ordering on the basis of the ${\text{M}}_{2}^{+}$ scheme below $\ensuremath{\sim}775\text{ }\text{K}$ but is replaced by the ${\ensuremath{\Gamma}}_{3}^{+}$ scheme below ${T}_{\text{c}}$. In contrast with the tilting and Jahn-Teller effects, magnetic ordering at the N\'eel temperature $(\ensuremath{\sim}180\text{ }\text{K})$ is accompanied by only the slightest volume strain and is not likely to influence the evolution of the other order parameters to any significant extent, therefore. An additional change in the volume strain below $\ensuremath{\sim}85\text{ }\text{K}$ is perhaps related to changes in magnetic structure at lower temperatures. Line broadening in powder diffraction patterns collected in the temperature interval $\ensuremath{\sim}150--260\text{ }\text{K}$ appears to be related to the presence of ferroelastic twins arising from octahedral tilting and draws attention to the fact that the $Pnma\ensuremath{\leftrightarrow}\text{IC}$ transition takes place in a material which already contains heterogeneities. Finally, correlation of the repeat distance of the IC structure with ${\ensuremath{\Gamma}}_{3}^{+}$ distortions of ${\text{MnO}}_{6}$ octahedra shows that the nature of the IC structure itself is also determined essentially by geometrical factors and strain.

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.

Interplay between Ferroelastic and Metal−Insulator Phase Transitions in Strained Quasi-Two-Dimensional VO2 Nanoplatelets

Formation of ferroelastic twin domains in vanadium dioxide (VO(2)) nanosystems can strongly affect local strain distributions, and hence couple to the strain-controlled metal-insulator transition. Here we report polarized-light optical and scanning microwave microscopy studies of interrelated ferroelastic and metal-insulator transitions in single-crystalline VO(2) quasi-two-dimensional (quasi-2D) nanoplatelets (NPls). In contrast to quasi-1D single-crystalline nanobeams, the 2D geometric frustration results in emergence of several possible families of ferroelastic domains in NPls, thus allowing systematic studies of strain-controlled transitions in the presence of geometrical frustration. We demonstrate the possibility of controlling the ferroelastic domain population by the strength of the NPl-substrate interaction, mechanical stress, and by the NPl lateral size. Ferroelastic domain species and domain walls are identified based on standard group-theoretical considerations. Using variable temperature microscopy, we imaged the development of domains of metallic and semiconducting phases during the metal-insulator phase transition and nontrivial strain-driven reentrant domain formation. A long-range reconstruction of ferroelastic structures accommodating metal-insulator domain formation has been observed. These studies illustrate that a complete picture of the phase transitions in single-crystalline and disordered VO(2) structures can be drawn only if both ferroelastic and metal-insulator strain effects are taken into consideration and understood.

Disorientation angles and compatible walls for phase transition hexagonal to monoclinic phase

Orientation of compatible domain walls and magnitude of disorientation angle of a ferroelastic domain twin resulting from phase transition hexagonal to monoclinic phases is expressed in crystallographic unit-cell parameters of the low-symmetry phase. These two characteristics, the orientation of the compatible wall and the disorientation angle, depend on the spontaneous strain in two single-domain states R 1, R 2 from which the domain twin is formed. They have been determined for all classes of the compatible domain walls as a function of the strain-tensor components [A. Authier, International Tables for Crystallography, in Physical Properties of Crystals, Chapter 3.4, Vol. D, A. Authier, ed., Kluwer Academic Publishers, Dordrecht, 2003, pp. 449–505]. If relative changes of crystal lattice are small, then the second rank symmetrical strain tensor u can be calculated from the crystallographic unit-cell parameters before and after the deformation [J.L. Schlenker, G.V. Gibbs, and M.B. Boisen Jr, Strain-tensor components expressed in terms of lattice parameters, Acta. Cryst. A 34 (1978), pp. 52–54; L. Jian and C.M. Wayman, Domain boundary and domain switching in a ceramic rare-earth Orthoniobate LaNbO4 , J. Am. Ceram. Soc. 79 (1996), pp. 1642–1648]. An alternative approach expresses the disorientation angle and orientation of the compatible domain wall [J. Přívratská, Disorientation angle expressed in terms of lattice parameters, Ferroelectrics 291 (2003), pp. 197–204] in terms of the crystallographic unit-cell parameters of the low-symmetry phase.

Trapping of oxygen vacancies in the twin walls of perovskite

The binding and pairwise interaction of oxygen vacancies in the ferroelastic (100) twin walls of the orthorhombic phase of ${\text{CaTiO}}_{3}$ perovskite $(Pbnm)$ have been investigated by numerical simulations using empirical force fields. An oxygen vacancy finds it energetically favorable to reside inside a twin wall, particularly when bridging two titanium ions located in the twin-wall plane. In such case, the binding energy of the vacancy to the wall is $0.7\ifmmode\pm\else\textpm\fi{}0.1\text{ }\text{eV}$, the error bar reflecting variability within two different force fields. A different disposition of the vacancy in the wall sees its binding energy reduced by a factor of 2. This implies that depending on the relative time scales for twin-wall motion and for oxygen-vacancy diffusion, anelastic motion of twin walls can display two different energy dissipation mechanisms associated to these point defects. The strongest interactions among oxygen vacancies in a twin wall are due to short-range repulsion so that no defect clusters were found. The vacancy-wall binding energy is found to increase substantially with pressure.

Ferroelastic interactions in bilayered ferroelectric thin films

We present a theoretical investigation of the elastic interactions in a heteroepitaxial bilayer consisting of a (001) tetragonal PbZrxTi1−xO3 and (001) rhombohedral PbZr1−xTixO3 on a thick (001) passive substrate. Analytical expressions for the elastic interaction energies between the layers and the resultant ferroelastic twin formation have been derived as a function of the lattice misfit strain (between layers and the substrate), composition of the ferroelectric and thickness. It is found that the elastic coupling between the tetragonal and rhombohedral layers leads to the equilibrium domain fraction in the tetragonal layer several time larger than that in single-layer films of similar thickness. Most critically, the model finds a significant change in the ferroelastic domain volume fraction in the presence of an applied electric field and hence enhanced piezoelectric properties compared to single-layered epitaxial PZT thin films.

Disorientation Twin Angles for the Hexagonal–Orthorhombic Phase Transitions

Orientation of compatible domain walls, magnitude of disorientation angles and shear angle of ferroelastic domain twins resulting from the hexagonal–orthorhombic phase transitions are discussed. Magnitude of shear angle is expressed using crystallographic unit-cell parameters of the low-symmetry phase.

Effect of ferroelastic twin walls on local polarization switching: Phase-field modeling

Local polarization switching in epitaxial ferroelectric thin films in the presence of ferroelastic domain walls was studied using phase-field approach. The nucleation bias profile across a twin wall was analyzed, and the localization of preferential nucleation sites was established. This analysis was further extended to a realistic domain structure with multiple twin boundaries. It was observed that the local nucleation voltage required for a 180° domain switching is closely related to the number of such local defects.

Oxygen deficient perovskites in the system CaSiO3–CaAlO2.5 and implications for the Earth’s interior

Oxygen deficient perovskites of the system CaSiO3–CaAlO2.5 have been synthesised at high-pressure and -temperature conditions relevant to the Earth’s transition zone in order to investigate their stabilities in the Earth’s mantle and determine structural properties associated with vacancy incorporation. Two polysomes of thermodynamically stable defect perovskites with Ca(Al0.4Si0.6)O2.8 and Ca(Al0.5Si0.5)O2.75 stoichiometry have been identified. The ordering of oxygen defects into pseudo-cubic (111) layers results in well-ordered ten- or eightfold superstructures, respectively. At all other compositions examined, a metastable formation of perovskites has been observed instead, which are assumed to grow initially disordered. These are now characterised by tiny domains, formed due to subsequent ordering of vacancies along various pseudo-cubic {111} layers. Both ordered defect perovskites show a large P–T stability field ranging from about 9–18 GPa and 4–12 GPa, respectively. Microstructural TEM analyses revealed the presence of growth and ferroelastic twins, which indicate a phase transition from rhombohedral to monoclinic symmetry during quenching. Electron energy loss spectroscopy of Si and Al K edges point at the presence of tetrahedral, octahedral and maybe some pentacoordinated silicon, whereas aluminium is predominantly octahedrally coordinated with minor fractions in lower coordination. Observed properties are interpreted in terms of a new structural model, explaining the observed phase transition and formation of different twin laws as well as giving reasons for the development of such large superstructures. With respect to phase relations of the transition zone, the potential occurrence of such defect perovskites in the Earth’s interior is discussed.

Large bulk polarization and regular domain structure in ceramic BiFeO3

Regularly twinned domain structures are observed by scanning piezoforce microscopy on single crystalline grains of BiFeO3 ceramics being grown by a special low temperature sintering process. The domains are considerably larger than those observed in thin films. Their spontaneous polarization comes close to that predicted theoretically and overcomes restrictions hitherto being set to bulk single crystals. The observed ferroelastic twin domain structure resembles that of classic T domains in rhombohedrally distorted NiO, but is additionally superimposed by ferroelectric twin domain patterns.

Effect of 90 deg ferroelastic twin walls on lattice dynamics of nanocrystalline tetragonal ferroelectric perovskites

A combined transmission electron microscopy (TEM) and Raman spectroscopy study has been performed on nanocrystalline Ba0.9Sr0.1TiO3 (BST) crystals and tubes. TEM investigations revealed the existence of 90 deg ferroelastic twins in the materials. Raman spectra showed an obvious shoulder (∼750 cm-1) from the broad band at ∼720 cm-1 that nominally represents the quasimode of E(LO4) and A1(LO3). The intensity of this shoulder increases with the twin population in the nanocrystalline materials, suggesting a correlation between the lattice dynamical characteristics and the long-range ferroelastic strain of the twin wall. The ferroelastic strain is mainly constrained along the c-axis of the BST unit cell, and the effect of this constraint is more pronounced in nanocrystalline materials than in bulks due to a significant wall volume ratio in twinned nano-materials. A1 phonons showing collective ion dynamics along the c-direction could be then hardened by the strain, while E symmetry exhibiting vibrations perpendicular to the c-axis would be less affected. The theoretically predicted giant LO–TO coupling in tetragonal ferroelectric perovskites [18] suggests that the hardening of the softest A1(TO1) mode in A1 symmetry is accompanied by that of the hardest A1(LO3) phonon. Consequently, the shoulder could be ascribed to the ferroelastic strain induced hardening of the quasimode with a considerable contribution from the A1(LO3) phonon.

Ferroelastic domain switching behaviors of superionic conductor M3H(SO4)2 (M=K, Rb, and NH4) single crystals

We have measured the temperature dependences of the optical polarizing microscopy and the stress-strain hysteresis curves in the K3H(SO4)2,Rb3H(SO4)2, and (NH4)3H(SO4)2 crystals grown by using the slow evaporation method. From these temperature dependences, it was determined that the three single crystals undergo the ferroelastic phase transitions near Tc. We also studied the ferroelastic domain switching that occurs in the three single crystals due to external mechanical stress. The critical stress values for switching from the ferroelastic twin domain to the paraelastic single domain were obtained. The ferroelastic domain switching stress of Rb3H(SO4)2 crystals (0.7 MPa) was found to be higher than those of K3H(SO4)2 and (NH4)3H(SO4)2 crystals (0.3 and 0.25 MPa, respectively). (NH4)3H(SO4)2 and K3H(SO4)2 can therefore be more easily transformed by a weak external mechanical stress. This domain switching from the ferroelastic twin domain to the paraelastic single domain is explained by the restriction of the rotation of the SO4 tetrahedron by the external stress.

Elastic coupling between 90° twin walls and interfacial dislocations in epitaxial ferroelectric perovskites: A quantitative high-resolution transmission electron microscopy study

A quantitative high-resolution transmission electron microscopy study has been performed on tetragonal, single-crystalline $\mathrm{Pb}({\mathrm{Zr}}_{0.4}{\mathrm{Ti}}_{0.6}){\mathrm{O}}_{3}$ islands grown on Nb-doped $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}(001)$ substrates, revealing the strain fields of a 90\ifmmode^\circ\else\textdegree\fi{} ferroelastic twin wall and the nearby interfacial dislocation. The twin wall, showing a width of $\ensuremath{\sim}1.5\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ and compressive strain features, is elastically coupled to the tensile-type strain of an edge dislocation having an out-of-plane Burgers vector, indicating an intimate interaction of the strain fields of both crystallographic defects. The long-range strain field of the dislocation core imposes a potential barrier on the twin wall, limiting its translational mobility under an applied electric field. The substrate clamping in the epitaxial island further acts as a restoring force on the electric-field-induced wall movement. The ensemble of these electromechanical boundary conditions thus indicates that the ferroelastic twin wall in the island should be immobile upon external electric fields. A further discussion also suggests that this complex interplay of the substrate clamping and the interfacial dislocation should account for the reported low twin-wall mobility in continuous, epitaxial ferroelectric perovskite films under an electric field.

Chemical turnstile

A chemical turnstile is a device for transporting small, well-characterized doses of atoms from one location to another. A working turnstile has yet to be built, despite the numerous technological applications available for such a device. The key difficulty in manufacturing a chemical turnstile is finding a medium which will trap and transport atoms. Here we propose that ferroelastic twin walls are suitable for this role. Previous work shows that twin walls can act as two-dimensional trapping planes within which atomic transport is fast. We report simulations showing that a stress-induced reorientation of a twin wall can occur. This behavior is ideal for chemical turnstile applications.

Orientation of Compatible Domain Walls Expressed in Terms of Lattice Parameters

Orientation of a compatible domain wall and disorientation angle of a ferroelastic domain twin resulting from phase transition tetragonal → monoclinic phases is expressed in crystallographic unit-cell parameters of the low-symmetry phase. These results are compared with those based on spontaneous strain tensor components.

The nature of spontaneous twisting of (NH4)2SO4 crystals at the curie point

Spontaneous twisting of (NH4)2SO4 crystals at the phase transition from the paraelectric phase Pnam to the ferroelectric phase Pna2 (TC = 223 K) was studied using the method of low-frequency torsion pendulum. It is shown that the macroscopic twisting of samples is caused by the rearrangement of ferroelastic twins with the {011} and {031} twinning planes existing in both the paraelectric and ferroelectric phases. A model interpreting the effect of the spontaneous twisting below the ferroelectric Curie point is proposed.

Application of real-time, stroboscopic x-ray diffraction with dynamical mechanical analysis to characterize the motion of ferroelastic domain walls

The dynamic response of ferroelastic twins to an alternating stress has been studied in situ at high temperature using a stroboscopic x-ray diffractometer and combined dynamical mechanical analyzer (XRD-DMA). The XRD-DMA is designed to allow x-ray rocking curves to be collected while the sample is undergoing simultaneous dynamical mechanical analysis in three-point-bend geometry. The detection of diffracted x-rays is synchronized with the applied load, so that rocking curves corresponding to different parts of the dynamic load cycle can be obtained separately. The technique is applied to single-crystal LaAlO3, which undergoes a cubic to rhombohedral phase transition at 550 °C, leading to the generation of characteristic “chevron” twins. The rocking-curve topology is calculated as a function of crystal orientation for each chevron type. Systematic changes in the rocking curves during heating and cooling under dynamic load demonstrate a clear preference for chevrons containing {100}pc walls perpendicular to the sample surface and {110}pc walls oriented at 45° to the sample surface. These domain walls are oriented favorably with respect to the applied stress (i.e., they separate domains with contrasting components of spontaneous strain parallel to the sample length). Below 200 °C, the superelastic strain is accommodated by rapid advancement/retraction of vertical {100}pc needle domains, with little effect on the dynamic rocking curves. Above 200 °C, a dynamic shift in peak position between rocking curves measured at the maximum and minimum applied loads is detected. The onset of a dynamic response correlates with the loss of the {100}pc needle domains and the transformation of the microstructure to 45° {110}pc walls. Superelastic strain is then accommodated by domain wall displacement/rotation, causing the wall to sweep back and forth across the x-ray beam and diffraction to occur from alternate domains at the maximum and minimum points of the stress cycle. A second sample, oriented so that domain walls in all possible chevrons are unfavorably oriented with respect to the applied stress, shows very different behavior. The rocking curves consist of several well-separated peaks at the minimum load and a single broad diffraction signal at the maximum load. This is caused by the creation of a very high density of twin walls across the sample above a critical applied stress, leading to corrugation of the sample surface.

Disorientation Angle Expressed in Terms of Lattice Parameters

Disorientation angle of a ferroelastic domain twin resulting from phase transitions cubic M tetragonal, tetragonal M orthorhombic and orthorhombic M monoclinic phases is expressed in crystallographic unit-cell parameters of the low-symmetry phase. These results are compared with those based on spontaneous strain tensor components.

White beam synchrotron X-ray topography studies of twinning in GdFeO3-type perovskite crystals

Abstract The twin structure of NdGaO3 and YAlO3 : Dy crystals was examined using white beam synchrotron X-ray topography. The relation of the orthorhombic lattice basis vectors has been obtained for every domain pair in the crystals with GdFeO3-type structure. A new computer program has been used to generate Laue simulation patterns and to calculate the image shifts in topographs. The proposed approach allow for the analysis of both, sample images for specified reflections and Laue patterns as a whole. Topography was used to map domain patterns, to show misorientations and to detect symmetric aspects of ferroelastic twins. Information on twin laws and the twin distribution was obtained simultaneously.