Improper Ferroelastic Transition Research Articles

Thermal and electric field induced phase transitions of Na0.5Bi0.5TiO3 single crystals

The phase transitions of unpoled and poled Na0.5Bi0.5TiO3 (NBT) single crystals were studied using structural, hysteresis loops, polarizing-microscope, dielectric, mechanical (the first measurement), thermal expansion strain and calorimetric measurements. It was found that phase transitions in NBT are first-order and clearly demonstrate ferroelastic aspects. Both rhombohedral-tetragonal and tetragonal-cubic transformations are accompanied by a softening of mechanical properties like in improper ferroelastic transitions. It was concluded that the difference in the internal friction between unpoled/poled states and between [001]c/[111]c poled states can be associated with a difference in the density of mobile ferroelastic twin walls in these states.

Theory of strain phase separation and strain spinodal: Applications to ferroelastic and ferroelectric systems

In the well-known phase decomposition process, a phase with a homogeneous composition separates into two phases with different local compositions that can be geometrically determined by the common tangent construction on the molar free energy versus composition curves. Here we consider an analogous phase destrain process in which a phase with a homogeneous strain separates into two phases with different local strains that can be geometrically determined by the common tangent construction on the volume free energy density versus strain curves. There is also a complete analogy between compositional and strain spinodals. Within the phase destrain model, we provide a general thermodynamic formulation for the phase rule, lever rule, equilibrium conditions of chemical potential, and coherent/incoherent strain spinodals. Using the cubic to tetragonal ferroelastic/ferroelectric transition as an example, we study the possible strain phase separation and spinodal phenomena, and calculate the strain-strain and strain-temperature phase diagrams for the first-order proper, first-order improper, and second-order improper ferroelastic transitions. The proposed phase destrain theory complements the existing compositional phase separation theory and can serve as guidance for the analysis and design of multi-domain/multi-phase structures during any phase transitions associated with structural changes.

A-site ordering and its effect on tilting transition in perovskite La0.75Sr0.25FeO3-δ investigated by mechanical spectroscopy

La0.75Sr0.25FeO3-δ polycrystalline samples were prepared by the solid state reaction at different sintering temperatures. An octahedral tilting Pnma↔R3¯c transition in La0.75Sr0.25FeO3-δ was detected by mechanical spectroscopy, where a dip of reduced modulus was observed and accompanied by a sharp internal friction peak. The modulus softening is due to the strain/order parameters coupling at this improper ferroelastic transition. The tilting transition shifts toward lower temperature with reducing sintering temperature in La0.75Sr0.25FeO3-δ samples, which is due to the detriment of A-site ordering in the ABO3 perovskite. A higher degree of A-site ordering favors more homogenous structural modulation, which stabilizes the low temperature Pnma phase and results in the shift of the transition to higher temperature. Another internal friction peak just below the tilting transition was observed, which is attributed to domain wall motions. A correlation between the mobility of ferroelastic domain walls in Pnma perovskite and the existence of the high temperature R3¯c phase was suggested.

Strain coupling, microstructure dynamics, and acoustic mode softening in germanium telluride

GeTe is a material of intense topical interest due to its potential in the context of phase-change and nanowire memory devices, as a base for thermoelectric materials and as a ferroelectric. The combination of a soft optic mode and a Peierls distortion contributes large strains at the cubic - rhombohedral phase transition near 625 K and the role of these has been investigated through their influence on elastic and anelastic properties by resonant ultrasound spectroscopy. The underlying physics is revealed by softening of the elastic constants by ~30-45%, due to strong coupling of shear and volume strains with the driving order parameter and consistent with an improper ferroelastic transition which is weakly first order. The magnitude of the softening is permissive of the transition mechanism involving a significant order/disorder component. A Debye loss peak in the vicinity of 180 K is attributed to freezing of the motion of ferroelastic twin walls and the activation energy of ~0.07 eV is attributed to control by switching of the configuration of long and short Ge-Te bonds in the first coordination sphere around Ge. Precursor softening as the transition is approached from above can be described with a Vogel-Fulcher expression with a similar activation energy, which is attributed to coupling of acoustic modes with an unseen central mode that arises from dynamical clusters with local ordering of the Peierls distortion. The strain relaxation and ferroelastic behaviour of GeTe depend on both displacive and order/disorder effects but the dynamics of switching will be determined by changes in the configuration of distorted GeTe6 octahedra, with a rather small activation energy barrier.

Ferroelasticity in a metal–organic framework perovskite; towards a new class of multiferroics

A metal–organic framework perovskite, [(CH2)3NH2][Mn(HCOO)3], exhibits a weakly first order ferroelastic phase transition at ∼272K, from orthorhombic Pnma to monoclinic P21/n, and a further transition associated with antiferromagnetic ordering at ∼8.5K. The main structural changes, through the phase transition, are orientational ordering of the azetidium groups and associated changes in hydrogen bonding. In marked contrast to conventional improper ferroelastic oxide perovskites, the driving mechanism is associated with the X-point of the cubic Brillouin zone rather than being driven by R- and M-point octahedral tilting. The total ferroelastic shear strain of up to ∼5% is substantially greater than found for typical oxide perovskites, and highlights the potential of the flexible framework to undergo large relaxations in response to local structural changes. Measurements of elastic and anelastic properties by resonant ultrasound spectroscopy show some of the characteristic features of ferroelastic materials. In particular, acoustic dissipation below the transition point can be understood in terms of mobility of twin walls under the influence of external stress with relaxation times on the order of ∼10−7s. Elastic softening as the transition is approached from above is interpreted in terms of coupling between acoustic modes and dynamic local ordering of the azetidium groups. Subsequent stiffening with further temperature reduction is interpreted in terms of classical strain–order parameter coupling at an improper ferroelastic transition which is close to being tricritical. By way of contrast, there are no overt changes in elastic or anelastic properties near 9K, implying that any coupling of the antiferromagnetic order parameter with strain is weak or negligible.

Ferroelastic aspects of relaxor ferroelectric behaviour in Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 perovskite

Elastic and anelastic properties of poled and depoled single crystals of Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 with compositions close to the morphotropic boundary have been investigated over the temperature range 5–700 K by resonant ultrasound spectroscopy (RUS) at frequencies of 0.1–1.2 MHz. Steep elastic softening occurs in a temperature interval of at least 250 K as the Vogel-Fulcher freezing interval and cubic → tetragonal transition point, Tc, are approached from above. This is understood in terms of coupling between acoustic modes and central peak mode(s) associated with dynamic polar nano regions (PNR's) below the Burns temperature. Acoustic losses occur in a temperature interval of ∼50 K above Tc, associated with slowing down of the PNR dynamics. The cubic ↔ tetragonal and tetragonal ↔ rhombohedral transitions are accompanied by steep minima in elastic properties, closely analogous to the pattern of softening and stiffening observed in sequences of improper ferroelastic transitions in other perovskites. Variations in the magnitudes of acoustic losses at T < Tc correlate with the density of ferroelastic twin walls, from lowest for [001]c-poled and [111]c-poled crystals in the stability fields of the tetragonal and rhombohedral phases, respectively, to highest for unpoled crystals. A simple model of Debye-like peaks in acoustic loss near 100 K has yielded activation energies and attempt frequencies in the same range as those observed from dielectric data in the Vogel-Fulcher freezing interval. These highlight the fact that, in addition to conventional ferroelectric/ferroelastic twin walls, relaxor ferroelectrics contain local structural heterogeneities coupled to strain, which are probably related to the presence of static PNR's preserved even in poled crystals. RUS also provides a convenient and effective means of determining the mechanical quality factor of relaxor ferroelectrics, as functions of both poling history and temperature.

Elastic and anelastic relaxations accompanying magnetic ordering and spin-flop transitions in hematite, Fe2O3

Hematite, Fe2O3, provides in principle a model system for multiferroic (ferromagnetic/ferroelastic) behavior at low levels of strain coupling. The elastic and anelastic behavior associated with magnetic phase transitions in a natural polycrystalline sample have therefore been studied by resonant ultrasound spectroscopy (RUS) in the temperature range from 11 to 1072 K. Small changes in softening and attenuation are interpreted in terms of weak but significant coupling of symmetry-breaking and non-symmetry-breaking strains with magnetic order parameters in the structural sequence . The transition at TN = 946 ± 1 K is an example of a multiferroic transition which has both ferromagnetic (from canting of antiferromagnetically ordered spin moments) and ferroelastic (rhombohedral → monoclinic) character. By analogy with the improper ferroelastic transition in Pb3(PO4)2, W and W′ ferroelastic twin walls which are also 60° and 120° magnetic domain walls should develop. These have been tentatively identified from microstructures reported in the literature. The very low attenuation in the stability field of the C2/c structure in the polycrystalline sample used in the present study, in comparison with the strong acoustic dissipation reported for single crystal samples, implies, however, that the individual grains each consist of a single ferroelastic domain or that the twin walls are strongly pinned by grain boundaries. This absence of attenuation allows an intrinsic loss mechanism associated with the transition point to be seen and interpreted in terms of local coupling of shear strains with fluctuations which have relaxation times in the vicinity of ∼10−8 s. The first order (Morin) transition occurs through a temperature interval of coexisting phases but the absence of an acoustic loss peak suggests that the relaxation time for interface motion is short in comparison with the time scale of the applied stress (at ∼0.1–1 MHz). Below the Morin transition a pattern of attenuation which resembles that seen below ferroelastic transitions has been found, even though the ideal low temperature structure cannot contain ferroelastic twins. This loss behavior is tentatively ascribed to the presence of local ferromagnetically ordered defect regions which are coupled locally to shear strains.

Ferroelastic transition and the relaxor state in SrTiO3-PbMg1/3Nb2/3O3

Dielectric and acoustic properties of the (1 − x)SrTiO3−xPbMg1/3Nb2/3O3 solid solutions (0 ⩽ x ⩽ 1) have been studied at temperatures ranging from 4.2 to 350 K. It has been found that the improper ferroelastic transition exists up to a concentration x = 0.4 and that the phase transition temperature grows with x increasing from 0 to 0.4. As the concentration of the second component is further increased, the transition becomes suppressed by the relaxor phase forming at xc ≈ 0.22. The results obtained are discussed in terms of the current concepts of relaxor ferroelectrics.

Effect of the phase transition on the infrared spectra of improper ferroelastic Hg2Cl2

The effect of the improper ferroelastic transition on the IR spectra of the Hg2Cl2 crystal is considered. It is shown that, due to lattice anharmonicity, the distortions caused by the phase transition give rise to mixing of the normal modes of the higher symmetry phase of the crystal, which results in the appearance of extra poles in the frequency dependence of the lattice permittivity. Experimentally, such extra poles manifest themselves in the appearance of extra lines in the IR absorption spectra. Symmetry analysis shows that this effect in Hg2Cl2 is strongly anisotropic in the plane normal to the tetragonal axis of the crystal.

High-temperature macroscopic piezoelectricity in Nb-dopedPbZr1−xTixO3ceramics driven by the existence of polar regions

The dielectric, elastic, and piezoelectric properties of a niobium-doped $\mathrm{Pb}{\mathrm{Zr}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{O}}_{3}$ ceramic with a composition located near the morphotropic phase boundary have been studied from $25\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}400\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. A strong softening of the elastic coefficients was observed far below the temperature corresponding to the dielectric permittivity maximum, ${T}_{\ensuremath{\epsilon}\mathrm{max}}=366\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$. The steep decrease of the stiffness coefficient ${c}_{44}$ from $400\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}350\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ is probably a stepwise anomaly which is expected at an improper ferroelastic transition. In addition, it was found that all macroscopic piezoelectric activity had disappeared well above ${T}_{\ensuremath{\epsilon}\mathrm{max}}$. This is explained by the combined effects of compositional fluctuations in the $\mathrm{Zr}∕\mathrm{Ti}$ sublattice and the presence of polar nanoregions. The elastic properties have an anomaly at the temperature at which the lattice becomes predominantly centrosymmetric. The piezoelectric activity vanishes when the polar nanoregions reach a critical size below which they can no longer interact coherently through the nonpolar matrix to induce a macroscopic piezoelectric response.

Elastic properties of minerals and the influence of phase transitions

Elastic anomalies that accompany cation ordering and displacive phase transitions can be understood in terms of coupling between strain components and the driving order parameter in Landau free energy expansions. Non-convergent cation ordering in spinel, MgAl 2 O 4 , is accompanied by changes in individual elastic constants, shear modulus, and bulk modulus that vary linearly with the order parameter. Convergent cation ordering, such as Al/Si ordering in anorthite, is expected to give changes in elastic properties that scale with the square of the order parameter. The elastic anomalies that develop in association with displacive phase transitions show greater diversity, due to the additional influence of the order parameter susceptibility. These are illustrated for the cases of the proper ferroelastic transition at high pressure in stishovite and the improper ferroelastic transition in SrTiO 3 perovskite. Low temperature transitions in lawsonite show a more complex pattern of softening and stiffening that depends on coupling with both cation ordering and displacive processes. Variations of the spontaneous strain and elastic constants are indicative of the underlying thermodynamic mechanism for a phase transition. If any such transitions occur in minerals of the Earth's crust or mantle they should be identifiable from their distinctive influence on seismic velocities.

Pressure-induced structural phase transition in the IV–VI semiconductor SnS

The structural behaviour of SnS under high-pressure has been investigated by angular dispersivesynchrotron powder diffraction up to 38.5 GPa. A structural phase transition from orthorhombicα-SnS tomonoclinic γ-SnSwas observed at 18.15 GPa. The fit of a Birch–Murnaghan equation-of-state gave the volume at zero pressure ofV0 = 192.6(3) Å3, the bulk modulusat zero pressure of B0 = 36.6(9) GPa and the pressure derivative of the bulk modulus for α-SnS and V0 = 160(1) Å, B0 = 86.0(5) GPa and for γ-SnS. The improper ferro-elastic transition is of first-order and is accompanied by a largevolume discontinuity of about 9.1%. The phase transition can be described in terms of agroup/subgroup relationship. The doubling of the unit cell indicates a wavevector(1/2,0,1/2) atthe U-point in the Brillouin zone.

Urotropin azelate: a rather unwilling co-crystal.

Urotropin (U) and azelaic acid (AA) form 1:1 co-crystals (UA) that give rise to a rather complex diffraction pattern, the main features of which are diffuse rods and bands in addition to the Bragg reflections. UA is characterized by solvent inclusions, parasite phases, and high vacancy and dislocation densities. These defects compounded with the pronounced tendency of U to escape from the crystal edifice lead to at least seven exotic phase transitions (many of which barely manifest themselves in a differential scanning calorimetry trace). These involve different incommensurate phases and a peritectoid reaction in the recrystallization regime (T(h) > 0.6). The system may be understood as an OD (order-disorder) structure based on a layer with layer group P(c)c2 and cell a(o) approximately 4.7, b approximately 26.1 and c approximately 14.4 A. At 338 K the layer stacking is random, but with decreasing temperature the build-up of an orthorhombic MDO (maximal degree of order) structure with cell a(1) = 2a(o), b(1) = b, c(1) = c and space group Pcc2 is begun (at approximately 301 K). The superposition structure of the OD system at T = 286 (1) K with space group Bmmb and cell â = 2a(o), b = b and ĉ = c/2 owes its cohesion to van der Waals interactions between the AA chains and to three types of hydrogen bonds of varied strength between U-U and U-AA. Before reaching completion, this MDO structure is transformed, at 282 K, into a monoclinic one with cell a(m) = -a(o) + c/4, b(m) = b, c(m) = -2(a(o) + c/2), space group P2(1)/c, spontaneous deformation approximately 2 degrees, and ferroelastic domains. This transformation is achieved in two steps: first a furtive triggering transition, which is not yet fully understood, and second an improper ferroelastic transition. At approximately 233 K, the system reaches its ground state (cell a(M) = a(m), b(M) = b, c(M) = c(m) and space group P2(1)/c) via an irreversible transition. The phase transitions below 338 K are described by a model based on the interaction of two thermally activated slip systems. The OD structure is described in terms of a three-dimensional Monte Carlo model that involves first- and second-neighbour interactions along the a axis and first-neighbour interactions along the b and c axes. This model includes random shifts of the chains along their axes and satisfactorily accounts for most features that are seen in the observed diffraction pattern.

A symmetry comparison of orientation-twin and antiphase domainwalls in Pb3(VO4)2

A group-theoretical comparison of domain walls in orientation twins andantiphase structures is presented for the improper ferroelastic transition inlead orthovanadate, Pb3(VO4)2. Six possible domains arise in thedaughter state: three orientation states and three translation-relatedantiphase states. The transition is driven by a three-component primary orderparameter belonging to the F+2 irrep, with secondary order parametersconsisting of elements of the spontaneous strain tensor. Order-parameterprofiles across domain walls which arise in structures composed of pairs ofthe allowed daughter states can be calculated by constructing theLandau-Ginzburg free energy and applying the Euler-Lagrange equations. Wepresent some solutions of the resulting differential equations, and note someinteresting features in the symmetries of the profiles described by thesesolutions. In particular, the antiphase wall is described by the same diperiodicgroup as the domains on either side of it, whereas the orientation-twin wallis described by a different diperiodic group to either of the two domainsbordering it.

Micro-Brillouin scattering study of ferroelastic phase transitions inKSc(MoO4)2

High-resolution micro-Brillouin scattering studies of ferroelastic ${\mathrm{K}\mathrm{S}\mathrm{c}(\mathrm{M}\mathrm{o}\mathrm{O}}_{4}{)}_{2}$ have been performed in the temperature range 293--125 K giving information about the temperature dependence of the acoustic phonons propagating in the [100], [010], and [001] directions. Strong anomalies in sound velocity and attenuation have been observed for the sound waves corresponding to the ${c}_{11},$ ${c}_{44},$ and ${c}_{66}$ elastic constants. These results indicate a $3\ifmmode\bar\else\textasciimacron\fi{}\stackrel{\ensuremath{\rightarrow}}{m}2/m$ improper ferroelastic transition at 260 K followed by two transitions into other ferroelastic and monoclinic phases at 240 and 180 K. The comparison of the observed anomalies with the results of phenomenological theory suggests the following phase transition sequence in ${\mathrm{K}\mathrm{S}\mathrm{c}(\mathrm{M}\mathrm{o}\mathrm{O}}_{4}{)}_{2}:$ $P3\ifmmode\bar\else\textasciimacron\fi{}m\stackrel{\ensuremath{\rightarrow}}{1}C2/\stackrel{\ensuremath{\rightarrow}}{c}C2/\stackrel{\ensuremath{\rightarrow}}{m}C2/c.$ The present results suggest that below 260 K a simultaneously ferroelastic and incommensurate phase may exist, in agreement with the previous reports.

Lattice dynamics representation theory versus isotropy subgroup method with application to M5mode instability in CsCl structure

Abstract The Landau theory for ferroic phase transitions occurring in materials with CsCl structure (space group O1 h, Pmm) induced by M− 5 mode softening is developed by two different procedures: (i) The physically transparent lattice dynamical approach in conjunction with standard group representation theory, and (ii) the abstract, powerful group theoretical approach employing the concepts of isotropy subgroups and subduction frequencies. These two methods are outlined and their respective merits compared. The Landau free energy is given up to sixth order in the six-component primary order parameter. All 26 symmetry allowed product phases are identified and described in terms of their atomic displacements. Specifically, an improper ferroelastic transition to a tetragonally distorted low symmetry phase (D1 4, 14/mmm) and its atomic displacements observed in x-ray and neutron scattering experiments on LaAg1-x Inx (x ∼ 0.2) are confirmed. For this transition another symmetry allowed secondary order paramet...

Theoretical model for the improper zone-centre ferroelastic transition in rare-earth elpasolites

Abstract The cubic to tetragonal transition in rare-earth elpasolites is the unique example of an improper ferroelastic transition induced by a zone-centre instability. The anomalies of various physical quantities found in the vicinity of Tc are interpreted as indications for the existence of an incommensurate intermediate structure which is stabilized by the coupling of the order-parameter to inhomogeneous spontaneous strains.

Temperature dependence of third-order elastic constants of potassium manganese fluoride.

The nonlinearity parameters along the three principal symmetry directions have been measured for ${\mathrm{KMnF}}_{3}$ from 298 to 350 K by means of acoustic second-harmonic generation. In conjunction with our earlier data on the temperature dependence of the pressure derivatives of the elastic constants, the complete set of the six third-order elastic (TOE) constants has been determined in this temperature range. For ${c}_{111}$, ${c}_{123}$, and ${c}_{166}$ the temperature dependence is linear, suggesting that the effect of the improper ferroelastic transition at 186 K is no longer present above 300 K. This permits us to eliminate the effects of zero-point and thermal motion and of the structural phase transition by linear extrapolation of the data to absolute zero temperature. The bare TOE constants thus obtained differ significantly from the room-temperature values. The bare (and the room-temperature) values exhibit large deviations from the Cauchy relations, indicating significant contributions from many-body forces.