The ferroelastic transition of betaine borate

The ferroelastic transition of betaine borate at about 142 K and the nonlinear temperature dependence of the corresponding critical elastic modulus are related to the softening of optical phonons. The transition has to be considered a ferroelastic one of the optic type, i.e. pseudoproper one, therefore. It is shown by Raman spectroscopic results that the transition is induced by a strong bilinear coupling between a homogeneous strain and at least two optic lattice modes which are of the same symmetry as the strain. Optic and dielectric, investigations support the second-order character of and the classical behaviour at this transition, which have been reported in the literature. Differences and similarities to the ferroelastic transition of betaine fumarate are discussed.     

The ferroelastic transition of betaine borate

The ferroelastic transition of betaine borate at about 142 K and the nonlinear temperature dependence of the corresponding critical elastic modulus are related to the softening of optical phonons. The transition has to be considered a ferroelastic one of the optic type, i.e. pseudoproper one, therefore. It is shown by Raman spectroscopic results that the transition is induced by a strong bilinear coupling between a homogeneous strain and at least two optic lattice modes which are of the same symmetry as the strain. Optic and dielectric, investigations support the second-order character of and the classical behaviour at this transition, which have been reported in the literature. Differences and similarities to the ferroelastic transition of betaine fumarate are discussed.     

Pattern formation in Ferroelastic Transitions

We study pattern formation in ferroelastic materials using the Ginzburg–Landau approach. Since ferroelastic transitions are driven by strain, the nonlinear elastic free energy is expressed as an expansion in the appropriate (i.e., order parameter) strain variables. However, the displacement fields are the real independent variables, whereas the components of the strain tensor are related to each other through elastic compatibility relations. These constraints manifest as an anisotropic long-range interaction which drastically influences the underlying microstructure. The evolution of the microstructure is demonstrated for (i) a hexagonal-to-orthorhombic transition using a strain-based approach with explicit long-range interactions; and (ii) a cubic-to-tetragonal transition by solving the force-balance equations for the displacement fields.     

Soft optical phonon in ferroelastic BiVO4

We report the observation of an underdamped q～O soft optical phonon in the Raman spectra of the paraelastic and ferroelastic phases of BiVO₄. This mode has the same symmetry as the ferroelastic strain. The temperature dependence of the soft optical phonon energy indicates that the ferroelastic transition is continuous and that the order parameter has a Landau-type behavior over a wide temperature range.     

Mechanism of the ferroelastic transition of BiVO4

BiVO₄ has a pure ferroelastic transition at T_c = 528°K and atmospheric pressure. We elucidated the mechanism of this transition by studying the q≈0 soft optical phonon, with the symmetry of the ferroelastic strain, under large hydrostatic prèssures at room temperature. A free-energy analysis, including the optical-acoustical phonon couplings, shows that the transition is driven by the q≈0 soft optical phonon.     

Acoustic study of the ferroelastic phase transition in LiCsSO4 crystal

The paper reports on an acoustic study of the temperature dependences of the ultrasonic-wave velocity and attenuation in a LiCsSO₄ crystal within the 190–295 K temperature region, which includes the interval of the pseudoproper second-order ferroelastic phase transition (202 K). The velocity of the transverse xy acoustic mode is found to decrease by more than six times at the phase transition. The possibility of performing ultrasonic studies both in the region of the ferroelastic phase transition temperature and below it is demonstrated. The results are treated in terms of Landau’s theory. Waves not associated with the soft mode are shown to exhibit anomalies which are supposedly due to an intermediate phase, whose existence was suggested in a number of publications.     

Theory of the isostructural extension-contraction phase transition in proper ferroelastics

Using the phenomenological Landau theory of phase transitions, a diagram of states and anomalies of physical characteristics are investigated in the area of conditions corresponding to isostructural transitions in a high-symmetric phase. A cubic phase with a two-component order parameter describing the ferroelastic extension-compression transition is considered as an example.     

3-d Model for strain ordering in steel: II Relaxational effects

The spring-defect model developed by us in the accompanying paper I to discuss ferroelasticity, exhibited in the BCT phase of α-iron (BCC metals), is used to analyse anelastic relaxation across the paraelastic to ferroelastic phase transition. The kinetics of the underlying Hamiltonian representing strain-strain interactions is treated within mean-field theory. The relaxation-response relation of the linear response theory is employed to derive explicit expressions for the anelastic strain, the frequency-dependent compliance and the internal friction in terms of the basic parameters of the spring-defect model.     

Giant thermodynamical optical effect near ferroelastic phase transition point in Cs3Bi2I9 layered crystal

For the first time we have found a new giant thermodynamical optical effect near the ferroelastic phase transition point in Cs₃Bi₂I₉ layered crystal. The effect is appeared as periodical oscillations in time of the reflection coefficient. This phenomenon is caused by the small temperature deviations in thermodynamical system the appearance of which in the reflection spectra is strongly amplified in the ferroelastic phase transition point. The optical oscillations are explained on the base of a model that takes into account the temperature dependence of the refractive index through the order parameter (spontaneous strain) of the crystal.     

Analysis of the parameters of a smeared orientational transition at 250–260 K in C60 crystals

The orientational structural transformation in C₆₀ crystals at temperatures of 250–260 K is investigated within the theory of smeared first-order phase transitions. The parameters of this transformation are analyzed using the experimental temperature dependences of the heat capacity and the inelastic (ferroelastic) strain rate in the phase transition range. The elementary volume of the transformation (11–83 nm³) in a correlated motion of C₆₀ molecules and the spontaneous shear strain of the lattice (2.4×10^?2) upon its transformation from the simple cubic to the face-centered cubic structure are determined.     

Internal strain and the ferroelectric transition in ferroelastic NH4HSO4 crystals as studied by EPR of VO2+ impurity probes

The ferroelectric phase transition and its relation to the spontaneous strain in ferroelastic NH₄HSO₄ crystals were investigated using VO²⁺ ions as an EPR probe. The impurity ions were found to be interstitially trapped at sites surrounded by crystallographically inequivalent NH₄⁺ and SO₄^2? ions. The polar VO²⁺ axes exhibited temperature-dependent displacements in two distinct directions with different energies. The differential properties of VO²⁺ ions in NH₄HSO₄ crystals were used to verify the presence of internal stress in the ferroelastic phases, and the corresponding strain was studied in the range between ?120 and + 100°C. The results indicate that the ferroelectric phase transition occurs as a consequence of lattice instability caused by the internal strain. At the second-order structural transition a dipolar lattice emerges in the crystal and the spontaneous polarization appears as a result of internal entropy transfer to the strained lattice.     

A single-crystal neutron scattering study of lattice melting in ferroelastic [Formula: see text

We present the results of an extensive single-crystal neutron scattering study of the ferroelastic phase transition in [Formula: see text]. This material has previously been demonstrated to undergo a continuous loss of long-range order at its ferroelastic transition, which is the phenomenon known as lattice melting. We show that our data are consistent with a special form of lattice melting where the long-range order appears to be destroyed in a two-dimensional sense, but is preserved in the third dimension.     

Ferroelastic phase transition in LiCsSO4 embedded into molecular sieves

Acoustic studies of a nanocomposite consisted of MCM-41 molecular sieves with nanoparticles of ferroelastic LiCsSO₄ within pores were carried out. The critical softening of the transverse ultrasound velocity was observed which evidenced the ferroelastic phase transition in confined particles. The transition was moved to low temperatures compared to that in bulk LiCsSO₄. It is shown that acoustic methods are very suitable to reveal the ferroelastic phase transitions under nanoconfinement.     

Raman scattering investigation of ferroelastic Sb5O7I crystals

Sb₅O₇I undergoes a displacive phase transition at 481 K where the symmetry is changed fromC _6h ² toC _2h ⁵ . In the low temperature monoclinic phase the crystal is ferroelastic. The polarized Raman spectra of Sb₅O₇I have been measured at various temperatures below and above the phase transition. The frequencies and symmetries of most of the theoretically expected Raman active phonons in the ferroelastic phase have been determined. The observation of a soft mode in the ferroelastic phase which disappears above the phase transition together with the fact that the unit cell of the ferroelastic phase is twice as large as that of the paraelastic structure permits the conclusion that the phase transition results from a phonon instability at the Brillouin zone boundaryM-point of the hexagonal phase. The temperature dependent splittings and intensity changes of several Raman lines are discussed with respect to the ferroelastic property of the crystal and the phase transition.     

Phase transition effects in polycrystalline Hg<Subscript>2</Subscript>Br<Subscript>2</Subscript> samples

The effects accompanying the ferroelastic phase transition in Hg₂Br₂ polycrystalline samples are compared in an x-ray diffraction study with similar effects observed to occur in Hg₂Br₂ single crystals. In particular, an analysis is made of the “orthorhombic” splitting of the basal plane reflections and the behavior with temperature of the Bragg and diffuse reflections from the X points of the Brillouin zone, which characterize the behavior of the order parameter and its fluctuations, respectively. Polycrystalline samples exhibit strong smearing of the phase transition effects originating from the existence of damaged surface layers and elastic and plastic strain fields which induce order parameter fluctuations over a wide temperature range.     

Phenomenological theory of first-order phase transitions characterized by a one-component order parameter

The Landau theory of phase transitions is generalized with regard to the change Δρ_inv in the charge distribution probability density that does not break the symmetry of the high-symmetry phase. It is shown that the inclusion of Δρ_inv makes it possible to describe first-order phase transitions in terms of a fourth-order non-equilibrium potential. The suggested theory leads to the conclusion that the ferroelastic transition in TeO₂ is a first-order phase transition.     

Features of sound propagation in the vicinity of “symmetry-dictated” isostructural phase transitions in ferroelastics

Using a proper ferroelastic phase transition of the tension-compression type as an example, it is shown that, if the order parameter characterizing a structural phase transition allows the existence of a third-power invariant in the Landau potential, then there must be “symmetry-dictated” isostructural phase transition lines in the vicinity of the line of that structural phase transition. These isostructural transitions may manifest themselves both directly and as supercritical anomalies in the behavior of elastic moduli and lattice parameters. These effects are discovered and investigated without invoking the perturbation theory in terms of which the second-order phase transitions are commonly described. A hypothesis is made on the basis of the results obtained that the sound velocity anomalies observed in orthoclase and sanidine crystals are due to the super-critical behavior of the lattice parameters in the vicinity of a symmetry-dictated isostructural phase transition in the prototype phase of these crystals.     

First-principles study of the Li2TiGeO5 ferroelastic phase transition

The electronic structures of ferroelastic lithium titanium germanate are investigated by first-principles method. The structure changes caused by the phase transition are discussed. It is shown that the orthorhombic structure is more stable than the tetragonal structure. The remarkable ferroelastic property largely originates from the Ge–O hybridization, which is enhanced by the Ti–O hybridization. The effective density and potential shows the changes of atoms bonding accompanying the ferroelastic phase transition.     

Local geometry of the isofrequency phonon surface and the spectral structure of generalized lamb waves on a bounded ferroelastic substance

The singularities in the spectrum of bulk acoustic phonons polarized in the sagittal plane are investigated on a plate made of a uniaxial ferroelastic material undergoing a proper ferroelastic transition from the paraelectric to the ferroelectric phase. The singularities are induced by anomalies in the reflection of this type of normal elastic vibrations at the crystal boundary.     

Origin of the structural local transition in the molecular impurity ion MnO<Stack><Subscript>4</Subscript><Superscript>2−</Superscript></Stack> in the K<Subscript>3</Subscript>Na(CrO<Subscript>4</Subscript>)<Subscript>2</Subscript> ferroelastic

A new model is proposed for a local transition in a Jahn-Teller impurity center in a crystal with a ferroelastic (ferroelectric) phase transition. This model is based on direct interaction of the order parameter of the phase transition in the matrix with the Jahn-Teller impurity degrees of freedom. It is shown that, under these conditions, the order parameter field can induce lifting of degeneracy of the electronic states active in the Jahn-Teller effect, which is accompanied by a transition from the Jahn-Teller effect to the pseudo-Jahn-Teller effect with its subsequent suppression. As a result, a decrease in temperature gives rise to a structural local transition in the region of the low-symmetry ferroelastic (ferroelectric) matrix phase from the many-well local adiabatic to a single-well potential. The model proposed allows interpretation of experimental data obtained in an EPR study of the molecular impurity ion MnO ₄ ^2? in the K₃Na(CrO₄)₂ ferroelastic.