Antiferroelectric phase transitions in single crystals PbZrO3:Sn revisited

This paper is a review of earlier results which have been completed with recent investigations on the nature and sequence of phase transitions evolving in the antiferroelectric PbZr_1–xSn_xO₃ single crystals (0 < x < 0.35). It was found that these crystals undergo several first-order phase transitions. To investigate these transitions, five experimental methods were used to characterize the crystal properties: birefringence, Raman light scattering, dielectric, thermodynamic and electromechanical methods, and the atomic force microscopy-piezoresponse force microscopy (AFM-PFM) method to focus also on nanoscale properties. Temperature dependencies have been tentatively measured in a wide range, including a region above T_C, where precursor dynamics is observed in the form of non-centrosymmetric regions existing locally in crystal lattices.

New experimental data (Raman light scattering and PFM) are presented mainly to revise the phase diagram and, at the same time, to complement other studies on the problem of pre-transitional effects. The phase transition mechanism in PbZr_1–xSn_xO₃ is discussed taking into account the incommensurability of crystal lattices, ferroelastic behavior of multicell cubic phases, electric field influence on antiferroelectric to ferroelectric transformation, and flexoelectric effect.     

Phase transitions in ferroelectric liquid crystals

Molecular chirality plays an important role in the science of liquid crystals, leading to cholesteric liquid crystal, blue phases, ferroelectric and antiferroelectric smectic phases and twist grain boundary phases. In all of these mesogens, chirality is an intrinsic property built into the chemical structure of mesogenic molecules. The study of ferroelectric liquid crystals has seen substantial experimental strides. In theoretical aspects, there has been relatively little basic work on this fascinating class of material. This review will try to present a comprehensive overview of the current status of the phase transitions in ferroelectric smectic liquid crystals. The article begins with a brief introduction about the symmetry and structure of ferroelectric mesophases. An attempt is made to identify a range of problems and related questions associated with the study of phase transitions. In the remaining parts of the article the important experimental and theoretical developments are summarized. Finally, some of the future directions have been identified.     

Editorial

This review contains up-to-date information about experimental and theoretical investigations of phase transitions and specific features of properties of mixed crystals involving the incipient ferroelectric KTaO₃ with the off-center Li⁺, Nb⁵⁺, Na⁺ impurities. Main attention is paid to the results of the study of the mixed systems by radiospectroscopy methods (ESR and NMR).

Theoretical criteria and experimental evidence of ferroelectric and ferroelastic phase transitions as well as of dipole and quadrupolar glass states induced by the off-center impurities are discussed. It is shown that at high enough concentrations of the off-center impurities phases with long-range order appear, but at low concentrations dipole glass states occur. At intermediate concentrations of the off-center impurities new phases appear in which the coexistence of long-range properties and those of dipole glasses is possible. These phases could be named ferroelectric or ferroelastic glasses to stress their similarity with the ferroglass phases which were discovered earlier in mixed magnetic systems. The usefulness of radiospectroscopy methods for the study of phase transitions induced by off-center impurities in mixed systems, which can be considered as model disordered systems, is underlined.

In conclusion, some questions on the physics of phase transitions in disordered systems which should be solved in the future are discussed.     

Acoustic studies of phase transitions in crystals and nanocomposites

A brief review of acoustic studies of phase transitions in crystals (ferroelectric, ferroelastic, and superionic ones) and nanostructured composite materials made on the basis of porous matrices is presented. The studies were carried out at the Laboratory of Quantum Acoustics and Ultrasonic Spectroscopy of the St. Petersburg State University.     

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.     

Ferroic phase transitions in β-LiNH4SO4

Abstract

The paper reviews the results of experimental and theoretical studies of ferroic phase transitions in β-LiNH₄SO₄ and its deuterated analogue. β-LiNH₄SO₄ undergoes succesive phase transitions: a paraelectric - ferroelectric phase transition at T₁ ? 462 K, a ferroelectric - ferroelastic phase transition at T₂ ? 283 K and a transition from one ferroelastic phase to the other at T₃ ? 28 K. Attention is focused on the influence of the order of phase transitions on the pattern of ferroelectric and ferroelastic domain structure, and also on the role played by the dynamics of molecular groups in the mechanism of transitions. The pre-transition effect connected with the ferroelectric-paraelectric transition: heterophase, capable of accounting for anomalies in different physical properties present 1-3 K below T₁ is shown. The anomalous temperature variation of spontaneous polarisation of the crystal is discussed within the framework of the phenomenological model of weak ferroelectrics.     

Paramagnetic defects as probes for the study of ferroelastic phase transition in lithium niobate and lithium tantalate under high pressure

It was found by optical polarization microscopy and the EPR study that lithium niobate and tantalate crystals undergo irreversible lattice changes under anisotropic hydrostatic compression. Regions having different cell orientations were registered. The observed changes were explained in terms of "strain switching" of ferroelastic domains. Possible sequence of phase transitions in these crystals ( Pm3m\leftrightarrow R\ \bar{3}\ c\leftrightarrow R\ 3\ c ) and the symmetry of the condensed soft modes ( R 25 and o 15 , correspondingly) were obtained by the analysis of the Gibbs free energy under external pressure.     

Internal friction in Cu6PS5Br superionic crystals and related composites

Mechanical properties of Cu₆PS₅Br single crystals and composites based on them have been investigated by the internal friction method. The measurements of the internal friction and the shear modulus have been performed in the temperature range of 80–300 K at deformation frequencies of 10–100 mHz in a mode of forced torsional vibrations. The maxima caused by the superionic and ferroelastic phase transitions have been found in temperature dependences of the internal friction. It has been shown that a more than two-fold decrease in the shear modulus with increasing temperature in the range of 150–230 K is caused by mobility unfreezing in the cation sublattice of the Cu₆PS₅Br single crystal during the superionic phase transition. An abrupt (more than threefold) increase in the shear modulus upon heating in the range of 260–270 K is caused by the ferroelastic phase transition of the Cu₆PS₅Br single crystal. Parameters of the internal friction of this single crystal in the course of mentioned phase transitions have been determined.     

Static and dynamic effects in the EPR spectra of [A(H2O)6]BF6 systems

EPR studies of [Mg(H₂O)₆]BF₆ (B=Si, Ge) crystals are performed by using Mn²⁺ paramagnetic probes. The temperature dependence of the EPR spectra shows that the crystals undergo a ferroelastic phase transition to a monoclinic phase. In both systems the ferroelastic phase transition is preceded by intermediate states. The spin Hamiltonian parameters determined in the low and high temperature phases of the systems are useful to precise some aspects of the local atomic displacements involved in the intermediate states. The nature of this state is analyzed in the framework of different models as well.     

A study on the structural phase transitions of ferroelastic [N(CH3)4]2CuCl4 from microhardness measurements

Measurements of Vickers microhardness (MHv) as a function of temperature has been carried out on [N(CH₃)₄]₂CuCl₄ single crystals. The suitability of this technique for the determination of transition temperatures in the paraelastic-incommensurate→ferroelastic (commensurate) phase transitions sequence is shown.     

Phase transition in the ternary fluorides Li3Alf6 and Li3CrF6

The phase transitions of two ternary fluorides have been reinvestigated by thermal and X-ray diffraction analyses. Four phase transitions have been detected at T ₁ = 483 ± 5 K, T ₂ = 548 ± 5 K, T ₃ = 765 ± 5 K and T ₄ = 867 ± 5 K for Li₃AlF₆. Only two transformations occurred at T ₁ = 550 ± 5 K and T ₂ = 660 ± 10 K for Li₃CrF₆. Dielectric and optical measurements performed respectively on ceramics and single crystals revealed a ferroelectric behaviour coupling partially with ferroelastic coupling for the two investigated fluorides.     

Changes in the optical properties at phase transitions in TEA2MeCl4 (Me=Zn, Mn, Hg, Cu) crystals

Optical properties of TEA₂MeCl₄ crystals, where Me is a divalent metal ion, have been studied under polarization microscope in temperatures ranging from 200 to 300 K. Abrupt changes in the interference colours and strong cracking of the sample have been observed for all crystals except the TEA₂CuCl₄ one, for which only brightening of the plate image has been noted. The cracks are approximately parallel to the cleavage planes. These changes occur in two stages. The brightening of the images of the crystal samples may suggest the ferroelastic deformation in microregions. No classical ferroelastic domain structure has been observed in the low-temperature phase.     

Optical studies of the ferroelastic phase transitions in KFe(MoO4)2

ABSTRACT

The ferroelastic phase transitions in KFe(MoO₄)₂ have been studied by means of polarized light microscopy. The crystal undergoes a sequence of ferroelastic phase transitions. It has been found that the second transition consists of two transitions separated by the temperature interval of about 0.4 K. Both these transitions are of the first order and are evidenced through a phase front passing, without the domain structure rebuilding. The disposition of optical indicatrix axes n_g, n_m has been established, and the birefringence has been measured in the plane (0001) in the temperature range covering all ferroelastic phases. From temperature studies of the morphic birefringence, a critical exponent of the order parameter has been estimated.     

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.     

Temperature dependence of the order parameter and of diffuse scattering in the Hg<Subscript>2</Subscript>Cl<Subscript>2</Subscript> model ferroelastics

The fundamental and diffuse x-ray reflections from Brillouin zone-edge X points of the paraelastic phase of Hg₂Cl₂ crystals (whose integrated intensity is related to the order parameter and its fluctuations) were studied. Information was obtained on the temperature dependence of the order parameter and of diffuse scattering, and the critical exponents were determined. The conclusion is drawn that the ferroelastic phase transition in these crystals is close to the tricritical point.     

Strain-gradient-induced polarization in SrTiO3 single crystals

Piezoelectricity is inherent only in noncentrosymmetric materials, but a piezoelectric response can also be obtained in centrosymmetric crystals if subjected to inhomogeneous deformation. This phenomenon, known as flexoelectricity, can significantly affect the functional properties of insulators, particularly thin films of high permittivity materials. We have measured strain-gradient-induced polarization in single crystals of paraelectric SrTiO3 as a function of temperature and orientation down to and below the 105 K phase transition. Estimates were obtained for all the components of the flexoelectric tensor, and calculations based on these indicate that local polarization around defects in SrTiO3 may exceed the largest ferroelectric polarizations. A sign reversal of the flexoelectric response detected below the phase transition suggests that the ferroelastic domain walls of SrTiO3 may be polar.     

Photoinduced non-linear optical diagnostic of InI ferroelastic nanocrystals

Photoinduced second harmonic generation was established in the centrosymmetric layered crystals of InI. The effect was grounded on occurrence of photoinduced optical second harmonic generation in the ferroelastic phase of the InI crystals. As a subject of investigations layered ferroelastic crystal of InI was chosen. It was found that the ferroelastic phase disappears during decrease of the nanolayers from 15 nm up to 6 nm. Such effects are explained by occurrence of anharmonic phonon modes confined by the walls of the layered crystals. We have found that the effect may be of importance for the further investigations of the layered nanocrystals. At the same time the giant value of the photoinduced SHG indicates on a possible using the nanolayered crystals like promising non-linear optical crystals.     

Light scattering by some nematic liquid crystals due to phase transitions

New computer modelling of light scattering and its propagation through liquid crystal has been presented using T-matrix method in the structural phase transition regions. Numerical aspects of light scattering process, which are based on numerically solving Maxwell's equations, were calculated for some nematic liquid crystals. Firstly, we described in detail T-matrix method for computing light scattering from nematic liquid crystals and presented results of benchmark computations for the considered model. We reported results of extensive calculations for polydisperse, randomly oriented rod-like multilayered systems (nematic liquid crystals). Our results are associated with light scattering by ferroelectric and ferroelastic materials.     

五磷酸钕晶体中铁弹畴界的X射线形貌研究

利用X射线衍射形貌法,研究了五磷酸钕(NdP₅O₁₄)晶体中铁弹畴界的衍射衬度。发现在μt=0.6—7范围内,畴界呈现黑的或白的衬度。畴界衍射衬度的特征可归结为(c₂-c₁=)△c∥g畴界衬度明显△c⊥g畴界衬度消失△c·g>0畴界呈黑衬度△c·g<0畴界呈白衬度利用Penuing-Polder波点迁移原理,对畴界的衬度形成原理做了定性解释。根据畴界的衍射衬度特征,定性讨论了畴界的结构特征。 关键词：