Commensurate incommensurate phase transitions

there are two types of Commensurate-Incommensurate Phase Transitions : t_I between the basic structure and the incommensurate phasis and t_L between the inc. phasis and the lock in phasis. They both have connected structures. So that, they must verify the relation between crystallographic groups in accordance with Landau's Theory. But we have to consider the three phases in the superspace - as we do at an ordered-disordered magnetic transition-because the inc. phasis ins't a crystal in the physical space; e.g., in order to cancel the “middle range order” of the inc. phasis at t_I, we are led to assume the grey (point) group to the basic structure in the superspace. Now both inc. phase and basic structure verify the connection between point-groups in the superspace in the same way as both para and ferro phases do at a ferroic transition in the physical space. We also show that the same type of relation is possible at t_L and we give the order parameter at both t_I and t_L.     

Magnetostructural phase transitions in manganese arsenide single crystals

The effect of an external magnetic field with a strength up to 140 kOe on the phase transitions in manganese arsenide single crystals has been investigated. The existence of unstable magnetic and crystal structures at temperatures above the Curie temperature T _C = 308 K has been established. The displacements of manganese and arsenic atoms during the magnetostructural phase transition and the shift in the temperature of the first-order magnetostructural phase transition in a magnetic field have been determined. It has been shown that the magnetocaloric effect in a magnetic field of 140 kOe near the Curie temperature T _C is equal to ??T ?? 13 K. A model of the superparamagnetic state in MnAs above the temperature T _C has been proposed using the data on the magnetic properties and structural transformation in the region of the first-order magnetostructural phase transition. It has been demonstrated that, at temperatures close to T _C, apart from the contribution to the change in the entropy from the change in the magnetization there is a significant contribution from the transformation of the crystal lattice due to the magnetostructural phase transition.     

Birefringence and phase transitions in liquid crystals

The birefringence of liquid-crystalline phases is the result of the parallel order of molecules exhibiting a polarizability anisotropy. The magnitude and sign of the birefringence are determined by the structure and order of the liquid-crystalline phase types as well as by the polarizability properties of the constituent molecules. The characteristic change of the birefringence at phase transitions between liquid-crystalline phases indicates more or less pronounced structural changes. The temperature dependence of the birefringence is due to the temperature change of the molecular order.

It is shown that the structural variety of the liquid crystalline state is reflected by a big variety of their optical anisotropy properties.     

Ordering and phase transitions in liquid crystals

Structures and properties of different types of liquid crystals are discussed from a uniform point of view. Apart from the traditional mesophases (nematics, cholesterics, smectics), some new examples, including polymeric, metalloorganic and ferromagnetic liquid crystals, are also investigated. Systems with several macroscopic scales on which the type of ordering may differ, are described and analysed. Phase transitions and certain types of critical behaviour in different liquid crystals are studied.     

Multipolar phase transitions in magnetic crystals

We have studied the possibility of successive multipolar phase transitions in magnetic crystals. A Hamiltonian including various (l ? 4) multipolar interactions is treated in the molecularfield approximation. If each interaction is introduced with its characteristic symmetry, three successive phase transitions at most are found in the absence of any crystalline field anisotropy.     

Reentrant phase transitions in liquid crystals

A comprehensive review of the recent developments regarding the phenomenon of reentrant phase transitions (RPT) in liquid crystals is presented. In addition to liquid crystals this phenomenon has been observed in amazingly diverse systems. A critical assessment of the experimental investigations concerning single and multiple reentrances is given. A brief account of the theoretical efforts is also given. The article ends with the identification of the factors which impede the proper understanding of the phenomenon.     

Commensurate and incommensurate modulated structures of Rb2ZnCl4

The commensurate and incommensurate structures of Rb₂ZnCl₄ have been refined using the four-dimensional formalism for modulated structures. They are characterized by a rigid body modulated rotation of the ZnCl₄ tetrahedra and by a translation motion of the Rb atoms.     

Field-induced phase transitions in antiferroelectric liquid crystals

A theoretical study is made of the process by which an antiferroelectric smectic liquid crystal undergoes a field-induced transition to ferroelectric alignment. We find that for cells of moderate thickness the initial departure from antiferroelectric alignment occurs as a continuous Fréedericksz transition. The following transition from partial alignment to complete ferroelectric ordering may occur as either a first-order or continuous transition, depending on the relative strength of some of the model parameters. The case where the transition is continuous provides a possible mechanism for some recently observed thresholdless transitions in these systems.     

Magnetic resonance investigations of phase transitions and modulation wave motions in incommensurate solids

We measured⁸⁷Rb nuclear magnetic resonance (NMR) and³⁵Cl nuclear quadrupole resonance (NQR) Hahn spin-echo magnetization decays in the incommensurate (I) phase of Rb₂ZnCl₄ and, in each case, obtained a Hahn echo decay that was shorter than the Carr-Purcell-Meiboom-Gill decay and one which decayed with a time constant proportional to the cube of the echo time. From these measurements we obtained from both the⁸⁷Rb NMR and³⁵Cl NQR measurements values for the diffusion coefficients that are comparable in magnitude, a fact that strongly supports the existence of slow modulation wave diffusionlike motions in the I phase, since such motions should affect both Rb and Cl ions similarly. In addition, we used⁸⁷Rb two-dimensional exchange-difference NMR to study atomic motions in the incommensurate (I) and paraelectric (P) phases to elucidate the nature of the I-P transition. We measured as a function of the mixing time the frequency shifts of the cross peaks from the main diagonal and observed a gradual increase towards an asymptotic value in the I phase but a sudden jump to the final value in the P phase. We interpreted the motions observed in the P phase as normal modes arising from simultaneous reorientations of ZnCl₄ tetrahedra and corresponding Rb ions displacements between two sites. These normal modes freeze out in the I phase and change to the diffusionlike motion of the modulation wave. We also performed³⁵Cl NQR lineshape andT ₁ measurements in K₂ZnCl₄ and obtained conclusive evidence for the presence of a narrow 1q (singly modulated) I phase between 146 and 149 K.     

On the structural phase transitions in the incommensurate Cs2CdBr4

Abstract

In the series of incommensurate A₂BX₄ halides with the β-K₂SO₄ type structure, Cs₂CdBr₄ exhibits an unusual behaviour since the “lock-in” phase transition occurs at the centre of the Brillouin zone. The observed phase sequence is the following: Pnma (Z = 4)?INC(k₀ ≈ 1/6a*)?P2_1/n(Z = 4)?P1 (Z = 4). These phase transitions have been studied by means of Raman scattering and ultrasonic measurements. It is shown that the Pnma?INC?P2_1/n sequence is governed by order-disorder processes due to CdB2-₄ tetrahedra reorientations coupled with translations of the Cs⁺ cations, and that the low-temperature P2_1/n?P1 transition is of a displacive nature, governed by a soft optical mode. The “pseudo-proper” ferroelastic character of these transformations is clearly established. A model potential developed in the framework of Landau theory is proposed; this model is able to reproduce the general trends observed in the temperature dependence of the soft-modes and of the elastic constants in the different phases.