Universal incommensurate structures

Certain phase transitions in quasiperiodic systems are characterized byuniversal structures. In these cases the functional form of the order parameter corresponding to the modulated phase,P(r), is determined by the symmetry properties of the system and is independent of the details of the associated Landau-Ginzburg model. Here we consider a simple one-dimensionalXY-like model corresponding to this type of phase transition. The universal modulated structure of this model is calculated numerically at various points along the critical line.     

On the thickness of domain walls in ferroelectrics and ferroelastics

Ferroelastic and ferroelectric domain walls are commonly described by wall profiles of the tanh(x/w)-type. We argue that this profile is still a good approximation if higher-order gradient energies are considered. Such energies are relevant for phase transitions close to structural incommensurations and also for phase transitions with dominant elastic interactions. Their effect on the wall profile is to influence the effective wall thickness. Positive gradient energies tend to widen domain walls beyond the values predicted in classic Landau-Ginzburg theory.     

Modelling of creep hysteresis in ferroelectrics

In the current paper, a macroscopic model is proposed to simulate the hysteretic dynamics of ferroelectric ceramics with creep phenomenon incorporated. The creep phenomenon in the hysteretic dynamics is attributed to the rate-dependent characteristic of the polarisation switching processes induced in the materials. A non-convex Helmholtz free energy based on Landau theory is proposed to model the switching dynamics. The governing equation of single-crystal model is formulated by applying the Euler–Lagrange equation. The polycrystalline model is obtained by combining the single crystal dynamics with a density function which is constructed to model the weighted contributions of different grains with different principle axis orientations. In addition, numerical simulations of hysteretic dynamics with creep phenomenon are presented. Comparison of the numerical results and their experimental counterparts is also presented. It is shown that the creep phenomenon is captured precisely, validating the capability of the proposed model in a range of its potential applications.     

Thermal hysteresis and memory effects in TIInS2

The dielectric susceptibility of layered TlInS₂ was studied in the temperature range of successive phase transitions. Thermal hysteresis was observed in the incommensurate phase. It was shown that after annealing the crystal at a fixed temperature within the incommensurate phase, the existing temperature interval of this phase reveals noticeable broadening. The thermal memory effect is discussed using a defect density wave model.     

Thermal hysteresis and memory effects in TlGaSe2 crystal with incommensurate phase

Temperature dependencies of dielectric permittivity of TlGaSe₂ have been measured under various thermal cycles. Peculiarities of anomalies in temperature dependencies of dielectric permittivity corresponding to structural phase transitions at 108 and 115?K are discussed. The coexistence of two different incommensurate structures in TlGaSe₂ was proposed. The phase transitions at 108 and 115?K are considered as commensurate lock-in transitions. As a result a new model of the structural phase transitions in TlGaSe₂ has been suggested.     

Conformal invariance in incommensurate phases

We study finite-size corrections to the free energy of free-fermion models on a torus with periodic, twisted, and fixed boundary conditions. Inside the critical (striped-incommensurate) phase, the free energy densityf(N, M) on anN×M square lattice with periodic (or twisted) boundary conditions scales asf(N, M)=f _–A(s)/(NM)+.... We derive exactly the finite-size-scaling (FSS) amplitudesA(s) as a function of the aspect ratios=M/N. These amplitudes are universal because they do not depend on details of the free-fermion Hamiltonian. We establish an equivalence between the FSS amplitudes of the free-fermion model and the Coulomb gas system with electric and magnetic defect lines. The twist angle generates magnetic defect lines, while electric defect lines are generated by competition between domain wall separation and system size. The FSS behavior of the free-fermion model is consistent with predictions of the theory of conformal invariance with the conformal chargec=l. For instance, the FSS amplitude on an infinite cylinder with fixed boundary conditions is found to be one-quarter of that with periodic boundary conditions. Finally, we conjecture the exact form of the FSS amplitudes for an interacting-fermion model on a torus. Numerical calculations employing the Bethe Ansatz confirm our conjecture in the infinite-cylinder limit.     

New compounds with incommensurate phases: Cs2CdI4 and Cs2ZnI4

Abstract

In this paper the results of birefringence studies and of optical observations in polarized light in a wide temperature region are presented for crystals Cs₂CdI₄ and Cs₂ZnI₄. There is the following sequence of phases: commensurate orthorhombic Pnma ? incommensurate ? monoclinic ferroelastic P2₁/n ? triclinic ferroelastic PT. A correlation was observed between the peculiarities of birefringence and NQR spectra temperature dependence. An assumption is made, that in Cs₂ZnI₄ crystal in a broad pre-transition region (T - T _i = 100 K) precursor clusters exist, which manifest themselves as coexistence of NQR spectra of two phases and as deviation of birefringence from the linear temperature dependence (“tail”).     

Phenomenological analysis of thermal hysteresis in Ni-Mn-Ga Heusler alloys

The manipulation of thermal hysteresis in Ni-Mn-Ga Heusler alloys with coupled magnetostructural phase transition is studied theoretically using the Landau theory, including magnetic, elastic and crystal lattice modulation order parameters as well as an external magnetic field. It is shown that for the assigned combination of phenomenological parameters, in the phase diagrams, the Austenite–Martensite first-order phase transition has a finite (critical) point in which the thermal hysteresis is disappeared. Moreover, this point depends on the relation between modulation and elastic constants as well as on the magnetic field. Obtained results have been compared with other theoretical end experimental data.     

Applications of optical activity to studies of phase transitions

This article reviews at an introductory level the physics of optical activity and its recent applications to studies of phase transitions of ferroelectrics. Optical activity is a kind of internal perturbation of the refractive index, and accordingly induces a resonating effect on the eigenstates of the susceptibility. This is the reason why optical activity provides us with unreplaceable information concerning the chirality of the structure and specific bonding nature of constituent atoms. The principles of our high accuracy universal polarimeter (defined as HAUP) method are described, which realized for the first time simultaneous measurements of birefringence, optical activity, and rotation angles of the indicatrices of any crystals, even those belonging to monoclinic and triclinic systems. The utility of the HAUP method is exemplified by our recent experiments. The origin of the occurrence of incommensurate states in some A₂BX₄ crystals was theoretically explained from the fact that they showed optical activity. It is of particular interest that the origin is also resonance of eigenstates of the dynamical matrix. The merits of the HAUP method have been extended to the evaluation of the soliton density in the incommensurate phase, discrimination of the twin mechanism of the ferroelectric domains, and search for the origin of ferroelectricity of Rochelle salt.     

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.     

Multicritical behavior in ferroelectrics

Solid state systems exhibit besides usual second order phase transitions a rich variety of multicritical phenomena like Lifshitz points (or lines), tricritical points (or lines) and even tricritical Lifshitz points. Realizations of such points are numerous and were also verified in the family of ferroelectrics of the type (Pb_ySn_1y)₂P₂(Se_xS_1-x)₆. A review of the critical behavior at such points is presented here. Because of the importance of the uniaxial dipolar interaction in ferroelectrics the critical behavior is different from systems with short range interaction only. Moreover the coupling to the elastic degrees of freedom may not be neglected, and leads under certain conditions to a critical temperature dependence in certain elastic constants. Crossover phenomena, which are expected in the experimental accessible region of experiments are also considered.     

Anomalies of dielectric properties of cs2hgci4 crystals in the vicinity of phase transitions

A short review of the published experimental data on various physical properties and some new results of the measurement of dielectric and electromechanical properties of Cs₂HgCI₄ crystals in a wide temperature range are presented. The crystal is shown to reveal anomalies at seven temperatures associated with structural phase transitions and hence to have eight phases. In two temperature regions there exists a small spontaneous polarization and the anomalous dielectric permittivity is a nonlinear function of the electric biasing field. Within the phase followed by the first polar phase on cooling the crystal, the effects of thermal, electrical and mechanical memory, specific for incommensurate phases, are observable.     

Existence of several surface-reconstructed phases in a two-dimensional lattice model

The zero-temperature phase diagram is rigorously obtained for a two-dimensional lattice model with four energy parameters. It is shown that the parameter space can be divided into regions, together with their boundaries, such that in each region the ground-state configurations are of one of seven different types. These types include one which is nondegenerate, four which are doubly degenerate, one which is infinitely degenerate but with no residual entropy, and one which is infinitely degenerate and has a nonzero residual entropy. The Pirogov-Sinai extension of the Peierls argument is used to establish the existence at low temperatures of four different types of ordered surface-reconstructed phases.     

Central peak of partially deuterated hydrogen-bonded ferroelectrics

A Green's function technique is used to investigate the dynamical structure factor and the central peak for mixed ferroelectric–ferroelectric systems below the phase transition temperature. The central peak is discussed in terms of its dependence on the deuteron concentration.     

铁电体中相界运动对压力的依赖性

在平均场理论的框架内研究了KNbO3 中的顺电—铁电相界在静水压的运动。纠缠解被用于不同压力下相界宽度和速度的计算。计算基于居里—外斯常数的实验数值和自由能的金兹堡—朗道展开式的参数。非经验性地研究了对静水压和三相点的响应。     

Dynamics of the domain structure in ferroelectrics with an incommensurate phase

The dynamics of the domain structure of ferroelectrics with an incommensurate phase (like sodium nitrite) is considered. The polarization properties of these ferroelectrics are described using the pseudospin formalism. The equation for the polarization is numerically solved together with the equation for acoustic waves. The obtained results are analyzed for various values of the parameters of the crystal and different initial conditions. It is shown that, after a sufficiently large time, the domain structure of the crystal becomes localized.     

Structural and dielectric properties of Pb5(Ge,Si)O11

The ferroelectric lead germanate (Pb₅Ge₃O₁₁) and its isomorphous compounds are important because of their uses as pyroelectric and electro-optic devices. Comparison of inter-planar d-spacings of Pb₅Ge_3−x Si _x O₁₁ (x=0, 0.3, 0.7 and 1.00) suggests that there is no change in basic structure of Pb₅Ge_3−x Si _x O₁₁ when Si is substituted for Ge in small quantity (x<1). The dielectric properties of the Si-substituted compounds have been studied as a function of temperature (30 to 200°C). The ferroelectric-paraelectric phase transition has been observed at 185°C. The Si doping causes (a) Curie point to shift towards low temperature, (b) peak value of the dielectric constant to decrease and (c) phase transition diffuse. The fast increase in dielectric constant of pure Pb₅Ge₃O₁₁ with temperature (beyond transition temperature) may be attributed to the development of space charge polarization in the system.