Landau-type Free Energy Function Research Articles

Nonlinear dielectric constant in Pb(Mg1/3Nb2/3)O3–PbTiO3 relaxor ferroelectrics

The nonlinear dielectric constant ε3 induced by the cube of the electric field was investigated in the paraelectric phase of the relaxor ferroelectric 70.5% Pb(Mg1/3Nb2/3)O3–29.5% PbTiO3. ε3 was confirmed to be positive near Tm at which the linear permittivity is maximum, and becoming negative at 158.5 °C. The temperature dependences of the linear and nonlinear dielectric susceptibilities are discussed on the basis of the Landau-type free energy function.

Phase Front Near the Critical End Point as the Boundary of the Polar Nanoregions in Relaxor Ferroelectrics

The static modulation structure of the phase front at the field-induced first-order transition point near the critical end point (CEP) was discussed on the basis of the Landau-type free-energy function. It was confirmed that the field E dependence of the thickness of the phase front is proportional to ( E CEP - E ) -1/2 , diverging at CEP ( E = E CEP ). It is pointed out that, in relaxor ferroelectrics, the boundary between the polar nanoregion (PNR) and the paraelectric matrix may be considered as a phase front, and that the contribution to the dielectric response of the phase front cannot be ignored.

Simple Landau model of the Smectic- [formula omitted] phase transition in binary mixture

Simple Landau-type free energy function is presented to describe the Smectic- C α ⁎ – Smectic ‐ C ⁎ transition in a liquid crystal mixture. The problem of the first or second order transition is explored by means of the variation of the concentration. The influence of the concentration on this transition is discussed by varying the coupling between the concentration variable and the order parameter. Within this model the Smectic- C α ⁎ – Smectic ‐ C ⁎ transition is found to be always first order transition that ends at a critical point. The presented analysis is in good agreement with the experimental results.

Nematic-smectic-A-smectic-C multicritical point: An alternative model

A new Landau-type phenomenological free-energy function to describe the nematic-smectic-A transition, smectic-A-smectic-C transition and nematic-smectic-C transition is proposed. The influence of pressure on the these phase transitions is discussed by varying the coupling between various order parameters. The phase diagram of the thermodynamic parameters is studied and a possible nematic-smectic-A-smectic-C bicritical point is predicted. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a bicritical point is observed in the phase diagram. The obtained topology of the pressure-temperature phase diagram is consistent with experimental results.

Field-Induced Phase Transition between Tetragonal and Rhombohedral Phases in Pb(Zn1/3Nb2/3)O3–8%PbTiO3

The field-induced phase transition between the rhombohedral and tetragonal phases was investigated in Pb(Zn1/3Nb2/3)O3–8%PbTiO3 by dielectric constant and electrostriction loop measurements. The temperature-electric-field phase diagram was clarified, and physical properties near the field-induced phase transition were discussed using the Landau-type free energy function.

Simple Landau model of the RIV-RIII-RV rotator phases of alkanes

Simple Landau-type free energy function is presented to describe the R(IV)-R(III)-R(V) rotator phase sequence and the transitions between them. The order parameters necessary to describe the above rotator phase transitions are identified. Varying the coupling between the order parameters, the R(IV)-R(III) and R(III)-R(V) transitions occur. Available experimental results are consistent with our model.

Landau Theory of Phase Transition in Ferroelectric Vinylidene Fluoride/Trifluoroethylene Copolymer Single Crystals: Hysteresis Loop

Ferroelectric hysteresis loops in vinylidene fluoride/trifluoroethylene, P[VDF/TrFE], copolymer single crystals are discussed on the basis of the Landau-type free energy function with the anisotropy parameter γ2. It was found that the coercive field strongly depends on the value of γ2, and decreases as γ2=0 is approached, because the Landau-type free energy function becomes isotropic in the order parameter space. We successfully reproduced the p–E hysteresis loop with a square shape and a small coercive field in P[VDF/TrFE] on the basis of the Landau theory with the anisotropy parameter γ2.

Phenomenology of Elastic Properties in Martensite Alloys

The phase diagram and elastic stiffness constants in Martensite alloys with the symmetry change from the cubic m\bar3m to the tetragonal 4/mmm and the orthorhombic mmm symmetries are discussed on the basis of the Landau-type free energy function expressed in terms of the strain components, u 1 , u 2 and u 3 . It was found that some of elastic stiffness constants corresponding to the shear deformation become extremely small not only in the vicinity of the transition temperature but also near the morphotropic phase boundary where the Landau-type free energy function is isotropic or less anisotropic in the order parameter space.

Simple Landau model of the smectic- A-isotropic phase transition

A simple Landau-type free energy function is presented to describe the smectic-A-isotropic phase transition. Varying the coupling between orientational and positional order parameters, a smectic-A-isotropic or a nematic-isotropic phase transition occurs. Within this model the smectic-A-isotropic phase transition is found to be always more strongly first order than the nematic-isotropic phase transition. The theoretical results are found to be in good agreement with all published experimental results.

Quantum paraelectricity in the mean-field approximation

Recently discovered [W. Kleemann et al., Phys. Rev. B 58, 8985 (1998)] scaling properties of the electric susceptibility of quantum paraelectric solid solutions ${\mathrm{SrTiO}}_{3}:\mathrm{C}\mathrm{a}$ are shown to emerge from a Landau-type free-energy function involving the quantum temperature ${T}_{Q}{=T}_{s}\mathrm{coth}{(T}_{s}/T)$ of Salje et al. [Z. Phys. B 82, 399 (1991)]. It is derived from both the Salje-Wruck-Thomas model and the transverse Ising model and applies also to cases where no phase transition is encountered.

Theory of Morphotropic Phase Boundary in Solid Solution Systems of Perovskite-Type Oxide Ferroelectrics: p-e Hysteresis Loop

The p-e hysteresis loop near the morphotropic phase boundary in the perovskite-type oxide solid solution system is discussed on the basis of a Landau-type free energy function. It was found that the coercive field in the p-e hysteresis loop decreases upon approaching the morphotropic phase boundary and vanishes at the morphotropic phase boundary, because of the instability in the direction perpendicular to the polarization.

Phenomenology of Magnetostrictive Alloys of the Rare-Earth Fe2Compound Family. I. Elastic Constants

Elastic stiffness constants in magnetostrictive alloys of the rare-earth Fe 2 compound family are discussed on the basis of the Landau-type free energy function expressed in terms of magnetization and strain components. It was found that some of elastic stiffness constants become extremely small in the vicinity of tetragonal-rhombohedral phase transition points.

Theory of Morphotropic Phase Boundary in Solid-Solution Systems of Perovskite-Type Oxide Ferroelectrics: Elastic Properties

Elastic stiffness constants in a perovskite-type oxide solid-solution system are discussed on the basis of the Landau-type free energy function expressed in terms of polarization and strain components. It is found that some of the elastic stiffness constants become extremely small in the vicinity of the morphotropic phase boundary.

A Theory of Morphotropic Phase Boundary in Solid-Solution Systems of Perovskite-Type Oxide Ferroelectrics

The origin of the appearance of the morphotropic phase boundary in perovskite-type oxide solid solution systems is clarified on the basis of a Landau-type free-energy function expressed in terms of polarization and strain components. The dielectric susceptibilities and piezoelectric constants are shown to increase in the vicinity of the morphotropic phase boundary.

Phenomenological description of the crystal-liquid crystal phase diagram

A new Landau-type phenomenological free energy function to describe the phase diagram of uniaxial anisotropic materials is proposed. The resulting phase diagram includes crystalline, smectic A, nematic and isotropic states, as well as a theoretically possible plastic solid state. Depending on the parameters of the free energy, smectic A phase may or may not be present for a given material. The obtained topologies of the temperature-pressure phase diagram qualitatively agree with results from computer simulations of model liquid crystalline materials.

Singularities near critical and bicritical end points: applications to an isomorphous transition

We study a system that has an isomorphous transition using an eighth-order Landau-type free energy function. The phase diagram of such system has a critical line that meets a first-order phase boundary at a critical end point. This phase boundary is also limited by two other critical lines that meet at a bicritical end point. We showed that this phase boundary close to the end point exhibits a nonanalytic behavior associated with the singularities of the critical line, confirming similar result we previously obtained using scaling arguments. Related universal amplitude ratios are then computed. Next, the critical lines near the bicritical end point are also analyzed and checked for singularities.

Successive Structural Phase Transitions in La2Mo4(M=Cu, Ni etc.) Compounds

A Landau-type free energy function is proposed to reproduce the phase sequences, which are given rise to by the instability of the modes at the X-point of the I4/mmm phase as seen in La 2 MO 4 (M=Cu, Ni etc.) compounds. Emphasis is placed on the appearance of the Pccn phase. Typical phase diagrams obtained by varying the coefficient values appearing in the free energy function are presented.

Note on Successive Phase Transitions in Hexagonal BaTiO3. II

The successive phase transitions in hexagonal BaTiO 3 is discussed on the basis of the Landau-type free energy function, putting the emphasis on the transition between the intermediate phase II and the lowest temperature phase III. It is pointed out that to induce the phase III with the space group P2 1 the twelveth order term in the order parameters, transforming under the symmetry operations as the bases of the two-dimensional E 2 u representation of the 6/mmm group, is required.

Theory of Polarization Reversals in Ferroelectrics Based on Landau-Type Free Energy

The rate equations based upon the Landau-type free energy function are solved to discuss the polarization reversals in ferroelectrics. The switching time ts is found to approximately depend upon the applied field E according to a power law, i.e., ts\\proptE-m, with m differing according to the definition of ts. The polarization reversal process fits the Kolmogorov-Avrami formula, where the index n describing the dimensionality of the reversed domains is found to be about 1.3.

On an Isomorphous Transition

A phase diagram and several physical quantities related to an isomorphous transition are studied on the basis of a Landau-type free energy function. Relationship with a two-sublattice model including an asymmetric double minimum potential is discussed.