Landau Model Of Phase Transitions Research Articles

Superlattice structures observed in the extraordinary phase sequence and analyzed by the phenomenological Landau model and the partially molecular model

We draw several electric-field-temperature (E-T) phase diagrams with electric-field-induced birefringence contours in the nOHFBBB1M7 (n=10) and nOTBBB1M7 (n=11) (C11) mixture system by changing the C11 concentration carefully; some of the mixtures show the unusual extraordinary phase sequence where subphases with the four-, five-, and six-layer superlattice structures emerge above the smectic-C(*) main phase. We try to understand the results in terms of two complementary models that have so far been proposed: the phenomenological Landau model of phase transitions by Dolganov et al. [P. V. Dolganov et al., Phys. Rev. E 86, 020701(R) (2012)] and the partially molecular Emelyanenko-Osipov model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)]. The observed E-T phase diagram can be well reproduced by the phenomenological model. An emergence of the subphase with the four-layer superlattice structure above smectic-C(*) is also understandable in terms of the partially molecular model. We discuss the pros and cons of the two models as well.

Ginzburg-Landau theory for multiband superconductors: Microscopic derivation

A procedure to derive the Ginzburg-Landau (GL) theory from the multiband BCS Hamiltonian is developed in a general case with an arbitrary number of bands and arbitrary interaction matrix. It combines the standard Gor'kov truncation and a subsequent reconstruction in order to match accuracies of the obtained terms. This reconstruction recovers the phenomenological GL theory as obtained from the Landau model of phase transitions but offers explicit microscopic expressions for the relevant parameters. Detailed calculations are presented for a three-band system treated as a prototype multiband superconductor. It is demonstrated that the symmetry in the coupling matrix may lead to the chiral ground state with the phase frustration, typical for systems with broken time-reversal symmetry.

Commensurate polar smectic structures with a two-component order parameter

Recently Wang [Phys. Rev. Lett. 104, 027801 (2010)] discovered a novel smectic-C* liquid-crystal commensurate structure with six-layer period. Challenged by this discovery, we show that the observed novel structure and the unusual sequence of polar phases can be explained in the framework of the discrete Landau model of phase transitions with a two-component order parameter. Peculiarities of the six-layer phase and the influence of short-range and long-range interactions on the formation of different phases and phase sequences are discussed.

Formation and structure of a soliton in an antiferroelectric liquid crystal in an electric field

The soliton structure in an antiferroelectric liquid crystal in an electric field is calculated in the discrete phenomenological Landau model for phase transitions. The anticlinic structure of the antiferroelectric crystal gives rise to nontrivial features of the soliton structure and the stability of the soliton. The soliton is topologically stable in a metastable state if the electric field is much higher than the field of antiferroelectric-helix unwinding. A structural transition with a step-like change in the orientation of molecules occurs as the soliton field varies. A peculiar soliton (synclinic pair) can be formed if the barrier between the anti- and ferroelectric structures is large. The calculation shows the possibility of a large electroclinic effect in the soliton, i.e., a variation in the molecular tilt angle in an electric field in the vicinity of the transition of the structure to the synclinic state.

Towards a microscopic theory of phase transitions: residual rays, correlation radii and critical indices

Bonds between atoms/molecules of condensed substances must be described within the framework of quantum electrodynamics (QED) as an exchange of virtual photons. Such representation is supported by the known conformity of latent heat with residual infrared (IR) rays and the possibility of latent heat removal by characteristic frequencies. These bonds are virtual if the duration of photons’ formation (their ‘dressing’) τ exceeds the duration of free path in substance ℓ = 1/σ tot N, i.e. if τ > ℓ/c. It is assumed that reversing this inequality corresponds to bond breakage and phase transitions. With low σ tot and τ frequencies, it leads to the universal radius of correlations, R c ∼ ω −ν, ν = 2/3, and allows refinement of the Ginzburg–Landau model of phase transitions by expansion of thermodynamic potentials over R c (instead of temperature distance), which results in the correct system of critical indices. Such a consideration offers an opportunity for the stimulation of definite phase transitions by resonant frequencies.

Analysis of ferroelectric switching in finite media as a Landau-type phase transition

A detailed analysis of polarization reversal in ferroelectrics has been performed, in the framework of the Landau model for phase transitions. Some important characteristics of homogeneous switching have been emphasized and later used in studying the more general case of inhomogeneous switching. The two extremes of switching current correspond to the inflexion points of the dielectric hysteresis loop. Hysteresis loops of poled ferroelectric samples are expected to include negative-susceptibility regions, for high-frequency applied electric fields. The switching current minimum is eliminated by the experimental method used for recording the switching responses. Equivalent Landau coefficients and electric fields have been defined, in order to integrate the size effects and inhomogeneity contribution to switching of the global order parameter. We correlated the size effects on the critical parameters of the switching (the coercive field) and the ferroelectric-to-paraelectric phase transition (the Curie temperature). Polarization reversal in small-size ferroelectrics can be regarded as a diffuse phase transition, whereas its character is closer to normal for large-size samples. The size dependencies of the reversal speed and maximum current result from the size dependencies of the equivalent Landau coefficients and electric field inducing reversal.

Magnetization measurements of nearly ferromagnetic compounds TiBe 2-xMx (M = Cu, Ag, Au, Fe) in low and high fields

It is shown that the substitution of minute amounts of Cu for Be in TiBe 2 causes the susceptibility to increase monotonically. Magnetization data for TiBe2-xCux at 1.24 K and 4.17 K in fields up to 213 kOe are analysed in the Landau model of phase transitions. The critical concentration for ferromagnetism, xc, is about 0.2. Ag and Au as solutes decrease the susceptibility of TiBe2 (preliminary results). The magnetic moment of Fe in TiBe2-xFe x is estimated to be smaller than 0.01 μB.

Investigation of a ferroelastic phase transition in NdP514 by EPR study of Gd3+ center

The ferroelastic phase transition between P21/c and Pncm structure of GdxNd1−xP5O14 is analyzed by EPR spectra, and the dependence of the resonance spectrum is studied from 77 to 421 K. It is shown that the orientation of the principal axis of the classical D tensor is mainly related to the spatial symmetry of the crystal by a rotation angle, and its temperature dependence is analyzed using the Landau model of phase transitions. Alternatively, the critical exponent of the order parameter near the phase transition has been found to be β = 0.33.

Some Experimental Effects in Films of Ordered Matter

The existence of boundary layers, having properties different from the bulk, influences considerably the ordering properties of thin films of condensed matter. First, we will review the problem of size effects in superconducting as well as in superfluid helium films. Liquid crystals films offer another class of ordered systems in which similar concepts can be applied. The physicochemical understanding of the boundary effects (role of the elastic distortion and of the interfacial chemical energy) and the bulk ordering mechanisms will be discussed and the analogies with the previous low temperature examples studied in the framework of the Landau model of phase transitions. A direct approach of the dynamic behavior is also possible due to macroscopic relaxation times.