Landau phenomenology

In a series of works by Salejda and Dzhavadov [148] and Stasyuk et al. [38-42], a microscopic description of the phase transitions in (NH4)3H(Se04)2 has been proposed. The results obtained have been compared with those obtained from the Landau phenomenological theory. The original Hamiltonian has been presented in a bilinear form... 

Liquid crystals manifest a number of transitions between different phases uprm variation of temperature, pressure or a craitent of various compounds in a mixture. All the transitions are divided into two groups, namely, first and second order transitions both accompanied by interesting pre-transitional phenomena and usually described by the Landau (phenomenological) theory or molecular-statistical approach. In this chapter we are going to consider the most important phase transitions between isotropic, nematic, smectic A and C phases. The phase transitions in ferroelectric liquid crystals are discussed in Chapter 13. 

If we integrate Equation 152 twice with respfx t to the fluctuating parameter we get a Hamiltonian in the fashion of the Landau phenomenological theory (section 2.5)... 

The third problem is the possible effect of stress or external field on isotropic-nematic phase transition. In equilibrium, this phase transition is usually described by the well-known Landau phenomenology or more specifically (however, less reliably because of large fluctuations) by the Maier-Saupe mean field theory [2] (see also Refs [30,31 ]). The assumption that the transition behavior of nematic elastomers is independent of stress was roughly confirmed while testing the LCE theory [3], where the parameters of anisotropy were assumed to be independent of stress. The possible dependences of scalar/tensor order parameter on stress/extemal field have been considered in molecular Doi theory [9, 11] or phenomenological approach by Ericksen [41]. 

Within the frameworks of Landau phenomenological theory of second-order transitions [61], the order parameter /, unequivocally connected with one of the most important thermodynamic properties which is entropy change AS, is determined as follows ... 

Here A, C and E are phenomenological coefficients in the Landau expansion in tenns of the smectic ordering ... 

The first step in studying phenomenological theories (Ginzburg-Landau theories and membrane theories) has usually been to minimize the free energy functional of the model. Fluctuations are then included at a later stage, e.g., using Monte Carlo simulations. The latter will be discussed in Sec. V and Chapter 14. 

As already mentioned in the Introduction, phenomenological models for amphiphilic systems can be divided into two big classes Ginzburg-Landau models and random interface models. 

Such continuous phase transitions are conveniently described in a phenomenological Landau free-energy expansion of the order parameter. Since we... 

For a binary A-B alloy, another independent parameter, Xb (or = 1 — Xg) must be added to the fixed-stoichiometry order parameters in the preceding section. The phenomenological form of the Landau expansion, Eq. 17.2, can be extended to include Xb and has been used to catalog the conditions for many transitions in two-component systems [3]. 

It has been shown that die BCS theory does lead to die phenomenological equations of London. Pippard and Ginzburg and Landau, and one may therefore state that the basic phenomena of superconductivity are now understood from a microscopic point of view, i.e., in terms of the atomic and electronic structure of solids. It is true, however, that we cannot yet, ub initio, calculate V For a given metal and therefore predict whether it will be superconducting or not. The difficulty here is our ignorance of the exact wave functions to be used in describing the electrons and phonons in a specific metal, and their interactions. However, we believe that the problem is soluble in principle at least. 

Summary. On the basis of phenomenological Ginzburg-Landau approach we investigate the problem of order parameter nucleation in a ferromagnetic superconductor and hybrid superconductor - ferromagnetic (S/F) systems with a domain structure in an applied external magnetic field H. We study the interplay between the superconductivity localized at the domain walls and between the domain walls and show that such interplay determines a peculiar nonlinear temperature dependence of the upper critical field. For hybrid S/F systems we also study the possible oscillatory behavior of the critical temperature TC(H) similar to the Little-Parks effect. 

The phenomenological equation that determines the motion of the magnetic moment of a ferromagnetic sample is known generically as the Landau-Lifshitz-Gilbert equation and has two basic modifications. The first form... 

W.L. Ginzburg and L. Landau developed a phenomenological theory, the GL theory , which makes no assumptions concerning the basic mechanism responsible for superconductivity. In this respect the approach is similar to the Devonshire phenomenological theory as applied to ferroelectrics (see Section... 

A phenomenological treatment of the hydration repulsion, based on a Landau expansion of the free energy density, was proposed by Marcelya and Radic.9 They showed that, if the free energy density is a function of an order parameter that varies continuously from the surface, and if only the quadratic terms in this parameter and its derivative are nonnegligible, an exponential decay... 

At a simple phenomenological level, the hydration force can be described via an exponentially decreasing force, additive to (and independent of) the DLVO double layer and van der Waals forces [10]. An alternative phenomenological description is to consider the existence of an order parameter" and a Landau-like expansion of the free energy in that parameter. When only some of the expansion terms are retained in the latter expansion, both phenomenological descriptions lead to similar behaviors for the hydration forces [11]. 

In the macroscopic and phenomenological Ginzburg109-Landau description of superconductivity, a complex "order parameter" P(r) = j/(r) exp(i) is proposed, which equals zero above Tc and whose magnitude determines... 

A simple quantitative model, with no adjustable parameters, is developed for the finite size effect of ferroelectric particles on the Curie transition temperature. As the size of ferroelectric particles decreases, the Curie temperature decreases. Based on our model for lattice contraction and the Landau-Ginsburg-Devonshire (LGD) phenomenological theory, size effects on Curie temperature of lead zirconate titanate PbZri. Ti Oj (PZT, x > 0.6) are considered. It is shown that Curie temperature of PZT (x > 0,6) decreases with decreasing particle size. The predictions of our equation are in agreement with the experimental results. 

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