Landaus phenomenological theory

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)... 

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 ... 

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. 

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 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. 

Recently, a quantitative model for the size-dependent Curie temperature has been established based on mechanic and thermodynamic considerations using the Landau-Ginsburg-Devonshire (LGD) phenomenological theory by equalizing free energies of the ferroelectrics and paraelectrics phases [1-4],... 

Equations (10.38) and (10.39) give a nonlinear integro-differential equation for W, and its mathematical handling is not easy. A guidance of how to proceed is obtained from the phenomenological theory in nematics. De Gennes showed that the dynamics of nematics is essentially described by the Landau theory of phase transition and proposed a phenomenological nonlinear equation fof the order parameter tensor... 

Interaction effects must be accounted for in considering those situations where the quasiparticle distribution function deviates from that of the equilibrium case. In the phenomenological Landau-FL theory the characteristic properties of the qnasiparticles, which can hardly be calculated microscopically, are expressed in terms of parameters which are determined from... 

In Landau s phenomenological theory of the mean field the thermodynamic potential G (or F) is considered as a series in terms of the order parameter Q. I he series coefficients, generally, depend on temperature and pressure. Depending on the presence of the series term with a certain power n Q ), on the coefficients values, and on the relationships between them, the thermodynamic potential assumes a functional dependence being characteristic for the first-order transitions, transitions of the continuous type or for the first-order ones of the near-continuous type. 

Sanchez (1984) has performed analysis of the binodal and spinodal amplitudes, using Flory-Huggins s theory in the fashion of Landau s phenomenological theory. 

The temperature dependence of the spontaneous polarization (Fig. 9.39) of the monomer crystal can be described in the framework of Landau s phenomenological theory assuming a tricritical phase transition [97]. The maximum experimental value of the electric polar-... 

The theoretical explanation of superconductivity remained a big puzzle for almost a half century after its discovery. Although extremely useful phenomenological theories were proposed to account for the various aspects of superconductivity, due to London and London [106], Pippard [107], Ginzburg and Landau [108], Abrikosov [109] and others, a theory based on microscopic considerations was lacking until 1957, when it was developed by J. Bardeen, L.N. Cooper and J.R. Schrieffer [110], who were awarded the 1972 Nobel prize for Physics for their contribution this is referred to as BCS theory. 

The situation with respect to Landau-type phenomenological theories is also contradictory. Drawing an analogy between the smec-tic-A phase of liquid crystals and the superconducting phase of metals, de Gennes22 23 constructed a phenomenological theory from which he concludes that the smectic-A to nematic phase transition can be second order. Halperin and Lubensky, on the other hand, have improved the analogy with superconductors and conclude that the transition will always be at least weakly first order. 

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