Ginzburg temperature

In water-in-oil droplet microemulsion systems undergoing a phase separation, we observed the crossover behavior of Belyakov and Kiselev and could determine the Ginzburg temperature Tq which is smaller in LCST case than and equal in UCST case to that of gas-liquid-phase transitions of low molecular weight as expected. 

Figure 5. Temperature development of the electronic density of states in fee FeaNi with the temperature dependent input taken from the Ginzburg-Landau theory (magnetic moments are given per atom).

Now — L is the Landau-Ginzburg free energy, where m2 = a(T — Tc) near the critical temperature, is a macroscopic many-particle wave function, introduced by Bardeen-Cooper-Schrieffer, according to which an attractive force between electrons is mediated by bosonic electron pairs. At low temperature these fall into the same quantum state (Bose-Einstein condensation), and because of this, a many-particle wave function (f> may be used to describe the macroscopic system. At T > Tc, m2 > 0 and the minimum free energy is at = 0. However, when T [Pg.173]

Here, the final three terms are a Ginzburg-Landau expansion in powers of i j. The coefficient t varies as a function of temperature and other control variables. When it decreases below a critical threshold, the system undergoes a chiral symmetry-breaking transition at which i becomes nonzero. The membrane then generates effective chiral coefficients kHp = k n>i f and kLS = which favor membrane curvature and tilt modulations, respec-... 

We will demonstrate below that the Ginzburg number Gi = AT/Tc), which determines the broadness of the energy region near the critical temperature, where fluctuations essentially contribute, is Gi A(Tc/iiq)4 with A 500 in our case. To compare, for clean metals A 100, p,q — fi,., the latter is the electron chemical potential. Thus Gi 1, if Tc is rather high, Tc (f -t- )p,q, and we expect a broad region of temperatures, where fluctuation effects might be important. 

Comparing the mean field (12) and the fluctuation (15) contributions to the specific heat (in the low and high temperature limiting cases one may use Eqs. (22), (24)) we may estimate the fluctuation temperature < Tc, at which the contribution of fluctuations of the order parameter becomes to be as important as the mean field one (so called Ginzburg - Levanyuk criterion),... 

Equilibrium data for the NH3-H2S-H2O subsystem have been reported by van Krevelen et al. at 20°, 40°, and 60°C(7 ), by Miles and Wilson at 80° and 120°C(46), and by Ginzburg et al. at temperatures from 57° to 87°C (obtained at constant total pressure rather than at constant temperature) (60,61) We correlated data having ionic strengths above 0.2 molal in terms of an equilibrium coefficient K4 ... 

NH3-NHJ, NH3-HCO3 and NH3-HS- were fitted to 68 selected ternary data points (partial pressures of weak electrolytes) measured by Otsuka et al. for NH3-CO2-H2O at 40, 60, 80 and 100 °C ( ) and Ginzburg et al. for NH3-H2S-H2O at temperatures between about 40 and 90 °C ( 1 0). While with the original -numbers the mean deviations... 

Here M is a mobility coefficient, which is assumed to be constant and r/(r.t) is the random thermal noise term, which for a system in equilibrium at temperature T satisfies the fluctuation-dissipation theorem. The free energy functional is taken to be of a Ginzburg-Landau form. In the notation of Qi and Wang (1996,1997) it is given by... 

Fig. 2.46 Cell-dynamical simulation of a symmetric block copolymer in two dimensions (64 X 64 lattice) (Hamley 1997).This structure forms from an initially homogeneous state via time-dependent Ginzburg-Landau kinetics at a temperature below the ODT.

Once the correlation length is known, one is able to estimate the range of validity of mean-field theory, as first demonstrated by Ginzburg [47]. By considering the magnitude of the fluctuations, Ginzburg derived a criterion for the temperature distance from the critical point up to which mean-field theory remains self-consistent. Ginzburg theory predicts that classical theory is only valid if... 

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. 

A primary focus of our work has been to understand the ferroelectric phase transition in thin epitaxial films of PbTiOs. It is expected that epitaxial strain effects are important in such films because of the large, anisotropic strain associated with the phase transition. Figure 8.3 shows the phase diagram for PbTiOs as a function of epitaxial strain and temperature calculated using Landau-Ginzburg-Devonshire (lgd) theory [9], Here epitaxial strain is defined as the in-plane strain imposed by the substrate, experienced by the cubic (paraelectric) phase of PbTiOs. The dashed line shows that a coherent PbTiOs film on a SrTiOs substrate experiences somewhat more than 1 % compressive epitaxial strain. Such compressive strain favors the ferroelectric PbTiOs phase having the c domain orientation, i.e. with the c (polar) axis normal to the film. From Figure 8.3 one can see that the paraelectric-ferroelectric transition temperature Tc for coherently-strained PbTiOs films on SrTiOs is predicted to be elevated by 260°C above that of... 

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