H. Karacali

Calculation of the free energies for the solid phases of ammonium halides

Using mean field theory, we calculate the free energies of the solid phases of ammonium halides. The temperature and pressure dependences of the free energies are obtained using experimental phase diagrams of the ammonium halides. From these dependences, we calculate numerically the specific heat as a function of temperature for the solid I–liquid, solid II–liquid and solid I–solid II transitions in the ammonium halides, in particular for NH4Cl. The critical behaviour of some other thermodynamic quantities is also predicted from the mean field theory.

Calculation of a generalised smectic–hexatic phase diagram in liquid crystals

This study gives a generalised smectic–hexatic phase diagram calculated by the Landau mean field theory. Our calculated phase line equations are fitted to the experimental phase lines, which represent first-order transition for the liquid crystals studied here. The temperature- and concentration-dependent phase lines calculated in this study describe the observed T–X phase diagram for the smectic–hexatic transitions. This indicates that the method of calculating the phase line equations from the mean field theory is general and it can be applied to other phase transitions in liquid crystals.

CALCULATION OF THE DAMPING CONSTANT AND ACTIVATION ENERGY FOR RAMAN MODES IN (NH4)2SO4

The temperature dependence of the damping constant is calculated for various Raman modes in (NH4)2SO4 by the expressions derived from the soft mode–hard mode coupling model and the energy fluctuation model. The expressions for the damping constant are fitted to the measured Raman bandwidths and then the activation energies are extracted, which are equal to ~0.2 eV for the Raman modes studied. The damping constant of a soft mode is also calculated and the activation energy (~0.1 eV) is deduced in this crystal. Values of the activation energies obtained here, can be compared with the value of kBTC = 0.02 eV for (NH4)2SO4. This indicates that this ferroelectric material undergoes an order–disorder transition. It is concluded that the observed behaviour of (NH4)2SO4 can be described reasonably by the soft mode–hard mode coupling model considered here.

Calculation of the Spontaneous Polarization and the Dielectric Constant for the Ferroelectric N(CH3)4HSO4 Using the Mean Field Model

Abstract The temperature dependences of the spontaneous polarization and the dielectric constant (susceptibility) are calculated using the mean field model for the ferroelectric N(CH3)4HSO4. Expressions derived from the mean field model for the spontaneous polarization and the inverse susceptibility are fitted to the experimental data from the literature. The fitting parameters in the expansion of the free energy in terms of the spontaneous polarization are determined within the temperature intervals in the ferroelectric and paraelectric phases of N(CH3)4HSO4. Our results show that the temperature dependences of the spontaneous polarization and the dielectric constant as predicted from our mean field model, describe adequately the observed behavior of N(CH3)4HSO4 in the ferroelectric and paraelectric phases.

A temperature-concentration (T-X) phase diagram calculated using the mean field theory for liquid crystals.

Phase-line equations for smectic–hexatic phase transitions in liquid crystals were derived using the Landau phenomenological theory. In particular, second-order transitions for the smectic-A–smectic-C (SmA–SmC) and hexatic-B–hexatic-F (or HexI) transitions were studied and the tricritical points for these transitions were located. The calculated phase-line equations were fitted (using experimental data for various liquid crystals) to construct a generalized T–X phase diagram. It was shown that the T–X phase diagram calculated from the free energy adequately describes the observed behavior of liquid crystals during smectic–hexatic transitions.

LINEWIDTH OF PHONONS IN ORDER–DISORDER PHASE TRANSITIONS WITH RANDOM TELEGRAPH NOISE

We derive an expression for the linewidth of phonons involved in the order–disorder phase transitions in solids. The linewidth is obtained as a function of the dwell time from which the activation energy can be computed. A new viewpoint is presented on the assumption that the fluctuations in the random variable of the noise, which is carried by the random particles involved in the order–disorder mechanism, affect the linewidth of the phonons.