We analyze the observed Raman frequencies of the three lattice modes (modes A, B and 70cm -1 ) near the melting point in biphenyl by calculating the temperature dependence of the order parameter from the mean field theory.This is based on the correlation between the frequency and the order parameter close to the melting temperature (Tm=343K) in biphenyl.The Raman frequencies of the modes A and B decrease rapidly as the melting temperature is approached, whereas the Raman frequency of the 70 cm -1 is smoothly decreasing, as observed experimentally.It is indicated that the structural phase change toward the melting point in biphenyl is associated with the decrease in the Raman frequencies of the lattice modes A and B, in particular mode A, as observed experimentally in this molecular crystal.This method of calculating the Raman frequency in relation to the order parameter as calculated from the mean field theory is significant in comparison with some previous methods such as using the quasi-harmonic approximation and also from the crystal volume by means of the mode Grüneisen parameter.
The Raman frequency of a soft mode (238 cm -1 ) is analyzed as a function of pressure at 20 o C for NH 4 F using the experimental data from the literature. This analysis is performed for the pressure dependence of the Raman frequency shifts (1 / n )( ¶ n / ¶ P) T of the soft mode close to the I - III, III - V and V – VI transitions in NH 4 F. The frequency shifts increase as the pressure increases toward the phase transitions at T = 20 o C (293 K) in this ammonium structure. From the frequency shifts of the soft mode studied, the pressure dependence of the isothermal compressibility is predicted through the mode Grüneisen parameter. Our calculated isothermal compressibility can be compared with the experimental measurements.
The temperature dependence of the dielectric susceptibility χg is recalculated by making the elastic modulus K temperature dependent for the chiral smectic C phase in HDOBAMBC. For this calculation, the experimental data for the spontaneous polarization PS, tilt angle θ and the helical pitch ρ are used from literature close to the AC* transition in HDOBAMBC. The temperature dependences of the wave vector of the helical modulation q, the elastic free energy F and the critical electric field EC are also calculated by using the temperature dependent elastic modulus K for the chiral smectic C phase close to the AC* transition in this ferroelectric liquid crystal.It is found that the critical behaviors of the dielectric susceptibility χg, the helical modulation q, elastic free energy F and the electric field EC, are modified as the temperature dependence of the elastic modulus K is taken into account. Predictions given here can be compared with the experimental measurement in the chiral smectic phase close to the AC* transition in HDOBAMBC.
The molar volume of solid and liquid benzene was calculated at various pressures (at constant temperatures), and the Pippard relations were examined close to the melting point in this organic molecule.The molar volume calculated is in good agreement with the observed data, which decreases as the pressure increases up to about 150 MPa. The Pippard relations are also valid within this pressure range at constant temperatures studied here for the solid and liquid phases of benzene.
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.
