a Self Consistent Average Phonon Equation of State for Solids.

In the present thesis the author has investigated the thermodynamical properties of solids and an equation of state for solids with particular reference to the rare gas solids and the ionic solids by developing a self consistent average phonon approximation scheme. The self consistent phonon (SCP) formalisms have proved to be very useful in calculating the anharmonic contributions to the lattice properties. Replacing the sums over the frequencies in the SCP formalism by appropriate functions of the average phonon frequencies yields simple equations of state for solids. This method is referred to as the self consistent average phonon (SCAP) formalism. In the first chapter the thermodynamical properties of Ne, Ar, Kr and Xe are presented. Using the Lennard -Jones potential, the lattice parameter, compressibility, coefficient of expansion etc., have been calculated. The SCAP results are compared with the experimental results as well as with ISCP. The agreement with the experiments is found to be very good. In the second chapter, a first principle self consistent average phonon equation of state and the thermodynamical quantities of the ionic solids with reference to NaCl have been studied. Using the Gordon and Kim potential the equation of state lattice constant, compressibility etc., have been obtained in the SCAP formalism. It is found that in the low and medium temperature range the agreement between the experimental values and the SCAP results is good but in the high temperature region near the melting point the agreement is not good. It is also found that at a critical temperature T(,c), a lattice instability occurs when B (--->) 0.0 at a physically unobservable temperature (above the melting point). Therefore such an instability does not have any physical significance relative to melting. In the quasiharmonic approximation such an instability occurs at a temperature close to the melting temperature. This closeness between the critical temperature and melting is a consequence of overestimating the vibrational pressure in the quasiharmonic approximation.