A detailed investigation of the dynamic and thermodynamic properties of liquid germanium

Abstract

Using Rao-Joardar's equation the potential energy of interaction in liquid germanium at a density of 46.5 nm^-1 is derived. The potential function shows a kink at 0.29 nm and an attractive minimum at 0.46 nm corresponding to the first and second nearest-neighbour distances. The values calculated by other methods is found to be in good agreement with the present values. The derivatives of the potential function are used to calculate the phonon frequencies using Bhatia-Singh's (BS) method and also by that of Hubbard and Beeby (HB). The agreement between the two methods is fair. Using Bhatia-Singh's method the elastic constans are calculated. They are also calculated through the use of velocities in the long-wave limit as obtained from the equations of Takeno and Goda and are from the phonon frequencies as obtained from Hubbard and Beeby's equations. The elastic constants calculated by different methods are found to be in good agreement with each other. Using the third and second derivatives of the potential the Gruneisen constant γ_g is evaluated. It is also calculated through pressure and energy of the vibrations. The values obtained by different methods are interconsistent. An average value of 1.39 for γ_g is obtained. The Gryuneisen constant is used to evaluate the pressure derivative of the diffusion coefficient.