Pressure derivatives of the melting point for Si and Ge

Abstract

The mean-square displacement of Si and Ge is studied theoretically using higher-order perturbation and the local Heine-Abarenkov model pseudopotential. The contribution of the acoustical phonon modes to the mean-square displacement is more temperature dependent and larger than the corresponding optical mode contribution except at low temperatures. The relative contribution from the acoustical modes is more predominant at higher temperatures. Lindeman's criteria for melting xm, which is defined as the ratio of twice the root-mean-square displacement to the nearest-neighbour distance, are found to be 0.272+or-0.03 and 0.249+or-0.03 for Si and Ge respectively. The volume effect on the melting temperature of Si and Ge is studied by keeping xm constants. The melting curve obtained decreases as a function of the compressed volume, and is qualitatively in agreement with the observed tendency. The pressure derivatives of the melting point obtained are -3.3+or-0.1 and -2.5+or-0.1 K kbar-1 for Si and Ge.