Ab initio study of the volume dependence of dynamical and thermodynamical properties of silicon

Motivated by the negative thermal expansion observed for silicon between 20 K and 120 K, we present first an ab initio study of the volume dependence of interatomic force constants, phonon frequencies of TA(X) and TA(L) modes, and of the associated mode Gruneisen parameters. The influence of successive nearest neighbors shells is analysed. Analytical formulas, taking into account interactions up to second nearest neighbors, are developped for phonon frequencies of TA(X) and TA(L) modes and the corresponding mode Gruneisen parameters. We also analyze the volume and pressure dependence of various thermodynamic properties (specific heat, bulk modulus, thermal expansion), and point out the effect of the negative mode Gruneisen parameters of the acoustic branches on these properties. Finally, we present the evolution of the mean square atomic displacement and of the atomic temperature factor with the temperature for different volumes, for which the anomalous effects are even greater.