Theoretical study of the structural, elastic and electronic properties of the GeX2O4 (X = Mg, Zn, Cd) compounds under pressure

The effect of high pressures, up to 30GPa, on the structural, elastic and electronic properties of GeX2O4, with X = Mg, Zn and Cd, were studied by means of the pseudo-potential plane waves method within the local density approximation for exchange and correlation. The results of bulk properties, including lattice constants, internal parameters, bulk modulus and derivatives are obtained. The band structures show a direct (Gamma-Gamma) band gap for the three compounds. All the calculated band gaps increase with increasing pressure and fit well to a quadratic function. The analysis of the density of states revealed that the lowering of the direct gap Gamma-Gamma from GeMg2O4 to GeZn2O4 to GeCd2O4 can be attributed to the p-d mixing in the upper valence band of GeZn2O4 and GeCd2O4. The elastic constants and their pressure dependence are calculated using the static finite strain technique. We have observed a linear dependence of the elastic moduli on the pressure. We derived the bulk modulus, shear modulus, Young's modulus and Poisson's ratio for ideal polycrystalline GeX2O3 aggregates. We estimated the Debye temperature of GeX2O4 from the average sound velocity.