Vibrational properties of amorphous germanium under pressure and its thermal expansion and Grüneisen parameters

We study the vibrational properties of amorphous germanium at high pressures using a constant pressure ab initio technique. With the application of pressure, the low-frequency modes gradually soften with a decrease in their acoustic-like nature while the high-frequency modes shift to larger frequencies. The acoustic-like vibrations are found to have negative Grüneisen parameters whereas the optic-like ones have positive values of about +1. A negative thermal expansion is produced below 200 K. Furthermore, we find that pressure reduces the number of localized states. Accompanied by the phase transition into a metallic high-density amorphous state, the nature of the low-frequency vibrations is changed from acoustic-like to optic-like and from bond bending to bond stretching.