First-principles study of the structural properties of Ge

With the use of an ab initio pseudopotential method, the structural properties of Ge are investigated at normal and high pressures. The pressure-induced structural phase transitions from cubic diamond to β-Sn, to simple hexagonal (sh), and to double hexagonal close packed (dhcp) are examined. With the possible exception of the dhcp structure, the calculated transition pressures, transition volumes, and axial ratios are in good agreement with experimental results. We find that sh Ge has characteristics similar to those of sh Si; the bonds between hexagonal layers are stronger than intralayer bonds and the transverse phonon modes become soft near the transitions from the sh to β-Sn and the sh to hcp structures. At normal pressures, we compare the crystal energies for the cubic diamond, hexagonal 2H, and hexagonal 4H structures. Because of the similar sp³ bonds in these structures, the structural energy differences are less than about 14 meV, and the 2H and 4H phases are metastable with respect to the cubic diamond structure. The equation of state is also presented and compared with experiment.