Temperature and dynamical effects on the high-pressure cubic-diamond <->beta-tin phase transition in Si and Ge

The cubic-diamond <-> beta-tin phase transition in Si and Ge is studied usi ng modern first-principles techniques based on density-functional theory (D FT) without making use of any experimental inputs. The relevant Gibbs energ ies, G(p, T) = U - TS + pV, are obtained in the quasi-harmonic approximatio n from static internal energies and free-energy vibrational contributions i n the two different phases, as computed by DFT and density-functional pertu rbation theory (DFPT), respectively. Our results show that the combination of the quasi-harmonic approximation and DFPT provides an efficient tool for the study of finite-temperature pressure-induced solid-solid phase transfo rmations.