A comprehensive study of the high-pressure–temperature phase diagram of silicon

A high-pressure–temperature (P–T) phase diagram of silicon (Si) has been constructed in a range of temperatures covering from 0 to 2000 K and pressures up to 80 GPa. In this system, there is a potential for the following phases to occur: cubic diamond, β-tin, simple hexagonal, double-hexagonal close-packed, hexagonal close-packed and face-centered cubic. Besides, the lattice vibrational energy and thermodynamic quantities of each phase were calculated, in combination with quasi-harmonic approximation using the first-principles phonon density of state. The calculated temperature dependencies of thermodynamic quantities are in good agreement with experimental and theoretical observations. Thereinto, the Gibbs free energy differences of these six phases, as a function of pressure and temperature, were used to define the phase boundaries of the P–T phase diagram of Si. The results in this work not only integrate previous experimental and theoretical investigations, but also successfully predict the phase relationships of the stable phases of Si under conditions of high temperature and pressure for the first time.