Thermodynamic properties of Si-Ge alloys

A combined electronic-structure and statistical-mechanical approach has been used to calculate the thermodynamic properties of ${\mathrm{Si}}_{\mathrm{x}}$ ${\mathrm{Ge}}_{1\mathrm{-}\mathrm{x}}$ alloys. Since the long-range ordered structures are found to be unstable, only the disordered alloys have been studied. The thermodynamic functions such as entropy, enthalpy, Gibbs free energy, and others are calculated as functions of temperature and concentration. The phase diagram is also calculated and the critical temperature is predicted to be around 360 K. The tendency to clustering is found to be very small which provides further support for the instability of ordered bulk Si-Ge structures. We have studied the effects of hydrostatic pressure on both the phase diagram and the thermodynamic functions. It has been found that by increasing the pressure the instability region shrinks and moves toward the Ge side, while the critical temperature increases.