Ab initio study of the beta$-tin->Imma->sh phase transitions in silicon and germanium

We have investigated the structural sequence of the high-pressure phases of silicon and germanium. We have focussed on the cd->beta-tin->Imma->sh phase transitions. We have used the plane-wave pseudopotential approach to the density-functional theory implemented within the Vienna ab-initio simulation package (VASP). We have determined the equilibrium properties of each structure and the values of the critical parameters including a hysteresis effect at the phase transitions. The order of the phase transitions has been obtained alternatively from the pressure dependence of the enthalpy and of the internal structure parameters. The commonly used tangent construction is shown to be very unreliable. Our calculations identify a first-order phase transition from the cd to the beta-tin and from the Imma to the sh phase, and they indicate the possibility of a second-order phase-transition from the beta-tin to the Imma phase. Finally, we have derived the enthalpy barriers between the phases.