Ideal crystal stability and pressure-induced phase transition in silicon

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Abstract
The structural response of diamond-cubic silicon under hydrostatic compression is analyzed using both an empirical interatomic potential proposed by Tersoff and ab initio total-energy calculations. The stability analysis based on elastic stiffness coefficients (which are generalized elastic constants at finite strain) gives a critical pressure of 64 GPa at which the ideal lattice becomes unstable against homogeneous tetragonal shear deformation. This prediction is explicitly verified by direct molecular-dynamics simulation, which shows that the instability causes the lattice to transform to the β-Sn structure. It is demonstrated that the large value of the transition pressure implies an intrinsic activation barrier, for which the Tersoff potential results agree well with ab initio calculations. This barrier exists for a transformation involving ideal crystal lattices that, while uniformly deformed from the equilibrium diamond-cubic structure, do not contain any point or extended defects. We suggest that, due to the neglect of lattice defects, the critical pressure corresponding to this transformation represents the upper bound on the limit of stability. A lower bound, corresponding to the barrierless transition, is obtained by equating free energies of different phases. Lower bounds calculated with the Tersoff potential and present ab initio results are 12.7 and 7.8 GPa, respectively, close to the range of experimental values for the diamond-cubic to β-Sn transition under compression. To support our conjecture on the role of defects we invoke certain analogies between the studied structural transitions in crystalline solids and melting.