(51b) Nonmonotonic Dependence of the Absolute Entropy On Temperature in Supercooled Stillinger-Weber Silicon

Using a recently developed thermodynamic integration method, we compute the precise values of the excess Gibbs free energy (G^e) of the high density liquid (HDL) phase with respect to the crystalline phase at different temperatures (T) in the supercooled region of the Stillinger-Weber (SW) silicon [F. H. Stillinger and T. A. Weber, Phys. Rev. B. 32, 5262 (1985)]. Based on the slope of G^e with respect to T, we find that the absolute entropy of the high density liquid (HDL) phase shows a nonmonotonic dependence on temperature at 1065 K close to the liquid--liquid transition temperature of T_LL=1060 K. Our result is consistent with the earlier observation of a nonmonotonic dependence of the enthalpy on temperature in molecular dynamics simulations starting in the HDL phase at a temperature just above T_LL [S. Sastry and C. A. Angell, Nat. Mater. 2, 739 (2003)]. Our result elucidates a thermodynamic route by means of which the liquid--amorphous transition occurs in SW silicon, and possibly, in real silicon.