Lattice dynamics and thermodynamic properties of the B-Sn phase in Si

The lattice dynamics of silicon in the metastable b-Sn structure is studied using the density-functional linear-response theory. The Gru¨neisen parameters and thermal expansion are calculated in the quasiharmonic approximation for the cubic diamond ~cd! and b-Sn phase and the thermodynamic properties are compared with the liquid phase at zero pressure. We relate the anomalously high entropy of fusion in Si to the difference in entropy between the b-Sn and the cd phase. The melting temperature and phase boundary slopes for the b-Sn phase at zero pressure are qualitatively different from those deduced from the experimental pressuretemperature phase diagram. This suggests that the reported experimental liquid-metallic solid phase boundary does not refer to the b-Sn phase.