First-principles study of the structural properties of Sn under pressure

The structural properties of Sn at normal and high pressures are investigated using a self-consistent ab initio pseudopotential method. The structural stability of various phases including \ensuremath{\alpha}-Sn, \ensuremath{\beta}-Sn, simple hexagonal (sh), hexagonal close packed (hcp), body-centered tetragonal (bct), body-centered cubic (bcc), and face-centered cubic (fcc) is examined. The T=0 scalar relativistic calculations show that \ensuremath{\alpha}-Sn undergoes a phase transition into \ensuremath{\beta}-Sn at 0.8 GPa. As pressure increases, we find successive phase transitions from \ensuremath{\beta}-Sn to bct at 19 GPa, to bcc at 46 GPa, and to hcp at 61 GPa. The transition sequence \ensuremath{\beta}-Sn\ensuremath{\rightarrow}bct\ensuremath{\rightarrow}bcc is consistent with experiment while bcc Sn was observed to be stable at room temperature up to 120 GPa. Examining two internal structural parameters, which induce a hcp-bcc transition, a small energy barrier that is less than thermal vibrational energy is found between bcc and hcp. This result suggests that the entropy term may be significant for the bcc phase at high pressures.