Ab initio pseudopotential study of high pressure properties of Sn

Abstract

Among group IV elements (C, Si, Ge and Sn), the structural properties of Sn have not been well studied. Since the covalent bonds in Sn are relatively weak, an entropy contribution to the total energy is considered to be somewhat important in determining the stable structures. An ab initio pseudopotential method within the local-density-functional approximation is used to investigate the structural stability of various phases in Sn including $\alpha$ -Sn, $\beta$ -Sn, body centered tetragonal(bct), body centered cubic(bcc), simple hexagonal(sh), and hexagonal closed pack (hcp). Relativistic effects on the phases stability are also examined. The $\beta$ -Sn structure is found to transform into the hcp phase at zero temperature as pressure increases whereas experimentally the $\beta$ -Sn to bct to bcc phase transition was observed at room temperatures. To see the effects of thermal energy on the phase stability, the structural relations between the bct, bcc and hcp phases are examined. For the bct phase, the c/a ratio increases from 0.87 to 1.0, which is equivalent to the axial ratio of the bcc phase, as pressure is applied. In this case, the total energy change is much smaller as compared to the room temperature energy of about 2 mRy. For the bcc phase, the transverse acoustic(TA) phonon frequency at the [110] N point in the Brillouin zone is calculated using frozen-phonon approximation. This phonon mode is directly related to the bcc to hcp phase transition. The calculated TA phonon frequency of 0.56 THz at the N-point is found to be soft, stabilizing the hcp phase with respect to the bcc phase. Since the energy difference between the bcc and hcp phases is about 3 mRy and this value is comparable to the thermal energy, the stable phase at room temperatures and at high pressures might be the bcc structure which is experimentally observed.