Ab Initio Study of Polonium

Polonium is the only element with a simple cubic (sc) crystal structure. Atoms in solid polonium sit at the corners of a simple cubic unit cell and no where else. Polonium has a valence electron configuration 6s²6^p4 (Z = 84). The low temperature α-phase transforms into the rhombohedral (trigonal) β structure at ∼348 K. The sc α-Po unit cell constant is a = 3.345 Å. The beta form of polonium (β-Po) has the lattice parameters, a_R = 3.359 Å and a rhombohedral angle 98°13'. We have performed an ab initio electronic structure calculation by using the density functional theory. We have performed the calculation with and without spin-orbit (SO) coupling by using both the LDA and the GGA for the exchange-correlations. The k-points in a simple cubic BZ are determined by R (0.5, 0.5, 0.5), Γ (0, 0, 0), X (0.5, 0, 0), M (0.5, 0.5, 0) and Γ (0, 0, 0). Other directions of k-points are Γ (0, 0, 0), X (0.5, 0, 0), R (0.5, 0.5, 0.5) and Γ (0, 0, 0). The SO splittings of p states at the Γ point in the GGA+SO scheme for α-Po are 0.04 eV and 0.02 eV while for the β-Po these are 0.03 eV and 0.97 eV. We have also calculated the vibrational spectra for the unit cells in both the structures. We find that exchanging of a Po atom by Pb atom produces several more bands and destabilizes the β phase.