Ab initio study of phonons and structural stabilities of the perovskite-type MgSi{O_3}

Using the local-density approximation, calculating the Hellmann-Feynman forces, applying the direct method and deriving the phonon dispersion relations, the stability of the perovskite-like structures of MgSiO₃ at T =0 have been studied. The cubic Pmm phase shows a dispersion-less soft phonon branch spreading from the R to M points of the cubic Brillouin zone. This soft branch persists up to high pressures of 150 GPa. The low-symmetry phases I4/mcm and Imma, P4/mbm can be considered as a result of the soft mode condensation at the M and R points, respectively. These phases prove to be unstable at T =0. The experimentally observed Pmnb phase is a consequence of the intersection of Imma and P4/mbm space groups. Thus, it can be regarded as a simultaneous condensation of two soft modes: one at the M and a second at the R high-symmetry points of the cubic Brillouin zone. The phonon dispersion relations of Pmnb show that this phase is stable and its optical phonons appear above 4.0 THz only. Received 15 October 1999 and Received in final form 14 January 2000