Ab initio study of phonons and structural stabilities of the perovskite-type <img src="/fulltext-image.asp?format=htmlnonpaginated&src=BRQ4U2QKKW825RHG_html\10051_2000_Article_49_TeX2GIF_Equ1.gif" border="0" alt="$$MgSi{O_3}$$ " />

Abstract:: 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 Pm$$Pm\overline 3 m$$m 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.