Ab initio lattice dynamics of Pb/sub 2/MgTeO/sub 6/ double perovskite

Pb/sub 2/MgTeO/sub 6/ is one of the few perovskites presenting an incommensurate phase at low temperature. We report calculations of the lattice dynamical properties (phonon band structure) for the cubic, (high-T) and the average rhombohedral, (low-T) structures of Pb/sub 2/MgTeO/sub 6/. The cubic phase presents two unstable phonons at Gamma . The first has a T/sub 1u/ character and is restricted to a small neighborhood near Gamma . The second has a T/sub 1g/ character in Gamma . Its lowest branch generates, in the reciprocal space, tube-like unstable regions along Gamma X. Its displacement pattern, in the real space, corresponds essentially to rotations of the TeO/sub 6/ octahedra. The rhombohedral average structure presents no instability in Gamma . However, an instability is obtained by interpolation along the 100 direction, around the q=< delta 00> point, with delta close to 0.1, in disagreement with a published interpretation of experimental data, claiming q=< delta delta delta >. Reexamination of the published electron diffraction spectra shows that the correct value of the modulation wavevector is q=< delta 00>.