Phase transitions of titanite CaTiSiO5 from density functional perturbation theory

Phonon dispersion of titanite CaTiSiO5 has been calculated using the variational density functional perturbation theory. The experimentally known out-of-center distortion of the Ti atom is confirmed. The distortion is associated with a B-u mode that is unstable for wave vectors normal to the octahedral chain direction of the C2/c aristotype structure. The layer of wave vectors with imaginary mode frequencies also comprises the Brillouin zone boundary point Y (0,1,0), which is critical for the transition to the P2(1)/c ground-state structure. The phonon branch equivalent to the imaginary branch of the titanite aristotype is found to be stable in malayaite CaSnSiO5. The unstable phonon mode in titanite leads to the formation of transoriented short and long Ti-O1 bonds. The Ti as well as the connecting O1 atom exhibit strongly anomalous Born effective charges along the octahedral chain direction [001], indicative of the strong covalency in this direction. Accordingly and in contrast to malayaite, LO-TO splitting is very large in titanite. In the C2/c phase of titanite, the Ti-O1-Ti distortion chain is disordered with respect to neighboring distortion chains, as all chain configurations are equally unstable along the phonon branch. This result is in agreement with diffuse x-ray scattering in layers normal to the chain direction that is observed at temperatures close to the P2(1)/c to C2/c transition temperature and above. The resulting dynamic chains of correlated Ti displacements are expected to order in two dimensions to yield the P2(1)/c ground-state structure of titanite.