Phase transitions of titanite CaTiSiO5 from density functional perturbation theory

Phonon dispersion of titanite ${\mathrm{CaTiSiO}}_{5}$ 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 $P{2}_{1}/c$ ground-state structure. The phonon branch equivalent to the imaginary branch of the titanite aristotype is found to be stable in malayaite ${\mathrm{CaSnSiO}}_{5}$. 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 $P{2}_{1}/c$ 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 $P{2}_{1}/c$ ground-state structure of titanite.