The modulated low-temperature structure of malayaite, CaSnOSiO₄

The crystal structure of the mineral malayaite has been studied by single-crystal X-ray diffraction at a temperature of 20 K and by calculation of its phonon dispersion using density functional perturbation theory. The X-ray diffraction data show first-order satellite diffraction maxima at positions q = 0.2606 (8)b*, that are absent at room temperature. The computed phonon dispersion indicates unstable modes associated with dynamic displacements of the Ca atoms. The largest-frequency modulus of these phonon instabilities is located close to a wavevector of q = 0.3b*. These results indicate that the malayaite crystal structure is incommensurately modulated by static displacement of the Ca atoms at low temperatures, caused by the softening of an optic phonon with B_g symmetry.