The modulated low-temperature structure of malayaite, CaSnOSiO(4)

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.