Abstract
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 Bg symmetry.
Highlights
Malayaite is the tin analogue of the common accessory mineral titanite, CaTiOSiO4 (Takenouchi, 1976; Higgins & Ribbe, 1977)
This instability is enhanced with the PBEsol XC functional, which predicts imaginary frequency for the transverse optical (TO) mode at the À point, due to larger LO/TO (LO = longitudinal optical) splitting compared with the PBE result
On the basis of the computational results, the crystal structure of malayaite at 20 K appears to be modulated by a soft Bg optic phonon, leading to a transverse modulation of the Ca position with a period of close to 34 Aalong [010]
Summary
Malayaite is the tin analogue of the common accessory mineral titanite, CaTiOSiO4 (Takenouchi, 1976; Higgins & Ribbe, 1977). The crystal structure of malayaite at room temperature is described in space group C2/c.1 It consists of parallel, kinked chains of corner-sharing SnO6 octahedra, laterally connected by isolated SiO4 tetrahedra. Pure titanite transforms from C2/c to P21/c at temperatures below 490 K (Taylor & Brown, 1976), forming a crystal structure with ordered out-of-centre displacements of the Ti atoms inside their distorted octahedral coordination environment (Higgins & Ribbe, 1976; Speer & Gibbs, 1976). CaO5SiSn 266.87 298 C2=c – 6.6667 (2) 8.8934 (3) 7.1520 (3) 113.323 (3) 389.39 (3) 4 X-ray, = 0.61992 A 5.52 0.16 Â 0.09 Â 0.09 tional prediction of the ordered titanite phase using density functional perturbation theory (DFPT), Malcherek & Fischer (2018) used malayaite as a reference system for the undistorted C2/c crystal structure. In the following we will describe another distortion of the malayaite structure that occurs at low temperatures and involves long-range modulation of the monoclinic malayaite structure
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