Molecular dynamics study and normal mode analysis of diffuse scattering in quartz

Abstract

X-ray scattering intensities in quartz were investigated in molecular dynamics (MD) simulation at different temperatures with the aid of normal mode analyses. The MD-simulated structure produced diffuse streaks most remarkably along a hexagon joining symmetry-equivalent points of index 400 in the hk0 plane, extending in ± c*. In addition, most Bragg spots were found to be associated by radial diffuse scattering in the six a* directions. The normal mode analysis and calculations of first-order scattering intensities showed that the lowest-lying branch in Γ-M is of transversal acoustic characters, and is responsible for the diffuse scattering radiating from Bragg reflections in the a*-directions. The transversal acoustic characters of atomic displacements in these modes provide the scattering in phase at points on the fourth hexagon. Phonon dispersion relations of the MD crystal were examined in view of symmetry-adapted atomic displacement patterns, and a possibility was suggested for two curves in Γ-M, optic soft branch and transversal acoustic branch polarized in the z axis (the second-lowest branch), to exchange the eigenvectors in the middle range of q (0.2–0.3).