Dynamic structure determination for two interacting modes at the M-point in α- and β-quartz by inelastic neutron scattering

Abstract

The eigenvectors of a temperature-independent and a strongly temperature-dependent M-point mode have been determined. Near the alpha - beta transition they exchange their eigenvectors. In both modes the SiO₄ tetrahedra stay rigid. In addition, in the temperature-dependent mode, all Si-Si distances (Si-O-Si bond angle) are unaffected, similar to the well known soft mode. In the beta phase a flat low-frequency dispersion branch in the Gamma -M direction connects the temperature-dependent mode at M with the soft mode of the Gamma point. This connection is permitted by group theory for the Gamma -M direction but not for the Gamma -K-M direction. The results are consistent with a domain model of the beta phase.