Study of theα−βQuartz Phase Transformation by Inelastic Neutron Scattering

Abstract

An inelastic neutron scattering investigation of high-temperature $\beta$ quartz by triple-axis spectrometry reveals the existence of a phonon branch with anomalously low and temperature-dependent frequencies. Near the Brillouin zone center, the mode is overdamped and unstable, and gives rise to a critical scattering intensity which diverges as ${(T-T_c)}^{-1\mathrm{}}$. Here $T_c$ is 10°C lower than the transition temperature $T_0=573\mathrm{}°$C. Measurements of the relative intensity of the critical scattering about various reciprocal-lattice points establishes that the general pattern of displacements associated with the $\alpha -\beta$ transformation is determined by this soft mode. At room temperature, the zone center phonon at 25.8 meV (208 ${\mathrm{cm}}^{-1\mathrm{}}$) is shown to strongly resemble the $\alpha -\beta$ displacements. This confirms the proposal by Scott that the renormalized soft mode interacts with and passes through another low-lying excitation. It is suggested that the anomalous elastic behavior of $\beta$ quartz results from virtual excitation of pairs of phonons in the soft branch with wave vectors directed oppositely along the hexagonal axis.