Lattice-Dynamical Theory of Structural Phase Transition in Quartz

A lattice dynamical theory is developed for the phase transition in quartz, and the behaviours of various quantities in the vicinity of the transition temperature are discussed. At temperatures well away from the transition, these behaviours can be interpreted within the framework of the Landau theory. However, drastic deviations from the theory appear in the vicinity of the transition. Therefore an attempt was made to improve the approximation. The present consideration made it possible to interpret qualitatively the behaviours near the transition. It was shown that the order parameter is proportional to the frequency of the soft mode regardless their temperature dependence and the discontinuous change of the elastic constants are attributed to this proportionality. The discontinuous change of the frequency of \(₁\) mode was predicted by the theory.