Lattice distortions and phase transitions in crystalline methanes

Abstract

An order parameter for orientational phase transitions in solid methane is obtained on the basis of molecular symmetry arguments. A Landau theory of the I-II transition at constant volume is proposed. Then coupling of the order parameter and the lattice strain tensor is introduced. In the case of light methane ${\mathrm{CH}}_{4}$, coupling to the lattice makes the I-II phase transition first order. It is suggested that these lattice effects are at least as important as crystalline field effects in the methane transition. Finally, applications to other plastic crystal phase transitions of molecules of symmetry ${T}_{d}$, ${C}_{3h}$, and ${D}_{3h}$ are mentioned.