Application of the Landau theory on the2d structural phase transition of CH4 on (0001) graphite

A few degrees before melting CH₄ absorbed on (0001) Graphite undergoes a structural phase transition from a commensurate to an incommensurate2d solid. In the commensurate phase the molecules show a hexagonal structure. Since it is known from specific heat measurements that the corresponding phase transition is of continuous type, Landau's theory of second order phase transition should be applicable. Application of this theory allows predicting that the structure of the CH₄ molecules in the incommensurate phase should show a rectangular distortion, driven by a one or two component symmetry breaking order parameter. The rectangular distortion is in agreement with other more general theoretical investigations.