One-dimensional crystal model for incommensurate phase .1. Small displacement limit

A simple one-dimensional crystal model was proposed in order to study the incommensurate phase formation and its properties were numerically analyzed. In this model each particle (molecule) of the crystal has two degrees of freedom so that a longitudinal sound wave propagation is possible. In the case of small displacements and incompressible molecules the model has the Hamiltonian identical to that for a linear chain with a local fourth order anharmonic potential and the harmonic nearest- and next-nearest-neighbor interactions. Particular emphasis has been placed on the analysis of the incommensurate phases caused by the soft modes with short wavelength which has not been studied in most of the previous investigations.