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 t wo degrees of freedom so that a longitudinal sound wave propagation is possible. In the case of small displacements and incompressible molec ules the model has the Hamiltonian identical to that for a linear chai n with a local fourth order anharmonic potential and the harmonic near est- and next-nearest-neighbor interactions. Particular emphasis has b een 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.