Microscopic model for incommensurate crystal phases

Abstract

As a model for a crystal with an incommensurate phase we studied a linear chain of classical particles interacting by harmonic forces between up to third neighbors and anharmonic nearest-neighbor forces. Such a system has an infinite number of stable equilibrium configurations, among which there are incommensurate ones. The system has translational invariance and consequently acoustic phonons. Other excitations may be identified as phasons and amplitudons. In a mean-field approximation the model exhibits a soft mode, a transition to an (in general) incommensurate phase, which develops via discommensurations to a superstructure at a lock-in transition.