Molecular-dynamics simulation of a model with incommensurate phases

Abstract

Two-dimensional models of displacive and order-disorder behavior, in the form of crystallites with free boundary conditions and with one-dimensional incommensurate and/or commensurate phases, have been studied using the molecular-dynamics method. The incommensurate phase can be characterized with any wave vector by the appropriate choice of potential-energy parameters. The ground-state devil’s staircases of the models are complete. By a series of cooling runs the phase diagram is established. The map of the particle configuration, a result of the cooling run, formed a nonideal incommensurate phase. In the diffraction pattern of that configuration the intensities of the satellites, especially those of higher order, are considerably lower. The displacive system shows a soft, underdamped phonon mode, which with lowering temperature condenses at the critical wave vector, producing the incommensurate phase, in which the phase and amplitude modes are observed. The phase-mode dispersion curve does not show a gap. Adding 2% point defects to the system does not influence the phase and amplitude modes. The kinetics of the variation of the wave-vector modulation of the incommensurate phase has also been studied. The relevant non- equilibrium devil’s staircase exhibits quasisteps at irrational numbers which are attributed to the nucleation and growth of new incommensurate periods observed as a stripple. Examples of nucleation inside and at the edges of the crystallite are given. Point defects hinder the propagation of the deperiodization line which borders the stripple.