Study on one-dimensional CI phase transition with triple-well interactions

Abstract

To study modulated structures and commensurate–incommensurate (CI) transitions, we generalize the Frenkel–Kontorova model to the Frenkel–Kontorova–Devonshire model where the interparticle interactions are the triple-well potential. By use of the so called effective potential method, numerical solutions of the eigenvalue problem are used to work out the exact phase diagrams of W, a triple-well potential. According to the winding number ω and the rotation number Ω, we analyze the periodicity of the phase diagram and find some complex but regular phase structures. These new structures result from the triple-well interatomic interactions. A series of new transition behaviors enrich the traditional understanding on the periodicity of CI transitions.