PHASE-DIAGRAM OF THE FRENKEL-KONTOROVA-DEVONSHIRE MODEL

We study a generalization of the Frenkel-Kontorova (FK) model where the usual harmonic spring potential between neighboring atoms is replaced by a phenomenological potential identical in form to a sixth-degree Landau free-energy functional proposed by Devonshire. The resulting model is a natural extension of current FK-type models with nonconvex interactions. It also provides a first step toward the construction of a theory of the structure of an epitaxial film that undergoes a first-order phase transition from a high-symmetry phase to a degenerate low-symmetry phase. The phase diagram is obtained as a function of temperature and misfit (for representative choices of the remaining parameters) by use of the effective potential method of Griffiths and Chou. Among other unusual features, we find commensurate phases and soliton structures in which all competing phases are present simultaneously.