A mesophase transition in a binary monolayer on a solid surface

Abstract On a solid surface, an epitaxial monolayer may separate into phases that self-assemble into patterns on the nanoscale. The self-assembly minimizes the combined free energy of mixing, phase boundary, and elasticity. Our recent numerical simulation has revealed an intriguing mesophase transition. The surface stress is a second-rank tensor and can be anisotropic. Depending on the degree of the anisotropy, the lowest energy stripes can be either parallel to, or at an angle from, a principal axis of the surface stress tensor. This paper further elucidates this transition. We show that the off-axis stripes compromise the elastic energy of the inplane and antiplane deformation. The transition between the along-axis and the off-axis stripes obeys the Landau theory of phase transition of the second kind. The off-axis stripes have two variants by symmetry. A set of the stripes of the same variant forms a colony. The two kinds of colonies organize into a mesoscale herringbone structure. Energy minimization sets an equilibrium size of the individual colony.