Elastic domain structure and the transition between polydomain and monodomain states in thin epitaxial films

We consider an interesting and practically important case of elastic domain structure, which is the analog of the c/a domain pattern with 90° domains in ferroelectric (FE) perovskites and is solvable analytically for arbitrary misfit strain. There is no critical thickness below which the domain structure cannot exist when the ``extrinsic'' misfit is zero and the domains are of equal width. At the boundary of the polydomain-monodomain transition the pattern consists of narrow domains of a minority phase with growing separation between them, which is characteristic of a continuous topological phase transition. The dynamic stiffness of the domain structure diverges while the static stiffness vanishes at this transition. We discuss the implications of the present results for FE films and ceramics.