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We study how the ferroelastic domain structure sets in in an epitaxial filmof a material with second order proper ferroelastic transition. The domainstructures considered are similar to either $a_{1}/a_{2}/a_{1}/a_{2}$ or$c/a/c/a$ structures in perovskite ferroelectrics. If the "extrinsic" misfitstrain, not associated with the transition, does not break the symmetry of thehigh-temperature phase, the phase transition in the film occurs at somewhatlower temperature compared to the bulk. The loss of stability then occurs withrespect to a sinusoidal strain wave, which evolves into the domain structurewith practically the same geometry and approximately the same period. In thepresence of the symmetry-breaking component of the misfit strain ("extrinsic"misfit) the character of the phase transition is qualitatively different. Inthis case it is a {\em topological} transition between single-domain andmulti-domain states, which starts from a low density of the domain walls.Comment: 7 pages, 2 figures, REVTeX 3.

Proper ferroelastic phase transitions in thin epitaxial films with symmetry-conserving and symmetry-breaking misfit strains