Theory of microstructure and mechanics of the ...a1/a2/a1/a2... domain pattern in epitaxial ferroelectric and ferroelastic films

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Abstract
The micromechanics of the lamellar ...a1/a2/a1/a2... domain pattern are developed for the case of epitaxial tetragonal ferroelectric or ferroelastic films grown on (001) substrates. This problem is treated in the framework of the theory of defects. Coherency defects are necessary to maintain epitaxy as a result of the symmetry‐reducing phase transition in the film (ferroelectric or ferroelastic transition). The defects include continuous distributions of edge and screw dislocations. The screw dislocation distributions are equivalent to an alternating Somigliana dislocation chain. Using this approach, fully analytic solutions are derived for the stress and strain in the film and substrate. These calculations include all the effects of the free surface. An integral expression is derived for the elastic energy. Using dipole and quadrupole approximations, analytic expressions are derived for the rotations of the crystal axes for individual domains, the elastic energy, and thickness dependence of the domain periodicity. We find, in agreement with previous work, that there is no critical thickness to form the ...a1/a2/a1/a2... domain pattern. For thick films the domain periodicity scales with the square root of the film thickness.