The micro-mechanics of a lamellar, ...a1/a2/a1/a2..., domain pattern were developed for the case of epitaxial tetragonal ferro-electric or ferro-elastic films grown onto (001) substrates. Coherency defects were necessary in order to maintain epitaxy, as a result of a symmetry-reducing ferro-electric or ferro-elastic transition phase transition in the film. The defects included a continuous distribution of edge and screw dislocations. The screw dislocation distributions were equivalent to an alternating Somigliana dislocation chain. By using this approach, fully analytical solutions were derived for the stresses and strains in the film and substrate. These calculations included all of the effects of the free surface. An integral expression was derived for the elastic energy. By using dipole and quadrupole approximations, analytical expressions were derived for the rotations of the crystal axes in individual domains, the elastic energy, and the thickness dependence of the domain periodicity. It was found that, in agreement with previous work, there was no critical thickness for the formation of the ...a1/a2/a1/a2... domain pattern. In the case of thick films, the domain periodicity scaled with the square root of the film thickness.

Theory of Microstructure and Mechanics of the ...a1/a2/a1/a2... Domain Pattern in Epitaxial Ferroelectric and Ferroelastic Films. A.E.Romanov, W.Pompe, J.S.Speck: Journal of Applied Physics, 1996, 79[8], 4037-49