Elastic energy contributions to the thermodynamics of twinning of a coherent film on a substrate, and of a thin layer which was sandwiched within the bulk, were considered. By using linear elasticity theory, exact analytical results were obtained for the elastic energy release and for the stress fields which were associated with the formation of a periodic array of twinned domains or with a single embedded twin domain. Corresponding results were also obtained for twinning within the bulk, and these results facilitated the comparison of twinning in a constrained situation with that in the presence of a traction-free boundary. An asymptotic analysis of substrate stress fields far from the film/substrate interface revealed that the domains could be represented as idealized defects in the form of elastic line force dipoles. Detailed results were given for the energetics of domain formation in the case of a tetragonal film on a cubic substrate. The elastic energy release was incorporated into a thermodynamic analysis of twinning, and equilibrium microstructures were determined as a function of film thickness, interfacial energy, transformation strain and elastic constants.

N.Sridhar, J.M.Rickman, D.J.Srolovitz: Acta Materialia, 1996, 44[10], 4085-96