Twinning in thin films .1. Elastic analysis

We examine the elastic energy contributions to the thermodynamics of twinning of a coherent film on a substrate and a thin layer, sandwiched within the bulk. Using linear elasticity, we obtain exact analytical results for the elastic energy release and stress fields associated with the formation of a periodic array of twinned domains, as well as for a single embedded twin domain. The corresponding results are also obtained for twinning within the bulk and these results facilitate comparisons between twinning in a constrained environment as opposed to twinning in an environment with a traction free boundary. An asymptotic analysis of the substrate stress fields far from the him-substrate interface reveals that the domains can be represented as idealized defects in terms of elastic line force dipoles. While the analysis is applicable to general misfit strain tensors, we present detailed results for the energetics of domain formation for a tetragonal film on a cubic substrate; a case commonly encountered in ferroelectric films. The elastic energy release, derived in this paper, is incorporated into a thermodynamic analysis of twinning and the equilibrium microstructures are determined as a function of the film thickness, interfacial energy, transformation strains and the elastic constants in the following paper. Copyright (C) 1996 Acta Metallurgica Inc.