The energetics of twinning in misfitting films were considered for the case of a coherent thin film with a cubic structure which transformed into a tetragonal crystal structure on an initially lattice-matched cubic substrate. The strain energy change during twinning, together with interfacial energy contributions, were incorporated into a thermodynamic analysis of twinning. The equilibrium twinned microstructure was determined as a function of film thickness, lattice misfit, elastic properties, film surface energy, film/substrate interface energy and twin boundary energy. Stability diagrams were developed which displayed the role that these parameters played in determining the equilibrium microstructure. The results showed that, for a given variant, a periodic array of domains was always energetically favored over a mono-variant film. There was therefore no critical thickness below which the mono-variant film was stable. However, the equilibrium wavelength of the twinning microstructure depended upon the normalized film thickness as well as upon the orientation of the domain boundaries with respect to the cubic substrate. Examination of the elastic energy as a function of the domain boundary orientation showed that boundaries which were oriented parallel to the (110) plane of the substrate were preferred. However, (100) oriented boundaries were less favorable from the point of view of interfacial energy. The equilibrium wavelength of the microstructure was related to the exponential of the inverse film thickness at small thicknesses. It was independent of the film thickness, or was proportional to the square root of the film thickness (at large film thicknesses), for (100)- and (110)-oriented boundaries, respectively. In the case of unlike variants, there was a critical thickness below which the mono-variant film was energetically favored. This critical thickness depended upon the relative misfit strains, the normalized twin boundary energy, the normalized film/substrate interfacial energy and the normalized surface energies.

N.Sridhar, J.M.Rickman, D.J.Srolovitz: Acta Materialia, 1996, 44[10], 4097-113