A Somigliana dislocation dipole model was developed in order to determine the critical thickness for misfit twin formation in an epilayer having differing elastic constants to those of its substrate. The critical dipole arm length was determined by minimizing the twin formation energy for a given epilayer thickness and lattice mismatch strain, while a zero value of the minimum formation energy determined the critical thickness for misfit twinning. The results obtained by the Somigliana dislocation dipole model were roughly consistent with those found by using the dislocation-based twinning model.

Critical Thickness for Misfit Twinning in an Epilayer. L.Liu, Y.Zhang, T.Y.Zhang: International Journal of Solids and Structures, 2008, 45[11-12], 3173-91