Exact solutions were obtained for the interaction energy between infinitely long parallel twins. The latter were of alternating orientation, and terminated at some distance below the free surface in an elastically isotropic half-space. The solution method involved the summation of pair-wise interaction energies between the partial dislocations which made up the twins. The results were compared with those obtained when the elastic interaction between parallel twins was approximated by the interaction between parallel dislocations. It was shown that, for twins lying on {111} planes in a half-space - with a surface normal of (001) - there was excellent agreement between the 2 solutions; except for unrealistically low values of the twin spacing. It was also shown that, for this geometry, the use of an approximate solution for the elastic interaction between alternating twins, gave essentially the same results as the exact solution. Additional calculations were used to compare the energetics of an array of alternating twins, which relieved misfit strain in a thin SiGe film on a Ge(001) substrate, with those of an array of 60º perfect dislocations which performed the same task. The role which was played by the twin boundary energy, in the evolution of the twin morphology with increasing film thickness, was illustrated by examining relaxation via twinning in thin Ag(001) and Pt(001) epitaxial films which were in a state of biaxial tension. A solution was also given for the energetics of the relaxation of misfit strain, in a linear isotropic elastic half-space, by means of twin-like defects. The defect thickness was here allowed to vary continuously, thus allowing for the determination of effective average twin thicknesses and spacings which themselves varied continuously during relaxation.

The Energetics of the Relaxation of Misfit Strain in Thin Epitaxial Films by Means of Twinning M.Dynna, A.Marty: Acta Materialia, 1998, 46[4], 1087-101