Analysis of a two-dimensional invariant line interface for the case of a general transformation strain and application to thin-film interfaces

An explicit solution is obtained for a general two-dimensional deformation matrix between two phases containing any combination of expansion/contracti on and/or shear. Application of the solution to various cases of deformatio n shows that in the presence of a shear, an invariant line can be obtained even when the deformations along orthogonal directions are both contraction s or expansions. Utilization of the solution in the design of thin-film ove rgrowths on substrates and the relationship between the solution eigenvecto rs in real and reciprocal space are discussed. (C) 2000 Acta Metallurgica l ire. Published by Elsevier Science Ltd. All rights reserved.