A systematic investigation of the development of the orientation relationship in an fcc/bcc system

An analytical method, based on the Burgers vector content (BVC) model with the singular value decomposition method, has been developed for a systematic examination of three-dimensional misfit distributions, especially in an invariant line (IL) strain condition. This method is applied to a face-centered cubic/body-centered cubic system in either a coherent or semi-coherent state. The preferred orientation relationships (ORs) and interface orientations in the coherent state have been determined according to the criterion of minimum BVC. The determined OR is not unique, and ILs with different orientations are possible in this state, which is in agreement with the observations reported in the literature. Disagreement was found between the predictions from the BVC model and two of three typical ORs predicted from the O-line model for semi-coherent interfaces. The difference has been discussed in terms of the development of the ORs during the growth of the precipitates and the interfacial energy. The present analytical method is also applicable to evaluating the misfit in other systems.