Edge-to-edge matching - a new approach to the morphology and crystallography of precipitates

An entirely new approach is taken to understanding the morphology and crystallography of partially coherent precipitates formed by diffusional processes - `edge-to-edge matching'. This approach is based on the simple, well founded result put forward by Shiflet and Van der Merwe - namely that minimization of interfacial energy results when rows of atoms match across the interface. The geometric conditions necessary to achieve this atom row matching are shown to be possible for a variety of lattice parameters in the fcc/bcc system provided there is edge-to-edge matching of planes containing these rows in each of the two phases. This new model does not rely on physical assumptions of dubious validity, such as the existence of a long-range correspondence. It also differs from the existing models in that it does not need to include the particular orientation relationship as part of the input data. Instead it is capable of predicting the orientation relationship from first principles. The development of the concepts behind edge-to-edge matching are described for the fcc/bcc system, predictions of orientation relationships and habit planes are made for a variety of different precipitates and shown to be in extremely good agreement with reported experimental results.