Secondary dislocation structures in a Ni-TiN system from the GMS and O-lattice theory

The preferred state in an interface is the key to evaluating misfit strain, especially for the interphase interfaces in secondary preferred state. The structure of good matching site (GMS) in a GMS clusters offers a guidance for the preferred state, especially for identifying the coincidence site lattice in two dimension for secondary preferred state and the Burgers vectors in a large misfit system. Here, we combine the GMS with O-lattice theory to calculate the secondary dislocation structure in the habit planes of the type II and III TiN precipitates in a Ni-TiN system. We find that under a slight elastic strain, the type III habit plane contains a single set of secondary dislocations, consistent with the experimental observation. The type II habit plane contains three sets of secondary dislocations, two of which can be relaxed to be nearly parallel and another of which may be invisible in diffraction contrast due to its short Burgers vector. The present study provides a reasonable interpretation to the observed interfacial dislocations, and also suggests Burgers vectors for the dislocations that are not determined experimentally.