O-lattice analyses of interfacial misfit. I. General considerations

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Abstract
Misfits between lattice points of intersecting crystals and between corresponding lattice planes are analysed using O-lattice constructions referred to both direct and reciprocal spaces. O-lattice planes are described by the same expression as the ‘Moiré planes’ formed by the mismatch of correlated planes, which facilitates the study of the O lattice from diffraction patterns. The normalized primary O-lattice planes (those related to the closest packed atomic planes) with the smallest interplanar spacing are considered to be planes of minimum mismatch, and hence to represent plausible low-energy interfaces. An interface of arbitrary orientation is assumed to be stepped microscopically along the primary O-lattice planes. The solution for the O-lattice cells is derived. Based on this cell structure, possible configurations of the misfit dislocations in a primary O-lattice plane are obtained; this provides a basic description of interfacial structure.