Bollmann's 0-Iattice theory; a geometrical approach to interface structure

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Abstract
The 0-lattice theory is a geometrical approach to interface structure. The basis of the theory is that interfaces are ordered. The 0-lattice theory is completely general and embodies many of the concepts of the theories of twinning, martensitic crystallography, and the coincidence site lattice, each of which may be regarded as a special case. The coincidence site lattice concept is generalized to include coincidences of any equivalent points, lines, or planes. Such coincidences are called 0-points, -lines, and -planes, respectively, and are regions of exact matching, or ‘minimum-strain points', between two interpenetrating crystal lattices. A further aspect of 0-points is that they are origins with respect to which the two crystal lattices are related by a particular transformation. The misfit between 0-elements is accommodated on dislocations which conserve low-energy structures. Since the theory is purely geometrical it is necessary to investigate in parallel the criteria for low-energy structures by observation or additional calculation. The 0-lattice method permits the dislocation content of an arbitrary interface to be specified and suggests a starting point for atomic relaxation. The theory has been used to predict periodic structures in previously unknown systems and to analyse observed structures. A powerful application of the theory is in the analysis of high-angle grain-boundary structure and the derivation of Burgers vectors for perfect grain-boundary dislocations, using the DSC lattice.