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http://www.gaoyang168.com/html/201601/9833515.html In coincident site lattice (CSL) theory, the degree of fit (Σ) between the structures of the two grains is described by the reciprocal of the ratio of coincidence sites to the total number of sites. In this framework, it is possible to draw the lattice for the 2 grains and count the number of atoms that are shared (coincidence sites), and the total number of atoms on the boundary (total number of site). For example, when Σ=3 there will be one atom each 3 that will be shared between the two lattices. Thus a boundary with high Σ might be expected to have a higher energy than one with low Σ. Low-angle boundaries, where the distortion is entirely accommodated by dislocations, are Σ1. Some other low-Σ boundaries have special properties, especially when the boundary plane is one that contains a high density of coincident sites. Examples include coherent twin boundaries (Σ3) and high-mobility boundaries in FCC materials (Σ7). Deviations from the ideal CSL orientation may be accommodated by local atomic relaxation or the inclusion of dislocations into the boundary. |
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