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When three grain boundaries having misorientations generating coincidence site lattices (CSLs) meet at a triple junction, a common (triple-junction) CSL is formed. A theory is developed as a set of theorems establishing the relationships between the geometrical parameters of the grain-boundary and triple-junction CSLs. Application of the theory is demonstrated in detail for the case of the cubic crystal system. It is also shown how the theory can be extended to an arbitrary crystal lattice.

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