Combination rule for deviant CSL grain boundaries at triple junctions

The well-known sigma combination rule governs the connectivity of coincidence site lattice (CSL) grain boundaries at triple junctions, but is only strictly applicable for ideal CSL boundaries. Here, we extend this relationship to boundaries that deviate from ideal CSL misorientations, and derive a complementary rule that relates their angular deviations. This "deviation limit rule" states that the angular deviation of one boundary at a triple junction is at most equal to the sum of the other two deviation angles. This analysis also provides insight into apparent violations of the sigma combination rule, which can arise when one boundary deviates beyond the allowable limit for CSL classification.