The rise and fall of Weber Indices

Abstract

Weber indices were introduced to provide a unique expression of a lattice direction with respect to the four-axis setting used for hexagonal and rhombohedral crystals. They are in general fractional indices, even in the case of a primitive hexagonal unit cell, but they are often carelessly reduced to integer values. This corresponds, on the one hand, to taking as direction indices the nodes of a lattice further from the origin and, on the other hand, to adopting a hybrid indexing between direct and reciprocal space. A critical analysis of the drawbacks of Weber indices is presented, which justifies the reluctance of crystallographers to adopt them, despite a more widespread use in fields like electron microscopy and metal science.