From Online Dictionary of Crystallography
Revision as of 13:49, 10 November 2017 by BrianMcMahon (Tidied translations and added German and Spanish (U. Mueller))
Indices de direction (Fr). Richtungssymbol (Ge). Indici di direzione (It). 方向指数(Ja). Índices de dirección(Sp).
Any direction in a Bravais lattice is identified by a set of N indices (where N is the dimensionality of the space), written in square brackets, called the direction indices.
In the three-dimensional space, the direction passing through the origin and the lattice nodes nu,nv,nw, where n is an integer, has direction indices [uvw]. This corresponds to taking the coordinates of the first lattice node on that direction after the origin as direction indices. The indices [-u, -v, -w] identify the same direction as [uvw] simply observed from the opposite side.
When a primitive unit cell is used, the direction indices are all integer; they may instead be rational when a centred unit cell is adopted.