From Online Dictionary of Crystallography
Revision as of 15:44, 29 November 2017 by BrianMcMahon (Style edits to align with printed edition)
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 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.