# Direction indices

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 Revision as of 13:49, 10 November 2017 (view source) (Tidied translations and added German and Spanish (U. Mueller))← Older edit Latest revision as of 15:44, 29 November 2017 (view source)m (Style edits to align with printed edition) Line 1: Line 1: - Indices de direction (''Fr''). Richtungssymbol (''Ge''). Indici di direzione (''It''). 方向指数(''Ja''). Índices de dirección(''Sp''). + 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'''. + 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. + 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. 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.

## Latest revision as of 15:44, 29 November 2017

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.