# Direction indices

### From Online Dictionary of Crystallography

BrianMcMahon (Talk | contribs) (Tidied translations and added German and Spanish (U. Mueller)) |
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- | <font color = "blue">Indices de direction</font> (''Fr''). <font color="red">Richtungssymbol</font> (''Ge''). <font color="black">Indici di direzione</font> (''It''). <font color="purple">方向指数</font>(''Ja''). <font color="green">Índices de dirección</font>(''Sp''). | + | <font color = "blue">Indices de direction</font> (''Fr''). <font color="red">Richtungssymbol</font> (''Ge''). <font color="black">Indici di direzione</font> (''It''). <font color="purple">方向指数</font> (''Ja''). <font color="green">Índices de dirección</font> (''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 | + | 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.