# Reduced cell

### From Online Dictionary of Crystallography

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+ | <font color="blue">Maille réduite</font> (''Fr''). <font color="black">Cella ridotta</font> (''It''). <font color="purple">規約単位胞</font> (''Ja''). | ||

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A primitive basis a, b, c is called a ‘reduced basis’ if it is right-handed and if the components of the [[metric tensor]] satisfy the conditions below. Because of [[lattice]] [[symmetry operation|symmetry]] there can be two or more possible orientations of the reduced basis in a given lattice but, apart from orientation, the reduced basis is unique. | A primitive basis a, b, c is called a ‘reduced basis’ if it is right-handed and if the components of the [[metric tensor]] satisfy the conditions below. Because of [[lattice]] [[symmetry operation|symmetry]] there can be two or more possible orientations of the reduced basis in a given lattice but, apart from orientation, the reduced basis is unique. | ||

The type of a cell depends on the sign of | The type of a cell depends on the sign of | ||

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If ''T'' > 0, the cell is of type I, if ''T'' ≤ 0 it is of type II. | If ''T'' > 0, the cell is of type I, if ''T'' ≤ 0 it is of type II. | ||

- | The conditions for a primitive cell to be a reduced cell can all be stated analytically as follows | + | The conditions for a primitive cell to be a reduced cell can all be stated analytically as follows. |

==Type-I cell== | ==Type-I cell== |

## Revision as of 15:48, 18 December 2017

Maille réduite (*Fr*). Cella ridotta (*It*). 規約単位胞 (*Ja*).

A primitive basis a, b, c is called a ‘reduced basis’ if it is right-handed and if the components of the metric tensor satisfy the conditions below. Because of lattice symmetry there can be two or more possible orientations of the reduced basis in a given lattice but, apart from orientation, the reduced basis is unique.
The type of a cell depends on the sign of

.

If *T* > 0, the cell is of type I, if *T* ≤ 0 it is of type II.

The conditions for a primitive cell to be a reduced cell can all be stated analytically as follows.

## Contents |

## Type-I cell

### Main conditions

- ≤ ≤
- ≤
- ≤
- ≤

### Special conditions

- if then ≤
- if then ≤
- if /2 then ≤
- if /2 then ≤
- if /2 then ≤

## Type-II cell

### Main conditions

- ≤ ≤
- ≤
- ≤
- ≤
- ≤
- ≤ 0
- ≤ 0
- ≤ 0

### Special conditions

- if then ≤
- if then ≤
- if then
- if /2 then
- if /2 then
- if then ≤