Reduced cell

From Online Dictionary of Crystallography

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:

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 ≤