Crystallography - Notation

Notation

• Coordinates in square brackets such as denote a direction vector (in real space).

• Coordinates in angle brackets or chevrons such as <100> denote a family of directions which are related by symmetry operations. In the cubic crystal system for example, <100> would mean, or the negative of any of those directions.

• Miller indices in parentheses such as (100) denote a plane of the crystal structure, and regular repetitions of that plane with a particular spacing. In the cubic system, the normal to the (hkl) plane is the direction, but in lower-symmetry cases, the normal to (hkl) is not parallel to .

• Indices in curly brackets or braces such as {100} denote a family of planes and their normals which are equivalent in cubic materials due to symmetry operations, much the way angle brackets denote a family of directions. In non-cubic materials,