Crystallography

Crystallography (from the Greek words crystallon = cold drop / frozen drop, with its meaning extending to all solids with some degree of transparency, and graphein = write) is the experimental science of determining the arrangement of atoms in solids. In older usage, it is the scientific study of crystals.

Notation

See Miller index for a full treatment of this topic.

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• Coordinates in square brackets such as denote a direction (in real space).
• Coordinates in angle brackets or chevrons such as <100> denote a family of directions which are equivalent due to symmetry operations. If it refers to a cubic system, this example could mean , , or the negative of any of those directions.
• Coordinates in parentheses such as (100) denote the direction of plane normals.
• Coordinates in curly brackets or braces such as {100} denote a family of plane normals which are equivalent due to symmetry operations, much the way angle brackets denote a family of directions.