Planes and Crystal Morphology

Abstract

Defining planes in a crystal is necessary to describe morphology and for visualisation and description of a diffraction pattern. Planes in crystals are defined relative to the unit cell using a set of three integers called Miller indices. Since a crystal is periodic by translation, Miller indices actually describe sets of planes through the crystal with a perpendicular separation known as the d-spacing. Each set of planes can be efficiently represented by its normal vector, which has its direction perpendicular to the planes. If the length of the normal vector is defined as the reciprocal of the d-spacing, the ends of the vectors representing many sets of planes define a lattice, called the reciprocal lattice. The crystal habit can be constructed by placing each external crystal face along the line of its associated normal vector at some defined distance from the crystal's centre. The resulting habit is dominated by the faces that lie closest to the origin.