Crystal Lattices

Abstract

A “crystal” is a solid object in which a basic pattern of atoms is repeated over and over in all three dimensions. In order to describe the structure of a crystal, it is thus only necessary to know the simplest repeating “motif” and the lengths and directions of the three vectors which together describe its repetition in space (Fig. 2.1). The motif can be a molecule, as in Fig. 2.1, or the building block of a network structure. Normally, it consists of several such units, which may be converted into one another by symmetry operations (as in Fig. 2.2). The three vectors a, b, c, which describe the translations of the motif in space are called the basis vectors.