Space Groups

Abstract

This chapter describes how the symmetry operations in a crystal combine to form a space group and how the space group provides a general framework to describe a crystal structure. The simplest space group comprises just the three translational symmetry operations of the crystal. Other space groups also include non-translational symmetry operations such as rotations, mirrors, inversions, screws and glides. The requirement for all of the symmetry operations to be consistent with each other, and in particular with the translational periodicity of the crystal, means that the number of possible space group types is limited to exactly 230. The relationships between the symmetry operations and the atomic coordinates are expressed by the general equivalent positions, which provide the information to generate the complete contents of the unit cell from a minimal set of coordinates called the asymmetric unit. Various ways are discussed in which crystals are classified by their symmetry, with an especially important distinction made between centrosymmetric, non-centrosymmetric and chiral space groups.