Symmetry and reflection conditions in reciprocal space

Abstract

This chapter focuses on symmetry in reciprocal space. It reviews the definitions of reciprocal space and dual (reciprocal) basis vectors (from Chapter 6), and presents the new concept of the reciprocal lattice. It introduces in a very general way the concept of Fourier transform of lattice functions, and explains how these can be naturally assigned to the ‘nodes’ of the reciprocal lattice, thereby producing a pattern that has no translational invariance but has nevertheless either the point-group symmetry of the crystal class or a higher symmetry (the Laue class). The chapter also describes in some detail the concept of extinction (or reflection) conditions, and explains how these conditions relate to the translational and roto-translational symmetry in the real space. The Patterson function, an important concept related to crystal structure solution, is also presented.