Reciprocal Lattice and Integrated Intensities of Crystals

Abstract

The Bragg law enables us to explain all the diffraction phenomena of X-rays by a crystal described in the previous chapters. However, there are some diffraction phenomena that may not be explained by the Bragg law. The diffuse scattering at non-Bragg angles is a particular example. For this purpose, we need a more generalized theory of diffraction using the vector representation. Particularly, the concept “reciprocal lattice” is extremely effective for handling all the diffraction phenomena. In other words, the reciprocal-lattice theory of diffraction, being general, is applicable to all diffraction phenomena of X-rays by a crystal from the simplest one to the most complex case. It may be added that the usual set of three-dimensional atomic coordinates is called the crystal lattice or real-space lattice, as opposed to the reciprocal lattice.