Chapter 2 - Crystal Structure in Reciprocal Space

Abstract

X-ray and neutron diffraction techniques provide information about the structure of solids in reciprocal space from which one can deduce the structure in real space. This chapter is devoted to the study of crystal structure in reciprocal space. It includes the Laue diffraction theory and the diffraction conditions have been derived. The concepts of the reciprocal space and reciprocal lattice have been introduced. The conventional primitive cell in the reciprocal space and the Brillouin zone have been defined and general diffraction conditions have been derived. The transformations required to go from the reciprocal to the crystal space and vice versa have been presented. These are helpful in studying the structure of solids in crystal space. The construction of the reciprocal lattice for one-, two-, and three-dimensional solids has been described in detail. The calculation of reciprocal lattice vectors, reciprocal lattices, and the Brillouin zones of sc, fcc, bcc, and hexagonal structures has been presented. The atomic scattering factor and the geometrical structure factor have been evaluated for simple structures.