ABSTRACT
The reciprocal lattice constitutes a special coordinate system, designed originally to simplify the study of diffraction phenomena. A plane in reciprocal space represents all real space planes that share a common direction. The components of any vector referred to the reciprocal basis represent the Miller indices of a plane whose normal is along that vector, with the spacing of the plane given by the inverse of the magnitude of that vector. This chapter discusses X-rays which typically penetrate a few micrometers of the surface of a sample, whereas neutrons can penetrate several centimeters. Neutrons can therefore be used to determine the state of residual stress that exists in a macroscopic sample that is otherwise at equilibrium. In neutron diffraction, the scattering factors can be quite different for atoms with similar atomic numbers so superlattice reflections can be detected more readily.
