1.1 Introduction

X-ray and neutron scattering are an important class of experimental tools for materials characterization. The scattering of X-ray and neutron beams by crystalline materials can be divided into two categories: elastic and inelastic. Elastic scattering, or diffraction, is referred to as a scattering process in which the incident X-ray or neutrons change direction without losing energy when they interact with the material. During inelastic scattering, the incident X-ray or neutrons change both direction and energy. The loss (or gain) of energy by the X-ray or neutron beams excites (or annihilates) fundamental excitations that describe the collective motion of atoms within the material. As will be seen below, diffraction by X-ray or neutrons allows us to determine the structure (i.e., how atoms are arranged), whereas inelastic scattering allows us to investigate the dynamic behavior (i.e., how atoms move) of materials.

It is perhaps an understatement that much of our understanding and use of advanced materials were made possible by advances in X-ray and neutron scattering techniques. For example, an important aspect of modern materials design is based on the establishment of a relationship between structure and physical properties. The structure referred to here includes the crystal, magnetic, and microstructure of the material. X-ray and neutron diffraction are ideal, in some cases the only, tools for the determination of these structures. In addition, study of lattice dynamics with inelastic neutron scattering elucidates in detail how a structural transition takes place (Stassis, 1986). In recognition...