High-resolution inelastic X-ray scattering II: Scattering theory, harmonic phonons, and calculations

Abstract

This chapter reviews nonresonant, meV-resolution inelastic X-ray scattering (IXS), as applied to the measurement of atomic dynamics of crystalline materials. In conjunction with a companion paper on spectrometers and sample science (Part I, also in this handbook), it is designed to be an introductory, though indepth, look at the field for those who may be interested in performing IXS experiments or those desiring a practical introduction to harmonic phonons in crystals at finite momentum transfers. The treatment of most topics emphasizes practical issues, as they have occurred to the author in 15 years spent introducing meV-resolved IXS to Japan, including designing and helping to build two IXS beamlines, spectrometers, and associated instrumentation, performing experiments, and helping users. This chapter, Part II, focuses on more formal aspects of scattering theory and on calculations, emphasizing relations that have been of practical use in experiments. This includes an introduction to many issues related to scattering from harmonic phonons, including basic nomenclature, intensities, anti-crossings, sum rules, and issues related to calculations and modeling. It is designed for a reader who has a basic knowledge of reciprocal space as used in X-ray scattering and wishes to extend this to atomic dynamics.