High-resolution inelastic x-ray scattering part 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 chapter 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 the last two decades spent introducing meV-resolved IXS in Japan, including designing and building two IXS beamlines, spectrometers, and associated instrumentation, performing experiments, and helping other scientists. This chapter, Part II, focuses on scattering theory and on calculations, emphasizing relations and ideas 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.