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Abstract
The lecture focuses on diffraction and scattering phenomena in materials science beyond basic Bragg diffraction. Introducing the Born approximation and Kirchhoff’s theory, diffraction from ideal and non-ideal crystals is treated including, e.g., temperature and size effects, ordering phenomena, small-angle scattering and dynamical diffraction theories for both electron and X-ray diffraction.
Objective
• To become familiar with advanced diffraction phenomena in order to be able to explore the structure and properties of (solid) matter and their defects. • To be able to judge what type of diffraction method is suitable to probe what type of materials information. • To build up a generally applicable and fundamental theoretical understanding of scattering and diffraction effects. • To be able to identify limitations of the methods and the underlying theory which is commonly used to analyze diffraction data.
Content
The course provides a general introduction to advanced diffraction phenomena in materials science. The lecture series covers the following topics: derivation of a general scattering theory based on Green’s function as basis for the introduction of the first-order Born approximation; Kirchhoff’s diffraction theory with its integral theorem and the specific cases of Fresnel and Fraunhofer diffraction; diffraction from ideal crystals and diffraction from real crystals considering temperature effects expressed by the temperature Debye-Waller factor and by thermal diffuse scattering, atomic size effects expressed by the static Debye-Waller factor and diffuse scattering due to the modulation of the Laue monotonic scattering as a consequence of local order or clustering; the basics of small-angle scattering; and finally approaches used to treat dynamical diffraction are introduced. In addition, the specifics of X-ray, electron and neutron scattering are being discussed. The course is complemented by a lab visit, selected exercises and short topical presentations given by the participants.
Resources
Lecture Notes
Full-text script is available covering within about 100 pages the core topics of the lecture and all necessary derivations.
Literature
- Diffraction Physics, 3rd ed., J. M. Cowley, Elsevier, 1994. - X-Ray Diffraction, B. E. Warren, Dover, 1990. - Diffraction from Materials, 2nd ed., L. H. Schwartz, J. B. Cohen, Springer, 1987. - X-Ray Diffraction – In Crystals, Imperfect Crystals and Amorphous Bodies, A. Guinier, Dover, 1994. - Aberration-corrected imaging in transmission electron microscopy, 2nd ed., R. Erni, Imperial College Press, 2015.