# 327-2139-00L Diffraction Physics in Materials Science

Semester | Spring Semester 2022 |

Lecturers | R. Erni |

Periodicity | yearly recurring course |

Language of instruction | English |

Abstract | The lecture focuses on diffraction and scattering phenomena in materials science beyond basic Bragg diffraction. Introducing the 1st-order Born approximation and Kirchoff’s theory, diffraction from ideal and non-ideal crystals is treated including, e.g., temperature and shape effects, ordering phenomena, small-angle scattering and dynamical diffraction theories. |

Learning 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 and exemplified by performing simulations. 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. |

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. |

Prerequisites / Notice | Basics of crystallography and the concept of reciprocal space, basics of electromagnetic and particle waves (but not mandatory) |