Single-Course Engelsk 5 ECTS

The structure and dynamics of materials studied with X-rays and neutrons

Overall Course Objectives

Experimental determination of the atomic scale structure and dynamics of materials is a crucial prerequisite for understanding their physical properties, and therefore also for the design and development of novel materials for quantum technology and the green energy transition.

Analysis of neutron and x-ray scattering data obtained at facilities such as the European Spallation Source (ESS) and MAX-IV in Lund, Sweden or the European X-ray Free Electron Laser (EuXFEL) in Hamburg, Germany, permit the extraction of the key structural parameters characterizing molecules, amorphous materials and crystals, including their magnetic structure. Similarly, experiments probing the elementary excitations of the relevant structural, electronic and magnetic degrees of freedom (such as molecular vibrations, phonons and magnons), either directly in the ultrafast time domain or via their spectroscopic signatures, allow the strengths of chemical bonds and magnetic interactions to be determined.

The goal of the course is to provide students with a theory-based introduction to key x-ray and neutron scattering techniques and hands-on experience in analysing data using state-of-the-art tools. The first three sessions of the course will cover the essential general theory underlying x-ray and neutron scattering techniques, emphasizing their complementarity. The following 10 sessions will focus on selected techniques: Small angle scattering, Powder diffraction, Single crystal diffraction, Time-domain scattering using x-rays and Neutron spectroscopy. For each of these five techniques, students will be introduced to essential technique-specific theory and instrumental considerations. They will then be tasked with analysing experimental data sets of increasing complexity using a range of analysis tools from standard programs to cutting edge research software. The results of the data analysis will be collected in group reports.

See course description in Danish

Explain methods for production of X-ray and neutron beams.
Discuss the complementary ways in which neutrons and x-ray photons interact with nuclei and electrons.
Explain the principles behind experimental techniques for studies of structure and dynamics, notably small angle scattering, powder diffraction, single-crystal diffraction, time-domain x-ray scattering and neutron spectroscopy.
Sketch how key optical components (guides, choppers, monochromators, mirrors, lenses, detectors, absorbers and beam-diagnostic tools) are applied in neutron and x-ray instruments.
Calculate scattering and absorption cross-sections quantitatively.
Analyse typical small angle scattering data in order to obtain particle shapes and distributions.
Analyse typical powder diffraction data using Rietveld refinement in order to determine crystal structures.
Analyse typical single-crystal diffraction data in order to determine crystal and magnetic structures.
Analyse typical time-domain x-ray scattering data in order to determine how ultrafast changes in atomic positions couple to the electronic excited state cascade following absorption of optical light in molecular systems relevant for photocatalysis or solar cells.
Analyse typical neutron spectroscopy data in order to determine the strengths of chemical bonds or spin-spin exchange interactions from phonon and magnon dispersion curves.

Scattering cross-sections, absorption, fluorescence, scattering amplitudes for single atoms, form factors, structure factors, optical components in neutron and x-ray scattering instruments, small angle scattering, powder diffraction, single-crystal diffraction, time-resolved x-ray scattering, inelastic neutron scattering, data analysis.

10036/10041/10080/10081/10102/10104/10303/10317, or equivalent courses in electromagnetism, quantum mechanics and solid state physics. Prior experience with diffraction or spectroscopy techniques is a not a prerequisite for taking this course.

Lectures, problem sessions and data analysis sessions.