Neutron and X-ray Scattering for Quantum Materials

Welcome to this master and PhD course on neutron and X-ray scattering!

Lecturers: 

Dr. Ellen Fogh (EPFL) and Dr. Thorsten Schmitt (PSI)

Location and time:

Room: PH H3 31

Time: Mondays 13:15-17:00

Outline:

We will cover the fundamentals of neutron and X-ray scattering, including derivation of scattering cross sections.

We will then look at practical aspects of instrumentation and different types of experiments.

The first half of the course is focused on neutron scattering and the second half to X-ray scattering.

Reading material:

For the neutron part, we will use lecture notes by Kim Lefmann from the University of Copenhagen (available here on Moodle).

For the X-ray part we will use the books "Elements of Modern X-ray Physics" by Jens Als-Nielsen and Des McMorrow (available online via the EPFL library) and "An Introduction to Synchrotron Radiation - Techniques and Applications" by Philip Willmott (available online via the EPFL library).

In case of missing information or if you have suggestions regarding the Moodle page, please get in contact with Ellen (ellen.fogh@epfl.ch).

Topics covered:

Introduction to course, format and contents.

Introduction to different kind of particle and light probes in condensed matter physics.

We will discuss the properties of neutrons, their usefulness as explorers of materials, and the basics of neutron scattering. We will touch on the history of neutron scattering and take a look at some of the more practical aspects regarding generating neutrons. Finally we will go through the basic neutron scattering theory that describes the interaction between neutrons and matter.

Reading:

Lefmann notes Chapters 1-2 and 4

Other useful information:

Neutron scattering lengths and absorption cross sections: https://www.ncnr.nist.gov/resources/n-lengths/

Neutron attenuation calculator: https://www.ncnr.nist.gov/instruments/bt1/neutron.html

Topics covered:

Diffraction from crystals.

This week we will focus on the usefulness of neutron scattering to determine the structure of crystalline materials. We will discuss the reciprocal lattice, review the basics of crystalline symmetry groups, and connect crystalline symmetry to the elastic neutron scattering structure factor discussed in the previous lecture. We also discuss diffraction from magnetic structures and we will touch on some practicalities of using neutrons to measure both single crystal and powder samples.

Reading: 

Lefmann notes Chapters 9-10 (skip sections 9.1.5-9.1.8)

Others:

Please download the Quizizz app to your phones. We will use that tool to stir our memories from last week's lecture.

https://next-gen.materialsproject.org/materials

Neutron instrumentation.

We will discuss the various different components making up a neutron scattering instrument. We will simulate an experiment and study a magnetic phase transition with magnetic neutron diffraction.

Reading:

Lefmann notes Chapter  5 + 19

Others:

Please install the ray-tracing simulation program McStas before coming to class: www.McStas.org

Topics covered:

Diffraction from magnetic structures and polarised neutrons.

This week we will derive the differential neutron cross section for magnetic structures and look at some examples where neutron diffraction was used to determine magnetic structures. We will also touch on the technique of using polarised neturons for magnetic structure determination.

For the exercises you will need data from the temperature scan that we did last week in McStas.You can download my data set here: https://www.transfernow.net/dl/20241007j8DBBT1S

Reading:

Lefmann notes Chapters 3 and 10

Topics covered:

Small angle neutron scattering and reflectometry

This week we will look at how more specific neutron scattering technologies can be applied to gain different kinds of information from real materials. We will focus on small angle neutron scattering, which allows us to study systems with a larger length scale than the materials discussed previously. We will talk about the small angle approximation for the scattering cross section and discuss its applications for particles in a solution. We will also talk about reflectometry which is an excellent technique to study interfaces.

Reading:

Lefmann notes Chapters 7 and 8

Topics covered:

Introduction to content of X-ray part of course.

We will discuss the history and give a brief introduction into X-ray physics illustrating the usefulness of X-rays for exploring materials. We will show how X-rays can be generated and explain the advantages of synchrotron radiation facilities for generating highly intense and focused X-ray beams. Finally we will go through the basic interactions of X-rays with matter.

Reading:

Chapter 1 in "Elements of Modern X-ray Physics" by Jens Als-Nielsen and Des McMorrow (available online via the EPFL library) and Chapter 1-2 in "An Introduction to Synchrotron Radiation - Techniques and Applications" by PHILIP WILLMOTT

Topics covered:

Inelastic neutron scattering

This week we will introduce a change in energy between incoming and outgoing neutrons and talk about inelastic scattering from phonons and from magnetic excitations. We will also examine how they are measured using both triple-axis and time-of-flight spectrometers.

Reading:

Lefmann notes Chapters 12, 14 and 17

Topics covered:

X-ray absorption spectroscopy

In this lecture we look at the quantum mechanical description of X-ray absorption and derive the general formula for the X-ray absorption cross section. We will discuss the transition matrix element for absorption and Fermi's Golden Rule. The different regions of X-ray absorption spectra, the Extended X-ray absorption fine structure (EXAFS) and X-ray absorption near edge structure (XANES), are introduced. We will give examples of employing the polarization of the incident X-ray photons for dichroic XANES experiments. The analysis strategy of EXAFS experiments is sketched to illustrate how it can probe the short range structure.

Reading:

Chapter 7 (section 7.1 – 7.5) in Willmott and Chapter 7 (section 7.1 – 7.3 + appendix A) in Nielsen/McMorrow

Topics covered:

X-ray scattering and diffraction:

Reading:

Chapters 4 & 5 in Nielsen/McMorrow and Chapter 6 in Willmott

Topics covered:

Reading:

Chapters 3 and 5 in Willmott and Chapters 2 and 3 in Nielsen/McMorrow

Topics covered:

Introduction to Resonant Inelastic X-Ray Scattering

Reading:

Read section 7.6 (7.6.1-7.6.3, page 727-731) in Willmott.

Prepare before the lecture:

Read section 7.6 (7.6.1-7.6.3, page 727-731) in Willmott.

Read the following two papers attached below (concentrate on one if going through the papers is too heavy at first):

Schlappa, J., Wohlfeld, K., Zhou, K. J., Mourigal, M., Haverkort, M. W., Strocov, V. N., … Schmitt, T. (2012). Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr₂CuO₃. Nature, 485(7396), 82-85. https://doi.org/10.1038/nature10974

Bisogni, V., Catalano, S., Green, R. J., Gibert, M., Scherwitzl, R., Huang, Y., … Schmitt, T. (2016). Ground-state oxygen holes and the metal-insulator transition in the negative charge-transfer rare-earth nickelates. Nature Communications, 7, 13017 (8 pp.). https://doi.org/10.1038/ncomms13017