Introduction to neutron scattering
Authors: Langel Walter 
Published: October 2023

Neutron scattering is a very high-performance method for studying the structure and dynamics of condensed matter with similar approaches in wide ranges of space and time, matching dimensions in space from single atoms to macromolecules and in time from atomic vibrations over crystal phonons to low-lying transitions in the microwave range, and to motions of large molecular units. Concerning the number and depth of physical concepts, neutron scattering may be compared to modern nuclear magnetic resonance. Neutrons have contributed essential results to the understanding of atomic and molecular processes and are, in this respect, complementary to other materials science probes. Among others, three properties of thermal neutrons make them especially appropriate for such work: the neutron mass is similar to atomic masses, and both neutron energies and the wavelengths of the neutron material wave match typical values for condensed matter. A further important feature of neutron scattering, making it especially valuable in biochemistry and polymer sciences, is that hydrogen and deuterium atoms very significantly and specifically contribute to the signal in both diffraction and spectroscopy. Additionally, neutrons are scattered at the nuclei and directly reflect the nuclear structure and motions. Results from neutron scattering are of great general interest. This paper aims to provide an introduction for chemists on a level understandable also to students and researchers who are not going to become part of the neutron community and will not be involved in the experiments, but shall be able to understand the basic concepts of the method and its relevance to modern chemistry. The paper focuses on basic theory, typical experiments, and some examples demonstrating the applications. As for many modern experimental techniques, the interpretation of the results of neutron scattering is based on theoretical models and requires a significant mathematical overhead. Most results are only meaningful when compared with computer simulations. For understanding this, in this paper, the theory of scattering is developed, starting with intuitive models and presenting typical concepts such as the scattering triangle, energy and momentum transfer, and the relation of inelastic and elastic scattering to space- and time-dependent information. The interaction of neutrons with matter, scattering cross sections, beam attenuation, and coherent versus incoherent scattering are explained in detail. Two further typical concepts that are not generally familiar to scientists outside the community are the use of wave and particle equivalence, and of handling results as a scattering function that depends simultaneously on momentum and energy transfers. The possibility of obtaining neutron beams for scattering experiments at a few research centers around high-performance sources is explained, and experimentally relevant features of research reactors and spallation sources are mentioned. As neutron experiments always have to deal with small flux and extended beams and shielding, experimental conditions are very far away from laboratory methods where handling of samples and instruments is concerned. Experimental details are given for making experiments more understandable and familiarizing the reader with the method. Related to this are extended possibilities for handling samples in a large variety of different environments. In a further part of the manuscript, a variety of techniques and typical instruments are presented, together with some characteristic applications bringing alive the theory developed so far. This covers powder diffraction and structure of liquid water, triple-axis spectrometers and lattice phonons, backscattering spectrometry and rotational tunneling, time-of-flight spectrometry, and simultaneously probing the energy and shape of low lying vibrations and diffusion, filter spectrometer and vibrational spectroscopy without selection rules, small-angle neutron scattering and protein unfolding, as well as micelles, neutron spin echo spectroscopy, and polymer dynamics.