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The basic principles and experimental configurations of neutron diffraction experiments are given in this chapter. First, the physics of neutrons and neutron diffraction, such as neutron-scattering lengths and neutron absorption, are reviewed briefly, with special emphases on the comparison of neutron and X-ray diffraction phenomena and on specific features of the interactions between neutrons and bio-macromolecules. The basic principles of neutron protein crystallography (NPC) and the method of obtaining the positions of hydrogen atoms in proteins are also discussed. Two types of neutron sources—steady-state, reactor neutron sources and pulsed, accelerator-driven neutron sources—are then introduced, along with the different techniques used with each source. Because neutron detection is a key technique in NPC, a section is devoted to describing different types of neutron detectors. Based on the preceding knowledge, reactor sources and pulsed sources, as used for NPC, can finally be compared at the end of the chapter.

This chapter introduces the basic idea of quasielastic neutron scattering as a probe for diffusion processes in condensed matter. Neutron scattering and solid state diffusion have in common that they both can be separated into two problems: the single event (scattering on a single nucleus or single diffusive jump, respectively) and the cooperative combination (in space and time) of those events in solids. The history of neutron scattering is outlined with the development of neutron sources and neutron scattering instruments. All large scale neutron scattering facilities, based on research reactors or on neutron spallation sources, are nowadays operated as user facilities with the consequence that neutron scattering is not ‘big science’ like high energy particle physics, but the practise of neutron scattering is characterized by a large variety of small groups working on many different scientific problems. A brief summary of the remainder of the book covers the fundamentals of quasielastic neutron scattering and its application to different material systems.

This chapter discusses ways to describe theoretically neutron scattering as a probe for condensed matter, first the scattering on a rigidly bound and isolated nucleus by the neutron-nucleus interaction as well as coherent and incoherent neutron scattering. Then the corresponding matrix element, in terms of perturbation theory of quantum mechanics, is derived which yields the double differential scattering cross-section of the sample as a function of momentum and energy transfer of the scattered neutrons. With the concept of the van Hove correlation functions, this matrix formulation is finally transformed into classical correlation functions, which are convenient if the particle motion can be described by classical dynamical models. In this way, the coherent scattering function S(Q, ω) is the double Fourier transform of the correlation function G(r,t), whereas the incoherent scattering function Si(Q, ω) is the double Fourier transform of the self-correlation function Gs(r,t). The convolution approximation relates S(Q, ω) to Si(Q, ω). The scattering intensity decreases with increasing Q due to the Debye–Waller factor which is directly connected to lattice vibrations.

In this chapter the theory of the static structure factor, which is closely related to the underlying fluid structure, is described. Different methods of calculating this quantity are presented, including perturbational approaches,, integral equations (including those based on the interaction site model), and computer simulations. Wherever possible the results of these calculations are compared with experimental data obtained from X-ray, neutron, and electron scattering. The range of fluids considered is broad, including simple inorganic species, polar and nonpolar organic liquids, water, and aqueous solutions. The effect of both temperature and pressure on the fluid structure is analysed and used to distinguish between competing molecular models. Quantum effects are considered where these are significant. The utility of Reverse Monte Carlo calculations and their particular limitations for molecular fluids are also discussed.

This chapter discusses structural crystallography and phase transitions. If all atoms in a crystal were exactly at their official lattice sites and there were no order-disorder ambiguity as to the position of these sites, then all the measurable physical quantities associated with the crystal would be exactly periodic functions reflecting the symmetry of the unit cell. The use of X-ray diffraction (XRD) in determining a crystal's static structure is explored, along with the general theory of XRD, structural classification for ferroelectrics, elastic neutron scattering and the problems of structure refinement, diffuse X-ray scattering and static displacement correlations, inelastic neutron scattering and dynamic crystallography, KTa_1-xNb_xO₃ and dynamics in perovskite soft modes, and dynamics in hydrogen bonds of KD₂PO₄.

In this chapter, aspects of the planning and optimization of a neutron scattering experiment are covered, including attenuation, multiple scattering, data normalization, counting statistics, resolution, corrections for polarization analysis, and spurions. Practical aspects of diffraction experiments are described, including instrumentation, Rietveld refinement, anisotropic displacement parameters, the Ewald sphere construction, Lorentz factors, extinction and multiple scattering. Practical aspects of spectroscopy are also described, including triple-axis, time-of-flight and backscattering spectrometers, direct and indirect geometry, and some specific points arising in time-of flight inelastic scattering.

Matters within the realm of spectroscopy—the interaction of molecules with radiation—are considered. The treatment focuses on three areas: the absorption and emission of infrared light, the scattering of light, and the scattering of neutrons. The theory is developed around a consideration of the time correlation functions representing the evolution of molecular dipole moments, polarizabilities, and positions and orientations; the corresponding spectra are the spatial and temporal Fourier transforms of these quantities. Particular attention is paid to the estimation of correlation functions from their short-time behaviour which may be calculated using spectral moments: these can be computed using equilibrium statistical mechanics. It is shown that such studies of allowed and induced spectra can yield valuable information concerning molecular interactions in both gases and liquids.

This chapter contains an overview of the different types of structural dynamics found in condensed matter, and the associated neutron scattering cross-sections. The scattering dynamics of the harmonic oscillator is discussed, and an expression for the Debye-Waller factor is obtained. In the case of crystalline solids, the vibrational spectrum in the harmonic approximation is described, including the phonon dispersion and the cross-sections for one-phonon coherent and incoherent scattering. Multi-phonon scattering is discussed briefly. For non-crystalline matter, the time-dependent van Hove correlation and response functions are introduced, and their relation to the scattering cross-section established. An approximate expression for the correlation function is obtained from the classical form. Partial correlation and response functions are defined for multicomponent systems. The technique of neutron Compton scattering as a probe of single-particle recoil dynamics is described. Quasielastic and neutron spin-echo spectroscopy are introduced, as well as examples of relaxational dynamics which these techniques can measure.

This chapter begins by describing and interpreting experiments with both negative and positive ions. It continues with the results of neutron scattering and concludes with a note on scattering by X-ray photons.

This chapter discusses the interaction of light with non-conducting crystals. Topics covered include infrared absorption, X-ray diffraction, effect of atomic vibrations, scattering of light, and scattering of neutrons.

Electron scattering, significantly stronger than that for X-rays, is sensitive to surfaces and small volumes of materials. Low-energy electron diffraction (LEED) provides information on surface reconstruction and the arrangement of adsorbed atoms. Reflection high energy electron diffraction (RHEED) probes surface crystallography, and monitors, in situ, mechanisms of thin film growth. Transmission electron diffraction reveals a planar cross-section of the reciprocal lattice, where intensities are products of the structure and lattice amplitude factors determined by the overall shape of the specimen. The amplitude of any diffracted beam at the exit surface oscillates with thickness (fringes) and the excitation error (bend contours). Selected area diffraction produce spot or ring patterns, where low-index zone-axis orientations reflect the symmetry of the crystal, and double-diffraction shows positive intensities even for reflections forbidden by extinction rules. Kikuchi lines appear as pairs of dark and bright lines, and help in tilting the specimen. A focused probe produces convergent beam electron diffraction (CBED), useful for symmetry analysis at nanoscale resolution. Neutrons interact with the nucleus and the magnetic moment of the atom via the spin of the neutron; the latter finds particular use in studies of magnetic order. The atomic scattering factor for neutrons shows negligible angular dependence.

This chapter discusses the basic concepts of X-ray and neutron scattering. For purposes of simplicity, the discussion will initially be limited to the case where there is no exchange of energy in the process. The scattering of an X-ray photon, or a neutron, by a sample is characterised by the resultant change in its momentum, P, and energy, E. The momentum and energy gained by the scattered particle is equal to that lost by the sample, of course, and vice versa. The definitions of P and E as ‘incident minus final’, rather than the other way around, is a matter of convention. An ideal scattering experiment consists of a measurement of the proportion of incident particles that emerge with a given energy and momentum transfer. This is encoded in a four-dimensional function S(P,E), traditionally called the ‘scattering law’, where the vector P has three components.

This chapter is devoted to the observation of microscopic magnetism, working out in some detail the most commonly used magnetic techniques. The basic aspects of these techniques are only briefly recalled, and indication is given of relevant text books which will give a sound background knowledge. However, it is the goal of the chapter to allow the reader to be able to read the current literature with some acceptable understanding. The magnetic techniques include microSQUID and micro Hall probe techniques and torque magnetometry; specific heat measurements, including equilibrium and out of equilibrium measurements; and magnetic resonance techniques, including EPR, NMR, and muon spin resonance. Mention of neutron techniques, including polarized neutron diffraction and inelastic neutron scattering, will conclude the section.

This chapter focuses on those effects that depend on small displacements of atoms from their equilibrium sites. It starts with the theory of anisotropic elasticity as applied to a crystalline material with the symmetry of ice Ih, and then gives the experimental parameters for mono-crystalline and polycrystalline ice. The basic thermal properties that arise from lattice vibrations are heat capacity, thermal expansion, and thermal conductivity. A major topic is then the spectroscopy of lattice vibrations as determined by infrared absorption, Raman scattering, and inelastic neutron scattering. These results are then interpreted in terms of the dispersion curves of the lattice, which are modelled by the translational, librational, and molecular modes of the structure.

This chapter examines the structure of ³He-⁴He mixtures with neutrons. It focuses on thermal neutron studies of the quasiparticle excitation spectrum and structure functions. It begins with the results of Raman scattering and concludes with some recent deep inelastic neutron scattering measurements.

The basic theory of magnetic scattering is presented. A response function for magnetic scattering is defined, and expressed in terms partial response functions. The relation between the partial response functions and the correlation function for components of the magnetization is obtained, and the dynamical part of the partial reponse functions is linked via the fluctuation-dissipation theorem to the absorptive part of the generalized susceptibility. It is shown how the dipole approximation can be used to simply the magnetic scattering operator for localized electrons, and the magnetic form factor is introduced. Examples of the use of the dipole magnetic form factor, as well as more general anisotropic magnetic form factors, are given. A comparison with the X-ray atomic form factor is given. Various sum rules for the magnetic response function and generalized susceptibility are obtained.

This chapter presents incoherent QENS studies performed on Li⁺, Na⁺, H^-, and Cl^- ions. Purely coherent QENS concerns F^- and O^2- conductors, whereas for Ag⁺ a mixture of coherent and incoherent QENS prohibits quantitative data evaluation. On the other hand, AgI is one of the best solid ionic conductors, and QENS studies are performed and combined with impedance spectroscopy at high frequencies. For this system, the well-known jump relaxation model is derived. Na⁺ motion in β-Al₂O₃ is investigated by QENS in detail. Much effort has been spent on Li⁺ diffusion motivated by applications of Li in batteries. For anionic conductors, the system best investigated by means of QENS is Cl^- diffusion in SrCl₂.

The basic principles of crystallography are reviewed, including the lattice, basis and reciprocal lattice. The Bragg diffraction law and Laue equation, which describe coherent scattering from a crystalline material, are derived, and the structure factor and differential cross-section are obtained in the static approximation. It is explained how the presence of defects, short-range order, and reduced dimensionality causes diffuse scattering. For non-crystalline materials, such as liquids and glasses, the pair distribution function and density-density correlation function are introduced, and their relation to the static structure factor established. For molecular fluids, the form factor is defined and calculated for a diatomic molecule, and the separation of intra- and inter-molecular scattering is discussed. The principles of small-angle neutron scattering are described.