Physics
Neutron Scattering
Neutron scattering is a technique used to study the structure and dynamics of materials at the atomic and molecular level. Neutrons are directed at a sample, and the way they scatter provides information about the sample's composition, crystal structure, and magnetic properties. This method is valuable for research in physics, chemistry, materials science, and biology.
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11 Key excerpts on "Neutron Scattering"
eBook - PDF- Albert Furrer(Author)
- 1999(Publication Date)
- World Scientific(Publisher)
1 INTRODUCTION TO Neutron Scattering P. BONI and A. FURRER Laboratory for Neutron Scattering ETHZ & Paul Scherrer Institut CH-5232 Villigen PSI, Switzerland E-mail: Peter. [email protected], Albert. [email protected] Neutron Scattering is a powerful and direct method for investigating the static and dynamic properties of materials in many fields of science. The weak interaction between neutron and sample allows in most cases the use of the first Born ap-proximation for the calculation of the scattering cross sections. In the following introduction we discuss some basic properties of the neutron, in particular its nu-clear and magnetic interaction with matter. We demonstrate that the measured scattering function S(Q,UJ) is related to the pair correlation function G(r,t) by a Fourier transform in space. As an illustration we discuss some typical experiments from the field of high temperature superconductivity. 1 Introduction Among most other methods, Neutron Scattering allows a detailed understand-ing of the static and dynamic properties on an atomic scale of materials that occur in our environment. Combined with x-ray scattering a very large range of momentum and energy transfers can be covered thanks to the high comple-mentarity of both techniques. The most relevant, unique character of neutrons that cannot be matched by any other technique, can be summarized as follows: • The neutron interacts with the atomic nucleus, and not with the elec-trons as x-rays do. This has important consequences: i) the response of neutrons from light atoms like hydrogen or oxygen is much higher than for x-rays, ii) neutrons can easily distinguish atoms of comparable atomic number, iii) neutrons distinguish isotopes: For example, deutera-tion of macromolecules allows to focus on specific aspects of their atomic arrangement or their motion. • For the same wavelength as hard x-rays the neutron energy is much lower and comparable to the energy of elementary excitations in matter.
- J Honig(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
II. SELECTED CHARACTERIZATION TECHNIQUES This page intentionally left blank Neutron Scattering TECHNIQUES IN MATERIALS RESEARCH N.S. Satya Murthy B.A. Dasannacharya R. Chakravarthy Nuclear Physics Division Bhabha Atomic Research Centre, Bombay I. INTRODUCTION Neutron Scattering techniques have established their versatility in the microscopic characterisation of condensed materials. Slow neutrons, having both wavelengths and energies comparable to lattice spacings and lattice excitations respec-tively, prove to be an ideal probe for investigating microsco-pic structure as well as dynamics of condensed matter, spanning a large region of energy-momentum space . Apart from the nuclear interaction, the magnetic moment of the neutron interacts with the unpaired electrons of the target material making it a unique tool for probing magnetism in solids . This article describes some investigations which illustrate the nature and scope of various Neutron Scattering techniques, through examples of amino-acids, ferroelectrics , magnetic materials, superconductors and disordered solids. The theory of Neutron Scattering will be briefly described before discussing the examples. PREPARATION AND CHARACTERIZATION Copyright ©1981 by Academic Press, Inc. OF MATERIALS 105 All rights of reproduction in any form reserved. ISBN 0-12-355040-8 106 N. S. SATYA MURTHY ET AL. II. PRINCIPLES OF Neutron Scattering The neutron-nuclear interaction can be taken to be a sum of 6-function potentials centred at each nucleus in the target and is given by V (r,t) = ^ — Zb 6(r - r (t)). (1) N ~ m , d ~d a Here m is the neutron mass, b is the scattering amplitude, and rjt) is the position of d-th nucleus. The neutron-nuclear ~d -14 -15 interaction is short ranged (10 to 10 m) and for slow neutrons (λ ^10 m), the scattering from a nucleus is isotropic.
- Robert A. Scott, Charles M. Lukehart, Robert A. Scott, Charles M. Lukehart(Authors)
- 2013(Publication Date)
- Wiley-Interscience(Publisher)
hν . These frequencies are usually dependent on the propagation direction in the crystal, the specific crystal structure, and its atomic composition. Rotational, vibrational, and librational motions can also be effectively studied with neutrons. Finally, using high surface-to-volume materials, neutrons can be employed to investigate surface phenomena. In the following sections, some of the mathematical formalism of the Neutron Scattering technique will be used and several examples that are aimed at illustrating the power of the technique, with the goal of stimulating additional interest and further reading in more advanced and specialized monographs and journals.2.3 Neutron Scattering Formalism
In a typical Neutron Scattering experiment, the intensity of the neutrons scattered from a beam incident on a sample is recorded. Usually, the scattering process will involve a deflection of the incident neutrons identified by a change in the wave vector,k, of the beam, and denoted by the scattering vector Q =ki −kf , where the subscripts i and f denote the incident and final directions, respectively. In addition to the change in wave vector, the scattering can also involve a change in the energy, E , of the neutrons. The magnitude of this energy change is usually associated with some dynamic process in the sample and hence we can represent that as an angular frequency, ω , such that E = hω . The scattered intensity measured in a neutron experiment is proportional to the dynamical structure factor, S (Q ,ω ) and hence is a function of both Q and ω . S (Q ,ω ) represents the Fourier transform of the temporal and spatial fluctuations of the atomic (spin) density in a normal (magnetic) Neutron Scattering process. There are many comprehensive discussions of Neutron Scattering formalism and the reader is directed to such monographs written by Marshall and Lovesey,5 Lovesey,6 Bacon7 and Squires8
eBook - PDF- Hans Rudolf Wenk(Author)
- 2018(Publication Date)
- De Gruyter(Publisher)
Neutron Scattering techniques are ideally suited for the study of the structure and dynamics of atoms and molecules physisorbed on surfaces (e.g., Larese 1997, 1999) including processes such as multi-layer development, melting and rotational tunneling on unreactive stable surfaces. Furthermore, structural and dynamical features associated with chemisorption involving the formation of surface hydroxyl groups that saturate the coordination of surface cations and complete the interrupted bulk crystalline network can be imaged by neutron methods. The dynamical behavior of fluids and gases contained within porous solids is controlled by processes occurring at the interface as well as the rates of supply and removal of mobile components. The richness and complexity of fluid behavior (e.g., phase transitions, molecular orientation and relaxation, diffusion, adsorption, wetting, Studies of Fluids & Fluid-Solid Interactions 317 capillary condensation, etc.) in confined geometries has been, and continues to be, the focus of numerous applications of Neutron Scattering. Objectives The focus of this chapter is the application of Neutron Scattering and diffraction methods to the study of fluids and their interaction with solid matrices. By way of numerous examples, emphasis is placed on what neutrons can tell us about the molecular-level properties and behavior of geo-fluids and the processes attendant with their interaction with solid surfaces. Discussion focuses on two main themes, homogeneous fluids with a major emphasis on both water and aqueous solutions containing dissolved constituents, and the structure and dynamics of fluids interacting with either solid surfaces or within confined geometries, again with an emphasis on water.
eBook - PDFVibrational Spectroscopy With Neutrons - With Applications In Chemistry, Biology, Materials Science And Catalysis
With Applications in Chemistry, Biology, Materials Science and Catalysis
- Philip C H Mitchell, Stewart F Parker, Timmy A J Ramirez-cuesta(Authors)
- 2005(Publication Date)
- World Scientific(Publisher)
Theory of inelastic Neutron Scattering 29 2.5 The theoretical framework of Neutron Scattering The theory of thermal Neutron Scattering has for its objective the interpretation of the experimental observables in terms of the microscopic, quantum-like, properties of the scattering sample. It is as well then to understand exactly what is being measured in neutron spectroscopy. (The theory is fully developed in Appendix 2.) In its simplest form a neutron spectrometer consists of a single detector (of modest area, A) held at some distance, d t , with respect to the sample and at some angle, 6, with respect to the direction of the incident neutron beam see Fig. 2.1. These quantities are its polar coordinates (df, 9). The solid angle, d/2, (subtended by an angular element, d9) is 2rc sin#d# Depending on the detailed design of the spectrometer the energy spectrum of the sample is scanned in some way and, as a function of this scan, the number of neutrons measured in the detector is recorded, per second (the final, or detected, neutron flux, J { ). This must be normalised to the number of incident neutrons reaching the sample, per second (the incident flux, J). The strength of the sample's response is, therefore, known as a function of energy, E, and, since the polar coordinates of the detector can be changed, also as a function of solid angle. The observable is the rate of change of the cross section with respect to the final energy, Ef, and solid angle, d/2. This is the double differential scattering cross section, (d 2 cr/dE{ dD), with units, barn eV 1 steradian 1 , where: d£ = 4 (2.27) «f The changes that occur during the scattering process must now be related to how the initial state of the system (scattering atom plus neutron) is transformed into the final state of the system. The nature of the neutrons in the incident beam is represented by their initial wavefunction, ^ ni , which at long distances from the scattering nucleus will be a simple plane wave.
eBook - PDF- Steven M. Girvin, Kun Yang(Authors)
- 2019(Publication Date)
- Cambridge University Press(Publisher)
4 Neutron Scattering We have learned that scattering experiments are very useful in probing spatial structures. Thus far we have focused on elastic scattering, which involves momentum transfer from the probing particle/wave to our system, but no energy exchange between them. 1 Inelastic scattering, on the other hand, involves energy exchange as well as momentum exchange, and thus tells us not simply the static structure, but rather the dynamics/excitation spectrum of the system. In fact, elastic scattering can be viewed as a very special case of inelastic scattering where the energy transfer happens to be zero. Thus studying inelastic scattering will deepen our understanding of elastic scattering. In this chapter we will learn why neutrons are excellent probes of crystalline solids and their exci-tations. We will develop the mathematics needed to understand inelastic scattering and to describe the dynamical correlation functions of atomic positions (and spins) that inelastic scattering can measure. 4.1 Introduction to Neutron Scattering Radioactive decay produces high-energy neutrons. Here we will be concerned with thermal neutrons (i.e. neutrons that have diffused around inside a solid long enough to come to thermal equilibrium with it). These low-energy neutrons can be made mono-energetic by using a crystal as a 3D Bragg diffraction grating (to select a single momentum, much as in X-ray scattering). This mono-energetic beam can then be scattered from a sample and the resulting energy and momentum transfer analyzed very accurately [ 24 ]. Hence one can measure the spectrum of lattice and electronic excitations in a solid much more precisely than with X-rays. Crudely speaking, since the speed of thermal neutrons is comparable to the speed of atoms vibrating in the sample, we cannot make the approximation of neglecting atomic motion during the scattering event (as we did for the case of X-ray scattering).
- Frank C. Hawthorne(Author)
- 2018(Publication Date)
- De Gruyter(Publisher)
Chapter 5 Subrata Ghose INELASTIC Neutron Scattering INTRODUCTION In crystals strong forces exist between neighboring atoms. Hence, if one atom is displaced from its mean equilibrium position, the neighboring atoms also undergo displacements. As a result, the atomic motions are collective rather than individual, which can be analyzed into a spectrum of normal modes of vibrations which travel as waves through the crystal. The energy of these waves is quantized. The pseudoparticles associated with these waves are known as phonons, which carry quantums of energy jW Phonons play a very important role in determining the transport and thermodynamic properties of solids, such as electrical resistivity, thermal conductivity, superconductivity and specific heat. Neutrons are ideally suited for the study of phonons, as well as the spin waves (magnons) in magnetic materials. Basic properties of the neutron Neutron is a subatomic particle with zero charge, mass m = 1.0087 atomic mass units, spin V 2 , and magnetic moment, Un = -1.9132 nuclear magnetons. These four properties make neutron a very effective tool for the study of condensed matter. The zero mass means the neutron has great penetrability in bulk samples with very little absorption. Depending on their energies, neutrons are classified as ultracold (0.00025 meV), cold (1 meV), thermal (25 meV) and epithermal (1000 meV). The thermal neutrons are usually obtained by slowing down high energy neutrons obtained from a steady state (reactor) or a pulsed (spallation) source by inelastic collisions in a moderating material containing light atoms. Their characteristics are listed in Table 1. Table 1.
eBook - PDF- Waldemar Alfredo Monteiro(Author)
- 2016(Publication Date)
- IntechOpen(Publisher)
Generally, it is convenient to describe the particle structure taking into account enough small elements to consider the scattering factors of these elements to be constant, independent of scattering angle over the whole domain where the structure factor of the considered particle is different from zero. This theory of small angle X-ray scattering can be adapted very easily to neutrons. Small angle Neutron Scattering is used where the X-rays cannot provide the desired informa‐ tion either of the lack of scattering contrast or of severe absorption of the studied material. The choice of thermal neutrons as a means of substance investigation was owed to their wave‐ lengths and their energies corresponding to the inter atomic distances and excitation energies of condensed matter. Neutron absorption from the matter is very low, thus resulting in the samples that can have thicknesses larger than in the X-rays case which are strongly absorbed with an increase in the volume of analyzed samples. We can say that SANS allows the investigation of materials in various conditions, such as in containers, furnaces, cryostats, etc. Due to its magnetic moment, the neutron provides unique possibilities to the study of magnetic structures, magnetic moment distribution, and magnetic excitations. Being a nuclear propriety, the nuclear scattering amplitude can be considerably different between various isotopes of a specific chemical species. For example, the big difference between the coherent scattering lengths of hydrogen and deuterium lead to the usage of phase contrast in the study of hydrogenate materials, allowing a good resolution in analyzing polymers and biological substances in general. Because thermal neutrons interact very low with the matter, this interaction can be theoretically treated on the base of first Born approximation [5, 6]. We will show further that the variation of the scattering density is very important in the study of condensed matter through SANS.
eBook - ePubExperimental Methods in Polymer Science
Modern Methods in Polymer Research and Technology
- Toyoichi Tanaka(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
is particularly useful for polymer science.2.2.2 Neutron Scattering AND CROSS SECTION
Neutrons are scattered by nuclei because of nuclear force. Because the range of the nuclear force is very short (10−13 –10−12 cm) and the size of nuclei is much smaller than that of an atom (≈10−8 cm), most of materials are “very dilute” for the “eye” of neutrons, as schematically illustrated in Figure 2.3 . Let us consider a case in which a flux of neutron Φ0 is irradiated by an object. According to Lambert’s law, the transmitted flux Φ is obtained byFigure 2.3 Comparison of the sizes of neutrons and atoms for Neutron Scattering.(8)where σT is the number rate of neutrons that collide with the atoms, N is the number of atoms in the sample volume V, and x is the path length of the object. σT is called the total cross section and consists of the absorption σa and the scattering cross sections σ, respectively;(9)If the scattering is isotropic, σ is given by(10)where b is the scattering length. The scattered intensity for an assembly of atoms of number N can be calculated by taking account of the phase of the scattered waves in the context of the Born approximation [18](11)where Ω is the solid angle, andbiand r i are respectively the scattering length and the position vector of the atom i ;〈…〉 denotes the average; and (d σ/d Ω) is called the differential cross section and q is the momentum transfer given by(12)where q is the magnitude of the momentum transfer (or scattering vector) and θ is the scattering angle. The q
eBook - PDFPhysics of Nuclear Radiations
Concepts, Techniques and Applications
- Chary Rangacharyulu(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
6 Interactions of Neutrons with Matter 6.1 Introduction This chapter is devoted to the interactions of neutrons with matter. This topic is of interest when we are looking for uses in science and technol-ogy or we are concerned with the radiation damage and hazards they pose. Neutron interactions with material media share some features with charged particles and some others with photons, but some aspects of these interactions are unique to them. We can talk about the slowing down of neutrons, i.e., neutrons losing energy by multiple elastic col-lisions along their path in the medium, in the same way as for charged particles. Their interactions resemble those of charged particles in that the neutron after scattering is the same one we started with except it is of lower energy and is deflected from its original path. Unlike the case of charged particles, which leave ionization trails along their paths, neutrons leave no track. Also, analogous to photon propagation, they may travel long distances without interactions and be absorbed in a single encounter. Neutrons interact mainly with atomic nuclei over a wide range of energies. This behavior is in contrast to the interaction of charged par-ticles and photons, for which energy loss or absorption is mainly due to interactions with electrons. To a lesser extent, they also interact with atomic/molecular electrons at low energies. 1 As they are electrically neutral, heavy and are of small size, neu-trons can penetrate deep into the interiors of atoms even at low ener-gies, get very close to atomic nuclei and thus be readily absorbed by them. The absorption is an exoergic process. It is generally followed by the emission of photons, sometimes charged particles and in some 1 See Section 6.6. 151 152 Physics of Nuclear Radiations: Concepts, Techniques and Applications cases by the well known nuclear fission. Quite often, the interactions produce radioactive nuclei which decay with their typical half-lives and emit radiations.
eBook - ePub- Toyoko Imae, Toshiji Kanaya, Michihiro Furusaka, Naoya Torikai, Toyoko Imae, Toshiji Kanaya, Michihiro Furusaka, Naoya Torikai(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
eq. (I.1.15) . This way magnetic multilayers can serve as powerful neutron beam polarizers by reflecting neutrons with one spin direction with much higher probability than those with the other (Mezei and Dagleish, 1977). A detailed description of the art of neutron reflectometry can be found in Chapter 1.I.1.8 Scattering, Interference, and CoherenceWe now turn our attention to the evaluation of the interference processes that can occur between neutron waves scattered by different atoms. This is the central subject for the study of matter on the atomic scale by actually any radiation (even including electron microscopy, where the atomic scale resolution often apparently achieved by direct imaging is also the result of shrewd processing and reconstruction). When particle waves scattered on different atoms are superposed, the interference between these waves is determined by the optical path length differences between waves scattered at different atoms. The optical path is defined as the real geometrical distance in the direction of wave propagation multiplied by the wave number of the radiation, cf. in eq. (I.1.4) . A change of the optical path comparable to unity implies substantial modification of the wave by a shift of its phase by a radian. Hence, the high sensitivity of neutron wave interference to distances comparable to 1/k = λ/2π offers us a spatial resolution capability not accessible by direct imaging methods.Let us consider the optical paths for scattering on a point-like object (nucleus) at a position , by comparing it to the optical path for a scattering object at r = 0. The incoming radiation will be considered as a plane wave with wave vector and the outgoing radiation as spherical waves from each scattering center with a wave number , cf. eq. (I.1.9) . Here we assume that the detection point is at a very large distance compared to the distance between the scattering points; therefore, the outgoing radiation arrives to the detector practically as a plane wave with wave vector , with a direction determined by the position of the neutron detection. As shown in Figure I.1.4 , the optical path difference between the two spherical waves scattered at the origin and
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