Diffraction of neutrons by crystals

Structure of the two independent molecules of decamethylsilicocene in the crystal (hydrogen atoms omitted). Adapted with permission from [58], Copyright 1986 Wiley-VCH Verlag GmhH Co. KG.  

Although both X-rays and neutrons can be used to study the structures of crystalline substanees, the vast majority of published struetures are based on X-ray diffraetion. This is because a nuclear reactor or a spallation source is necessary to produce the neutrons required. Nowadays, there are about 20 high-flux 

The much slower fall-off of scattering power with scattering angle for neutrons than for X-rays makes neutron diffraction particularly well suited for high-resolution studies. In combination with X-ray diffraction, neutron diffraction can be used to determine the vibrational displacement of atomic nuclei and therefore decouple and separate this effect from deformations in electron density. 

Another advantage of neutrons over X-rays comes from the fact that neutrons are particles with a nuclear spin. The interaction of this with the electronic spin of a sample allows the determination of the magnetic stmcture of magneticaUy-active compounds. For example, in this way it is possible to distinguish between parallel and anti-parallel spins in ferromagnetic and antiferromagnetic materials [63]. This topic is beyond the scope of this book, so we refer to a more specialized text [64]. 

The section yttrium hydride in the on-line supplement for chapter 10 describes a study of an yttrium hydride, with one p.4-H atom in the center of an Y4 tetrahedron, one p-a-H atom capping one of the faces of the tetrahedron, and six P2-H atoms bridging its edges. In this study, data from two completely separate sources were analyzed. This is rarely done, but it can show up systematic errors that might otherwise not be noticed. 

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In the first part of this experiment the diffraction of neutrons by a single crystal is demonstrated and neutron wave properties experimentally verified. To do this, a crystal spectrometer is aligned in a beam of neutrons and a rocking curve is measured. The resolution of the spectrometer is calculated. The energy spectrum of neutrons coming out of the reactor beam hole is then measured and compared with the calculated theoretical distribution. The approximately Maxwellian shape of the beam spectrum is thus shown. The use of the experimental spectrum plot as a direct method for obtaining the effective neutron temperature is demonstrated. 

Several types of diffraction by crystals are now studied. Neutron diffraction can be used with great effectiveness to give information on molecular structure. These results complement those from X-ray diffraction studies, because there are different mechanisms for the scattering of X rays and of neutrons by the various atoms. X rays are scattered by electrons, while neutrons are scattered by atomic nuclei. Neutron diffraction is important for the determination of the locations of hydrogen atoms which, because of their low electron count, are poor X-ray scatterers. Electron diffraction, while requiring much smaller crystals and therefore being potentially useful for the study of macromolecules, produces diffraction patterns that are more complicated. Their interpretation is hampered by the fact that the diffracted electron beams are rediffracted within the crystal much more than are X-ray beams. This has limited the practical use of electron diffraction in the determination of atomic arrangements in crystals to studies of surface structure. 

The diffraction of neutrons provides a way of locating hydrogen atoms in compounds and is used to complement X-ray study of crystals especially by locating and characterising water molecules in hydrates (Bacon, 1958). 

Two years after de Broglie s prediction, C. Davisson (1882-1958) and L. H. Germer (1896-1971) at the Bell Telephone Laboratories demonstrated diffraction of electrons by a crystal of nickel. This behavior is an important characteristic of waves. It shows conclusively that electrons do have wave properties. Davisson and Germer found that the wavelength associated with electrons of known energy is exactly that predicted by de Broglie. Similar diffraction experiments have been successfully performed with other particles, such as neutrons. 

The flux generated by neutron sources is generally 4 to 5 orders of magnitude less than a standard X-ray source. This means that large crystals and long exposures are required. As a result of improved instrumentation in detector systems and in data handling, the size of a crystal required for a neutron experiment has been reduced from about 20 to 1.5 mm [246]. Nevertheless, neutron diffraction studies are limited to those proteins for which very large crystals can be obtained. With X-rays, a crystal of this size would lead to severe absorption. Fortunately, the absorption of neutrons by most atoms is very low. 

Measurements of dispersion curves provide information about the interatomic forces in solids. In fact, a dispersion curve is a function of the vibration frequency V on the wavelength X. The methods of neutron spectroscopy based on the phenomenon of diffraction of heat neutrons by crystals enables one to graph the dispersion curves of solids. The most accurate measurements of these curves are obtained by the inelastic neutron scattering using triple axis spectrometers. 

Diffraction of X-rays or neutrons by crystals have provided very rich material on inter-nuclear distances R. If explicit determination of angles is not required, electron diffraction of gaseous molecules, or X-ray and neutron diffraction of vitreous materials, solutions, etc. may many times provide acceptable R values. If one asks for the distribution of distances from a given point in a gas of geometrical points, the density in a shell between R and R -1- dR is jaroportional to 4nR dR = P. This is also valid in actual compounds and alloys for very long R, but not at all for short R. Fig. 1 is a qualitative probability distribution of R values (normalized by division with P) for nuclei of a given element, or for a combination of two definite elements Zj and Zj. Contrary... 

Many scientifically and teclmologically important substances caimot be prepared as single-crystals large enough to be studied by single crystal diffraction of x-rays and, especially, neutrons. If a sample composed of... 

The classical approach for determining the structures of crystalline materials is through diflfiaction methods, i.e.. X-ray, neutron-beam, and electron-beam techniques. Difiiaction data can be analyzed to yield the spatial arrangement of all the atoms in the crystal lattice. EXAFS provides a different approach to the analysis of atomic structure, based not on the diffraction of X rays by an array of atoms but rather upon the absorption of X rays by individual atoms in such an array. Herein lie the capabilities and limitations of EXAFS. 

The crystal lattices of a series of ternary alkali metal-silver acetylenediide [M Ag(C=C)] (M1 = Li 161, Na, K 162, Rb, Cs 163) have been analyzed by Ruschewitz and co-workers using X-ray powder diffraction.209 Neutron powder diffraction experiments have also been performed on 161-163 for obtaining precise bond lengths. It has been found that for 161 and 162, the [Ag(C C)] chains were packed parallel to each other, whereas for 163, they were aligned in layers that were rotated by 90° with respect to each other (see Figure 51). 

Most of the crystal-structure analyses report hydrogen-atom positions these are less accurate than those of the non-hydrogen atoms by a factor of ten, except in the case of neutron diffraction, where the accuracies are comparable. 

Since these early X-ray diffraction experiments, several other crystals have been subjected to analysis by X-ray and neutron diffraction and the F bond length has remained virtually unchanged. The location of the proton has been the point at issue. Early ir studies on KHF2 were interpreted as evidence for a double minimum potential well (Ketelaar, 1941 Glocker and Evans, 1942), but later studies questioned this (Pitzer and Westrum, 1947 Cote and Thompson, 1951 Newman and Badger, 1951) and led to a revision of earlier opinions (Ketelaar and Vedder, 1951). 

Diffraction analysis—whether employing x-rays, electrons, or neutrons—is the method of choice for obtaining structural information on crystalline substances. The application of the well understood principles and methods of diffraction analysis to single crystals of sufficient size and perfection can lead to a detailed determination of the crystal structure, without recourse to any auxiliary methodology. Hundreds of mono- and oligosaccharide molecules have been characterized by these means (1), yielding not only an increased understanding of their structures in the solid state, but also a data base useful for extrapolation to other states and molecular interactions. 

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