Diffraction of neutrons

D) DIFFRACTION OF NEUTRONS FROM NONMAGNETIC AND MAGNETIC CRYSTALS... 

Since the recognition in 1936 of the wave nature of neutrons and the subsequent demonstration of the diffraction of neutrons by a crystalline material, the development of neutron diffraction as a useful analytical tool has been inevitable. The initial growth period of this field was slow due to the unavailability of neutron sources (nuclear reactors) and the low neutron flux available at existing reactors. Within the last decade, however, increases in the number and type of neutron sources, increased flux, and improved detection schemes have placed this technique firmly in the mainstream of materials analysis. 

As noted earlier, the diffraction of X-rays, unlike the diffraction of neutrons, is primarily sensitive to the distribution of 00 separations. Although many of the early studies 9> of amorphous solid water included electron or X-ray diffraction measurements, the nature of the samples prepared and the restricted angular range of the measurements reported combine to prevent extraction of detailed structural information. The most complete of the early X-ray studies is by Bon-dot 26>. Only scanty description is given of the conditions of deposition but it appears likely his sample of amorphous solid water had little or no contamination with crystalline ice. He found a liquid-like distribution of 00 separations at 83 K, with the first neighbor peak centered at 2.77 A. If the pair correlation function is decomposed into a superposition of Gaussian peaks, the area of the near neighbor peak is found to correspond to 4.23 molecules, and to have a root mean square width of 0.50 A. 

The diffraction of X-rays and electrons is due to interaction with the orbital electrons of the atoms they encounter. The diffraction of neutrons (p. 5) springs from different causes. 

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). 

Neutron diffraction examples will be discussed when deemed necessary, even though in this book we have no intent to cover diffraction of neutrons (and electrons) at any significant depth. Interested readers can find more information on electron and neutron diffraction in some of the references provided at the end of this chapter. 

It is worth noting that it is the radial distribution of core electrons in an atom, which is responsible for the reduction of the intensity when the diffraction angle increases. Thus, it is a specific feature observed in x-ray diffraction from ordered arrangements of atoms. If, for example, the diffraction of neutrons is of concern, they are scattered by nuclei, which may be considered as points. Hence, neutron scattering functions (factors) are independent of the diffraction angle and they remain constant for a given type of nuclei (also see Table 2.2). 

C. Gliss, H. Clausen-Schaumann, R. Gunther, S. Odenbach, O. Randl, and T. M. Bayler Direct detection of domains in phospholipid bilayers by grazing incidence diffraction of neutrons and atomic force microscopy. Biophys. J., 1998, 74, 2443-2450. 

At the same time, the use of new means of observation by diffraction of neutrons and photons has led to a better experimental knowledge of the critical behaviour. Finally, at the juncture between theory and experiment, the development of computers has, by means of network simulation, enabled interesting results to be obtained. 

One can also compare the neutron diffraction and X-ray diffraction experiments where there is the diffraction of neutrons on nuclei and the diffraction of X-rays on electrons, respectively [64, 65]. As a consequence the positions of nuclei and the positions of maxima of the electron density are determined in neutron diffraction and X-ray diffraction measurements, respectively. Thus in a case of neutron diffraction the results correspond to the common understanding of molecular stmcture where the bond length is the distance between atoms nuclei. In a case of X-ray results the positions of electron density local maxima are practically the same as the positions of nuclei but only for non-hydrogen atoms. For the H-atom, as it was described earlier... 

The original and most extensively employed method of evaluating g R) experimentally is the study of the X-ray diffraction pattern by liquids. Recently, diffraction of neutrons has been found increasingly useful for this purpose. The principal idea of converting diffraction patterns into pair distribution functions is common to both methods, though they differ both in experimental detail and scope of information that they provide. 

By virtue of these factors, diffraction of neutrons by polycrystalline matter yields far more information than that of X rays. Thicker layers of material can be penetrated, and preferred orientations can be eliminated. Useful intensities can be measured out to large diffraction angles. 

Neutron diffraction is less commonly used than X-ray diffraction because of the limitations and costs of sources of neutrons. However, because the technique relies upon the diffraction of neutrons by atomic nuclei, neutron diffraction... 

Diffraction of neutrons is essentially similar to that of X-rays but is dependent only on nuclear properties and not on electron density. There can be dramatic differences between adjacent elements (e.g. Cr, Mn, Fe as shown in Fig.2) and both +ve and -ve values are possible. Unfortunately there is little improvement in discrimination between Al and Si, though there is an appreciable improvement for Mg and Al. 

We may return to the meaning of interatomic distances and of the coordination number JV. It is a minor detail that diffraction of X-rays indicates the centre of electronic density and diffraction of neutrons (disregarding the effects of partly filled shells observed in magnetically ordered compounds) indicates the position of the nuclei. Even when not demanded by symmetry, these two techniques agree very closely, and actually, the electronic densities seem to be a superposition of standard atomic quantities, with the marginal exception of hydrogen atoms, which are deformed and somewhat contracted (as predicted by... 

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. 

This Appendix points out the major design criteria used in the construction of the present spectrometer, and suggests many improvements possible for this or a new spectrometer. The spectrometer shown in Fig. 29.9 and described below was constructed as a prototype and a demonstration unit. With it, the diffraction of neutrons at low reactor power (about 200 W) was demonstrated, and the spectrum of the neutron radiation was measured in a student experiment at the International Institute. 

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