DIFFRACTION, NEUTRONS

Neutron diffraction is one of the most widely used techniques for the study of liquid structure. In the experiment, neutrons are elastically scattered off the nuclei in the sample and are detected at different scattering angles, typically 3° to 40°, for the purpose of measuring intermolecular structure whilst minimizing inelasticity corrections. The resultant scattering profile is then analyzed to provide structural information. 

The data taken is normally presented as the total structure factor, F(Q). This is related to the neutron scattering lengths hi, the concentrations C , and the partial structure factor Sy(Q) for each pair of atoms i and j in the sample, by Equation 4.1-1  

The real space pair distributions gy(rj is the inverse Fourier transform of (Sy(Q)-l), that is  

Quantum effects require that neutrons have a wavelike as well as particle nature with wavelengths dependent on the velocity ( = hlmx, where m is the mass of the neutron and v its velocity). Neutrons emerging from a nuclear reactor, after many atomic collisions in passing through a graphite 

Another advantage of neutron diffraction is that neutrons have a spin and so interact with the magnetic structure of the solid, which arises from the alignment of unpaired electron spins in the structure. The magnetic ordering in a crystal is quite invisible to X-rays, but is revealed in neutron diffraction as extra diffracted beams and hence a change in unit cell. 

Many experiments can be performed with either X rays or neutrons. Neutron radiation is some orders of magnitude more expensive and so is not a candidate for studies that can be done equally well or belter (because of the higher intensity) with X rays [127], ]128]. 

An important application of neutron diffraction is based on the fact that the dependence of scattering power on atomic number is different for neutrons and X rays. For X rays, the atomic form factor is directly proportional to the atomic number, but the relationship is more complicated for neutron radiation, and there is a correlation with the energy states of isotopes. Between hydrogen and deuterium, for example, there is an appreciable difference in scattering power. The fact that neutrons, unlike X-ray quanta, are scattered by atomic nuclei means that the scattering power is virtually independent of the diffraction angle. A further advantage of the use of neutrons is the lower absorption. 

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. 

For most structure problems investigated with neutrons, an X-ray structure analysis already exists. The task is to improve or refine certain parameters. There are four essential problems  

2) To distinguish between atoms of similar atomic number 

Neutrons in thermal equilibrium at 298 K can be used for diffraction in a similar way to X-rays, since they also have wavelengths comparable to interatomic spacings. In contrast to X-ray diffraction, the powder neutron diffraction experiment is much more common than single crystal neutron diffraction, since the beam intensity tends to be 1000 times less than for X-ray diffraction, so that single crystals of a sufficient size to collect good data are difficult to grow. 

The neutron technique is very much a complementary technique to the X-ray experiment as neutrons can interact very differently with isotopes and also, unlike X-rays, interact strongly with light elements. The neutron diffraction experimental technique varies slightly and is described below, but the general principles are similar to the X-ray experiment. 

The Bragg equation is utilized in two different ways in two sorts of powder neutron diffraction experiment  

Fixed wavelength (similar to X-rays), using a reactor source 

Fixed theta (angle of incidence), using a spallation source 

But the main point is that the heavy atom clearly will not swamp out the H position under these circumstances, and, as a result, M-H distances can be determined much more accurately with neutrons than with X-rays (the difference in precision is typically one or two orders of magnitude). 

Certain elements pose problems for neutron diffraction work. Elements such as B, Cd, Sm, Eu and a few others are often difficult to work with because of their high absorption cross-sections for neutrons. Fortunately, with the exception of boron, these elements are not commonly encountered in organometallic complexes. For boron-containing compounds, there are two ways of getting around the absorption 

Such a situation may arise if data collection time on the nuclear reactor is limited, or if the crystal is too small to give an adequate number of data. 

HaU and coworkers used density functional theory calculations to assign the inelastic neutron scattering derived vibrational spectrum of the elongated dihydrogen complex, (Tp )Rh(H)2(/ -H2) [66], They conclude that the H-H distance derived from neutron diffraction for the (Tp )Rh(H)2( / -H2) complex may in fact correspond to the average of the H-H distances of the tetrahydride and bis-hydride/// -H2 species. 

Ever since the discovery of the first / -H2 complex by Kubas, there has been the fingering question after coordination to a metal center, what remains of the H-H bond A series of experimental methods for answering this question are presented below. 

There are several experimental tools available for the determination of the H-H distance and the degree of the H-H bonding interaction. Neutron diffraction studies provide an accurate measure of the H-H distance. The measurement of the spin-lattice proton relaxation time, Ti, for an tf -V 2 complex or the proton-deuteron couphng constant, Jhd. for the corresponding isotopically substituted rf -WT) complex via H nuclear magnetic resonance (NMR) spectroscopy provides a quantitative measure of the H-H distance. The frequency of the v(H-H) stretching band, as determined by Raman or infrared (IR) spectroscopy of / -H2 complexes provides semiquantitative information about the strength of the H-H interaction. 

The two main methods for the determination of the three-dimensional (3-D) structures of molecules are single crystal X-ray diffraction and single-crystal 

The magnitude of the NMR coupling constant between atoms A and B, Jab, is related to the spatial orientation of those atoms. Non-interacting atoms have Jab values at or near 0 Hz. The largest values of Jab occur when atoms A and B are connected by a direct chemical bond. 

Recall that X rays are diffracted by the electrons that surround atoms, and that images obtained from X-ray diffraction show the surface of the electron clouds that surround molecules. Recall also that the X-ray diffracting power of elements in a sample increases with increasing atomic number. Neutrons are diffracted by nuclei, not by electrons. Thus a density map computed from neutron diffraction data is not an electon-density map, but instead a map of nuclear mass distribution, a nucleon-density map of the molecule (nucleons are the protons and neutrons in atomic nuclei). 

The collimated, monochromatic neutron beam is delivered to the sample on a diffractometer, and diffraction is detected by an area detector (Chapter 4, Section III.C). The most common type is a multiwire area detector that uses helium-3 as the active gas, according to this reaction  

A second type of image-plate detector employs gadolinium oxide, which absorbs a neutron and emits a gamma ray, which in turn exposes the image plate. Image plates have higher spatial resolution but lower efficiency than multiwire detectors. 

The great advantage of neutron diffraction is that small nuclei like hydrogen are readily observed. By comparison with carbon and larger elements, hydrogen is a very weak X-ray diffractor and is typically not observable in electron-density maps of proteins. But hydrogen and its isotope deuterium (2H or D) diffract neutrons very efficiently in comparison with larger elements. 

Data from C. R. Cantor and P. R. Schimmel. (1980). Biophysical Chemistry, Part 11 Techniques for the Study of Biological Structure und Function. W. H. Freeman and Company, San Francisco, p. 830. 

Physical adsorption isotherms involve measuring the volume of an inert gas adsorbed on a material s surface as a function of pressure at a constant temperature (an isotherm). Using nitrogen as the inert gas, at a temperature close to its boiling point (near 77K), such isotherms are used to determine the amount of the inert gas needed to form a physisorbed monolayer on a chemically unreactive surface, through use of the Brunauer, Emmett, and Teller equation (BET). If the area occupied by each physisorbed N2 molecule is known (16.2A ), the surface area can then be determined. For reactive clean metals, the area can be determined using chemisorption of H2 at room temperature. Most clean metals adsorb one H atom per surface metal atom at room temperature (except Pd, which forms a bulk hydride), so if the volume of H2 required for chemisorption is measured, the surface area of the metal can be determined if the atomic spacings for the metal is known. The main use of physical adsorption surface area measurement is to determine the surface areas of finely divided solids, such as oxide catalyst supports or carbon black. The main use of chemisorption surface area measurement is to determine the particle sizes of metal powders and supported metals in catalysts. 

Further discussion of this subject is given, for example, by Loretto [50], 

Let us first examine the scattering of a neutron plane wave by a single atom, which is supposed fixed. The behaviour of this system is represented by the wave equation 

Here V(r) is the potential energy of interaction of the neutron and the nucleus of the atom. 

Let the incident wave be represented by exp (i r). Using the Bom approximation (the Born approximation is explained in most standard texts on quantum mechanics) the approximate solution of this equation is given by 

For an incoming wave having unit amplitude the scattered neutron flux in a solid angle dfl is 

The epoxide information is straightforward. Electron density from the lone pairs is simply located on oxygen as expected, somewhat out away from the nucleus so that the center of electron density for the oxygen atom is shifted by 0.013 A. The nitrile 

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The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. 

The structure of a fluid is characterized by the spatial and orientational correlations between atoms and molecules detemiiued through x-ray and neutron diffraction experiments. Examples are the atomic pair correlation fiinctions (g, g. . ) in liquid water. An important feature of these correlation functions is that... 

The correlation functions provide an alternate route to the equilibrium properties of classical fluids. In particular, the two-particle correlation fimction of a system with a pairwise additive potential detemrines all of its themiodynamic properties. It also detemrines the compressibility of systems witir even more complex tliree-body and higher-order interactions. The pair correlation fiinctions are easier to approximate than the PFs to which they are related they can also be obtained, in principle, from x-ray or neutron diffraction experiments. This provides a useful perspective of fluid stmcture, and enables Hamiltonian models and approximations for the equilibrium stmcture of fluids and solutions to be tested by direct comparison with the experimentally detennined correlation fiinctions. We discuss the basic relations for the correlation fiinctions in the canonical and grand canonical ensembles before considering applications to model systems. 

In general, anions are less strongly hydrated than cations, but recent neutron diffraction data have indicated that even around the halide ions there is a well defined primary hydration shell of water molecules, which, in... 

As with synchrotron x-rays, neutron diffraction facilities are available at only a few major research institutions. There are research reactors with diffraction facilities in many countries, but the major ones are in North America, Europe and Australia. The are fewer spallation sources, but there are major ones in the United States and the United Kingdom. 

The development of neutron diffraction by C G Shull and coworkers [30] led to the detennination of the existence, previously only a hypothesis, of antiferromagnetism and ferrimagnetism. More recently neutron diffraction, because of its sensitivity to light elements in the presence of heavy ones, played a cmcial role in demonstrating the importance of oxygen content m high-temperature superconductors. 

For bulk structural detemiination (see chapter B 1.9). the main teclmique used has been x-ray diffraction (XRD). Several other teclmiques are also available for more specialized applications, including electron diffraction (ED) for thin film structures and gas-phase molecules neutron diffraction (ND) and nuclear magnetic resonance (NMR) for magnetic studies (see chapter B1.12 and chapter B1.13) x-ray absorption fine structure (XAFS) for local structures in small or unstable samples and other spectroscopies to examine local structures in molecules. Electron microscopy also plays an important role, primarily tlirough unaging (see chapter B1.17). 

The main problem with x-ray (and neutron) diffraction is that the infonnation it is made to yield is essentially... 

Brunger, A. T., Karplus, M. Polar hydrogen positions in proteins Empirical energy placement and neutron diffraction comparison. Proteins Struct. Func. Genet. 4 (1988) 148-156. 

The two major databases containing information obtained from X-ray structure analysis of small molecules are the Cambridge Structural Database (CSD) [25] and the Inorganic Crystal Structure Database (ICSD) [26] both are available as in-house versions. CSD provides access to organic and organometallic structures (mainly X-ray structures, with some structures from neutron diffraction), data which are mostly unpublished. The ICSD contains inorganic structures. 

All of these crystal structures have been analyzed using X-ray or neutron diffraction... 

Fig. 5.37 Comparison of the calculated phonon dispersion curve for Al with the experimental values measured using neutron diffraction. (Figure redrawn from Michin Y, D Farkas, M ] Mehl and D A Papaconstantopoulos 1999. Interatomic Potentials for Monomatomic Metals from Experimental Data and ab initio Calculations. Physical Review 359 3393-3407.)...

F H, O Kennard, D G Watson, L Brammer, A G Orpen and R Taylor 1987.1 ables of Bond Lengths determined by X-ray and Neutron Diffraction. 1. Bond Lengths in Organic Compounds. Journal of he Chemical Society Perkin Transactions 11 51-519. 

A variety of experimental techniques have been employed to research the material of this chapter, many of which we shall not even mention. For example, pressure as well as temperature has been used as an experimental variable to study volume effects. Dielectric constants, indices of refraction, and nuclear magnetic resonsance (NMR) spectra are used, as well as mechanical relaxations, to monitor the onset of the glassy state. X-ray, electron, and neutron diffraction are used to elucidate structure along with electron microscopy. It would take us too far afield to trace all these different techniques and the results obtained from each, so we restrict ourselves to discussing only a few types of experimental data. Our failure to mention all sources of data does not imply that these other techniques have not been employed to good advantage in the study of the topics contained herein. 

In discussing molecular symmetry it is essential that the molecular shape is accurately known, commonly by spectroscopic methods or by X-ray, electron or neutron diffraction. 

The stmcture of Pmssian Blue and its analogues consists of a three-dimensional polymeric network of Fe —CN—Fe linkages. Single-crystal x-ray and neutron diffraction studies of insoluble Pmssian Blue estabUsh that the stmcture is based on a rock salt-like face-centered cubic (fee) arrangement with Fe centers occupying one type of site and [Fe(CN)3] units randomly occupying three-quarters of the complementary sites (5). The cyanides bridge the two types of sites. The vacant [Fe(CN)3] sites are occupied by some of the water molecules. Other waters are zeoHtic, ie, interstitial, and occupy the centers of octants of the unit cell. The stmcture contains three different iron coordination environments, Fe C, Fe N, and Fe N4(H20), in a 3 1 3 ratio. 

Ca(I) sites have been shown to be responsible for most of the observed luminescence, whereas emission from the Mn " ions on the Ca(Il) sites occur only for higher Mn concentrations. Neutron diffraction studies have also confirmed these results (10). 

A detailed account is given in Reference 20. The techniques giving the most detailed 3-D stmctural information are x-ray and neutron diffraction, electron diffraction and microscopy (qv), and nuclear magnetic resonance spectroscopy (nmr) (see Analytical methods Magnetic spin resonance X-ray technology). 

Silver in the +3 oxidation state, including silver peroxide, ie, black oxide, marketed as AgO, is obtained by the action of the vigorous oxidising agent S20 g on Ag20 or other Ag compounds. X-ray and neutron diffraction analyses show the nominal AgO unit cell to be Ag20 Ag202- Both Ag" and Ag " are present. Another compound of potentially important commercial value is Ag O, which has a unit cell of two Ag and two Ag ions. Its preparation is as follows ... 

Conformation. Neutron diffraction studies of sucrose revealed the presence of two strong intramolecular hydrogen bonds 0-2—HO-1 and 0-5—HO-6 in the crystal form (7,8). These interactions hold the molecule in a weU-ordered and rigid conformation. The two rings are disposed at an angle close to 90°, with the glucopyranosyl and fmctofuranosyl residues adapting chair and T" twist conformations, respectively. 

X-ray crystallographic analysis of the sodium thiosulfate pentahydrate [10102-17-7] crystal indicates a tetrahedral stmcture for the thiosulfate ion. The S—S bond distance is 197 pm the S—O bond distance is 148 pm (5). Neutron diffraction of a barium thiosulfate monohydrate [7787-40-8] crystal confirms the tetrahedral stmcture and bond distances for the thiosulfate ion (6). 

Physical Properties. Table 3 contains a summary of the physical properties of L-ascorbic acid. Properties relating to the stmcture of vitamin C have been reviewed and summarized (32). Stabilization of the molecule is a consequence of delocalization of the TT-electrons over the conjugated enediol system. The highly acidic nature of the H-atom on C-3 has been confirmed by neutron diffraction studies (23). 

For x-ray investigations, the diffractometer method is generally used. The lattice constants indicate purity or composition of soHd solutions the rapid counting-tube goniometric method can be used at the manufacturing plant for quaUty control. The rotating-crystal and neutron diffraction methods are sometimes used for stmcture elucidation. 

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