X-Ray and Neutron Diffraction Experiments

As pointed out in section 2.5, there are significant differences between results from X-ray and neutron diffraction experiments because of the way these species are scattered by the atoms of the liquid. In the case of X-rays the scattering is due to the electrons around each nucleus, and the scattering amplitude increases with 

Because of the important differences between the two diffraction experiments, the strategies used in carrying out these studies are not the same. X-ray experiments are certainly more common since the equipment used is easily obtained. Neutron experiments are carried out at a nuclear reactor site or at an accelerator with the appropriate facilities. In the following sections, some results from diffraction experiments are presented with emphasis on the structural information which has been obtained regarding ion solvation in electrolyte solutions. 

Because the scattering amplitudes/ (ko) vary with reciprocal distance, a normalized structure function H kjf is usually defined in reporting X-ray diffraction data. Thus, 

Many X-ray diffraction studies of electrolyte solutions have been carried out in aqueous solutions [Gl, 4, 5]. Values of the most probable distance, between the oxygen atom in water and a number of monoatomic ions are summarized in table 5.1. In the case of the cations, this distance reflects the radius of the cation plus the effective radius of the water molecule measured in the direction of the lone pairs on oxygen. In the case of alkali metals, the effective radius of water increases from 122 pm for Li to 131 pm for Cs when the Shannon and Prewitt radii are assumed for the cations (see section 3.2), the average value being 127 pm. This result can be attributed to the observation that the coordination number for water molecules around an alkali metal or alkaline metal earth cation changes with cation size and electrolyte concentration. In the case of the Li ion, this number decreases from six in very dilute solutions to four in concentrated solutions [5]. Because of the electrostatic character of the interaction between the cation and water molecules, these molecules exchange rapidly with other water molecules in their vicinity. For this reason, the solvation coordination number should be considered as an average. 

In the case of transition metal cations, the coordinated water molecules are covalently bonded to the cation, and the coordination number can be interpreted as fixed in the absence of other ligands. If the cations Mn, Fe, Co, and Ni are assumed to be in the high spin state, then the effective radius of coordinated water molecules in these systems is 123 pm on the basis of the X-ray data. 

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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... 

Thble 6.1 shows some comparisons of values determined by X-ray and neutron diffraction studies for O-H and H- -O bond lengths for some carbohydrate crystal structures that have been analyzed by both methods. Application of the normalization reduces the discrepancy between the H - - O distances obtained by X-ray and neutron diffraction experiments from 0.102 A to 0.033 A. Similar results have been reported for NH -0=C bonds [387], where the random errors in the X-ray N-H and H 0 distances varied between 0.02 and 0.17 A with a mean of 0.065 A when compared with the same neutron diffraction values. Cor-... 

The symmetry around the dimer is, however, usually low in crystals. The degeneracy of configurations (a) and (b) in Fig. 9, therefore, is removed by an environmental effect, which is sometimes called a site-splitting effect. The presence of two non-equivalent configurations in crystals has been confirmed by X-ray and neutron diffraction experiments. Although the... 

Hydration Numbers for Some Alkali Metal and Halide Ions Obtained from MD Calculations and X-Ray and Neutron-Diffraction Experiments ... 

Fig. 10. The variation of the bond lengths of (ND4)2Cu(D20)6(S04)2 as a function of temperature. Symbols show data from X-ray and neutron diffraction experiments, while the solid line shows the results from EXAFS measurements...

The protein-solvent interface was studied in an explicit solvent environment of 3182 water molecules by MD simulations performed on metmyoglobin [31].Both the structure and dynamics of the hydrated surface of myoglobin are similar to that obtained by experimental methods calculating three-dimensional density distributions, temperature factors and occupancy weights of the solvent molecules. On the basis of trajectories they identified multiple solvation layers around the protein surface including more than 500 hydration sites. Properties of theoretically calculated hydration clusters were compared to that obtained from neutron and X-ray data. This study indicates that the simulation unified the hydration picture provided by X-ray and neutron diffraction experiments. 

In powder diffraction, x-ray photons or neutrons (in x-ray and neutron diffraction experiments, respectively) are registered by the detector as random events. The measured intensity is directly proportional to the number of counts and therefore, the accuracy of intensity measurements is governed by statistics. Even though below we will refer to x-ray diffraction and photons, all conclusions remain identical when neutron diffraction and neutron count is considered. 

The overall pair correlation function for acetonitrile is obtained by X-ray and neutron diffraction experiments. List the component pair correlation functions which make up G r) in each experiment. Devise a strategy for separating these based on isotopic substitution. 

The electron denstiy distribution p(r) of an atom or molecule is an observable property that can be measured by a combination of X-ray and neutron diffraction experiments [22]. Also, it is easy to calculate p(r) once the MOs and the wave function of a molecule have been determined. The distribution p(r) is invariant with regard to any unitary transformation of the MOs. It has been shown by Hohenberg and Kohn that the energy of a molecule in its (nondegenerate) ground state is a unique functional of p(r) [23]. In other words, the physical and chemical properties of a molecule can be related to p(r). Thus, p(r) represents the best starting point for an analysis of chemical bonding. 

The structure of LiaAIDe as seen by X-ray diffraction and neutron diffraction. The size of the spheres illustrates the contribution from the different elements to the scattering. With X-rays, scattering from lithium and deuterium is nearly invisible, and X-ray diffraction gives only the position of the aluminium atoms. With neutrons, the strongest scattering is from deuterium, with both aluminium and in particular lithium weaker. This illustrates clearly the importance of combined X-ray and neutron diffraction experiments. 

This section provides guidance on laboratory-scale crystallization of small organic compounds. It does not deal with the more specialized area of crystallization of proteins. Crystal structure reports in journals rarely, if ever, detail crystallization information beyond the solvent used. Textbooks also tend to be limited in value because they vary so much in scope and focus. What we present here combines information gathered from textbooks with our own experience of growing single crystals for X-ray and neutron diffraction experiments, and keeps the natural products chemist very much in mind. 

The spatial extent of adsorbed water on smectite surfaces is a matter of some controversy. Infrared spectroscopy, NMR relaxation, and X-ray and neutron diffraction experiments all point to a thickness of the adsorbed water film of around 1.0 nm. However, certain thermodynamic data, summarized for Na-montmorillonite in Table 2.5, suggest a thickness as great as 10 nm or more." These data are for partial and apparent specific properties of montmorillonite-water systems whose variation with water... 

In the past few years, there have been advances in the detailed understanding of the crystalline structures through x-ray and neutron diffraction experiments. These advances were possible because synchrotron x-ray beams are much more powerful than ordinary laboratory beams, giving double or triple the amount of diffraction data. Neutron diffraction permits location of deuterium atoms so the hydrogen bonding systems can be worked out on samples that have had the hydroxyl hydrogen atoms substituted with deuterium atoms. Also, new methods have been used to prepare samples that are much more crystalline, also leading to more diffraction data. 

Liquid water also has tetrahedral symmetry because the melting process is not disruptive enough to disorder the water molecules fully. This is known from the radial distribution functions for liquid water that are observed in x-ray and neutron-diffraction experiments. Figure 29.6 shows the radial distribution functions of two liquids, water, and argon. 

Figure 10.61 shows some details of the bonding and electronic stmcture of the organolithium compound [ 2-(Me3Si)2CFiC5H4N 2], determined by combined X-ray and neutron diffraction experiments [65], which demonstrates the ability of neutron diffraction to give precise information on distances between light atoms (H, Fi). 

Perhaps the most basic of the physical properties of the liquid R s is their mass density. Knowledge of this parameter is of interest in itself, but is also essential to studies of a wide variety of other properties of these liquids, ranging from determinations of structural information from X-ray and neutron-diffraction experiments, to studies of electronic and of thermodynamic properties of pure R s and their alloys. 

Another approach, utilizing the intensities of layer reflections from both X-ray and neutron diffraction experiments to obtain estimates for has been applied to the SmA, SmB and smectic E phases of IBP-BAC[126]. 

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