Neutron diffraction, application

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. 

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). 

Some of the techniques included apply more broadly than just to surfaces, interfaces, or thin films for example X-Ray Diffraction and Infrared Spectroscopy, which have been used for half a century in bulk solid and liquid analysis, respectively. They are included here because they have by now been developed to also apply to surfaces. A few techniques that are applied almost entirely to bulk materials (e.g.. Neutron Diffraction) are included because they give complementary information to other methods or because they are referred to significantly in the 10 materials volumes in the Series. Some techniques were left out because they were considered to be too restricted to specific applications or materials. 

Neutron Diffraction and Its Application in Inorganic Chemistry G. E. Bacon... 

Papoular, R.J., Ressouche, E., Schweizer, J. et al. (1993) MaxEnt enhancement of 2D projections from 3D phased Fourier data an application to polarised neutron diffraction, In Maximum Entropy and Bayesian Methods, Mohammad-Djafari, A. and Demoments, G. (Eds.), Kluwer Academic Publisher, Dordrecht, Vol. 53, pp. 311-318. 

Without any doubt, the zeolite framework porous characteristics (micropores sizes and topology) largely govern the zeolite properties and their industrial applications. Nevertheless for some zeolite uses, as for instance, host materials for confined phases, the zeolite inner surface characteristics should be precised to understand their influence on such low dimensionality sorbed systems. In that paper, we present illustrative examples of zeolite inner surface influence on confined methane phases. Our investigation extends from relatively complex zeolite inner surface types (as for MOR structural types) to the model inner surface ones (well illustrated by the AFI zeolite type). Sorption isotherm measurements associated with neutron diffraction experiments are used in the present study. 

Physical properties and detection of liquid Zintl compounds have been discussed and problems of gradual development of stoichiometries in non-clustering liquid ionic alloys, and their agreement with those persisting in the solid, have been considered. Neutron diffraction techniques and the results of their applications (Ga, Tl, alkali alloys) have been described. 

Recent progress in electron diffraction has significantly broadened its applications from a primary a microstructure characterization tool to an accurate structure analysis technique that traditionally belongs almost exclusively to the domain of X-ray and neutron diffraction. This development is timely since the focus of modem materials feature size is increasingly on nanoscale stmctures, where the electron high spatial... 

Structure determination from X-ray and neutron diffraction data is a standard procedure. Starting with a rough model, the accurate structure is determined using a least-squares structure refinement, which is based on kinematic diffraction and in which the differences between calculated and experimental intensities are minimized. X-ray and neutron diffraction are not applicable to all crystals. To determine crystal structures of thin layers on a substrate or small precipitates in a matrix (see figure 1) only electron diffraction (ED) can lead you to the crystal structure. 

The structures of iron oxides have been determined principally by single crystal X-ray diffraction or neutron diffraction with supplementary information coming from infrared spectroscopy, electron diffraction and high resolution electron microscopy. A few years after the first successful application of X-ray diffraction to crystal structure determination, this technique was used to establish the major features of the structures of magnetite (Bragg, 1915 Nishikawa, 1915) and hematite (Bragg Bragg, 1918). 

The five years since last considering specifically recent developments in X-ray and neutron diffraction methods for zeolites [1] have witnessed substantial progress. Some techniques, such as high resolution powder X-ray diffraction using synchrotron X-rays, have blossomed from earliest demonstrations of feasibility to widespread and productive application. Others, such as neutron powder diffraction, have shown steady progress. For still others, notably microcrystal diffraction, a variety of circumstances have contributed to extended gestation periods. Additionally, opportunities scarcely considered earlier (such as single crystal Laue diffraction, and certain developments in computer simulations that complement diffraction work) now command broad attention and warrant the commitment of substantial further investment. 

Other techniques previously described for general investigation of tautomeric equilibria (76AHC(S1)1> involve heats of combustion, relaxation times, polarography, refractive index, molar refractivity, optical rotation, X-ray diffraction, electron diffraction, neutron diffraction, Raman, fluorescence, phosphorescence and photoelectron spectroscopy, and mass spectrometry. The application of several of these techniques to tautomeric studies has been discussed in previous sections. Other results from the more important of these will be referred to later in this section. 

Soper, A.K., Tests of the empirical potential structure refinement method and a new method of application to neutron diffraction data on water, Mol. Phys., 99, 1503-1516,2001. 

X-ray and neutron diffraction methods and EXAFS spectroscopy are very useful in getting structural information of solvated ions. These methods, combined with molecular dynamics and Monte Carlo simulations, have been used extensively to study the structures of hydrated ions in water. Detailed results can be found in the review by Ohtaki and Radnai [17]. The structural study of solvated ions in lion-aqueous solvents has not been as extensive, partly because the low solubility of electrolytes in 11011-aqueous solvents limits the use of X-ray and neutron diffraction methods that need electrolyte of -1 M. However, this situation has been improved by EXAFS (applicable at -0.1 M), at least for ions of the elements with large atomic numbers, and the amount of data on ion-coordinating atom distances and solvation numbers for ions in non-aqueous solvents are growing [15 a, 18]. For example, according to the X-ray diffraction method, the lithium ion in for-mamide (FA) has, on average, 5.4 FA molecules as nearest neighbors with an... 

Other diffraction methods include electron diffraction, which may be used to determine the structures of gases or of volatile liquid substances that cannot be obtained as crystals suitable for x-ray diffraction, and neutron diffraction, which has special application for crystals in which the exact location of hydrogens is desired. Hydrogen does not have sufficient scattering power for x rays to be located precisely by x-ray diffraction. 

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