Neutron diffraction experimental

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. 

Liquid structure a very strict test of the quality of the force field used in a simulation is represented by the comparison between the structural results obtained from the trajectory and X-ray or neutron diffraction experimental data. When a good agreement between theory and experiment is found, one can be sure that the molecular dpmamics simulation provides a reliable and correct description of the structural properties of the system under investigation. 

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. 

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.)...

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. 

The most important experimental task in structural chemistry is the structure determination. It is mainly performed by X-ray diffraction from single crystals further methods include X-ray diffraction from crystalline powders and neutron diffraction from single crystals and powders. Structure determination is the analytical aspect of structural chemistry the usual result is a static model. The elucidation of the spatial rearrangements of atoms during a chemical reaction is much less accessible experimentally. Reaction mechanisms deal with this aspect of structural chemistry in the chemistry of molecules. Topotaxy is concerned with chemical processes in solids, in which structural relations exist between the orientation of educts and products. Neither dynamic aspects of this kind are subjects of this book, nor the experimental methods for the preparation of solids, to grow crystals or to determine structures. 

The order occurring among the spins of the atoms in the unit cell can be determined experimentally by neutron diffraction. Since a neutron itself has a spin and a magnetic moment, it is diffracted by an atom to an extent which depends on the orientation of the magnetic moment. 

Zheludev, A., Grand, A., Ressouche, E. et al. (1994) Experimental determination of the spin density in the tetracyanoethenide free radical, [TCNE]-, by single-crystal polarized neutron diffraction, a view of a 71 orbital, J. Am. Chem. Soc., 116,7243-7249. 

The model reference density pref is a good approximation to the dominant part of p appearing very close to the nuclei, and so Ap(r) will be very small everywhere and is assumed to be experimental noise. If the peaks in p are located, then the nuclear positions are known and the structure is resolved. Because they have no core, hydrogen atoms produce only very small maxima, and thus their positions are difficult to locate with any accuracy. If it is important to locate their positions accurately, this can be done by neutron diffraction. Neutrons are scattered by nuclei rather than electrons, and so the positions of the nuclei are obtained directly. Neutron diffraction is particularly important for the accurate determination of the positions of hydrogen atoms. 

Figure 9.24 A radial distribution function (RDF) for a DRP of monospheres (right) and a scheme for its evaluation (left), Nmeenl4nR2 is an equivalent of IA(R), where A/mean is the mean number of spheres in the intervals of 0.2R. The solid curve illustrates the data obtained from neutron diffraction in liquid argon 1,2 are the experimental data by Scott [128] and Bernal [127] obtained for the models of steel spheres (cited in [127]).

The location of the hydrogen atoms in hydrogen bonded systems is often difficult to ascertain. When X-ray diffraction is used there is an experimental limitation to face, as it is usually difficult to locate the very light H-atom in Fourier maps and, even when this is possible, the technique can provide information on electron density centroids rather than on the position of the light nucleus. Neutron diffraction is required for an unambiguous location of the H-atom. In ionic hydrogen bonds the situation may occur where a knowledge of the proton position in a donor-acceptor system is necessary to know whether proton transfer, i.e. protonation of a suitable base, has occurred or not. 

In this way and by numerical evaluation, Driessens (2) proved that the experimental activities could be explained on the basis of substitutional disorder, according to Equation (27), within the limits of experimental error. It seems, therefore, that measurements of distribution coefficients and the resulting activities calculated by the method of Kirgintsev and Trushnikova (16) do not distinguish between the regular character of solid solutions and the possibility of substitional disorder. However, the latter can be discerned by X-ray or neutron diffraction or by NMR or magnetic measurements. It can be shown that substitutional disorder always results in negative values of the interaction parameter W due to the fact that... 

A very sensitive test of the model is the comparison of calculated and observed structure functions this is shown in Figs. F and G. Note that the central force model yields the characteristic double peak in sh(s) near 2.5 A-1. That the theoretical curve oscillates with greater amplitude than the experimental data indicates that the predicted distribution of near neighbor 00 separations is too narrow. The comparison with neutron diffraction data shows that the theoretical... 

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