Radial distribution analysis

Katada, K. Studies on the Radial Distribution Analysis in Diffraction Methods. J. Phys. Soc. Japan 13, 51 (1958). 

Datta, A. K., B. K. Mathur, B. K. Samantaray, and S. Bhattacharjee. 1987. Dehydration and phase transformation in chrysotile asbestos a radial distribution analysis study. Bull. Mater. Sci. 9(2) 103-10. 

McKeown, D. A. (1987) Radial Distribution Analysis of a Series of Silica-rich Sodium Alumino-silicate Glasses Using Energy Dispersive X-ray Diffiaction, Phys. Chem. Glasses, 28, 156-163. 

The essence of analyzing an EXAFS spectrum is to recognize all sine contributions in x(k)- The obvious mathematical tool with which to achieve this is Fourier analysis. The argument of each sine contribution in Eq. (8) depends on k (which is known), on r (to be determined), and on the phase shift

characteristic property of the scattering atom in a certain environment, and is best derived from the EXAFS spectrum of a reference compound for which all distances are known. The EXAFS information becomes accessible, if we convert it into a radial distribution function, 0 (r), by means of Fourier transformation ... 

The power of X-ray methods can be extended to investigate the local structure on a scale of a few angstroms by means of the analysis of the fine structure and the radial distribution function. 

Figure 9. Data reduction and data analysis in EXAFS spectroscopy. (A) EXAFS spectrum x(k) versus k after background removal. (B) The solid curve is the weighted EXAFS spectrum k3x(k) versus k (after multiplying (k) by k3). The dashed curve represents an attempt to fit the data with a two-distance model by the curve-fitting (CF) technique. (C) Fourier transformation (FT) of the weighted EXAFS spectrum in momentum (k) space into the radial distribution function p3(r ) versus r in distance space. The dashed curve is the window function used to filter the major peak in Fourier filtering (FF). (D) Fourier-filtered EXAFS spectrum k3x (k) versus k (solid curve) of the major peak in (C) after back-transforming into k space. The dashed curve attempts to fit the filtered data with a single-distance model. (From Ref. 25, with permission.)...

Abstract. We present metallicities for 487 red giants in the Carina dwarf spheroidal (dSph) galaxy that were obtained from FLAMES low-resolution Ca triplet (CaT) spectroscopy. We find a mean [Fe/H] of —1.91dex with an intrinsic dispersion of 0.25 dex, whereas the full spread in metallicities is at least one dex. The analysis of the radial distribution of metallicities reveals that an excess of metal poor stars resides in a region of larger axis distances. These results can constrain evolutionary models and are discussed in the context of chemical evolution in the Carina dSph. 

The vapor sample under investigation may not eontain only one kind of speeies. It is desirable to learn as mueh as possible about the vapor composition from independent sources, but here the different experimental conditions need to be taken into account. For this reason, the vapor composition is yet another unknown to be determined in the electron diffraction analysis. Impurities may hinder the analysis in varying degrees depending on their own ability to scatter electrons and on the distribution of their own intemuclear distances. In case of a conformational equilibrium of, say, two conformers of the same molecule may make the analysis more difficult but the results more rewarding at the same time. The analysis of ethane-1,2-dithiol data collected at the temperature of 343 kelvin revealed the presence of 62% of the anti form and 38% of the gauche form as far as the S-C-C-S framework was concerned. The radial distributions calculated for a set of models and the experimental distribution in Figure 6 serve as illustration. 

Results similar to those for the nitrogen compounds discussed here have been obtained by analysis of C, N, and O atoms in a number of nucleotides and nucleosides (Pearlman and Kim 1985). Finally, a test of the kappa refinement using the theoretical densities of 28 diatomic molecules proved it to be quite successful in reproducing the theoretical radial distribution of the spherical component of the atomic density (Brown and Spackman 1991). 

Sodium fluoride, NaF, is a favorable choice for X-ray analysis of the lattice energy of an ionic crystal. Both Na and F are relatively light atoms, and the Na 3s-radial distribution, though diffuse, is not quite as spread out as the Li 2s shell (single-C values are 0.8358 and 0.6396 au-1, respectively see appendix F), and therefore contributes to a larger number of reflections. 

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