Crystal fitting procedure

The long Cu-S(Met) bond (2.9 A) does not contribute to the EXAFS fit for PCu(II) under a variety of conditions, including studies on orientated single crystals at liquid He temperatures [38]. From fitting procedures reported the two Cu-N(His) bonds at 1.97 A are 0.1 A less and the Cu-S(Cys) distance 2.11 A (0.02 A smaller) than those obtained from the X-ray crystal structure determination [16]. 

For pure WO3 the fine structure of the W(4f) peak shows considerable changes after reduction of the crystal. With the nonreduced stoichiometric crystal only two levels 4f7yj and 4f5/2 are observed, but after reduction the superposition of two doublets induces broadened features. Shifts due to the transformation of W to are revealed by a curve fitting procedure however, more drastic reduction can only be effected by hydrogen and argon ion-bombardment when W " " and W° states appear (Fig. 19). 

This is undertaken by two procedures first, empirical methods, in which variable parameters are adjusted, generally via a least squares fitting procedure to observed crystal properties. The latter must include the crystal structure (and the procedure of fitting to the structure has normally been achieved by minimizing the calculated forces acting on the atoms at their observed positions in the unit cell). Elastic constants should, where available, be included and dielectric properties are required to parameterize the shell model constants. Phonon dispersion curves provide valuable information on interatomic forces and force constant models (in which the variable parameters are first and second derivatives of the potential) are commonly fitted to lattice dynamical data. This has been less common in the fitting of parameters in potential models, which are onr present concern as they are required for subsequent use in simulations. However, empirically derived potential models should always be tested against phonon dispersion curves when the latter are available. 

In addition to structural analysis and purity evaluation, Raman spectroscopy can also be used to estimate the crystal size of nanostructured solids. In most cases size characterization using Raman spectroscopy is based on the phonon confinement model (PCM), which uses changes in Raman frequency and Raman peak shape to estimate the crystal size. Although several attempts have been made to relate confinement-induced changes in the Raman spectrum of ND to the crystal size, the agreement between calculated and experimental data and the accuracy of the fitting procedure are still unsatisfactory. A detailed discussion of the limitations of the PCM and the accuracy of previous studies on ND powders is given in Ref [86]. 

The crystal-setting procedure illustrated in Fig. 8-21 can be carried out whether or not the indices of the various poles are known. If the Laue pattern of a crystal is difficult to solve, any spot on it can be indexed by using a Laue camera and a diffractometer in sequence [8.4]. In addition, a goniometer is required that fits both instruments. The procedure is as follows ... 

Coupling in PDA Crystals. The polarized specular reflection spectra for the most highly reflective principal directions are shown in Figure 1. For the first three members of the series, the characteristic LT spectrum is observed. Backreflection was a severe problem because of the thinness of the crystals and, in the case of the less reflective principal direction, structure was altered sufficiently to render the spectra unuseable. Thus, direct measurement of exciton splitting, if present, was not possible. In the spectra reported, the backreflection in the intensely reflecting principal directions was corrected using a curve fitting procedure described elsewhere (21). 

EXAFS measurements were performed at the MRCAT undulator beam-line equipped with a double-crystal Si (111) monochromator with resolution of better than 4 eV at 11.5 keV (Pt L3 edge). Spectra of the metal solutions contained in plastic cuvettes were taken in fluorescence mode and those of solids as pressed powders in transmission mode. Phase-shift and backscattering amplitudes were obtained from various solid reference compounds. Details of the experimental and fitting procedures can be found in [6]. 

The results of the fitting procedure (table i) reveal chat the divalent iron phase is Szomolnokite (FeS04 H20). The trivalent iron phase is probably a hydroxylated basic iron sulfate like Butlerite (FeSC>40H 2H20) [8]. The data also reveal that the catalysts after operation contain well crystallized Szomolnokite, as follows from the observed small line width of its spectral contribution. The presence of die sextuplet in the spectrum of the used catalyst B shows that still some iron(III) oxide is present as also found by XRD. 

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