Crystal structure refinement

Yu N et al (2006) Critical assessment of quantum mechanics based energy restraints in protein crystal structure refinement. Protein Sci 15(12) 2773-2784... 

Although simple intensity correction techniques can be used to develop very adequate XRPD methods of quantitative analysis, the introduction of more sophisticated data acquisition and handling techniques can greatly improve the quality of the developed method. For instance, improvement of the powder pattern quality through the use of the Rietveld method has been used to evaluate mixtures of two anhydrous polymorphs of carbamazepine and the dihydrate solvatomorph [43]. The method of whole pattern analysis developed by Rietveld [44] has found widespread use in crystal structure refinement and in the quantitative analysis of complex mixtures. Using this approach, the detection of analyte species was possible even when their concentration was less than 1% in the sample matrix. It was reported that good quantitation of analytes could be obtained in complex mixtures even without the requirement of calibration curves. 

Sheldrick, G.M. (1997) SHELXL-97, Program for Crystal Structure Refinement, University of Gottingen, Germany, Windows version by McArdle by National University of Ireland, Galway, Ireland. 

An interesting feature of the conduction mechanism in these materials and the LISICONS is that it is, at least partially, an interstitialcy mechanism. Both structure types contain examples of face-sharing tetrahedral sites. Fig. 2.13. Such sites are much too close together for both to be occupied simultaneously. Crystal structure refinements show that often, on average, one site of each pair contains a Li ion but the occupancy appears to be random. This means that, during conduction, one site of each pair may contain a Li ion but this is ejected when an incoming... 

G.M. Sheldrick, SHELXL, Program for crystal structure refinement. University of Gottingen, Germany 1999. 

J. Jansen, D. Tang, H.W. Zandbergen and H. Schenk, MSLS, a least-squares procedure for accurate crystal structure refinement from dynamical electron diffraction patterns. Acta Cryst. A54 91-101,1998. 

Francis C. A. and Ribbe R H. (1980). The forsterite-tephroite series, I Crystal structure refinement. Amer. Mineral, 65 1263-1269. 

The number of reflection intensities measured in a crystallographic experiment is large, and commonly exceeds the number of parameters to be determined. It was first realized by Hughes (1941) that such an overdetermination is ideally suited for the application of the least-squares methods of Gauss (see, e.g., Whittaker and Robinson 1967), in which an error function S, defined as the sum of the squares of discrepancies between observation and calculation, is minimized by adjustment of the parameters of the observational equations. As least-squares methods are computationally convenient, they have largely replaced Fourier techniques in crystal structure refinement. 

In these zeolites the Si/Al ratio is normally very near 1.5 [33]. Therefore, disorder is due to an Al->Si substitution between A1 and Sil. In this case, according to Loewenstein s rule. Si must occupy both A1 sites, and the Si atom substituted by A1 in Sil will occupy one Si2 site, the other Si2 site being occupied by the residual A1 (see Fig. lb). Therefore the crystal structure refinement must give an Al-fraction in site Sil, equal to the Si-fraction in site A1 and two times the Al-fraction in site Si2. These ratios have been found when disorder is low, as in some natrolites, in mesolite and scolecite but when the Al-fraction in Sil reaches values about 10 %, the disorder in the 4-ring formed by the T2 sites increases till it reaches complete disorder, with the same Al-fraction both in Tl and T2 (see Table 4 and Fig. 2). Curiously, complete disorder, which is not present in the majority of so-called disordered zeolites, has sometimes been found in these zeolites which are often taken as an example of order. 

Szymanski, J. T. Scott, J. D. 1982. A crystal structure refinement of synthetic brannerite, UTi206, and its bearing on rate of alkaline-carbonate leching of brannerite in ore. Canadian Mineralogist, 20, 271-279. 

Zeolite structures pose unconventional problems for crystal structure refinement. These problems arise from positional disorder pseudo-symmetry, twinning, high mobility of some atoms, and (sometimes) the inaccessibility of single-crystal data. Methods are discussed for investigating split atoms, Si-Al distribution, pseudo-symmetry, and for dealing with parameter correlation and limited data sets. Some additional techniques which have not been applied to zeolite structures are mentioned. 

The filled skutterudite antimonides appear to represent excellent examples of electron-crystal, phonon-glass materials. The incoherent rattling of the loosely bound lanthanide atoms in these materials is inferred from the large values of the ADP parameters obtained in single-crystal structure refinements. This rattling lowers the thermal conductivity at room temperature to values within two to three times Km... 

P. Muller, R. Herbst-Irmer, A. Spek, T. Schneider and M. Sawaya, Crystal Structure Refinement A Crvslallog rap her s Guide to SHELXL, Oxford University Press, Oxford, 2006. 

Crystal structure refinement a crystallographer s guide to SHELXL P. Muller, editor... 

Compositional variations of intensity of the absorption band at 23,400 to 24,000 cm-1 attributed to Ni2+/M2 site cations have provided site occupancy data for the Mg2+-Ni2+ olivines (Hu et al., 1990). The results obtained from crystal field spectra showing strong cation ordering of Ni2+ ions in the olivine Ml sites are in good agreement with estimates from crystal structure refinements (e.g. Bostrom, 1987 Ottonello etal., 1989) described later ( 6.7.1.2). 

Analyses of electron density distributions have enabled the positions of major elements of high atomic weights such as iron and other transition elements to be located relative to lighter elements such as magnesium and aluminium in mineral crystal structures. The widespread availability of automated X-ray dif-fractometry and least squares refinement programs have increased the availability of site occupancy data for transition metal ions in most contemporary crystal structure refinements. 

A number of X-ray crystal structure refinements of lunar and terrestrial Mg2+-Fe2+ olivines spanning wide composition ranges have revealed that Fe2+ ions are often slightly enriched in the smaller Ml sites (e.g., Finger, 1970 Brown... 

Cation distributions in amphibole structures, the site occupancy data for which were obtained mainly from X-ray crystal structure refinements, Mossbauer spectroscopy and hydroxyl stretching frequency measurements in the infrared region, have been critically reviewed (Strens, 1974 Hawthorne, 198 la,b 1983). 

Crystal structure refinements show that Fe3+ and Mn3+ ions are strongly enriched in the very distorted M3 site of the epidote structure (Dollase, 1968 Gabe et al., 1973 Stergiou and Rentzeperis, 1987), but these cations also appear to occupy Ml sites, too, in manganiferous epidotes (Dollase, 1969). These site occupancies correlate with Mossbauer spectral data for Fe3+ (Bancroft et al., 1967 Dollase, 1971 ) and crystal field spectra of Mn3+ in piemontites (Bums and Strens, 1967 Smith et al., 1982) described in 4.4.2 and 5.4.4. EPR measurements of clinozoisites (Vassilikou-Dova and Lehmann, 1987) indicate that Cr3+ and Fe3+ ions occupy the M3 sites. 

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