Rietveld Structure Refinement

Advanced structure refinement. The Rietveld refinement structural method has been taken further in a number of directions. One of the most appealing is to combine it with the maximum entropy method (MEM), in which... 

Wilson, R.M., Elliott, J.C. and Dowker, S.E.P. (1999) Rietveld refinement of the crystallographic structure of human dental enamel apatites. American Mineralogist, 84, 1406-1414. 

In this paper a detailed study on the relation between structural modifications due to reaction condition induced cation mobility and Ag,Co-FER catalytic activity, studied by XRD and UV-Vis DRS Rietveld refinement, is reported. 

According to the chemical analysis and coordination distances, the Rietveld refinement of the crystal structure at room temperature revealed 1.2 Co2+ atoms per unit cell at the Col and Co2 sites, whereas the 1.4 Ag+ cations are spread over the Co3 site, from now on referred to as Ag5 for clarity, and two new sites, Ag2 and Ag3, located near Co2 in the 10-membered ring (Fig. 3). In addition, for this catalyst the presence of Ag° clusters outside the zeolite structure was recognized by the detection of a strong reflection at about 40° 28. In agreement with the lower Ag content, in Ag2.7Co2.8AF the Ag3 site... 

Figure 3. Ag3.7Co2.6AF and Ag2.7Co3.8AF structure by Rietveld refinement...

Unsubstituted, unsolvated complexes have been observed for all metals, but their low solubility prevents the growth of quality single crystals. This problem was recently overcome with data collected on a powder sample on a synchrotron X-ray source followed by Rietveld refinement.17-19 Not surprisingly, the structures display polymeric chains with alternating metal and Cp units. 

Neumann, M.A., Tedesco, C., Destri, S., Ferro, D.R., Porzio, W., 2002, Bridging the gap - structure determination of the red polymorph of tetrahexylsexithiophene by Monte Carlo simulated annealing, first princple DFT calculations and Rietveld refinement, Journal of Applied Crystallography, 35, 3, 296-303. 

Rietveld refinements of the structures of Mg Al - CO3 LDHs (n = 2.0, 5.0) have been reported [39]. The oxygen atoms of both carbonate ions and water molecules were found to occupy a single set of 18(fi) sites distributed aroimd the three-fold O- 0 axis with a 3Ri polytype stacking (space group R5m). 

Key words electron diffraction, structure determination, Rietveld refinement... 

Information content in a powder diffraction pattern is reduced as compared to that in single crystal diffraction, due to the collapse of the three dimensional reciprocal space into a one dimensional space where the only independent variable is the scattering angle. The poorer the resolution of the diffraction method, the less the information content in the pattern (Altomare et al. 1995 David 1999). As a consequence, structure of less complex phases can be determined from power diffraction alone (fewer atoms in the asymmetric unit of the unit cell). However, refinement of the structure is not limited so seriously with resolution issues, so powder diffraction data are used in Rietveld refinement more frequently than in structure determination. Electron powder diffraction patterns can be processed and refined using public domain computer programs. The first successful applications of electron diffraction in this field were demonstrated on fairly simple structures. 

B. (1994) Rietveld refinement of the crystal structure of the synthetic porous zincosihcate VPl-7. Zeolites, 14,... 

Rietveld refinement [25, 26] is a method of whole pattern refinement, where a calculated diffraction pattern for a structure model is a least-squares fit to an observed diffraction pattern. Originally, it was used as a means of verifying proposed structure models. For zeolites, Rietveld refinement is still used for the same purpose and provides details of the structure including atomic positions of framework atoms and cation sittings. Data with accurate intensities and well-resolved peaks are needed for the most accurate work, and so often a synchrotron source is used for data collection since it can provide higher intensity and peak resolution than an in-house diffractometer. However, modern in-house diffractometers often provide good enough data for some refinements. 

Zeolitic materials have been prominent amongst those so far studied by high resolution powder diffraction using synchrotron X-rays [36]. High definition synchrotron PXD data has been helpful in a number of framework structure determinations and has facilitated studies of planar faulting (see below). Successful Rietveld refinements of the framework structures of zeolite ZSM-11 [37, 38] and silica-ZSM-12 [39], and of the complete structures of zeolite Y containing cadmium sulfide [40] and cadmium selenide [41] clusters have been described. 

Once Te-III was identified as incommensurate, subsequent analysis was conducted on the previously-collected powder-diffraction data using the formalism of 4D superspace [234], and the JANA2000 software for structure refinement [235]. The Rietveld refinement of the incommensurate Te-III diffraction profile is shown in Fig. 9, and the modulated structure is shown in Fig. 10. Tellurium was only the second element found to have a modulated crystal structure at high-pressure, the... 

Fig. 13 Rietveld refinement of Sc-II at 23 GPa using the C-centred guest structure. Reflections are indexed using their hklm indices. The upper tick marks show the calculated peak positions for hklG) host reflections and (hkOO) host/guest reflections, and lower ones mark (hkOm) guest-only reflections. The difference between the observed and calculated profiles is shown below the tick marks. The inset shows an enlarged view of the asymmetric peak at 17.5°, showing that it is accounted for by the (4400) and (0002) peaks. The vertical dashed line is a guide to the eye...

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