Rietveld refinements

The Te Bail method is a clever extension of the original work of Rietveld. The key difference between the two methods is that the Te Bail method uses iteratively the values of intensities obtained from the previous least squares cycle, and assumes unit values for all the peaks to initiate the refinement. Rietveld s method, on the other hand, uses the intensities calculated based on an initial model for the structure. 

The analysis of siUcon carbide involves identification, chemical analysis, and physical testing. For identification, x-ray diffraction, optical microscopy, and electron microscopy are used (136). Refinement of x-ray data by Rietveld analysis allows more precise deterrnination of polytype levels (137). 

Fig. 4.8 Powder X-ray diffraction pattern of pure single-phase Prb-IVand Rietveld refinement.

Fig. 1. Quantification of framework Ti sites and unit cell expansion versus Ti contents using XPS 2p transition lines ( O ). XANES profiles at Ti K-edge (A) and Rietveld refinement of the XRD powder patterns ( ). Solid data points for TS-1 prepared as in ref [9].

The Rietveld analysis is mainly used for refining the structures of crystalline phases and to perform quantitative analysis of multiphase samples. The quantitative analysis is possible since the Rietveld method can easily deal with diffraction patterns with strongly overlapped peaks, while preferred orientation can be quantitatively treated. 

Even if the main intent of the Rietveld analysis is the structure refinement in material science, sometimes the information relative to the structure is not the heart of the matter. 

Quantitative Phase Analysis by Rietveld Refinement. The quantitative analysis can be performed through the Rietveld method because the number of the elemental cells of each phase is NccKV, where K and are the refined scale factor and the cell volumes, respectively. So, the weight fraction of the /th phase is given by ... 

This formula works only if all the phases in the sample are crystalline and are refined in the Rietveld procedure so that the relative scale, cell volume and cell composition are known. 

Figure 57.13. The Rietveld XRD refinement for CA53 after being leached 45 min at rt for the determination of the Ni fee (A), Ni/Al bcc (B) and the Ni2Al3 (C) contents. The residual error analysis of the curve fit is displayed in hne D.

Figure 57.14. The wt.% of Ni fee, Ni/Al bcc and Ni2Al3 as Al was leached from the CA53 as calculated by the Rietveld refinement method.

Synthesis, characterization, and Rietveld refinement of tungsten-framework-doped porous manganese oxide (K-OMS-2) material. Chemistry of Materials, 20, 6382-6388. 

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. 

SGW wish to thank, IIT Bombay for providing FT Raman and Technical University Graz for providing X-ray Rietveld refinement of Nal and Agl-SOD. 

Historically (1960 s and 1970 s) mostly used on single crystals, it has since then been generalised for powders using Rietveld refinement procedures. 

In this paper the relation between cation mobility and catalytic activity in lean SCR NOx by CH4 on (Ag,Co)- and (Co,Ag)-FER have been studied by combining XRD Rietveld refinement in fresh and used catalysts with SCR catalytic testing performed in dry and wet conditions. UV-Vis DRS measurements were also performed. 

Keywords CoAg-FER, CH4NOx-SCR, cation siting, Rietveld refinement... 

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. 

XRD powder patterns of fresh and used catalysts, measured at room temperature on a Bruker D8 Advance diffractometer equipped with Sol-X detector, were subjected to Rietveld structure refinement in Immm space group using the GSAS package (Larson and Von Dreele, 1994). 

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...

On the basis of the very low Ag content, from the Co4.6AgO.2AF Rietveld refinement (Fig.5) Col, Co2 and also Ag2 were attributed to Co2+, whereas Ag5 must be partially occupied by Co2+ (for simplicity, site Ag2 will be indicated in Fig 5 and called Co4 from now on). As expected, no metallic Ag° was detected. After catalytic testing a fairly similar distribution of the 3.2 extraframework cations per unit cell was found. The most remarkable modification induced by the dry-wet SCR cycle was the migration of Co atoms from the Co2 to the Co4 site, an effect of particular interest as Co4 is, as stated earlier, nearer than Co2 to the Co2a position, i.e. the most active oc-site. 

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