Rietveld treatment

In order to obtain detailed structure, a knowledge of diffraction intensities is essential, the intensities being related to the structure factor. Computer-controlled single-crystal X-ray diffractometers with structure (software) packages have made structure elucidation a routine matter. The availability of synchrotron X-radiation of continuously variable wavelength has made X-ray diffraction a still more powerful structural tool for the study of solids. A technique of great utility to solid state chemists is the Rietveld treatment of powder X-ray diffraction profiles (Rietveld, 1969 Manohar, 1983). Automated structure packages for the determination of unknown structures by this method are now commercially available (see section 2.2.3). In Fig. 2.1, we show a typical set of profile data. 

P.Y. Zavalij, T. Chirayil, and M.S. Whittingham, Layered tetramethylammonium vanadium oxide [N(CH3)4]V307 by x-ray Rietveld refinement, Acta Cryst. C53, 879 (1997) tma - tetramethylammonium [N(CH3)4]. The material in a form of a black crystalline powder was prepared by hydrothermal treatment at 185°C of a mixture of V2O5, tmaOH, and LiOH taken in 1 2 1 molar ratio and acidified with CH3COOH to pH = 6,5. 

The residual difference after a successful DDM refinement or/and decomposition can be considered as a scattering component of the powder pattern free of Bragg diffraction. The separation of this component would facilitate the analysis of the amorphous fraction of the sample, the radial distribution function of the non-crystalline scatterers, the thermal diffuse scattering properties and other non-Bragg features of powder patterns. The background-independent profile treatment can be especially desirable in quantitative phase analysis when amorphous admixtures must be accounted for. Further extensions of DDM may involve Bayesian probability theory, which has been utilized efficiently in background estimation procedures and Rietveld refinement in the presence of impurities.DDM will also be useful at the initial steps of powder diffraction structure determination when the structure model is absent and the background line cannot be determined correctly. The direct space search methods of structure solution, in particular, may efficiently utilize DDM. 

Wasdell MB, Jan JE, Bomben MM, Freeman RD, Rietveld WJ, Tai J, Hamilton D, Weiss MD (2008) A randomized, placebo-controUed trial of controlled release melatonin treatment of delayed sleep phase syndrome and impaired sleep maintenance in children with neurodevelopmental disabilities. J Pineal Res 44 57-64. 

Investigations into the possibility of incorporation of chromium or copper into the tin(IV) oxide were made by indexing and refining the XRD patterns by the Rietveld method. No lattice incorporation is induced by thermal treatment. 

Fig. 4. Elliptical channel and position of water dimers within the channel as determined from Rietveld refinement treatment of powder X ray diffraction pattern recorded step by step (0.02° 2Q steps) (from ref. 50).

Through Rietveld analysis, the atomic positions appear unchanged after flux treatment, at the notable exception of europium, that tends to transfer from the regular nBR site to the interstitial nmO and antiphase n05 ones (Fig. 1). 

Beyond the improvement of the initial performances, the flux treatments also appear as an efficient way to alleviate the degradation undergone by the BAM phosphor during baking. The combined study of degraded samples using EPR, XPS, Rietveld analysis and fluorescence [6] reveal several new aspects of the oxidation mechanism. 

The transformation mechanism of amorphous precursors to Ml and M2 phases in 220-600°C range was demonstrated previously [6]. Final phase compositions of the catalysts form upon heat treatment at 600°C. XRD patterns of the samples after high-temperature treatment are shown in Fig. 4. The content of constituent phases was calculated by Rietveld refinements of X-ray powder diffraction data (Table 1). 

Figure 4.2 XRD scan of a portland cement (CEM I 52.5 N) (top) and its pattern decomposition calculated by Rietveld QPA (downwards from XRD scan). At right the QPA results are presented for indicative purposes. Arcanite was identified by means of a salicylic acid/methanol selective dissolution treatment.

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