Powder diffraction Rietveld refinement

A perfect crystal structure model is very helpful for theoretical calculations, reaction mechanism analysis, and some physical property analysis such as conductivity, magnetic susceptibility, chemical potential, etc. Powder XRD (or neutron diffraction) Rietveld refinement is one of the most popular methods used to characterize crystal structure. 

Powder X-Ray diffraction was employed to identify the crystalline phase of the prepared powder samples. Rietveld refinement was then performed on the XRD data to obtain the lattice constants. The electrochemical properties of LiCo,YyMn2 x.y04 powders were characterized in Li/LiCo,.YyMn2.,..y04 cells. The working electrodes were prepared by mixing polyvinylidene fluoride(PVDF), carbon black and LiCo,YyMn2.x.y04 powders in the ratio of 8 12 80% w/w, respectively. Electrochemical measurements were performed using lithium metal as counter and reference electrodes. The electrolyte was 1. OM anhydrous LiC104 dissolved in a 1 1 v/v ethylene carbonate and dimethyl carbonate mixture. The cell was cycled at a current rate of 0.2C between 3.6 and 4.3V, unless otherwise specified. 

The Rietveld method was originally devised for the refinement of crystal structures using neutron powder diffraction (Rietveld 1969) and was later extended to XRD (Young et al. 1977) and eventually to QPA (Bish and Howard 1988 Hill and Howard 1987). For an in-depth description of the various aspects and applications of the Rietveld method, the reader is referred to Dinnebier and Billinge (2008) and Young (1993). The following notes will focus on the application of the Rietveld method to QPA. 

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

Recent developments and prospects of these methods have been discussed in a chapter by Schneider et al. (2001). It was underlined that these methods are widely applied for the characterization of crystalline materials (phase identification, quantitative analysis, determination of structure imperfections, crystal structure determination and analysis of 3D microstructural properties). Phase identification was traditionally based on a comparison of observed data with interplanar spacings and relative intensities (d and T) listed for crystalline materials. More recent search-match procedures, based on digitized patterns, and Powder Diffraction File (International Centre for Diffraction Data, USA.) containing powder data for hundreds of thousands substances may result in a fast efficient qualitative analysis. The determination of the amounts of different phases present in a multi-component sample (quantitative analysis) is based on the so-called Rietveld method. Procedures for pattern indexing, structure solution and refinement of structure model are based on the same method. 

Most of the unknown structures is determined from single crystal diffraction and refined from powder diffraction. Refinement is done with the Rietveld method, which is a least square fitting of the computed pattern to the measured one, while structure parameters are treated as the primary fitting parameters. This is in contrast to the procedure in pattern decomposition, which is outlined above (where not the structure parameters, but the peak intensities were the primary fitting parameters). Beside the... 

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. 

Rietveld, H.M. (1967) line profiles of neutron powder-diffraction peaks for structure refinement. Acta Crystallogr.,... 

Fig. 16 Experimental (-1- marks), calculated solid line) and difference lower line) powder X-ray diffraction profiles for the three-component material after final Rietveld refinement, as reported by the authors [64]. (Reprinted with permission from Cheung et al. (2003) J Am Chem Soc 125 14658. Copyright 2003 American Chemical Society)...

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... 

Syntheses of near-single phases of the lead-substituted thallium monolayer phases with up to 6 Cu-O layers i.e., Pb-doped 1212, 1223, 1234, 1245, and 1256, have been recently reported (21). Reactant mixtures of various proportions of Tl2Os, PbO, CaO, Ba02, and CuO were pelletized, wrapped in gold foil, and sintered at 860-900°C under flowing oxygen for 10-30 h. The Tc value reached a maximum of 121 K for the 1234 compound and declined with further increase in the number of Cu-O layers. X-ray powder diffraction data for the different phases were refined using the Rietveld method and a consistent increase in the c-axis accompanied the increase in number of Cu-O layers. 

During the last five years, a powerful new method of getting crystal structural information from powder diffraction patterns has become widely used. Known variously as the Rietveld method, profile refinement1, or, more descriptively, whole-pattern-fitting structure refinement, the method was first introduced by Rietveld (X, 2) for use with neutron powder diffraction patterns. It has now been successfully used with neutron data to determine crystal structural details of more than 200 different materials in polycrystalline powder form. Later modified to work with x-ray powder patterns (3, X) the method has now been used for the refinement of more than 30 crystal structures, in 15 space groups, from x-ray powder data. Neutron applications have been reviewed by Cheetham and Taylor (5) and those for x-ray by Young (6). 

The metastable y-form crystal structure prior to the slow phase transitions was determined by the X-ray crystallographic analysis, but the crystal structures of three other new polymorphs ( -, r)- and e-forms) were undetermined by the same X-ray analysis, because these polymorphs were obtained as powder samples. Since the nearly racemic e-form crystals could be obtained as the monophasic powder sample by just leaving the crystallization mixture untouched, its crystal structure was solved from its X-ray diffraction (XRD) data by the direct-space approach using the Monte Carlo algorithm with the subsequent Rietveld refinement.26,27 Consequently, the Rwp value has been satisfactorily converged to 9.1%. 

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