Rietveld structural refinement

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). 

R. M. Wilson, J.C. Elliott, S.E.P. Dowker, R.l. Smith, Rietveld structure refinement of precipitated carbonate apatite using neutron diffraction data. Biomaterials 25 (2004) 2205-2213. 

Table 17.26 Available Rietveld structure refinement software. 

Table 17.30 Available quantitative phase analysis software (also refer to list of Rietveld structure refinement software).

Rietveld structure refinements have also been undertaken on synthetic precipitated COsAps as model systems for biological apatites. The reduction in apparent PO4 volume, and P and Ca2 occupancies seen in dental enamel were also seen in Na-free precipitated COsAps with CO3 contents of 4 wt % produced by the reaction between CaCOs and CaHP04 at 100°C (Morgan et al. 2000). COsAps precipitated in the presence of Na ions... 

Bigi A, Falini G, Foresti E, Gazzano M, Ripamonti A, Roveri N (1996) Rietveld structure refinements of calcium hydroxyapatite containing magnesium. Acta CrystallogrB52 87-92... 

Figure 2 shows the dependency of the lattice parameter oo with substitution level x and includes also data for shock-synthesized j sialons from Ref. [11]. For direct comparability, structural data of the equivalent yS-sialons with hexagonal lattice symmetry are plotted as the cube root of the volume of eight formula units (for spinel Z = 8). The same trend of a lattice expansion upon [Al-0] insertion is evident for both and j sialons. In the spinel structure, two different cation environments, a tetrahedral and an octahedral, exist. Rietveld structure refinement of j Si2A10N3 revealed that the size of the octahedral cation site had slightly increased with respect to Si3N4, while the tetrahedral site had decreased. This indicates a site preference of the bulkier A1 ion for the octahedral coordination, which would mean that Si2A10N3 is a partially inverse spinel [9]. 

Zeolites with high La and Ce contents, which have been calcined in the presence of steam or not, have been studied using Rietveld structure refinement [13]. As depicted in Fig. 3, several crystallographic sites may be found in the Y-zeofite framework. 

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. 

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. 

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

Akaganeite (named after the Akagane mine in Japan) is isostructural with hollan-dite. Compounds with this structure have a tetragonal or monoclinic unit cell. Bernal et al. (1959) and Keller (1970) both concluded that the unit cell of akaganeite was tetragonal with a = 1.000 nm and c = 0.3023 nm. The structural refinement of a natural sample using XRD and Rietveld analysis indicated, however, that the unit cell is monoclinic with a = 1.060 nm, b = 0.3039 nm, c = 1.0513 nm and p = 90.24° (Post Buchwald, 1991). There are eight formula units per unit cell. 

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... 

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 whole-pattern-fitting structure-refinement method, which was first introduced by Rietveld and used for neutron diffraction powder patterns, does yield from x-ray diffraction patterns correct, refined structural information for linear polymers. Remarkably precise lattice parameters are obtained incidentally in the use of the method. The method lends itself to improved estimations of the fraction of amorphous and crystalline materials, or of two polymorphic forms, present. As improved profile functions come in to use, the method promises to provide crystallite size information, almost as a spin-off benefit. 

Neutron diffraction patterns of powder samples were taken on a neutron diffractometer (X = 1.085 A) mounted on the thermal column of a WR-SM nuclear reactor [3]. The DBW-3.2 program for the Rietveld neutron diffraction line shape analysis was used in calculations and structure refinement [4]. A DRON-3M X-ray diffractometer (CuK - radiation) was used to measure X-ray powder diffraction patterns. 

Lennie AR, Redfem SAT, Schofield PF, Vaughan DJ. Synthesis and Rietveld crystal structure refinement of mackinawite, tetragonal FeS. Miner Mag 1995 59 677-83. 

The best structure solution (i.e. the structure with lowest Rwp in the final generation) for the a phase is shown in Fig. 5a and the best structure solution for the f5 phase is shown in Fig. 5b. For comparison, the known crystal structures [61,62] of the a and (5 phases are also shown. In each case, the structure solution obtained from the GA calculation is in excellent agreement with the known structure. In each case, the maximum distance between an atom in the structure solution and the corresponding atom in the known crystal structure is less than 0.5 A, and the structure refines readily (using the Rietveld method) to the known crystal structure. We emphasize that the L-glutamic acid molecule has a significantly different conformation in the a and f3 phases, and the GA structure solution calculations have successfully found the correct conformation for each phase. 

A survey of the usovite phases obtained up to now [5,15,18] shows that Al3+, Ga3+ and all the 3D tervalent ions from V3+ to Fe3+ readily occupy the M"3+ site all the 3D divalent ions from Mn2+ to Cu2+ can be used as M 2+ as for M2+, it may be Ca2+, Cd2+ or Mn2+ almost every combination of choices in these three series of possibilities will allow to obtain an usovite for the stoichiometry Ba2MM M"2F14 (with however some exceptions as BaMnFeF7 [19]). The correctness of the original structure determination has now been confirmed by several full X-ray structure refinements on single crystals and by Rietveld profile analyses on powder neutron diffractograms, so that this structural type is now firmly established and may be seen as rather common among fluorides. 

In the pharmaceutical community, quantitative analyses has conventionally been based on the intensity of a characteristic peak of the analyte. It is now recognized that phase quantification will be more accurate if it is based on the entire powder pattern.This forms the basis for the whole-powder-pattern analyses method developed in the last few decades. Of the available methods, the Rietveld method is deemed the most powerful since it is based on structural parameters. This is a whole-pattern fitting least-squares refinement technique that has also been extensively used for crystal structure refinement and to determine the size and strain of crystallites. 

Hull, A. A new method of X-ray analysis. Phys. Rev. 10, 661-696 (1917). Young, R. A. Application of the Rietveld method for structure refinement with powder diffraction data. Adv. X-ray Anal. 24, 1-23 (1981). 

Following this principle, some authors [74] have S3mthesized first europium phosphate Eui/3Zr2(P04)3 and then americium phosphate Ami/3Zr2(P04)3 [75] and classified them as members of the NZP family. The IR spectra and structure refinement of the Eu phosphate were carried out by the Rietveld method which... 

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