Conventional Rietveld Research Articles

Rare Earth doped ceria: a combined X-ray and neutron pair distribution function study

Rare Earth doped ceria materials (Ce1–xRExO2–x/2) are widely studied for their application in solid oxide fuel cell devices. In this work, RE(Yb, Y, Nd, La)-doped ceria samples at constant (x = 0.25) doping rate were subjected to a combined synchrotron radiation and neutron powder diffraction study. The dopants were chosen in order to cover a wide range of dopant-ionic radii. The effect of doping on the average structure is investigated using conventional Rietveld analysis, while the Pair Distribution Function technique is used to explore the spatial extent of disorder as well as the local structure. Two models for mapping the local structure, in terms of oxygen relaxation and nano-phase separation, are presented.

Local disorder in yttrium doped ceria (Ce1−xYxO2−x/2) probed by joint X-ray and Neutron Powder Diffraction

Yttrium doped ceria materials (Ce1−xYxO2−x/2) are widely studied for their application in Solid Oxide Fuel Cells devices. An anomalous decrease in the isothermal ionic conductivity at increasing Y3+ concentration above a critical value has been observed and attributed to the formation of defect clusters / domains at the nanometric scale, the crystallographic structure of which is still under debate. In this context we present a combined Synchrotron Radiation and Neutron Powder Diffraction study. In particular, neutrons allow to determine accurately oxygen related parameters, the contribution of which in terms of X-ray scattering power is almost negligible when compared to that of cations. The effect of doping on the average structure is investigated using conventional Rietveld analysis, while the Pair Distribution Function (PDF) technique is used to explore structural distortions and the spatial extent of disorder as well. The local structure observed in the real space is not consistent with the mean crystallographic one and is better modeled considering a biphasic model.

Quantitative X-ray Rietveld analysis of metallic aluminum content in nano-aluminum powders

Accurate analysis of the content of metal aluminum (Al) in nano-Al powders is a difficult task due to the high reactivity of nano-Al powders. Here, the X-ray Rietveld quantitative phase analysis (QPA) method was applied to analyze the content of metal aluminum in nano-Al powders produced by three methods. A good agreement between the observed and calculated diffraction pattern was obtained and the conventional Rietveld factors (R p, R wp and GOF) converged to satisfactory values, which suggested that Al content was evaluated accurately. At the same time, the mixture sample of 89.77 wt.% micro-Al + 10.23 wt.% α-Al 2O 3 was study and the fitting pattern and R factors were satisfactory, which further verified the reliability of the X-ray Rietveld QPA method.

Application of a theory for particle statistics to structure refinement from powder diffraction data

A new methodology is proposed for structure refinement using powder diffraction data, from which models for particle statistics and any other statistical errors can be formally optimized. This method is nothing but a straightforward implementation of the maximum-likelihood method, extended to the error estimation. Structure parameters refined by the method for fluorapatite [Ca5(PO4)3F], anglesite (PbSO4) and barite (BaSO4) become significantly closer to those obtained by single-crystal structure analyses in comparison with the results of the conventional Rietveld method.

Local structural properties of CuI at low temperatures

This study examined the local structural properties of CuI at low temperatures of10–300 K by x-ray diffraction (XRD) and extended x-ray absorption fine structure(EXAFS) measurements at the Cu K edge. The XRD data were refined usingtwo models, split (distorted zinc-blende structure) and non-split (zinc-blendestructure), using a conventional Rietveld refinement combined with a maximumentropy method (MEM). MEM/Rietveld analyses showed that both the split andnon-split models could fit the data. EXAFS revealed the split model fit to be betterthan the non-split model. The split distance of Cu–I pairs was approximately0.03 Å at 15 K andincreased to 0.07 Å at 300 K. XRD and EXAFS combined together suggested that the CuI crystal was ina metastable state with a distorted zinc-blende structure at low temperatures.

Three approaches to total quantitative phase analysis of organic mixtures using an external standard

Three different approaches for a total quantitative phase analysis of organic mixture data were presented and subsequently tested on a set of ten ternary powder mixtures consisting of α-glycine, α-lactose monohydrate and paracetamol form I. In each of these methods, an external standard was used (in the present study, diamond) to determine the diffractometer constant, which was employed to place the crystalline intensities of all other samples on an absolute scale. In Method A, pure component diffractograms were also measured. In Methods B and C, no pure component diffractograms were used. Using Methods A–C, both the absolute crystalline compositions and all the amorphous compositions of the samples were determined. These methods outperform the quantitative phase analysis provided by conventional Rietveld analysis. An average error of less than 0.5 wt% was achieved with the present approaches, whereas the average error from conventional Rietveld analysis wasca1.3 wt%.

A multicomponent calibration approach to the microabsorption problem involving inorganic mixtures

Microabsorption may present a serious obstacle to performing accurate quantitative phase analysis by the Rietveld method for samples that contain phases with high X-ray absorption contrast. In this study, a multicomponent calibration approach is introduced to reduce the systematic bias that is not accounted for in conventional Rietveld analysis. In order to demonstrate this approach, six ternary inorganic mixtures containing components with diverse mass absorption coefficients were prepared. Two of the six mixtures were chosen as a calibration set to obtain the corresponding calibration parameters. These parameters were used to predict accurately the compositions of the remaining mixtures. Additionally, several other issues concerning sample preparation, the choice of the calibration set and the inclusion of complimentary techniques to determine the calibration parameters are addressed. The present approach offers practical advantages over the frequently used Brindley method, since it does not require any additional information concerning particle size and morphology.

Multipole electron-density modelling of synchrotron powder diffraction data: the case of diamond

Accurate structure factors are extracted from synchrotron powder diffraction data measured on crystalline diamond based on a novel multipole model division of overlapping reflection intensities. The approach limits the spherical-atom bias in structure factors extracted from overlapping powder data using conventional spherical-atom Rietveld refinement. The structure factors are subsequently used for multipole electron-density modelling, and both the structure factors and the derived density are compared with results from ab initio theoretical calculations. Overall, excellent agreement is obtained between experiment and theory, and the study therefore demonstrates that synchrotron powder diffraction can indeed provide accurate structure-factor values based on data measured in minutes with limited sample preparation. Thus, potential systematic errors such as extinction and twinning commonly encountered in single-crystal studies of small-unit-cell inorganic structures can be overcome with synchrotron powder diffraction. It is shown that the standard Hansen-Coppens multipole model is not flexible enough to fit the static theoretical structure factors, whereas fitting of thermally smeared structure factors has much lower residuals. If thermally smeared structure factors (experimental or theoretical) are fitted with a slightly wrong radial model (s(2)p(2) instead of sp(3)) the radial scaling parameters (kappa' parameters) are found to be inadequate and the ;error' is absorbed into the atomic displacement parameter. This directly exposes a correlation between electron density and thermal parameters even for a light atom such as carbon, and it also underlines that in organic systems proper deconvolution of thermal motion is important for obtaining correct static electron densities.

Comparison of short-range ion–ion correlations in the α, β and δ phases of Bi 2O 3

Neutron total scattering data for α-Bi 2O 3 and δ-Bi 2O 3, considering both the Bragg and diffuse components, have been analysed by the reverse Monte Carlo (RMC) method to extract experimental information concerning the short-range correlations between pairs of ions. These results complement the average structural information provided by conventional Rietveld refinement of the Bragg scattering alone. The radial and angular distribution functions in the stable ambient temperature α phase and superionic δ phase of Bi 2O 3 are presented and compared with the corresponding data for the metastable β phase reported previously. These data provide an important insight into the nature of the anion disorder within the highly conducting δ phase and the relationship between the δ phase and its ordered α and β counterparts.

Structure-property relationships of fast copper ion conductor cubic CuI

Structure-property relationships of fast copper ion conductor cubic γ-CuI (300 K) and α-CuI (773 K) has been investigated using the time-of-flight (TOF) neutro powder diffraction over the Q-range up to 30 Å − 1 . Crystal structure of the both γ- and α-phases were refined using the conventional Rietveld methods combined with the maximum-entropy-method (MEM), whilst the local structures were analyzed by means of the pair distribution function (PDF) combined with the reverse Monte Carlo (RMC) simulation. The crystal structure analysis revealed temperature dependence of large thermal displacement of copper ions along <111> directions, with average copper ions density mostly distributed at the 8 c center of tetrahedrally-coordinated by I ions. The PDF analysis estimated the new peak position of Cu–Cu pairs shifted from 4.27 Å in the γ-phase to 2.49 Å in the α-phase and estimation of coordination number decreases from 12.1 to 5.8, respectively. The local structure analysis found the new split peaks of g Cu–Cu( r) at r about 2.47 Å and 2.72 Å in the α-phase that roughly correspond to the Cu–Cu diagonally distance between nearest neighboring tetrahedral corner 32 f-32 f sites and between tetrahedral center 8 c-32 f sites such as represented by the splitting Cu site model of Fm-3m.

A method for quantitative pyrite abundance in mine rock piles by powder X-ray diffraction and Rietveld refinement

Abstract The abundance of pyrite and other sulfide minerals in mine rock piles is a potentially significant if not a determinative factor in terms of the geochemical and geomechanical evolution of the dumps as oxidation produces acid solutions that drive hydrolysis reactions. A technique is presented here that supports the quantitative determination of pyrite abundance in mine rock dumps by heavy liquid mineral separation to concentrate pyrite for powder X-ray diffraction and then Rietveld method refinement of the diffraction data on a large number of samples using commonly available laboratory equipment. In order to improve and constrain the accuracy of XRD results, binary (pyrite-quartz) and 6-part mineral mixtures (pyrite and rock-forming andesite minerals) spanning a wide range of pyrite concentrations were prepared gravimetrically and run as standards. These standards were then used to minimize errors in pyrite abundance data by constraining key input parameters in the Rietveld refinement. A new polynomial relationship was derived between diffracting crystallite size and the Brindley microabsorption correction input size. This method provides a means to determine uncertainties in pyrite abundance, whereas conventional Rietveld refinement techniques done without the use of standards yield only statistical measures of the least-squares fit, rather than absolute uncertainties in mineral constituent weight percentages. The technique was applied to a number of mine rock pile samples and the uncertainty in the results determined by applying the relationship derived from the 6-part gravimetric standards to the results of the Brindley corrected Rietveld refinements. Uncertainties determined by this method are found to be on the order of ±10% for samples with pyrite content greater than ∼10 wt% and ±30% for samples with pyrite content less than 10 wt%. In order to evaluate the technique’s improvement upon traditional visual mineral abundance estimation the quantitative results are compared to manual volumetric estimates.

A new crystalline phase of the boron-rich metal-boride family: the Mg 2B 25 species

A new complex magnesium boride, the Mg 2B 25 species, has been prepared and its crystal structure determined from laboratory X-ray powder diffraction data by the simulated annealing technique, followed by a conventional Rietveld refinement procedure. The title compound is R-centered trigonal (with a = 11.0402 ( 3 ) Å and c = 24.198 ( 1 ) Å , hexagonal setting), space group R-3m, and is isomorphous with β-boron and with the rhombohedral compounds of the boron-rich metal-boride family. The magnesium atoms occupy interstitial sites with partial occupancies which can be interpreted with the aid of the analysis of “forbidden” interatomic Mg Mg contacts. The Mg atom in the F site is vicariant with the B(4) atom and falls into a pseudometallocenic environment with the 10 nearest-neighbour B atoms; all other magnesium atoms are placed in lattice cavities within corrugated slabs normal to c, with Mg(D) and Mg(E) occupying sites already known to be populated in other metal borides, and Mg(N) in a new one. These slabs present two equiprobable, but self excluding, configurations of ordered Mg atoms, which randomly stack along the c-axis. Mg 2B 25 shows a significant increase of the c-axis of the rhombohedral lattice with respect to the other members of the family, which we attribute both to the larger metallic radius of Mg, vs. those of 3d transition metal atoms and to the anisotropic stacking of the Mg atoms, and, possibly, to the presence of the rather stuffed Mg sublattices.

Quantitative Rietveld analysis of CAC clinker phases using synchrotron radiation

The quantitative Rietveld analyses of twenty samples of CAC from four different manufacturers over the world, one synthetic mixture and a NIST standard were performed using synchrotron radiation. As compared with conventional XRD, synchrotron powder diffraction permitted to find new minor phases, improve the characterization of solid solutions of iron rich CAC phases and reduce preferential orientation and microabsorption effects. Diffraction data were complemented with XRF and TG/DT analyses. Synchrotron results were used as a reference test to improve the performance of conventional powder diffraction, by an accurate selection of refinable profile and structural parameters, and permitted to extract several recommendations for conventional quantitative Rietveld procedures. It is shown that with these recommendations in mind, conventional XRD based Rietveld analyses are comparable to those obtained from synchrotron data. In summary, quantitative XRD Rietveld analysis is confirmed as an excellent tool for the CAC cement industry.

Ferroelastic phase transitions and domain structures in powders

Abstract Powder patterns of samples resulting from ferroelastic phase transitions generally show typical line profiles: asymmetry into the direction of the position of the corresponding hypothetical high symmetry reflection and strongly anisotropic line broadening. An approximate model is presented that describes the characteristic distribution of individual line widths based on the variation of lattice spacings within the domain walls. The variation with temperature is governed by the competition of decreasing spontaneous strain and increasing wall widths and/or wall densities. It is argued that conventional Rietveld refinements can easily lead to erroneous results and a simplified method is proposed to approximate the actual line profiles via the introduction of a second phase with anisotropic strain broadening to take into account the scattering fom the domain walls.

Distribution of Fe&lt;sup&gt;3+&lt;/sup&gt; in a synthetic (Ca,Na)&lt;sub&gt;2&lt;/sub&gt;(Mg,Fe&lt;sup&gt;3+&lt;/sup&gt;)Si&lt;sub&gt;2&lt;/sub&gt;O&lt;sub&gt;7&lt;/sub&gt;-melilite: &lt;sup&gt;57&lt;/sup&gt;Fe M&amp;ouml;ssbauer and X-ray Rietveld studies

Crystal structure and the 57Fe Mossbauer spectrum of synthetic (Ca1.53Na0.47)(Mg0.52Fe3+0.49)Si1.99O7-melilite have been investigated to confirm the location of Fe3+ at the T1 site, and to evaluate the effect of an incommensurate structure on 57Fe Mossbauer hyperfine parameters. A conventional Rietveld refinement with occupancies of Ca(W), Na(W), Mg(T1), Fe3+(T1) and Si(T2) fixed to 0.765, 0.235, 0.515, 0.485 and 2.00, respectively, converged well with an Rwp (R-weighted pattern) of 13.14% and a goodness-of-fit of 1.337, indicating exclusive Fe3+ distribution at the T1 site. However, the Mossbauer spectrum consists of two doublets with an isomer shift of 0.19 mm/s and quadrupole splitting of 0.75 and 1.04 mm/s, which can be attributed to Fe3+ at the T1 site. There are two sorts of T1 site with distinguishable distortion in the synthetic Na-Fe3+-melilite, which might be attributed to the existence of an incommensurate phase at room temperature.

Structure Determination and Refinement of Acid Strontium Oxalate from X-Ray and Neutron Powder Diffraction

The structure of acid strontium oxalate Sr(HC2O4)·12(C2O4)·H2O has been determined by conventional X-ray powder diffractometry. The diffraction pattern was indexed from a monoclinic unit cell with cell parameters a=6.341(1) Å, b=16.880(2) Å, c=5.7798(8) Å, and β=97.60(1)°; space group, P21/n (No. 14) with Z=4. Final (isotropic) Rietveld refinement of the neutron powder data yielded RB=4.57%, RF=2.87%, and Rwp=7.87% as conventional Rietveld parameters. Strontium is eight-fold coordinated and can be described as a distorted bicapped trigonal prism. The SrO8 polyhedra form one-dimensional chains along the c-axis by sharing edges. In contrast to all other known strontium oxalates, in this compound H2O acts as bridging ligand between two Sr atoms. SDPD-D classification (1): Sr(HC2O4)-12(C2O4)-H2O, P21/n, C1=14, Nc=42, C2=11, XC1+N/TREOR-97 & DICVOL-91, EXTRA, EQUI, SIRPOW-92 (DM), GFOURIER, FULLPROF.

Synthesis of potassium cyanamide, and crystal structure determination by pareto optimisation of the cost functions ‘lattice energy’ and ‘powder intensities’

Abstract The synthesis of K2CN2 was carried out by reaction of potassium hydrogen cyanamide (KHCN2) with potassium amide (KNH2) in liquid ammonia. The crystal structure has been determined by global optimisation techniques using the lattice energy and the difference between observed and calculated X-ray intensities as cost functions, simultaneously. The structure refinement has been performed by conventional Rietveld profile fitting of X-ray powder data (monoclinic, C 2/m, a=5.7877(1), b=5.7030(1), c=5.7857(2) A; β=109.016(1) °; Z=2). The CN22− units are linear exhibiting a C–N bond length of 1.234(2) A, while potassium is coordinated by five nitrogen atoms forming a square pyramid. The structural relationships to aristotypic K2NiO2 are pointed out.

多目的パターン・フィッティングシステムＲＩＥＴＡＮ‐２０００とその微細孔物質への応用

A heavy-duty system of high performance, RIETAN-2000, has recently been developed for Rietveld refinement, Le Bail refinement, whole-pattern fitting based on a maximum-entropy method (MEM), and individual profile fitting. An original feature called partial profile relaxation is applicable to (nearly) isolated reflections with relatively large residuals, which leads to better fits in these reflections. The state-of-the-art technology of MEM-based wholepattern fitting allows us to represent positional disorder, chemical bonds, and anharmonic thermal motion more adequately than the conventional Rietveld method. Four examples of applying RIETAN-2000 to microporous materials are introduced to demonstrate its high ability to analyze structural details.

Fourier modelling of the anisotropic line broadening of X-ray diffraction profiles due to line and plane lattice defects

A new model of line-profile broadening due to the effect of linear and planar lattice defects has been incorporated into the conventional Rietveld algorithm for the structural refinement and whole-pattern fitting of powder data. The proposed procedure, applied to face-centred cubic (f.c.c.) structure materials, permits better modelling, even in the case of anisotropic line broadening and otherhkl-dependent effects that can be related to the presence of dislocations and planar defects (stacking faults and twinning). Besides better quality of the profile fitting, detailed information on the defect structure can be produced: dislocation density and cut-off radius, stacking- and twin-fault probabilities can be refined together with the structural parameters. For each phase (in different samples or in multi-phase samples) the appropriatesize–strainmodel can be selected. The Fourier formalism, which is the basis of the line-profile modelling, also permits an easy adaptation to different lattice-defect models. New approaches can be easily introduced and tested against or together with the existing ones. Finally, the devised program can also be used for the simulation of powder patterns for materials with different types and amounts of line and plane lattice defects.

Synchrotron and Conventional X-Ray Rietveld Study of Clouded Plagioclase from Southern Sweden

Synchrotron and Conventional X-Ray Rietveld Study of Clouded Plagioclase from Southern Sweden