Journal articles: 'Rietveld method'

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Rietveld, Hugo M. "The Rietveld method." Physica Scripta 89, no. 9 (August 1, 2014): 098002. http://dx.doi.org/10.1088/0031-8949/89/9/098002.

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Sleight, A. W. "The Rietveld method." Materials Research Bulletin 29, no. 6 (June 1994): 695. http://dx.doi.org/10.1016/0025-5408(94)90128-7.

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Dünkel, L. "The Rietveld Method." Zeitschrift für Physikalische Chemie 196, Part_2 (January 1996): 280–81. http://dx.doi.org/10.1524/zpch.1996.196.part_2.280.

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Rietveld, H. M. "The Rietveld Method: A Retrospection." Zeitschrift für Kristallographie 225, no. 12 (December 2010): 545–47. http://dx.doi.org/10.1524/zkri.2010.1356.

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Oishi-Tomiyasu, R., M. Yonemura, T. Morishima, A. Hoshikawa, S. Torii, T. Ishigaki, and T. Kamiyama. "Application of matrix decomposition algorithms for singular matrices to the Pawley method inZ-Rietveld." Journal of Applied Crystallography 45, no. 2 (March 15, 2012): 299–308. http://dx.doi.org/10.1107/s0021889812003998.

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Z-Rietveldis a program suite for Rietveld analysis and the Pawley method; it was developed for analyses of powder diffraction data in the Materials and Life Science Facility of the Japan Proton Accelerator Research Complex. Improvements have been made to the nonlinear least-squares algorithms ofZ-Rietveldso that it can deal with singular matrices and intensity non-negativity constraints. Owing to these improvements,Z-Rietveldsuccessfully executes the Pawley method without requiring any constraints on the integrated intensities, even in the case of severely or exactly overlapping peaks. In this paper, details of these improvements are presented and their advantages discussed. A new approach to estimate the number of independent reflections contained in a powder pattern is introduced, and the concept of good reflections proposed by Sivia [J. Appl. Cryst.(2000),33, 1295–1301] is shown to be explained by the presence of intensity non-negativity constraints, not the intensity linear constraints.

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Wiessner, Manfred, and Paul Angerer. "Bayesian approach applied to the Rietveld method." Journal of Applied Crystallography 47, no. 6 (October 17, 2014): 1819–25. http://dx.doi.org/10.1107/s1600576714020196.

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The application of the Rietveld method for lattice constant and crystal structure refinement has been undertaken with great success. More routinely, this method is used to estimate quantitative phase amounts and to get information on the coherent diffracting length and the lattice defect density. In this paper an innovative combination of the Rietveld method with the Bayes approach is presented, to obtain directly the distribution of the refined parameters from a measured diffractogram, while the conventional Rietveld technique enables only the deduction of the most probable parameter and the estimation of its precision by confidence intervals. Furthermore, the goal of this work is to promote the development of a robust and automatable Rietveld algorithm. A detailed description of the modified algorithm is presented. Such a modified Rietveld approach is applied to anin situhigh-temperature experiment on a steel sample, including the temperature-dependent α → γ phase transformation reaction during heating and the martensitic transformation during the cooling phase.

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Balić-Žunić, T. "Quantitative powder diffraction phase analysis with a combination of the Rietveld method and the addition method." Powder Diffraction 17, no. 4 (December 2002): 287–89. http://dx.doi.org/10.1154/1.1523872.

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The Rietveld method can be combined with the addition method to determine the absolute quantities of the phases treated by Rietveld refinement plus the quantity of phase(s) not treated by it (amorphous or unobserved). If q is the added proportion of a defined phase already present in the sample, and a1 and a2 its relative proportions as determined by Rietveld refinement prior and after the addition, the proportion of the amorphous (untreated) phase(s) in the original sample is calculated as xo=[a2−(1−q)a1−q]/(1−q)(a2−a1). The absolute quantities of the phases treated by Rietveld refinement are then determined by a correction for the content of the amorphous phase(s), or they can be calculated directly from specific equations. The advantage of the method is that no new variables are introduced in the refinement when the added standard already is a part of the original mixture.

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Schneider, J. "Rietveld method runs on IBM-AT." Acta Crystallographica Section A Foundations of Crystallography 43, a1 (August 12, 1987): C295. http://dx.doi.org/10.1107/s0108767387077535.

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Mitra, G. B., and P. Das Gupta. "The Rietveld method – an alternative approach." Acta Crystallographica Section A Foundations of Crystallography 43, a1 (August 12, 1987): C236. http://dx.doi.org/10.1107/s0108767387079170.

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Rietveld, HM. "The Rietveld Method ? A Historical Perspective." Australian Journal of Physics 41, no. 2 (1988): 113. http://dx.doi.org/10.1071/ph880113.

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differences between observed and calculated values was already well established in crystallography. From there it was, in retrospect, only a small step to refrain from using the integrated intensities as observed values but to use the actual measured profile intensities obtained by step scanning the powder diagram. The Rietveld method was first reported at the I.U.Cr. congress in Moscow in 1966. However, it was not until 1975, when it was also applied to X-ray diffraction, that it became widely accepted. Nowadays its use is no longer confined to elastic neutron powder diffraction, but to all diffraction techniques producing complex diffraction diagrams.

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Taylor, J. C., I. Hinczak, and C. E. Matulis. "Rietveld full-profile quantification of Portland cement clinker: The importance of including a full crystallography of the major phase polymorphs." Powder Diffraction 15, no. 1 (March 2000): 7–18. http://dx.doi.org/10.1017/s0885715600010769.

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Crystalline phases present in the three NIST SRM Standard Portland cement clinkers 8486, 8487, and 8488 have been quantified from XRD powder patterns, (CoKα radiation), using the full-profile Rietveld method. Included in the Rietveld refinement are rhombohedral (R), monoclinic (M), and triclinic (T) crystal polymorphic forms of C3S, as well as crystal polymorphs of C2S and C3A. It is necessary to specify the phase crystallography including polymorphs, because of the extreme superposition of alite and belite XRD lines in the clinker patterns. Unsatisfactory results occur when only one or two of the C3S polymorphs are used in the Rietveld quantification; best results occur when all three polymorphs for C3S are included. The latter are called RMT-type refinements. The Rietveld full-profile XRD method is as precise as the microscope point-counting (MPC) method, but much less labor-intensive. The Rietveld method can quantify the C3S phase polymorphs, as well as total C3S. Rietveld and MPC methods give the same phase weight percentages for the three NIST standard clinkers. Calculated oxide weight percentages obtained from Rietveld phase weight percentages agree well with oxide percentages determined by XRF analysis. Bogue mineral weight percentages do not agree with Rietveld or MPC data, while transformation of the Bogue mineral percentages to oxides does not compare well with XRF analysis.

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Takata, Masaki, Eiji Nishibori, Yoshiki Kubota, and Hiroshi Tanaka. "Nanoporous Structural Science Developed by the MEM/Rietveld Method." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C1467. http://dx.doi.org/10.1107/s2053273314085325.

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Wide-spread functionalization research of Metal Organic Frameworks(MOFs) has brought rapid increase in variety of materials since the beginning of structural study in nanoporous of MOFs were made by SR(Synchrotron Radiation) powder diffraction using the MEM(Maximum Entropy Method)/Rietveld Method(Kitaura et al, 2002). The MEM/Rietveld method has successfully applied to refine the structural position of absorbed molecules and to investigate a bonding nature between the molecules and MOF's pore walls. Noise-resistance electron density mapping with incomplete data set was a key advantage of MEM to visualize unmodeled feature of molecules in nanoporous. Since then, the charge density studies by the MEM/Rietveld Method have uncovered various ordering structure of absorbed molecules into nanoporous more and more(Takata, 2008). Those findings ignited trends to design the nanoporous as the space to be functionalized. Recently, the MEM/Rietveld method has been further developed as the method to map an electrostatic potential and electric field(Tanaka 2006). This technique is making a progress in structural science of MOFs since the visualized electrostatic potential in the nanoporous ought to provide information of interplay between the molecule and the pore walls. The talk will present the recent progress and challenges of the MEM/Rietveld method to the structural science of the MOFs.

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Calligaris, Guilherme, Ana Paula Ribeiro, Adenilson dos Santos, and Lisandro Cardoso. "Rietveld Method Applied for Triacylglycerol Polymorphism Analysis." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C1764. http://dx.doi.org/10.1107/s2053273314082357.

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The characterization of the fat components becomes very useful in the formulation of shortening, margarines and fatty products due to their unique properties of plasticity, texture, solubility and aeration. The qualitative analysis obtained by X-ray diffraction (XRD) can be further improved in order to fulfill the lack of information on the triacylglycerol (TAG) in the hardfat systems aiming a complete polymorph characterization. In this work, as an attempt to quantify the distinct β and β' TAG polymorphs, XRD was combined with Rietveld refinement method and applied to two types of samples: mixtures (M) and blended hardfats (B) samples involving fully hydrogenated of soybean (FHSO) and palm (FHPO) oils. M-samples were prepared with linear concentrations of FHSO (β) and FHPO (β') and their Rietveld analysis have provided the expected content trend through the involved polymorphic phases with a very good agreement (~5%). This result validates the Rietveld method applicability on this kind of materials. The Rietveld method applied for B-samples has shown that β' polymorphic form prevails over the β-form, even for samples originally prepared with FHSO (β)/FHPO (β') = 60/40 ratio (see figure). This result indicates the influence of the seeding process (earlier crystallization of β' phase). This first quantitative approach for blended samples represents a very useful contribution towards the full characterization of fats.

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Ran, Xu, Jun Guo Ran, Li Gou, Ji Yong Chen, and Jiao Min Luo. "Structure of Carbonated Hydroxyapatite Based on Rietveld Method." Key Engineering Materials 368-372 (February 2008): 1187–89. http://dx.doi.org/10.4028/www.scientific.net/kem.368-372.1187.

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The crystalline structures of B-type carbonated hydroxyapatite (CHA) powders sintered at 700, 900 and 1100°C, respectively, were studied by Rietveld analysis of powder X-ray diffraction (XRD) data. A series of structure parameters, including lattice parameters (a and c), bond length and the distortion index of PO4 tetrahedron (Dind) were calculated by Rietveld method to characterize the fine structure of CHA. The broadening effect of XRD reflections was separated to calculate the micro-strain and crystalline size. The results showed that CHA become more stable with the increase of sintering temperature, but the CO3 2- is almost lost at temperature of 1100°C. The quantitative results about crystal structure of CHA based on crystalline structure simulated by Rietveld method are obtained.

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Scardi, Paolo, Matteo Ortolani, and Matteo Leoni. "WPPM: Microstructural Analysis beyond the Rietveld Method." Materials Science Forum 651 (May 2010): 155–71. http://dx.doi.org/10.4028/www.scientific.net/msf.651.155.

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The basics of the Whole Powder Pattern Modeling and its implementation in the PM2K software are briefly reviewed. The main features and functionalities, and most common line broadening models are introduced with the aid of working examples related to the instrumental profile and to a plastically deformed metal. A summary of the main expressions is reported in the appendix, together with a list of useful references.

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David, W. I. F., Matteo Leoni, and Paolo Scardi. "Domain Size Analysis in the Rietveld Method." Materials Science Forum 651 (May 2010): 187–200. http://dx.doi.org/10.4028/www.scientific.net/msf.651.187.

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The implementation of a physically-sound size broadening model for peak profiles in the Rietveld method is presented. TOPAS macros are provided and the results compared with analogous modelling performed according to advanced analysis methods such as the Whole Powder Pattern Modelling.

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Scardi, Paolo. "Diffraction Line Profiles in the Rietveld Method." Crystal Growth & Design 20, no. 10 (August 21, 2020): 6903–16. http://dx.doi.org/10.1021/acs.cgd.0c00956.

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Blanton, Tom. "Hugo Rietveld, the Person and the Method." Powder Diffraction 31, no. 4 (December 2016): 257–58. http://dx.doi.org/10.1017/s0885715616000567.

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Bish, D. L., and S. A. Howard. "Quantitative phase analysis using the Rietveld method." Journal of Applied Crystallography 21, no. 2 (April 1, 1988): 86–91. http://dx.doi.org/10.1107/s0021889887009415.

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Young, R. A. "International Workshop on the Rietveld Method (RW2000PL)." Powder Diffraction 16, no. 1 (March 2001): 48. http://dx.doi.org/10.1154/1.1490544.

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Hill, R. J. "Expanded Use of the Rietveld Method in Studies of Phase Abundance in Multiphase Mixtures." Powder Diffraction 6, no. 2 (June 1991): 74–77. http://dx.doi.org/10.1017/s0885715600017036.

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AbstractSimple relationships exist between the individual phase scale factors derived from Rietveld analysis of multiphase mixtures and (i) the ‘reference intensity ratio’ used in traditional methods of discrete-peak phase analysis, (ii) the phase abundance itself and (iii) the relative pattern intensities in simulated powder patterns. These relationships are shown to follow naturally from the fundamental integrated-intensity phase-analysis equations provided in standard texts. In the event that preferred orientation, crystallinity, extinction and/or microabsorption cannot be adequately incorporated into the Rietveld models for individual phases, it is demonstrated that the Rietveld ab initio ‘pattern intensity constants’ can be scaled/calibrated experimentally, as in other whole-pattern methods of analysis, while retaining all the advantages of the Rietveld method.

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Toraya, Hideo. "Profile fitting method, whole-powder-pattern decomposition method and rietveld method." Bulletin of the Japan Institute of Metals 28, no. 3 (1989): 189–94. http://dx.doi.org/10.2320/materia1962.28.189.

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Feret, Frank R. "Selected applications of Rietveld-XRD analysis for raw materials of the aluminum industry." Powder Diffraction 28, no. 2 (May 2, 2013): 112–23. http://dx.doi.org/10.1017/s088571561300016x.

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In the last few decades, X-ray diffraction (XRD) systems have been paramount and irreplaceable in controlling bauxite exploration, as well as Bayer and reduction processes. XRD quantitative phase analysis in the aluminum industry witnessed a steady deployment of the Rietveld method, which at present progressively replaces existing methodologies in research and plant laboratories. Rietveld analysis not only helped to surpass traditional XRD calibration methods, it also opened the door for new applications previously not possible. The use of the Rietveld method to characterize selected materials unique to the aluminum industry, such as bauxite, red mud, and alumina is demonstrated and discussed. This paper also presents how synchrotron-based diffractograms obtained for bauxite and red mud samples allowed a much better understanding of mineralogical representation, and made it possible to leverage their Rietveld quantification. Despite clear advantages, the Rietveld method also has limitations that are revealed. For alumina phase quantification, a dedicated Rietveld analytical program was built with structure data for eight alumina mineralogical phases: alpha, beta (β-Al2O3 = Na2O•11Al2O3), delta, gamma (2), kappa, sigma, and theta. The paper gives unique examples of phase quantification in aluminas of various origins and phase composition.

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Stinton, Graham W., and John S. O. Evans. "Parametric Rietveld refinement." Journal of Applied Crystallography 40, no. 1 (January 12, 2007): 87–95. http://dx.doi.org/10.1107/s0021889806043275.

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In this paper the method of parametric Rietveld refinement is described, in which an ensemble of diffraction data collected as a function of time, temperature, pressure or any other variable are fitted to a single evolving structural model. Parametric refinement offers a number of potential benefits over independent or sequential analysis. It can lead to higher precision of refined parameters, offers the possibility of applying physically realistic models during data analysis, allows the refinement of `non-crystallographic' quantities such as temperature or rate constants directly from diffraction data, and can help avoid false minima.

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Lesniewski, Joseph E., Steven M. Disseler, Dylan J. Quintana, Paul A. Kienzle, and William D. Ratcliff. "Bayesian method for the analysis of diffraction patterns usingBLAND." Journal of Applied Crystallography 49, no. 6 (December 1, 2016): 2201–9. http://dx.doi.org/10.1107/s1600576716016423.

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Rietveld refinement of X-ray and neutron diffraction patterns is routinely used to solve crystal and magnetic structures of organic and inorganic materials over many length scales. Despite its success over the past few decades, conventional Rietveld analysis suffers from tedious iterative methodologies, and the unfortunate consequence of many least-squares algorithms discovering local minima that are not the most accurate solutions. Bayesian methods which allow the explicit encoding ofa prioriknowledge pose an attractive alternative to this approach by enhancing the ability to determine the correlations between parameters and to provide a more robust method for model selection. Global approaches also avoid the divergences and local minima often encountered by practitioners of the traditional Rietveld technique. The goal of this work is to demonstrate the effectiveness of an automated Bayesian algorithm for Rietveld refinement of neutron diffraction patterns in the solution of crystallographic and magnetic structures. A new software package,BLAND(Bayesian library for analyzing neutron diffraction data), based on the Markov–Chain Monte Carlo minimization routine, is presented. The benefits of such an approach are demonstrated through several examples and compared with traditional refinement techniques.

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Stacey, P. "A study to assess the performance of an “X-ray powder diffraction with Rietveld” approach for measuring the crystalline and amorphous components of inhalable dust collected on aerosol sampling filters." Powder Diffraction 34, no. 3 (May 21, 2019): 251–59. http://dx.doi.org/10.1017/s0885715619000423.

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This work was undertaken in preparation for a survey to assess the exposure of carpenters to hazardous dust working in construction. Inhalable dust, in this industry, was expected to contain both crystalline mineral and amorphous phases (wood dust). The Rietveld method was applied to provide a simultaneous multicomponent analysis. To assess its performance, mixtures of aerosolised calcite, gypsum, quartz, kaolinite, and wood dust were collected onto quartz fibre filters (n = 41) using the Button inhalable sampler. Results obtained using Rietveld were compared with loaded mass and those from external standard calibrations. The measured content of a component in 14 samples was used as an internal standard by Rietveld to determine amorphous content (wood). The performance of the Rietveld and external standard methods was similar. The 95% confidence interval for the absolute differences between the two methods was 15%. Only one relative difference of more than 15% had a mass loading >0.5 mg. An approach for assessing the limits of detection with relative intensity ratios was applied and gave comparable values with the usual method using calibration coefficients from the external standard method. Rietveld is therefore a potentially useful multicomponent method for the measurement of dust aerosol to help better understand workers' exposures.

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Negrão, Leonardo, and Herbert Pöllmann. "THE PHASE ADDITION METHOD TO EVALUATE RIETVELD MINERAL QUANTITATIVE ANALYSIS OF HYDRATED CEMENTS." BOLETIM DO MUSEU DE GEOCIÊNCIAS DA AMAZÔNIA 7 (2020), no. 2 (December 1, 2020): 1–7. http://dx.doi.org/10.31419/issn.2594-942x.v72020i2a3lban.

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X-ray powder diffraction (XRPD) analysis combined with the Rietveld method is commonly used in the mineralogical quantification of a range of different samples, including soil, rocks, and many industrial materials. The combination of this technique with the addition method, i.e. the successive addition of a mineral phase to the investigated sample, offers a simple and reliable method to test Rietveld results without the need for third techniques. Four different hydrated cement samples were successive mixed (at 1, 5, and 10%) with one of the main mineral-related phases (ettringite, larnite, ternesite, or ye’elimite) occurring in them. The Rietveld quantified amounts of these phases show a very good agreement with their added amounts, all resulting in regression lines with R2>0.99. The respective line equations permitted the calibration of the quantified amounts of the studied mineral phases, which presented standard deviations lower than 0.3. Keywords: Rietveld; addition method; hydrated cement, calcium sulphoaluminate.

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McCusker, L. B., R. B. Von Dreele, D. E. Cox, D. Louër, and P. Scardi. "Rietveld refinement guidelines." Journal of Applied Crystallography 32, no. 1 (February 1, 1999): 36–50. http://dx.doi.org/10.1107/s0021889898009856.

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A set of general guidelines for structure refinement using the Rietveld (whole-profile) method has been formulated by the International Union of Crystallography Commission on Powder Diffraction. The practical rather than the theoretical aspects of each step in a typical Rietveld refinement are discussed with a view to guiding newcomers in the field. The focus is on X-ray powder diffraction data collected on a laboratory instrument, but features specific to data from neutron (both constant-wavelength and time-of-flight) and synchrotron radiation sources are also addressed. The topics covered include (i) data collection, (ii) background contribution, (iii) peak-shape function, (iv) refinement of profile parameters, (v) Fourier analysis with powder diffraction data, (vi) refinement of structural parameters, (vii) use of geometric restraints, (viii) calculation of e.s.d.'s, (ix) interpretation ofRvalues and (x) some common problems and possible solutions.

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David, William I. F. "On the equivalence of the Rietveld method and the correlated integrated intensities method in powder diffraction." Journal of Applied Crystallography 37, no. 4 (July 17, 2004): 621–28. http://dx.doi.org/10.1107/s0021889804013184.

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The Rietveld method is the most straightforward and statistically correct approach for the refinement of crystal structure parameters from powder diffraction data. The equivalent two-stage approach, involving the refinement of structural parameters based on integrated intensities extracted using the Pawley method, is extremely useful in circumstances such as the global optimization methods of structure determination, where a great many refinements need to be performed very quickly. The equivalence is emphasized in a simple mathematical relationship between the goodness of fits obtained in Rietveld, Pawley and correlated integrated intensities refinements. A rationale is given for determining the estimated standard deviations for structural variables from powder diffraction data.

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Wang, Xiaoli, and Hejing Wang. "Structural Analysis of Interstratified Illite-Smectite by the Rietveld Method." Crystals 11, no. 3 (February 28, 2021): 244. http://dx.doi.org/10.3390/cryst11030244.

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Rietveld method is a powerful tool in obtaining structural information of clay minerals by using of X-ray diffraction (XRD) patterns. However, the interstratified illite-smectites (I-S) show various stacking defects preventing the direct application of this method. It was shown that the Rietveld method combined with a recursive structure-factor calculation can be used for describing the stacking disorder of I-S. In this study, a series of samples with different stacking sequences and different proportions of layer types were chosen to verify the applicability of Rietveld method in determination of structural parameters of I-S. The Rietveld refinements were carried out on powder samples and oriented specimens in air-dry (AD) and ethylene glycol (EG) state. The structural information obtained by X-ray fluorescence (XRF) and thermal analysis were used as an independent test of the reliability of the refinements. The refined and experimental results were compared systematically and the relationship between structural parameter was discussed. For powder and oriented specimens, the refined results of occupancies of potassium and iron and the proportion of illitic layers showed consistent results. The refined value of cis-vacant layers was in good agreement with the experimental data. The reliability of the refinements increased with increasing proportion of illitic layers.

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Martin, Joannie, Martin Beauparlant, Jacques Lesage, and Huu Van Tra. "Development of a quantification method for quartz in various bulk materials by X-ray diffraction and the Rietveld method." Powder Diffraction 27, no. 1 (March 2012): 12–19. http://dx.doi.org/10.1017/s0885715612000036.

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Crystalline silica is known for its health hazards, and since 1997 has been listed as Group 1, Carcinogenic to Humans, by the International Agency for Research on Cancer. This issue is particularly important in the industrial environment, and there is still no method that allows quantification of the different polymorphs of crystalline silica. Many analytical methods have been proposed, and the major problem in almost all cases is attributable to the very large variety of matrixes encountered. This study evaluates the potential of X-ray diffraction techniques and an automated Rietveld analysis in order to overcome this problem and to adapt the quantitative analysis of quartz, the most prevalent crystalline silica polymorph, to routine analysis in the health and safety environment. Matrix simulations are done and many parameters are optimized. Sample preparation, the acquisition program, pattern treatment, and Rietveld refinement are evaluated, and a general procedure is determined. Automation of Rietveld refinement leads to a significant reduction in analysis time, but cannot be applied to every type of sample.

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HASHIZUME, Daisuke. "Structure Refinements of Organic Crystal Using Rietveld Method." Nihon Kessho Gakkaishi 53, no. 5 (2011): 299–306. http://dx.doi.org/10.5940/jcrsj.53.299.

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Hušák, M., and J. Had. "Quantitative Analysis of Organic Compounds by Rietveld Method." Materials Science Forum 166-169 (July 1994): 745–48. http://dx.doi.org/10.4028/www.scientific.net/msf.166-169.745.

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Sagawa, T. "Quantitative Hydration Analysis of Concrete by Rietveld Method." Concrete Journal 56, no. 5 (2018): 448–53. http://dx.doi.org/10.3151/coj.56.5_448.

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Lutterotti, Luca, Henry Pillière, Christophe Fontugne, Philippe Boullay, and Daniel Chateigner. "Full-profile search–match by the Rietveld method." Journal of Applied Crystallography 52, no. 3 (May 14, 2019): 587–98. http://dx.doi.org/10.1107/s160057671900342x.

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A new search–match procedure has been developed and tested which, in contrast to previously existing methods, does not use a set of lines identified from a diffraction pattern, but an optimized Rietveld fitting on the raw data. Modern computers with multicore processors allow the routine to be fast enough to perform the entire search in a reasonable time using quite large databases of crystal structures. The search–match is done using the crystal structures for all phases and the instrumental geometry, and as such can be applied to every kind of diffraction experiment, including X-rays, thermal/time-of-flight neutrons and electrons. The methodology can also be applied to nanocrystalline samples for which peak identification may be a problem. A web interface has been developed to permit easy testing and evaluation of the procedure. The quality of the results mainly depends on the availability of the sought phase in the structure database. The method permits not only phase identification but also a rapid quantification of the phases and their gross microstructural features, provided the instrumental function is known.

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Khan, R. T. A., J. Bashir, N. Iqbal, and M. Nasir Khan. "Crystal structure of LaVO3 by Rietveld refinement method." Materials Letters 58, no. 11 (April 2004): 1737–40. http://dx.doi.org/10.1016/j.matlet.2003.10.059.

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Baricco, M., S. Enzo, T. A. Baser, M. Satta, G. Vaughan, and A. R. Yavari. "Amorphous/nanocrystalline composites analysed by the Rietveld method." Journal of Alloys and Compounds 495, no. 2 (April 2010): 377–81. http://dx.doi.org/10.1016/j.jallcom.2009.11.024.

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Li, Hua, Jia Ping Liu, and Wei Sun. "Quantitative Analysis of Cement-Based Materials and Sulfate Attack Products by XRD-Rietveld Analysis." Applied Mechanics and Materials 357-360 (August 2013): 1362–69. http://dx.doi.org/10.4028/www.scientific.net/amm.357-360.1362.

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XRD-Rietveld method has been adopted for quantitative analysis of phases in cement powder, phases in mixed samples of cement and pure calcium hydroxide, and sulfate attack products in cement pastes, based on the TOPAS software. The results show that, Rietveld analysis values show good agreement with the actual levels of mixed samples, and the accuracy degree of Rietveld method is at least as well as that of TG/DSC method which is commonly used in quantitative analysis of calcium hydroxide. By adding appropriate internal standard substance, XRD-Rietveld analysis method can be effectively used in quantitative analysis of sulfate attack products in cement-based materials. This work has practical significance on the study of sulfate attack of cement-based material.

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Zeitler, Todd R., and Brian H. Toby. "Parallel processing for Rietveld refinement." Journal of Applied Crystallography 35, no. 2 (March 22, 2002): 191–95. http://dx.doi.org/10.1107/s0021889802000109.

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A method for speeding Rietveld refinements using parallel computing is presented. The method can be applied to most, if not all, Rietveld refinement programs. An example implementation for the Los AlamosGeneral Structure Analysis System(GSAS) package is described. Using a cluster with seven processors, least-squares refinements are completed 2.5 to 5 times faster than on an equivalent single-processor computer.

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Ida, Takashi, and Fujio Izumi. "Analytical method for observed powder diffraction intensity data based on maximum likelihood estimation." Powder Diffraction 28, no. 2 (April 16, 2013): 124–26. http://dx.doi.org/10.1017/s0885715613000195.

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A new methodology based on maximum likelihood estimation for structure refinement using powder diffraction data is proposed. The method can not only optimize the parameters adjusted in Rietveld refinement but also parameters to specify errors in a model for statistical properties of the observed intensity. The results of structure refinements with relation to fluorapatite Ca5(PO4)3F, anglesite PbSO4, and barite BaSO4 are demonstrated. The structure parameters of fluorapatite and barite optimized by the new method are closer to single-crystal data than those optimized by the Rietveld method, while the structure parameters of anglesite, whose values optimized by the Rietveld method are already in good agreement with the single-crystal data, are almost unchanged by the application of the new method.

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Ibanez, Jordi, Jose Fernandez-Turiel, Josep Elvira, Marta Rejas, and Soledad Alvarez. "Fast quantitative analysis of the amorphous content with the Rietveld method." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C949. http://dx.doi.org/10.1107/s2053273314090500.

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The characterization of the mineralogy and chemical composition of multi-phase mixtures is of chief importance in many different contexts, from industry to basic research. In the case of industrial processes, it is often necessary to perform fast and reliable quantitative phase analyses (QPAs) in large amounts of samples that contain amorphous phases. Rietveld refinement from powder x-ray diffraction (XRD) data is widely employed for this purpose. The quantification of the amorphous content with the Rietveld method is usually performed by spiking the samples with an internal standard, and this implies increased processing times. Alternatively, in samples exhibiting the typical, broad XRD signal from the amorphous (glassy) matrix, a poorly-crystalline structure can be used to represent the amorphous phase during the Rietveld analysis [1]. This procedure provides highly consistent data, but is limited because the particular crystal structure used for the QPAs is strongly sample dependent. Recently, it has been shown that fast Rietveld QPAs of coal fly ashes can be carried out with no sample spiking by initially calibrating the XRD signal from the glass [2]. In this work, we evaluate the usefulness of the calibration Rietveld-based approach on two different types of samples: fly ashes from coal combustion plants, and volcanic ashes. While the mineralogy of the fly ashes considered here is relatively simple (they mainly contain quartz, mullite and glass), the volcanic ashes contain sizable amounts of crystalline compounds with both simple and complex structures, including quartz, feldspars, biotite, pyroxene or iron oxides. We show that the calibration approach provides a suitable method to assess in a fast and consistent manner the amount of crystalline and amorphous phases in both types of samples. This method may be extended to industrial characterization processes involving large numbers of complex samples, reducing considerably the analytical times.

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Brinatti, André Maurício, Yvonne Primerano Mascarenhas, Vitor Paulo Pereira, Carmen Silvia de Moya Partiti, and Álvaro Macedo. "Mineralogical characterization of a highly-weathered soil by the Rietveld Method." Scientia Agricola 67, no. 4 (August 2010): 454–64. http://dx.doi.org/10.1590/s0103-90162010000400013.

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The mineralogical characterization through mineral quantification of Brazilian soils by X-ray diffraction data using the Rietveld Method is not common. A mineralogical quantification of an Acric Ferralsol from the Ponta Grossa region, state of Paraná, Brazil, was carried out using this Method with X-Ray Diffraction data to verify if this method was suitable for mineral quantification of a highly-weathered soil. The A, AB and B3 horizons were fractioned to separate the different particle sizes: clay, silt, fine sand (by Stokes Law) and coarse sand fractions (by sieving), with the procedure free of chemical treatments. X-ray Fluorescence, Inductively Coupled Plasma Atomic Emission Spectrometry, Infrared Spectroscopy and Mössbauer Spectroscopy were used in order to assist the mineral identification and quantification. The Rietveld Method enabled the quantification of the present minerals. In a general way, the quantitative mineralogical characterization by the Rietveld Method revealed that quartz, gibbsite, rutile, hematite, goethite, kaolinite and halloysite were present in the clay and silt fractions of all horizons. The silt fractions of the deeper horizons were different from the more superficial ones due to the presence of large amounts of quartz. The fine and the coarse sand fractions are constituted mainly by quartz. Therefore, a mineralogical quantification of the finer fraction (clay and silt) by the Rietveld Method was successful.

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Zeng, Wei Jin, Chao Zeng, and Wei He. "Quantitative Phase Analyses of a Slag Using X-Ray Powder Diffraction." Advanced Materials Research 881-883 (January 2014): 1241–44. http://dx.doi.org/10.4028/www.scientific.net/amr.881-883.1241.

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The quantitative phase analyses of a slag have been successfully carried out by using both of the full-profile Rietveld and RIR methods from X-ray powder diffraction data. The qualitative phase analysis indicates that the slag contains mayenite (CaO)12(Al2O3)7, olivine Ca2(SiO4), gehlenite Ca2Al (AlSiO7), lemite Ca2(SiO4) and hibonite CaO(Al2O3)6. The quantitative analysis from Rietveld refinement shows that the weight concentrations of mayenite, olivine, gehlenite, lemite and hibonite for the slag are 48.8(4) wt.%, 32.2(5) wt.%, 11.0(9) wt.%, 6.2(1.1) wt.% and 1.8 (1.2) wt.%, respectively. The quantitative phase analysis results obtained by Rietveld method are more precise then those by RIR method.

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Kaduk, James A. "A Rietveld tutorial—Mullite." Powder Diffraction 24, no. 4 (December 2009): 351–61. http://dx.doi.org/10.1154/1.3257610.

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The crystal structure of the mullite in a commercial material was refined by the Rietveld method using laboratory X-ray powder diffraction data. In this one refinement, most of the common challenges—including variable stoichiometry (partially occupied sites), multiple impurity phases, amorphous material, constraints, restraints, correlation, anisotropic profiles, microabsorption, and contamination during grinding—are encountered and the thought processes during the refinement are described step-by-step. Interpretation of the refinements includes bulk chemical analysis, chemical composition of the mullite, assessment of the geometry, bond valence sums, the displacement coefficients, crystallite size and microstrain, comparison to similar structures to assess chemical reasonableness, and the nature of the amorphous phase.

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Missyul, Alexander, Ivan Bolshakov, and Roman Shpanchenko. "XRD study of phase transformations in lithiated graphite anodes by Rietveld method." Powder Diffraction 32, S1 (May 9, 2017): S56—S62. http://dx.doi.org/10.1017/s0885715617000458.

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Commercial anodes with different state of charge are investigated by X-ray diffraction technique using Rietveld method for data collected with standard laboratory equipment. It is shown that full profile refinement gives good approximation for quantitative description of the charge/discharge process and may be used for estimation of real state of charge (SoC). Careful analysis of the diffraction profile with Rietveld method allows us to quantitatively distinguish the contribution of different LixC6 phases and estimate the real SoC.

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Gualtieri, A. "Modal analysis of pyroclastic rocks by combined Rietveld and RIR methods." Powder Diffraction 11, no. 2 (June 1996): 97–106. http://dx.doi.org/10.1017/s0885715600009052.

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The modal analysis of samples belonging to the zeolite-rich pyroclastic formation named “Neapolitan yellow tuff” (Central and Southern Italy) has been determined by full-profile refinement of X-ray powder diffraction (XRPD) data using a combined Rietveld–RIR method. The quantitative analysis and especially the zeolite content is a profitable source for geo-petrographic and genetic considerations and as well an essential source to assess the physical and chemical properties of the bulk material for a feasible use in industrial applications. Albeit a wealth of methods are used for the quantitative determination of zeolite content in pyroclastites they all fail for lack of accuracy as far as concerns the absolute standard deviation of the quantitative data. The outstanding outcomes achievable by using the Rietveld method make it as the most promising technique to fulfill this lack. The glass content in each sample is calculated by a combined Rietveld–RIR method in which a known amount of an internal standard is added to the mixture to rescale the Rietveld refined weight fractions into absolute values. Then, it is reasonable to designate this method as an external method according to the definition given by Hill and Howard (1987). Its counterpart is the internal method developed by Riello etal. (1995a,b). Other techniques such as the addition method and the background scattering volume calculation are developed to accomplish a further determination of the glass content. The results are compared to the values obtained from the Rietveld–RIR analysis. These experimental methods yield an over-estimation of the amorphous phase because the incoherent scattering contribution (air, absorption, sample holder, Compton scattering) is accounted for as the amorphous fraction itself. The glass content of each sample acquired from the Rietveld–RIR refinement on the “raw data” is compared to that accomplished from the refinement of incoherent scattering subtracted data. In addition, some largely used XRPD quantitative techniques such as the external standard and RIR (reference intensity ratio) and the influence of the sample loading method are accounted for in an internally consistent comparison among different procedures of analysis.

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Soleimanian, V., and S. R. Aghdaee. "Comparison methods of variance and line profile analysis for the evaluation of microstructures of materials." Powder Diffraction 23, no. 1 (March 2008): 41–51. http://dx.doi.org/10.1154/1.2888763.

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A comparison of different methods of X-ray diffraction analysis for the determination of crystallite size and microstrain; namely, line profile analysis, Rietveld refinement, and three approaches based on the variance method, is presented. The analyses have been applied to data collected on a ceria sample prepared by the IUCr Commission on Powder Diffraction. In the variance method, split Pearson VII, the Voigt function, and its approximation pseudo-Voigt function were fitted to X-ray diffraction line profiles. Based on the fitting results, the variances of line profiles were calculated and then the crystallite size and root mean square strain were obtained from variance coefficients. A SS plot of Langford as well as a Fourier analysis and Rietveld refinement have been carried out. The average crystallite size and microstrain were determined. The values of area-weighted domain size determined from the variance method are in agreement with those obtained from line profile analysis within a single (largest) standard uncertainty, and the volume-weighted domain sizes derived from the SS plot, Fourier size distribution, and Rietveld refinement agree within a single standard uncertainty. The results of rms strain calculated from variance and Pearson VII shape function and those from Rietveld refinements fall within a single esd. However, the variance method in conjunction with pseudo-Voigt and Voigt functions produce rms strains substantially larger than those determined from line profile analysis and Rietveld refinements.

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Aylmore, Mark G., and Graham S. Walker. "The quantification of lateritic bauxite minerals using X-ray powder diffraction by the Rietveld method." Powder Diffraction 13, no. 3 (September 1998): 136–43. http://dx.doi.org/10.1017/s0885715600009982.

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The application of the Rietveld method to quantify mineral components of bauxite and lateritic samples was carried out in order to determine the ability of the method to obtain accurate mineralogical abundances for these materials. The method was initially applied to synthetic mixtures using both Cu and Co Kα radiations, and it was shown that Rietveld-derived data compared favourably with the weighed compositions. Application to two types of natural bauxite resulted in a high correlation between Rietveld predicted values and those calculated by proportioning peak intensities with chemical assays. The use of the whole pattern rather than selected peak intensities gives greater accuracy, confirmed by a strong correlation between derived oxide concentrations from XRF assays. Accuracy and precision were improved by the determination of isomorphous substitution of aluminum in goethite and hematite by refinement of unit cell dimensions. Importantly, the ability of the Rietveld program to successfully model several goethites with different levels of isomorphous substitution improved the correlation between predicted and calculated values. In addition, crystallinity and crystallite size that influence the reactivity of the mineral components can be derived from refined peak profiles.

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Taylor, JC. "Technique and Performance of Powder Diffraction in Crystal Structure Studies." Australian Journal of Physics 38, no. 3 (1985): 519. http://dx.doi.org/10.1071/ph850519.

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A common use of powder diffraction data is for crystal structure studies. Since the pioneering papers of Rietveld (1967, 1969), powder diffraction has been improved in many ways. Some advances in powder diffraction techniques since an earlier review (Cheetham and Taylor 1977) are described, and an indication is given of how the Rietveld method is performing with X-ray and neutron diffraction. This method has been more popular with crystallographers than the integrated-intensity method since it attacks the superposition problem directly and allows more complex structures to be refined. It has been asserted (Sakata and Cooper 1969) that calculated e.s.d. values in the Rietveld method are low by a factor of about two, although the derived positional parameters have never been faulted. This does not negate the value of the method as corrections to the e.s.d. values can be computed (Cooper et aZ. 1981; Scott 1983). The problem of precision versus accuracy is universal; in fact most e.s.d. values published in single-crystal studies are probably low by a similar amount because of the widespread practice of omitting large amounts of 'weak' data in order to artificially lower the residuals and e.s.d. values. It is shown that powder methods, especially the Rietveld, have performed well in a variety of applications.

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Madsen, I. C., and R. J. Hill. "QPDA – A User-Friendly, Interactive Program for Quantitative Phase and Crystal Size/Strain Analysis of Powder Diffraction Data." Powder Diffraction 5, no. 4 (December 1990): 195–99. http://dx.doi.org/10.1017/s0885715600015785.

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AbstractRecent developments in the Rietveld method for the analysis of powder diffraction data have seen the method evolve from its original purpose of crystal structure refinement to include the determination of phase abundance in polycrystalline mixtures and the estimation of crystal size and strain parameters. However, the Rietveld method is not easy to use and may deter many powder diffractionists, who are not interested in structure refinement per se, from using the method in its non-structural applications.In order to overcome the difficulties in using the Rietveld method, a program, QPDA (for Quantitative Powder Diffraction Analysis), has been written that sets the conditions necessary for a single or multi-phase refinement, runs the Rietveld program and extracts phase abundance and size/strain information from the refined parameters. The program comprises a user-friendly, default-driven system of subroutines, written initially in VAX Fortran, and operates from a database of inorganic materials frequently encountered in a wide range of minerals and materials science industries.

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Journal articles on the topic 'Rietveld method'

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