The direct‐derivation (DD) method is a new technique for quantitative phase analysis (QPA) Toraya (2016). J. Appl. Cryst. 49, 1508–1516. A simple equation, called the intensity–composition (IC) ...formula, is used to derive weight fractions of individual components (wk; k = 1–K) in a mixture. Two kinds of parameters are required as input data of the formula. One is the parameter Sk, which is the sum of observed powder diffraction intensities for each component, measured in a wide 2gθ range and corrected for the Lorentz–polarization factor. The other is the parameter ak−1, defined by ak−1 = Mk−1∑nik2, where Mk is the chemical formula weight and nik is the number of electrons belonging to the ith atom in the chemical formula unit. The parameter ak−1 was originally derived by using the relationship between the peak height and the integrated value of the peak at the origin of the Patterson function, implicitly assuming the presence of periodic structures like crystals. In this study, the formula has been derived theoretically from a general assemblage of atoms resembling amorphous material, and the same expression as the original formula has been obtained. The physical meaning of ak−1, which represents `the total scattering power per chemical formula weight', has been reconfirmed in the present formulation. The IC formula has been tested experimentally by using two‐, three‐ and four‐component mixtures containing SiO2 or GeO2 glass powder. In the whole‐powder‐pattern fitting (WPPF) procedure, incorporated into the DD method, a background‐subtracted halo pattern is directly fitted as one of the components in the mixture, together with profile models for crystalline components. In the WPPF, an interaction was observed between the parameters of the background function (BGF) and the parameter for scaling the halo pattern, and this resulted in systematic deviations of wk from weighed values. The deviations were ≤0.7% in the case of binary mixtures when the BGF was fixed at the correct background height, supporting the hypothesis that the DD method is applicable to the QPA of amorphous components.
The direct‐derivation method has been applied to the quantitative phase analysis of mixtures containing amorphous components. A theoretical basis has been given to the formula for deriving individual weight fractions from observed intensity data. The formula has been experimentally tested by whole‐powder‐pattern fitting to the observed patterns of mixtures containing amorphous components.
A formula for quantitative phase analysis (QPA), called the intensity–composition (IC) formula, can be used for deriving weight fractions of individual crystalline phases in a mixture from sets of ...observed integrated intensities, measured in a wide 2gθ range, with chemical composition data Toraya (2016). J. Appl. Cryst.49, 1508–1516; Toraya (2017). J. Appl. Cryst.50, 820–829. In this study, the IC formula has been incorporated into the whole‐powder‐pattern fitting (WPPF) procedure to conduct QPA. The fitting function for calculating the profile intensity at each step of the scattering angle consists of three sub‐functions that represent the individual component diffraction patterns. The first sub‐function calculates the diffraction pattern using a set of integrated intensities, the parameter values of which are determined by the least‐squares fitting of the whole‐powder pattern as is usually done by the whole‐powder‐pattern decomposition (WPPD) method. The second sub‐function uses a set of integrated intensity parameters, which are preliminarily prepared by WPPD or may be calculated from a crystal structure model. These intensity parameters, multiplied by a scale factor, are fixed at their original values while the scale factor is adjusted in WPPF. The third sub‐function uses an observed or calculated diffraction pattern multiplied by a scale factor. This diffraction pattern can be fitted directly by adjusting the scale factor. Therefore, one can fit patterns consisting of heavily broadened and degraded diffraction lines, like those of clay minerals, without being concerned with the problem of peak overlap in decomposing the diffraction pattern. The IC formula uses the total sums of the intensities under the diffraction patterns of individual phases as observed data sets; therefore, it can equally treat these intensity data sets irrespective of differences in the profile models used by the three sub‐functions. The three sub‐functions can arbitrarily be chosen and linearly combined, and then they can simultaneously be fitted to the observed diffraction pattern of a target mixture. The capability of the above method has been demonstrated with QPA of mixtures consisting of α‐quartz, albite and kaolinite. Theories of currently used QPA techniques are reviewed from a viewpoint of the present theory and they can be interpreted as being based on the same principle, whereby the total observed intensities of individual phases are divided by the standard reference intensity per unit weight.
The intensity–composition formula, which can be used for directly deriving weight fractions of individual crystalline phases from sets of observed integrated intensities and chemical composition data, has been incorporated into the whole‐powder‐pattern fitting procedure. Mixtures containing known structure, unknown structure, and high and low crystalline materials can be quantified by using the present procedure.
Whole powder pattern modelling macros for TOPAS Scardi, Paolo; Azanza Ricardo, Cristy L.; Perez-Demydenko, Camilo ...
Journal of applied crystallography,
December 2018, 2018-12-01, 20181201, Volume:
51, Issue:
6
Journal Article
Peer reviewed
Macros implementing the main concepts of the whole powder pattern modelling approach have been written for TOPAS. Size and strain broadening components of the diffraction line profiles can be ...convolved with the instrumental profile already available among the standard commands of TOPAS. Specific macros are presented with examples of applications including plastically deformed powders and atomistic simulations. A macro is presented for the modelling of surface relaxation effects in spherical nanocrystals.
Macros implementing the main concepts of the whole powder pattern modelling approach have been written for TOPAS, taking into account the size and strain broadening components of the diffraction line profiles.
CONEX is a Windows application for converting series of two‐dimensional X‐ray powder patterns measured on flat two‐dimensional detectors into one‐dimensional scattering patterns. It is based on the ...rigorous use of scattering patterns of calibration samples to determine the three‐dimensional position of the detector, with respect to the sample and to the beam. This enables correction of the data for geometric distortions, even when the detector is highly tilted and not centred on the beam.
Equation (16) and some entries in Table 1 in the article by Scardi & Leoni (2001), Acta Cryst. A57, 604–613 are corrected.
Errors in the article by Scardi & Leoni (2001), Acta Cryst. A57, 604–613 are ...corrected.
Photocatalysis with TiO2 is one of the most promising methods for combatting environmental pollution. Of commercially available photocatalysts, Evonik Aeroxide (formerly Degussa) P25® titania is ...probably the most extensively used. In this communication, we quantitatively characterise the full phase composition (both crystalline and amorphous content) of P25®, as well as the microstructure of individual phases (crystalline domain size distribution and dislocation density). This was achieved with advanced X-ray diffraction (XRD) methods: Rietveld-RIR and whole powder pattern modelling (WPPM). Quantitative phase analysis (QPA) showed the precise composition of P25 to be 76.3wt% anatase, 10.6wt% rutile and 13.0wt% amorphous, and microstructural details are given for the two crystalline phases.
•First time fully quantitative X-ray characterisation of Evonik Aeroxide TiO2 P25®.•P25® composed of 76.3wt% anatase, 10.6wt% rutile, and 13.0wt% amorphous phase.•Anatase phase had an average crystalline domain size of 15.5nm.•Rutile phase had a larger average crystalline domain size of 19.3nm.
Gadolinium metal-organic frameworks (Gd-MOFs) and Eu-doped Gd-MOFs have been synthesized through a one-pot green approach using commercially available reagents. The 1,4-benzenedicarboxylic acid ...(H2-BDC) and 2,6-naphthalenedicarboxylic acid (H2-NDC) were chosen as ditopic organic linkers to build the 3D structure of the network. The Gd-MOFs were characterized using powder X-ray diffraction (XRD), FT-IR spectroscopy, field emission scanning electron microscopy (FE-SEM) and N2 adsorption–desorption analysis. The Gd-MOF structures were attributed comparing the XRD patterns, supported by the FT-IR spectra, with data reported in the literature for Ln-MOFs of similar lanthanide ionic radius. FE-SEM characterization points to the effect of the duration of the synthesis to a more crystalline and organized structure, with grain dimensions increasing upon increasing reaction time. The total surface area of the MOFs has been determined from the application of the Brunauer–Emmett–Teller method. The study allowed us to correlate the processing conditions and ditopic linker dimension to the network surface area. Both Gd-MOF and Eu-doped Gd-MOF have been tested for sensing of the inorganic ions such as Fe3+ and Cr2O72−.
A new procedure has been developed for separating a multi‐component powder diffraction pattern into its individual component patterns without utilizing the pattern model for one of the components. In ...currently used whole‐powder‐pattern fitting (WPPF) techniques, pattern models are required for all components in a target material that are not in negligible amounts. When the pattern model is unavailable for one of the components due to, for example, low crystallinity, the straightforward application of the WPPF procedure becomes difficult. In the present procedure, WPPF can be conducted even when the pattern model is not available for one of the components. The pattern model for that component can be automatically generated from a seed pattern by filling in the difference between the observed intensity and the sum of intensities calculated for the remaining components at each step in 2θ. The WPPF is conducted by iterative applications of linear least squares to scale the individual component patterns and of direct search (DS) to optimize the parameters, such as the peak positions and profile widths, of the modeled components. The procedure has been incorporated into a computer program for Rietveld refinement, and the simplex method is used for the DS. It has been tested by using intensity data sets of artificially mixed materials with different degrees of complexity in their powder diffraction patterns. The reliability of the procedure has been tested in quantitative phase analysis using separated intensity data sets. The errors in the derived weight fractions are of the same order (0.5 to 2.0 wt%) as those obtained by conventional techniques. Intensity data extracted as unknown patterns were also tested by Rietveld refinement.
A new procedure for separating a multi‐component powder diffraction pattern into individual component patterns has been developed. It can separate the patterns without utilizing the pattern model for one of the components. It can be used for the powder data analysis of materials containing a component material of low crystallinity, of an unknown material coexisting with known materials etc.
The degradation of electrochemical performance during the long-term operation of the solid oxide fuel cell is a critical issue. This challenge is confronted through an innovative approach of ...in-operando gas switching. Here, we developed a novel double perovskite electrode Sr2ScTi1-xMoxO6; x = 0.1 and 0.5, for the symmetrical solid oxide fuel cell. The crystallite phase and chemical stability of the perovskite are examined by X-ray diffraction whole powder pattern fitting. The electrochemical impedance analysis confirmed that the electrodes are exhibiting significant catalytic activity for hydrogen and methane oxidation, as well as the reduction of oxygen. Evolution of the cubic ScTiO3 due to the topotactic oxidation, improve the oxygen reduction activity of Sr2ScTi0.5Mo0.5O6, whereas the in-situ exsolution of Ti-ions enables the Sr2ScTi0.9Mo0.1O6 to exhibits of higher catalytic activity for fuel oxidation. The electrochemical performance, stability, and the effect of in-operando gas switching are investigated on large area (5 × 5 cm2) symmetrical solid oxide fuel cells supplying humidified CH4 and air. The galvanostatic test concludes the in-operando switching suppress the performance degradation of the SSOFC completely.
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•Novel double perovskite Sr2ScTi1-xMoxO6; x = 0.5, and 0.1 electrode for SSOFC.•Electrode, x = 0.5, exhibits higher ORR, while x = 0.1 shows excellent HOR.•In situ ex-solution of Ti exhibits for x = 0.1 electrode.•Pmax of the SSOFC with x = 0.5 is 3.5 W at 800 °C in CH4 and air.•in-operando gas switching suppresses the degradation of performance.
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