Rietveld refinements are widely used for many purposes in the physical sciences. Conducting a Rietveld refinement typically requires expert input because correct results may require that parameters ...be added to the fit in the proper order. This order will depend on the nature of the data and the initial parameter values. A mechanism for computing the next parameter to add to the refinement is shown. The fitting function is evaluated with the current parameter value set and each parameter incremented and decremented by a small offset. This provides the partial derivatives with respect to each parameter, along with information to discriminate meaningful values from numerical computational errors. The implementation of this mechanism in the open-source
program is discussed. This new method is discussed as an important step towards the development of automated Rietveld refinement technology.
The results of both a line‐broadening study on a ceria sample and a size–strain round robin on diffraction line‐broadening methods, which was sponsored by the Commission on Powder Diffraction of the ...International Union of Crystallography, are presented. The sample was prepared by heating hydrated ceria at 923 K for 45 h. Another ceria sample was prepared to correct for the effects of instrumental broadening by annealing commercially obtained ceria at 1573 K for 3 h and slowly cooling it in the furnace. The diffraction measurements were carried out with two laboratory and two synchrotron X‐ray sources, two constant‐wavelength neutron and a time‐of‐flight (TOF) neutron source. Diffraction measurements were analyzed by three methods: the model assuming a lognormal size distribution of spherical crystallites, Warren–Averbach analysis and Rietveld refinement. The last two methods detected a relatively small strain in the sample, as opposed to the first method. Assuming a strain‐free sample, the results from all three methods agree well. The average real crystallite size, on the assumption of a spherical crystallite shape, is 191 (5) Å. The scatter of results given by different instruments is relatively small, although significantly larger than the estimated standard uncertainties. The Rietveld refinement results for this ceria sample indicate that the diffraction peaks can be successfully approximated with a pseudo‐Voigt function. In a common approximation used in Rietveld refinement programs, this implies that the size‐broadened profile cannot be approximated by a Lorentzian but by a full Voigt or pseudo‐Voigt function. In the second part of this paper, the results of the round robin on the size–strain line‐broadening analysis methods are presented, which was conducted through the participation of 18 groups from 12 countries. Participants have reported results obtained by analyzing data that were collected on the two ceria samples at seven instruments. The analysis of results received in terms of coherently diffracting, both volume‐weighted and area‐weighted apparent domain size are reported. Although there is a reasonable agreement, the reported results on the volume‐weighted domain size show significantly higher scatter than those on the area‐weighted domain size. This is most likely due to a significant number of results reporting a high value of strain. Most of those results were obtained by Rietveld refinement in which the Gaussian size parameter was not refined, thus erroneously assigning size‐related broadening to other effects. A comparison of results with the average of the three‐way comparative analysis from the first part shows a good agreement.
Materials for learning use of GSAS-II Ginell, K. M.; Horn, C.; Von Dreele, R. B. ...
Powder diffraction,
06/2019, Volume:
34, Issue:
2
Journal Article
Peer reviewed
Open access
The General Structure Analysis System (GSAS-II) package provides materials and crystallographic analysis for all types of diffraction data. It was initially made available with very limited ...capabilities, but over much of the last decade the features have been expanded, so that GSAS-II is now a comprehensive tool for nearly all types of structural and materials characterization studies. The need to provide materials to teach use of GSAS-II, while the software has been undergoing constant revision and expansion, has required new approaches for documentation. This has included providing tutorials, as each major new capability has been added, and context-sensitive help for each section of the program. Comments in the code are also expanded into a software reference guide. Most recently, video versions of more than half of the tutorials were created and others were provided with animated graphics. All GSAS-II documentation is web-based.
A description and justification of the EXPGUI program is presented. This program implements a graphical user interface and shell for the GSAS single‐crystal and Rietveld package. Use of the Tcl/Tk ...scripting language allows EXPGUI to be platform independent. Also included is a synopsis of how the program is implemented.
Zeolites and related crystalline microporous oxides-tetrahedrally coordinated atoms covalently linked into a porous framework-are of interest for applications ranging from catalysis to adsorption and ...ion-exchange. In some of these materials (such as zeolite rho) adsorbates, ion-exchange, and dehydration and cation relocation can induce strong framework deformations. Similar framework flexibility has to date not been seen in mixed octahedral/tetrahedral microporous framework materials, a newer and rapidly expanding class of molecular sieves. Here we show that the framework of the titanium silicate ETS-4, the first member of this class of materials, can be systematically contracted through dehydration at elevated temperatures to 'tune' the effective size of the pores giving access to the interior of the crystal. We show that this so-called 'molecular gate' effect can be used to tailor the adsorption properties of the materials to give size-selective adsorbents suitable for commercially important separations of gas mixtures of molecules with similar size in the 4.0 to 3.0 A range, such as that of N2/CH4, Ar/O2 and N2/O2.
The Edgeworth series model for the modification of diffraction peak shapes because of axial divergence is compared with the peak shapes computed by a numerical convolution method that is ...computationally slow. It is shown that if the width of an approximately Gaussian instrumental peak shape is comparable with the width of the modifying function, a condition that is generally satisfied in fixed‐wavelength neutron diffraction and in many laboratory X‐ray diffraction instruments, but not with synchrotron X‐ray instruments, the Edgeworth model is nearly identical to the convolution model, while the computation is much simpler.
In contrast to classical phase transitions driven by temperature,a quantum critical point (QCP) defines a transition at zero temperature that is driven by non-thermal parameters. In the known quantum ...critical d-electron systems, tuning the electronic bandwidth by means of changing the applied pressure or unit-cell dimensions, or tuning the d-state population, is used to drive the criticality. Here we describe how a novel chemical parameter, the breaking of bonds in Ge-Ge dimers that occurs within the intermetallic framework in SrCo2(Ge1−xPx)2, results in the appearance of a ferromagnetic (FM) QCP. Although both SrCo2P2 and SrCo2Ge2 are paramagnetic, weak itinerant ferromagnetism unexpectedly develops during the course of the dimer breaking, and a QCP is observed at the onset of the FM phase. The use of chemical bond breaking as a tuning parameter to induce QCP opens an avenue for designing and studying novel magnetic materials.
Several different approaches have traditionally been used for detection of X‐ray powder diffraction patterns, including area detectors, point detectors and position‐sensitive detectors. Each has ...advantages. This paper discusses use of a low‐cost CCD detector attached to a diffractometer arm, where line‐by‐line readout of the CCD is coupled to continuous motion of the arm. When this type of detector is used and where X‐ray optics are employed to focus the source image onto the detector plane both high‐resolution and rapid measurements can be performed, with data collection over a complete 2θ range. This is particularly advantageous for synchrotron applications but valuable also for Guinier diffractometer laboratory instruments. Peak resolutions are shown to be moderately better than what can be obtained with a position‐sensitive detector and significantly better than with an area detector. Many samples have intrinsically broadened peak shapes for which little improvement in data quality could be obtained with an analyzer‐crystal detector. With comparable numbers of modules, these CCD data collection speeds can be close to those with position‐sensitive detectors, but without the low‐angle asymmetry seen in the latter.
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