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A scripting interface for GSAS-II

The GSAS-II suite is a complete crystallographic analysis package for all types of X-ray and neutron diffraction data, suited for fitting models ranging from simple materials to proteins, and designed around an integrated graphical user interface. This article describes a new module within GSAS-II , GSASIIscript­able , which provides access to the GSAS-II data structures and an extensible mechanism to run a significant fraction of GSAS-II functionality, particularly for powder diffraction applications, from within Python scripts or directly from commands in a shell/batch script. In conclusion, this allows parallelization in a high-performance computing environment; near ideal speedup is seen with up to 240 simultaneous processes.

47 OTHER INSTRUMENTATION↗

Stochastic and Deterministic Crystal Structure Solution Methods in GSAS-II: Monte Carlo/Simulated Annealing Versus Charge Flipping

One of the goals in developing GSAS-II was to expand from the capabilities of the original General Structure Analysis System (GSAS) which largely encompassed just structure refinement and post refinement analysis. GSAS-II has been written almost entirely in Python loaded with graphics, GUI and mathematical packages (matplotlib, pyOpenGL, wxpython, numpy and scipy). Thus, GSAS-II has a fully developed modern GUI as well as extensive graphical display of data and results. However, the structure and operation of Python has required new approaches to many of the algorithms used in crystal structure analysis. The extensions beyond GSAS include image calibration/integration as well as peak fitting and unit cell indexing for powder data which are precursors for structure solution. Structure solution within GSAS-II begins with either Pawley or LeBail extracted structure factors from powder data or those measured in a single crystal experiment. Both charge flipping and Monte Carlo-Simulated Annealing techniques are available; the former can be applied to (3+1) incommensurate structures as well as conventional 3D structures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Materials for learning use of GSAS-II

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. Finally, 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.

97 MATHEMATICS AND COMPUTING↗

Determining magnetic structures in GSAS-II using the Bilbao Crystallographic Server tool k-SUBGROUPSMAG

The embedded call to a special version of the web-based Bilbao Crystallographic Server tool k-SUBGROUPSMAG from within GSAS-II to form a list of all possible commensurate magnetic subgroups of a parent magnetic grey group is described. It facilitates the selection and refinement of the best commensurate magnetic structure model by having all the analysis tools including Rietveld refinement in one place as part of GSAS-II. It also provides the chosen magnetic space group as one of the 1421 possible standard Belov–Neronova–Smirnova forms or equivalent non-standard versions.

36 MATERIALS SCIENCE↗

GSAS-II (GENERAL STRUCTURE AND ALAYSIS SYSTEM-II)

GSAS-II is a comprehensive data analysis and simulation software package for determining atomistic structures from single-crystal and powder diffraction data. X-ray, neutron and electron data may be used. Constant-wavelength, time-of-flight and pink-beam sources may be employed and analyses may combine different types of data. The package is oriented towards materials characterization problems, but protein crystallography, pair-distribution function analysis, small-angle scattering and reflectometry analysis are all included. GSAS-II provides tools for indexing and solving structures from powder diffraction data, in addition to structure, data and results visualization tools

TOBY, BRIANH↗

Determination of physically based pseudo-Voigt powder diffraction profile terms from the fundamental parameters approach

In this study, a methodology is developed where a fundamental parameters approach (FPA) description of a laboratory powder diffraction instrument (configured in divergent-beam Bragg–Brentano geometry) is used to determine GSAS-II profile parameters for peak asymmetry and instrumental peak widths. This allows the instrumental contribution to peak shapes to be robustly determined directly from a physical description of the instrument, even though GSAS-II does not directly implement FPA for peak shape computation. The FPA-derived parameters can be used as the starting point for instrument characterization, or to characterize sample broadening without the use of a standard to determine the instrument profile function. This new method can facilitate generation of training sets for machine learning. A plot is generated that shows the differences between the two approaches, demonstrating upper bounds for the accuracy of the GSAS-II profile model for a particular instrumental configuration.

47 OTHER INSTRUMENTATION↗

Microstructural analysis of undoped and moderately Sc-doped TiO2 anatase nanoparticles using Scherrer equation and Debye function analysis

Highlights: • UV light sensitive undoped and moderate Sc-doped anatase nanocrystallites were prepared without post-synthesis annealing. • Elongated nanocrystallites were found by Scherrer equation and Debye Function Analysis applied to XRD data and also HRTEM. • 4 at.% Sc doping reduced the amount of Ti vacancies by half. • Doping showed ~0.3% growth of lattice parameters. - Abstract: UV light sensitive undoped and moderate (4 at.%) Sc-doped anatase nanocrystallites were prepared by an efficient and environmentally benign method based on homogeneous hydrolysis of TiOSO{sub 4} and Sc{sub 2}(C{sub 2}O{sub 4}){sub 3.5}H{sub 2}O aqueous solutions using urea as a precipitation agent, without post-synthesis calcination or annealing. X-ray diffraction study of the obtained powders revealed single phase anatase in both samples. Two different methods were applied to estimate the anatase crystallite size and shape from the X-ray diffraction data. The first one is based on the more conventional Scherrer equation (as implanted in GSAS-II program) while the second one is based on Debye function analysis (as implanted in DUBUSSY suite version 2.2), which is considered to be more adequate for nanocrystallites. Although each program has its own shape models, both methods indicated similar results of elongated nanocrystallite geometry for Sc-doped TiO{sub 2}: (i) GSAS-II confirmed ellipsoid shape with equatorial size of 5.1(0) nm and axial size of 6.8(0), (ii) DEBUSSY suite 2.2 showed cylinder shape with diameter of equivalent circle in the ab-plane, D{sub ab} = 4.9(1.0) nm and crystallite length along the c-axis, L{sub c} = 5.4(3.2) nm. For the undoped TiO{sub 2} sample, equatorial size of 5.5(0) nm and axial size of 7.3(0) nm for the ellipsoid shape was determined according to GSAS-II, while D{sub ab} = 5.5(1.3) nm and L{sub c} = 6.0(2.2) nm for the cylinder shape was determined by DEBUSSY suite 2.2. These outcomes were found to corroborate with HRTEM analysis. Doping with 4 at.% Sc caused ~0.3% growth of lattice parameters from a = 3.7979 [4] Å, c = 9.4995 [9] Å for the undoped sample to a = 3.8110 [7] Å, c = 9.5274 [16] Å for the moderately Sc doped sample, while reduction in the Ti vacancies by half was confirmed by both methods. The introducing of Sc as electronically active secondary species into the crystal lattice of TiO{sub 2} can greatly alter its optical absorption. The incorporation of Sc into the crystal lattice of TiO{sub 2} favors the substitution of Ti, as both have approximately the same ionic size, and generates surface oxygen vacancies which can act as trapping center for the photogenerated electrons and reduce the recombination of electron–hole pairs. We can expect Sc doped TiO{sub 2} nanomaterials to have applications as effective photocatalysts for selective photocatalytic oxidation of various environmental organic pollutants.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

PRISMA: PARALLEL REFINEMENT AND INTEGRATION SYSTEM FOR MULTI-AZIMUTHAL ANALYSIS

The Parallel Refinement and Integration System for Multi-azimuthal Analysis (PRISMA, version 1.1.0) is a Python application for processing X-ray diffraction (XRD) image data. PRISMA wraps GSAS-II to perform azimuthally-binned peak refinement, computes per-frame strain and d-spacing from those fits, and provides three PyQt5 graphical interfaces: (1) a Recipe Builder for selecting GSAS-II control (.imctrl) files, optional mask (.immask) files or threshold-ased masking, reference and experiment image sets, peaks, zimuthal range and bin size, and an optional ceria-based auto-calibration; (2) a Batch Processor that uses Dask on local workstations and pure MPI (mpi4py.futures.MPICommExecutor) on HPC to distribute GSAS-II refinement across cores or compute nodes and write results to a 4-dimensional (peaks x frames x azimuths x measurements) Zarr dataset; and (3) a Data Analyzer that renders heatmaps of fit parameters, strain, frame-to-frame deltas, and percent-change-vs-reference, and exports user-defined subsections to CSV or Excel. The peak-refinement algorithm is deterministic. Benchmark on ALCF Crux: a 20,000-image set, single-peak fit in frame mode with 44 azimuthal bins on 128 nodes x 128 workers, 48 seconds total wall time.

Lorenzo Martin, Maria De La Cinta [Argonne Nationa↗

POWTEX visits POWGEN

The high-intensity time-of-flight (TOF) neutron diffractometer POWTEX for powder and texture analysis is currently being built prior to operation in the eastern guide hall of the research reactor FRM II at Garching close to Munich, Germany. Because of the world-wide 3 He crisis in 2009, the authors promptly initiated the development of 3 He-free detector alternatives that are tailor-made for the requirements of large-area diffractometers. Herein is reported the 2017 enterprise to operate one mounting unit of the final POWTEX detector on the neutron powder diffractometer POWGEN at the Spallation Neutron Source located at Oak Ridge National Laboratory, USA. As a result, presented here are the first angular- and wavelength-dependent data from the POWTEX detector, unfortunately damaged by a 50 g shock but still operating, as well as the efforts made both to characterize the transport damage and to successfully recalibrate the voxel positions in order to yield nonetheless reliable measurements. Also described is the current data reduction process using the PowderReduceP2D algorithm implemented in Mantid [Arnold et al. (2014). Nucl. Instrum. Methods Phys. Res. A , 764 , 156–166]. The final part of the data treatment chain, namely a novel multi-dimensional refinement using a modified version of the GSAS-II software suite [Toby & Von Dreele (2013). J. Appl. Cryst. 46 , 544–549], is compared with a standard data treatment of the same event data conventionally reduced as TOF diffraction patterns and refined with the unmodified version of GSAS-II . This involves both determining the instrumental resolution parameters using POWGEN's powdered diamond standard sample and the refinement of a friendly-user sample, BaZn(NCN) 2 . Although each structural parameter on its own looks similar upon comparing the conventional (1D) and multi-dimensional (2D) treatments, also in terms of precision, a closer view shows small but possibly significant differences. For example, the somewhat suspicious proximity of the a and b lattice parameters of BaZn(NCN) 2 crystallizing in Pbca as resulting from the 1D refinement (0.008 Å) is five times less pronounced in the 2D refinement (0.038 Å). Similar features are found when comparing bond lengths and bond angles, e.g. the two N—C—N units are less differently bent in the 1D results (173 and 175°) than in the 2D results (167 and 173°). The results are of importance not only for POWTEX but also for other neutron TOF diffractometers with large-area detectors, like POWGEN at the SNS or the future DREAM beamline at the European Spallation Source.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A simple solution to the Rietveld refinement recipe problem

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 GSAS-II program is discussed. This new method is discussed as an important step towards the development of automated Rietveld refinement technology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Oil-Pressure Based Apparatus for In-Situ High-Energy Synchrotron X-Ray Diffraction Studies During Biaxial Deformation

Background: Understanding biaxial loading response at the microstructural level is crucial in helping better design sheet manufacturing processes and calibrate/validate material deformation models. Objective: The objective of this work was to develop a low-cost testing apparatus to probe, with sufficient spatial resolution, the micro-mechanical response of a sheet material in-situ under biaxial loading conditions. Methods: The testing apparatus fabricated as a part of this study operates in a similar fashion to a standard bulge test and uses oil pressure to generate biaxial loading conditions. This biaxial testing apparatus was operated within a synchrotron beamline to characterize the mechanical response of a flash-processed steel sheet using in-situ high-energy X-ray diffraction (XRD) measurements. Further, the GSAS-II package was utilized to develop a workflow for the analysis of the large volume of diffraction data acquired. The workflow was then used to extract the peak position, width, and integrated intensity of the XRD peaks corresponding to the major body-centered cubic phase. Results: The equi-biaxial nature of the loading in the measured area was independently corroborated using experimental (XRD) and simulation (finite element analysis) methods. Furthermore, we discuss the evolution of elastic strain in the major body-centered cubic phase as a function of applied oil pressure and location on the steel sheet. Conclusions: A key advantage of the biaxial apparatus fabricated in this synchrotron study is demonstrated using the results obtained for the flash-processed steel sheet – i.e., mapping the lattice plane-dependent response to biaxial loading for a relatively large sample area in a spatially resolved manner.

36 MATERIALS SCIENCE↗

Structure determination of oxamic acid from laboratory powder X-Ray diffraction data and energy minimization by DFT-D

The structure determination from laboratory X-ray powder diffraction data of oxamic acid, a derivative of the biologically active oxalic acid and the simplest organic acid containing an amide group, is presented in this contribution. An energy minimization analysis by DFT-D was carried out. The structure was determined with the program TALP and refined by the Rietveld method with GSAS-II in space group Cc (No. 9). The final unit-cell parameters are a = 9.4989 (6), b = 5.43796 (9), c = 6.8637 (9) Å, β = 107.152 (5)°, V = 338.772 (10) Å3, Z = 4. The refinement converged to the figures of merit: Re = 0.01674, Rp = 0.03270, Rwp = 0.05652 and GoF = 3.378 with a good fit between the calculated pattern of the structural model and the experimental pattern. The DFT-D calculations show an excellent reproduction of the experimental structure, validating the correctness of the structure. Furthermore, the non-centrosymmetric nature of the structure was confirmed by SHG measurements. In the crystal structure, the molecules are close to planar and form a complex 2D hydrogen-bonding pattern based on the cyclic amide-acid heterosynthon.

36 MATERIALS SCIENCE↗

Spotlight: efficient automated global optimization in rietveld analysis of diffraction data

Performing reliable Rietveld analysis on tens or hundreds of powder diffraction datasets from parametric or time-resolved experiments often poses a bottleneck in extracting meaningful results from the data. While automated analysis of data has recently been demonstrated, high temperature annealing studies, during which phase transformations occur and lattice parameters may change due to repartitioning of elements, are prime examples where automation by a simple phase identification from a database of room temperature structures or automation by sequential refinements is likely to fail. To enable reliable, efficient, automated Rietveld analysis, we present a Python package named Spotlight , building on established Rietveld packages such as MAUD, GSAS , or GSAS-II , which extends the refinement of best fit parameters to a global optimization using an ensemble of optimizers leveraging hierarchical parallel execution on high-performance computing clusters. Spotlight further enables the efficient design of refinement plans through the iterative automated machine-learning of a surrogate for the refinement on which the global optimizations are performed until results from the surrogate converge to the response surface data. We demonstrate Spotlight with the analysis of uranium molybdenum and Ti–6Al–4V datasets, as well as in two open-source tutorials analyzing aluminium oxide and lead sulphate.

36 MATERIALS SCIENCE↗

Improved calibration of area detectors using multiple placements

Calibration of area detectors from powder diffraction standards is widely used at synchrotron beamlines. From a single diffraction image, it is not possible to determine both the sample-to-detector distance and the wavelength, but, with images taken from multiple positions along the beam direction and where the relative displacement is known, the sample-to-detector distance and wavelength can both be determined with good precision. Finally, an example calibration using the GSAS-II software package is presented.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

XRD-PUAT (X-Ray Diffraction - Parameter Uncertainty Analysis Toolkit)

This XRD uncertainty toolkit was built to investigate uncertainty and local least squares topology over a specified parameter space on a single histogram in a gpx GSAS-II file. The parameter uncertainty can be investigated using either a frequentist F-test approach or a Bayesian Inference statistical inversion method on a weighted least squares or peak fit refinements.SAND Number: SAND2020-12227 M Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Moore, Alexander↗