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DOE OSTI2020

Algorithms in Diffraction Profile Analysis

This chapter introduces several approaches to crystallographic structure refinement from diffraction profile data including the Rietveld method, global optimization methods, and Bayesian modeling. First, the Rietveld method and related nonlinear least squares approaches to analyzing diffraction profiles are briefly discussed. We then review the most common algorithms within global optimization as alternative methods of structure solution: grid search, simulated annealing, and genetic algorithms. As the Rietveld method is the standard tool for analyzing diffraction profile data, we catalogue its challenges and limitations. A Bayesian approach to diffraction profile analysis is presented as an alternative, along with several sampling algorithms including Gibbs sampling, variants of Metropolis sampling, Hamiltonian Monte Carlo, and approximate Bayesian computing. These sampling algorithms are applied to the fitting of a neutron diffraction profile from a National Institute of Standards and Technology silicon standard reference material, and their results are compared.

Singh, Susheela↗

DOE OSTI2025

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↗

DOE OSTI2021

Accelerated microwave-assisted synthesis and in situ X-ray scattering of tungsten-substituted vanadium dioxide (V 1-x W x O 2 )

Vanadium dioxide (VO 2 ) has been widely studied due to its metal-insulator phase transition at 68°C, below which it is a semiconducting monoclinic phase, P2 1 /c, and above it is a metallic tetragonal phase, P4 2 /mnm. Substituting vanadium with transition metals allows transition temperature tunability. An accelerated microwave-assisted synthesis for VO 2 and 5d tungsten substituted VO 2 presented herein decreased synthesis time by three orders of magnitude while maintaining phase purity, particle size, and transition character. Tungsten substitution amount was determined using inductively coupled plasma-optical emission spectroscopy. Differential scanning calorimetry, superconducting quantum interference device measurements, and in-situ heating and cooling experiments monitored through synchrotron x-ray diffraction (XRD) confirmed the transition temperature decreased with increased tungsten substitution. Scanning electron microscopy analyzed through the line-intercept method produced an average particle size of 3 – 5 μm. Average structure and local structure phase purity was determined through Rietveld analysis of synchrotron XRD and least-squares refinement of pair-distribution function data.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Magnetic structures and excitations in sawtooth olivine chalcogenides Mn 2 SiX 4 (X = S, Se)

The Mn lattice in olivine chalcogenide Mn 2 SiX 4 (X = S, Se) compounds forms a sawtooth, which is of special interest in magnetism owing to the possibility of realizing flat bands in magnon spectra, a key component in magnonics. In this work, we investigate the Mn 2 SiX 4 olivines using magnetic susceptibility, and X-ray and neutron diffraction. We have determined the average and local crystal structures of Mn 2 SiS 4 and Mn 2 SiSe 4 using synchrotron X-ray, neutron diffraction, and X-ray total scattering data followed by Rietveld and pair distribution function analyses. It is found from the pair distribution function analysis that the Mn triangle that constitutes the sawtooth is isosceles in Mn 2 SiS 4 and Mn 2 SiSe 4 . The temperature evolution of magnetic susceptibility of Mn 2 SiS 4 and Mn 2 SiSe 4 shows anomalies below 83 K and 70 K, respectively, associated with magnetic ordering. From the neutron powder diffraction measurements the magnetic space groups of Mn 2 SiS 4 and Mn 2 SiSe 4 are found to be Pnma and Pnm'a', respectively. Here, we find that the Mn spins adopt a ferromagnetic alignment on the sawtooth in both Mn 2 SiS 4 and Mn 2 SiSe 4 but along different crystallographic directions for the S and the Se compounds. From the temperature evolution of Mn magnetic moments obtained from refining neutron diffraction data, the transition temperatures are accurately determined as T N (S) = 83(2) K and T N (Se) = 70.0(5) K. Broad diffuse magnetic peaks are observed in both the compounds, and are prominently seen close to T N , suggesting the presence of a short-range magnetic order. The magnetic excitations studied using inelastic neutron scattering reveal a magnon excitation with an energy corresponding to approximately 4.5 meV in both S and Se compounds. Spin correlations are observed to persist up to 125 K much above the ordering temperature and we suggest the possibility of short-range spin correlations responsible for this.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Local and long-range atomic/magnetic structure of non-stoichiometric spinel iron oxide nanocrystallites

Spinel iron oxide nanoparticles of different mean sizes in the range 10–25 nm have been prepared by surfactant-free up-scalable near- and super-critical hydrothermal synthesis pathways and characterized using a wide range of advanced structural characterization methods to provide a highly detailed structural description. The atomic structure is examined by combined Rietveld analysis of synchrotron powder X-ray diffraction (PXRD) data and time-of-flight neutron powder-diffraction (NPD) data. The local atomic ordering is further analysed by pair distribution function (PDF) analysis of both X-ray and neutron total-scattering data. It is observed that a non-stoichiometric structural model based on a tetragonal γ-Fe 2 O 3 phase with vacancy ordering in the structure (space group P 4 3 2 1 2) yields the best fit to the PXRD and total-scattering data. Detailed peak-profile analysis reveals a shorter coherence length for the superstructure, which may be attributed to the vacancy-ordered domains being smaller than the size of the crystallites and/or the presence of anti-phase boundaries, faulting or other disorder effects. The intermediate stoichiometry between that of γ-Fe 2 O 3 and Fe 3 O 4 is confirmed by refinement of the Fe/O stoichiometry in the scattering data and quantitative analysis of Mössbauer spectra. The structural characterization is complemented by nano/micro-structural analysis using transmission electron microscopy (TEM), elemental mapping using scanning TEM, energy-dispersive X-ray spectroscopy and the measurement of macroscopic magnetic properties using vibrating sample magnetometry. Notably, no evidence is found of a Fe 3 O 4 /γ-Fe 2 O 3 core-shell nanostructure being present, which had previously been suggested for non-stoichiometric spinel iron oxide nanoparticles. Finally, the study is concluded using the magnetic PDF (mPDF) method to model the neutron total-scattering data and determine the local magnetic ordering and magnetic domain sizes in the iron oxide nanoparticles. The mPDF data analysis reveals ferrimagnetic collinear ordering of the spins in the structure and the magnetic domain sizes to be ∼60–70% of the total nanoparticle sizes. The present study is the first in which mPDF analysis has been applied to magnetic nanoparticles, establishing a successful precedent for future studies of magnetic nanoparticles using this technique.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗