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Results for “atomic pair distribution function analysis (PDF)”

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Illustrated formalisms for total scattering data: a guide for new practitioners

The total scattering method is the simultaneous study of both the real- and reciprocal-space representations of diffraction data. While conventional Bragg-scattering analysis (employing methods such as Rietveld refinement) provides insight into the average structure of the material, pair distribution function (PDF) analysis allows for a more focused study of the local atomic arrangement of a material. Generically speaking, a PDF is generated by Fourier transforming the total measured reciprocal-space diffraction data (Bragg and diffuse) into a real-space representation. However, the details of the transformation employed and, by consequence, the resultant appearance and weighting of the real-space representation of the system can vary between different research communities. As the worldwide total scattering community continues to grow, these subtle differences in nomenclature and data representation have led to conflicting and confusing descriptions of how the PDF is defined and calculated. This paper provides a consistent derivation of many of these different forms of the PDF and the transformations required to bridge between them. Some general considerations and advice for total scattering practitioners in selecting and defining the appropriate choice of PDF in their own research are presented. This contribution aims to benefit people starting in the field or trying to compare their results with those of other researchers.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Structural Changes during the Growth of Atomically Precise Metal Oxido Nanoclusters from Combined Pair Distribution Function and Small-Angle X-ray Scattering Analysis

The combination of in situ pair distribution function (PDF) analysis and small-angle X-ray scattering (SAXS) enables analysis of the formation mechanism of metal oxido nanoclusters and cluster–solvent interactions as they take place. Herein, we demonstrate the method for the formation of clusters with a [Bi 38 O 45 ] core. Upon dissolution of crystalline [Bi 6 O 5 (OH) 3 (NO 3 ) 5 ]∙3 H 2 O in DMSO, an intermediate rapidly forms, which slowly grows to stable [Bi 38 O 45 ] clusters. To identify the intermediate, we developed an automated modeling method, where smaller [Bi x O y ] structures based on the [Bi 38 O 45 ] framework are tested against the data. [Bi 22 O 26 ] was identified as the main intermediate species, illustrating how combined PDF and SAXS analysis is a powerful tool to gain insight into nucleation on an atomic scale. PDF also provides information on the interaction between nanoclusters and solvent, which is shown to depend on the nature of the ligands on the cluster surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

In situ synchrotron pair distribution function analysis to monitor synthetic pathways under electromagnetic excitation

Electromagnetic (EM) fields, specifically microwave radiation (MWR), can significantly influence the synthesis of ceramic oxide materials and promote rapid, low-temperature growth. However, the mechanisms by which EM fields affect the phase formation process are not well understood. A major limitation to increasing this understanding has been the lack of information regarding dynamic changes in local atomic structure during MWR exposure compared to conventional hydrothermal synthesis routes. Here, we utilize in situ synchrotron X-ray pair distribution function (PDF) analysis to monitor MWR-assisted SnO 2 nanoparticle synthesis. A clear impact of the EM field is demonstrated, with MWR inducing changes in nearest neighbor distances and peaks in oxygen atomic displacement that do not occur during synthesis without MWR exposure. The observed local structural disorder serves as a precursor to rapid rutile SnO 2 nanoparticle crystallization, suggesting that EM field-assisted growth is mediated by changes to the oxygen sublattice. These findings further our understanding of the mechanisms underlying MWR-assisted synthesis and represent a step towards utilizing EM fields to engineer tailored atomic structures for a broad range of applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Effect of solvothermal synthesis parameters on the crystallite size and atomic structure of cobalt iron oxide nanoparticles

We here investigate how the synthesis method affects the crystallite size and atomic structure of cobalt iron oxide nanoparticles. By using a simple solvothermal method, we first synthesized cobalt ferrite nanoparticles of ca. 2 and 7 nm, characterized by Transmission Electron Microscopy (TEM), Small Angle X-ray scattering (SAXS), X-ray and neutron total scattering. The smallest particle size corresponds to only a few spinel unit cells. Nevertheless, Pair Distribution Function (PDF) analysis of X-ray and neutron total scattering data shows that the atomic structure, even in the smallest nanoparticles, is well described by the spinel structure, although with significant disorder and a contraction of the unit cell parameter. These effects can be explained by the surface oxidation of the small nanoparticles, which is confirmed by X-ray near edge absorption spectroscopy (XANES). Neutron total scattering data and PDF analysis reveal a higher degree of inversion in the spinel structure of the smallest nanoparticles. Neutron total scattering data also allow magnetic PDF (mPDF) analysis, which shows that the ferrimagnetic domains correspond to ca. 80% of the crystallite size in the larger particles. A similar but less well-defined magnetic ordering was observed for the smallest nanoparticles. Finally, we used a co-precipitation synthesis method at room temperature to synthesize ferrite nanoparticles similar in size to the smallest crystallites synthesized by the solvothermal method. Structural analysis with PDF demonstrates that the ferrite nanoparticles synthesized via this method exhibit a significantly more defective structure compared to those synthesized via a solvothermal method.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2022

Atomic structure and Mott nature of the insulating charge density wave phase of 1T-TaS 2

Here, using x-ray pair distribution function (PDF) analysis and computer modeling, we explore structure models for the complex charge density wave (CDW) phases of layered 1T-TaS 2 that both well capture their atomic-level features and are amenable to electronic structure calculations. The models give the most probable position of constituent atoms in terms of 3D repetitive unit cells comprising a minimum number of Ta–S layers. Structure modeling results confirm the emergence of star-of-David (SD) like clusters of Ta atoms in the high-temperature incommensurate (IC) CDW phase and show that, contrary to the suggestions of recent studies, the low-temperature commensurate (C) CDW phase expands upon cooling thus reducing lattice strain. The C-CDW phase is also found to preserve the stacking sequence of Ta–S layers found in the room temperature, nearly commensurate (NC) CDW phase to a large extent. DFT based on the PDF refined model shows that bulk C-CDW 1T-TaS 2 also preserves the insulating state of individual layers of SD clusters, favoring the Mott physics description of the metal-to-insulator (NC-CDW to C-CDW) phase transition in 1T-TaS 2 . Our work highlights the importance of using precise crystal structure models in determining the nature of electronic phases in complex materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Octahedral oxide glass network in ambient pressure neodymium titanate

Abstract Rare-earth titanates form very fragile liquids that can be made into glasses with useful optical properties. We investigate the atomic structure of 83TiO 2 -17Nd 2 O 3 glass using pair distribution function (PDF) analysis of X-ray and neutron diffraction with double isotope substitutions for both Ti and Nd. Six total structure factors are analyzed (5 neutron + 1 X-ray) to obtain complementary sensitivities to O and Ti/Nd scattering, and an empirical potential structure refinement (EPSR) provides a structural model consistent with the experimental measurements. Glass density is estimated as 4.72(13) g cm −3 , consistent with direct measurements. The EPSR model indicates nearest neighbor interactions for Ti-O at $$\overline{r}_{TiO}$$ r ¯ TiO = 1.984(11) Å with coordination of $$n_{TiO}$$ n TiO = 5.72(6) and for Nd-O at $$\overline{r}_{NdO}$$ r ¯ NdO = 2.598(22) Å with coordination of $$n_{NdO}$$ n NdO = 7.70(26), in reasonable agreement with neutron first order difference functions for Ti and Nd. The titanate glass network comprises a mixture of distorted Ti-O 5 and Ti-O 6 polyhedra connected via 71% corner-sharing and 23% edge-sharing. The O-Ti coordination environments include 15% nonbridging O-Ti 1 , 51% bridging O-Ti 2 , and 32% tricluster O-Ti 3 . This structure is highly unusual for oxide glasses melt-quenched at ambient pressure, as it consists of Ti-O x predominantly in octahedral (with nearly no tetrahedral) coordination.

36 MATERIALS SCIENCE↗
NASA NTRS2002

Examination of Short- and Long-Range Atomic Order Nanocrystalline SiC and Diamond by Powder Diffraction Methods

The real atomic structure of nanocrystals determines unique, key properties of the materials. Determination of the structure presents a challenge due to inherent limitations of standard powder diffraction techniques when applied to nanocrystals. Alternate methodology of the structural analysis of nanocrystals (several nanometers in size) based on Bragg-like scattering and called the "apparent lattice parameter" (alp) is proposed. Application of the alp methodology to examination of the core-shell model of nanocrystals will be presented. The results of application of the alp method to structural analysis of several nanopowders were complemented by those obtained by determination of the Atomic Pair Distribution Function, PDF. Based on synchrotron and neutron diffraction data measured in a large diffraction vector of up to Q = 25 Angstroms(exp -1), the surface stresses in nanocrystalline diamond and SiC were evaluated.

Palosz, B.↗
DOE OSTI2025

Structure refinement and anisotropic atomic displacement parameters of 1M Illite: Rietveld and pair distribution function analysis using synchrotron X-ray radiation

Illite, a widespread clay mineral, plays a pivotal role in geological processes, notably as an indicator in diagenetic and hydrothermal alteration environments, and possesses significant industrial relevance in applications including ceramics, construction and catalysis. However, challenges including its nanoscale crystallinity, structural disorder and frequent interstratification with other clay minerals have hindered detailed structural characterization using conventional X-ray diffraction (XRD) techniques. This study employs integrated synchrotron XRD and pair distribution function (PDF) analysis to elucidate the crystal structure of the 1M illite polytype, yielding the first determination of its anisotropic atomic displacement parameters (U aniso ). TheseU aniso parameters provide critical insights into atomic dynamics and static disorder within the structure, enabling a more refined understanding of structure–property relationships. This integrated approach, combining synchrotron XRD, Rietveld refinement and PDF analysis, yields a comprehensive structural characterization, capturing both average crystallographic and local atomic arrangements. Considering illite's widespread geological occurrence and industrial importance, this high-precision structural dataset, especially the determinedU aniso values, provides a crucial benchmark for future modeling and simulation efforts targeting accurate prediction of its physicochemical behavior.

Chemistry↗
DOE OSTI2023

Exploring the mobility of Cu in bimetallic nanocrystals to promote atomic-scale transformations under a reactive gas environment

Bimetallic nanocrystals (NCs) often show improved catalytic activities compared to their monometallic counterparts, but to optimize the performance it is crucial to understand how they behave under actual reaction conditions, i.e. in gas environments. Here, in this study, we use powder X-ray diffraction (PXRD), total scattering (TS) with pair distribution function (PDF) analysis and in situ high-resolution transmission electron microscopy (HR-TEM) to provide new insights into the atomic-scale behaviour of NC catalysts under a reactive gas environment. By investigating Au, Cu, Pd, PdCu, AuPd and AuCu NCs, we observe that the properties of bimetallic NCs differ significantly from their monometallic counterparts. While metal oxide phases formed for monometallic Pd and Cu under O 2 -exposure, bimetallic PdCu and AuCu NCs showed loss of metallic Cu in the crystalline phases after exposure to O 2 . However, upon introducing the bimetallic NCs to a reducing atmosphere, the Cu was found to reappear and reincorporate into a crystalline phase, forming the initial bimetallic structures. By combining TS, PDF analysis and in situ HR-TEM, we saw that Cu segregates to the NC surfaces or forms small CuO domains under O 2 -exposure. Our results thus indicate that the Cu mobility promotes segregation and formation of CuO along with the formation of a monometallic phase, which ultimately changes the resulting active surface sites of the nanocatalyst. Understanding the dynamical structure–property relations of nanocatalysts is key to enable rational design of efficient and robust catalysts for controlled catalytic reactions.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Crystal Structure of Moganite and Its Anisotropic Atomic Displacement Parameters Determined by Synchrotron X-ray Diffraction and X-ray/Neutron Pair Distribution Function Analyses

The crystal structure of moganite from the Mogán formation on Gran Canaria has been re-investigated using high-resolution synchrotron X-ray diffraction (XRD) and X-ray/neutron pair distribution function (PDF) analyses. Our study for the first time reports the anisotropic atomic displacement parameters (ADPs) of a natural moganite. Rietveld analysis of synchrotron XRD data determined the crystal structure of moganite with the space group I2/a. The refined unit-cell parameters are a = 8.7363(8), b = 4.8688(5), c = 10.7203(9) Å, and β = 90.212(4)°. The ADPs of Si and O in moganite were obtained from X-ray and neutron PDF analyses. The shapes and orientations of the anisotropic ellipsoids determined from X-ray and neutron measurements are similar. The anisotropic ellipsoids for O extend along planes perpendicular to the Si-Si axis of corner-sharing SiO4 tetrahedra, suggesting precession-like movement. Neutron PDF result confirms the occurrence of OH over some of the tetrahedral sites. We postulate that moganite nanomineral is stable with respect to quartz in hypersaline water. The ADPs of moganite show a similar trend as those of quartz determined by single-crystal XRD. In short, the combined methods can provide high-quality structural parameters of moganite nanomineral, including its ADPs and extra OH position at the surface. This approach can be used as an alternative means for solving the structures of crystals that are not large enough for single-crystal XRD measurements, such as fine-grained and nanocrystalline minerals formed in various geological environments.

58 GEOSCIENCES↗
DOE OSTI2021

Validation of non-negative matrix factorization for rapid assessment of large sets of atomic pair distribution function data

The use of the non-negative matrix factorization (NMF) technique is validated for automatically extracting physically relevant components from atomic pair distribution function (PDF) data from time-series data such as in situ experiments. The use of two matrix-factorization techniques, principal component analysis and NMF, on PDF data is compared in the context of a chemical synthesis reaction taking place in a synchrotron beam, applying the approach to synthetic data where the correct composition is known and on measured PDFs from previously published experimental data. The NMF approach yields mathematical components that are very close to the PDFs of the chemical components of the system and a time evolution of the weights that closely follows the ground truth. Lastly, it is discussed how this would appear in a streaming context if the analysis were being carried out at the beamline as the experiment progressed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Pair distribution function analysis of discrete nanomaterials in PDFgui

Pair distribution functions (PDFs) are a leading tool for atomic structure analysis of nanomaterials. However, the most widely used programs for refining atomic structure against PDF data are based on extended crystallographic models, which cannot be applied to discrete, whole nanoparticles. Furthermore, this work describes a straightforward approach to simulate and refine atomistic models of discrete clusters and nanoparticles employing widely used PDF modelling programs such as PDFgui that utilize extended crystallographic models. In this approach, the whole particle to be modelled is contained within an expanded, and otherwise empty, unit cell that is sufficiently large to avoid correlations between atoms in neighbouring unit cells over the r range analyzed. The PDF of the particle is simulated as a composite using two conventional `phases': one that calculates the atom–atom correlations and one that approximates the local number density. This approach is first validated for large nanoparticles that are well modelled by a conventional shape factor model, and then applied to simulate the PDF of discrete particles and low-dimensional materials (graphene and MXene) and to model the experimental PDF data for single-layer FeS nanosheets. A comparison of this approach with the DiffPy-CMI program, which calculates the PDF of discrete species, shows that the composite modelling approach is equally or more accurate. Example input files for implementing this approach within PDFgui and TOPAS, and recommendations for selecting model parameters for reliable application of this refinement strategy, are provided.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Symmetry-mode analysis for local structure investigations using pair distribution function data

Symmetry-adapted distortion modes provide a natural way of describing distorted structures derived from higher-symmetry parent phases. Structural refinements using symmetry-mode amplitudes as fit variables have been used for at least ten years in Rietveld refinements of the average crystal structure from diffraction data; more recently, this approach has also been used for investigations of the local structure using real-space pair distribution function (PDF) data. Here, the value of performing symmetry-mode fits to PDF data is further demonstrated through the successful application of this method to two topical materials: TiSe2, where a subtle but long-range structural distortion driven by the formation of a charge-density wave is detected, and MnTe, where a large but highly localized structural distortion is characterized in terms of symmetry-lowering displacements of the Te atoms. Here, the analysis is performed using fully open-source code within the DiffPy framework via two packages developed for this work: isopydistort, which provides a scriptable interface to the ISODISTORT web application for group theoretical calculations, and isopytools, which converts the ISODISTORT output into a DiffPy-compatible format for subsequent fitting and analysis. These developments expand the potential impact of symmetry-adapted PDF analysis by enabling high-throughput analysis and removing the need for any commercial software.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Atomic structure and grain shape evolution of nanodiamond during annealing in oxidizing atmosphere from neutron diffraction and MD simulations

In this work, real space pair-distribution function (PDF) analysis in conjunction with molecular dynamics (MD) simulations was applied to characterize crystal structure, shape and surface structure of diamond nanoparticles annealed in air up to 880 °C. MD simulated models of individual nanodiamond particles of various shapes and sizes were used to calculate theoretical radial distribution functions G(r) for powders with different grain size distributions. The calculated curves, showing distinct differences for the explored parameter space, were compared to the experimental G(r) functions obtained from neutron scattering for annealed detonated nanodiamond samples in a search for a model best describing the actual powders. It was found that as-synthesized nanodiamond grains are terminated by equally abundant (100), (110) and (111) crystallographic faces and their structure does not change upon annealing in air up to 280 °C. The shape and size of grains annealed above 480 °C changes due to surface etching. The etching rate differs between crystals faces and depends on temperature, resulting in the observed differences in grain shape. Below 680 °C the share of the (110) facets gradually increases and at 680 °C the grains become rhombic dodecahedra terminated solely by (110) surfaces. Further increase of the annealing temperature promotes formation of (111) surfaces and at 880 °C the preferred grain shape becomes an octahedron terminated by a variant of (111) surfaces possessing three dangling sp3 bonds per atom. At lower temperatures all grains become smaller and the size distribution moves towards the lower values. Furthermore, as the annealing temperature increases, the smallest grains disappear entirely and the average grain size grows back.

36 MATERIALS SCIENCE↗
NASA NTRS2004

High Pressure X-Ray Diffraction Studies of Nanocrystalline Materials

Experimental evidence obtained for a variety of nanocrystalline materials suggest that the crystallographic structure of a very small size particle deviates from that in the bulk crystals. In this paper we show the effect of the surface of nanocrystals on their structure by the analysis of generation and distribution of macro- and micro-strains at high pressures and their dependence on the grain size in nanocrystalline powders of Sic. We studied the structure of Sic nanocrystals by in-situ high-pressure powder diffraction technique using synchrotron and neutron sources and hydrostatic or isostatic pressure conditions. The diffraction measurements were done in HASYLAB at DESY using a Diamond Anvil Cell (DAC) in the energy dispersive geometry in the diffraction vector range up to 3.5 - 4/A and under pressures up to 50 GPa at room temperature. In-situ high pressure neutron diffraction measurements were done at LANSCE in Los Alamos National Laboratory using the HIPD and HIPPO diffractometers with the Paris-Edinburgh and TAP-98 cells, respectively, in the diffraction vector range up to 26 Examination of the response of the material to external stresses requires nonstandard methodology of the materials characterization and description. Although every diffraction pattern contains a complete information on macro- and micro-strains, a high pressure experiment can reveal only those factors which contribute to the characteristic diffraction patterns of the crystalline phases present in the sample. The elastic properties of powders with the grain size from several nm to micrometers were examined using three methodologies: (l), the analysis of positions and widths of individual Bragg reflections (used for calculating macro- and micro-strains generated during densification) [I], (2). the analysis of the dependence of the experimental apparent lattice parameter, alp, on the diffraction vector Q [2], and (3), the atomic Pair Distribution Function (PDF) technique [3]. The results of our studies show, that Sic nanocrystals have the features of two phases, each with its distinct elastic properties. and under pressures up to 8 GPa.

Palosz, B.↗
DOE OSTI2020

Mechanistic insight of KBiQ 2 (Q = S, Se) using panoramic synthesis towards synthesis-by-design

Solid-state synthesis has historically focused on reactants and end products; however, knowledge of reaction pathways, intermediate phases and their formation may provide mechanistic insight of solid-state reactions. With an increased understanding of reaction progressions, design principles can be deduced, affording more predictive power in materials synthesis. In pursuit of this goal, in situ powder X-ray diffraction is employed to observe crystalline phase evolution over the course of the reaction, thereby constructing a “panoramic” view of the reaction from beginning to end. We conducted in situ diffraction studies in the K–Bi–Q (Q = S, Se) system to understand the formation of phases occurring in this system in the course of their reactions. Powder mixtures of K 2 Q to Bi 2 Q 3 in 1:1 and 1.5:1 ratios were heated to 800 °C or 650 °C, while simultaneously collecting diffraction data. Three new phases, K 3 BiS 3 , β-KBiS 2 , and β-KBiSe 2 , were discovered. Panoramic synthesis showed that K 3 BiQ 3 serves an important mechanistic role as a structural intermediate in both chalcogen systems (Q = S, Se) in the path to form the KBiQ 2 structure. Thermal analysis and calculations at the density functional theory (DFT) level show that the cation-ordered β-KBiQ 2 polymorphs are the thermodynamically stable phase in this compositional space, while Pair Distribution Function (PDF) analysis shows that all α-KBiQ 2 structures have local disorder due to stereochemically active lone pair expression of the bismuth atoms. The formation of the β-KBiQ 2 structures, both of which crystallize in the α-NaFeO 2 structure type, show a boundary where the structure can be disordered or ordered with regards to the alkali metal and bismuth. A cation radius tolerance for six-coordinate cation site sharing of ($\frac{r^+}{r^{3+}}$) ~ 1.3 is proposed. The mechanistic insight the panoramic synthesis technique provides in the K–Bi–Q system is progress towards the overarching goal of synthesis-by-design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Atomic structural mechanism for ferroelectric-antiferroelectric transformation in perovskite NaNbO 3

Sodium niobate (NaNbO 3 or NN) is described as “the most complex perovskite system,” which exhibits transitions between, as well as coexistence of, several ferroelectrics (FE) and antiferroelectric (AFE) phases at different temperatures. Recently, solid solutions of NN with stabilized AFE phases(s) have gained attention for energy-related applications, such as high-density energy storage and electrocaloric cooling. A better understanding of the atomic mechanisms responsible for AFE/FE phase transitions in NaNbO 3 can enable a more rational design of its solid-solution systems with tunable functional properties. In this work, we have investigated changes in the average and local atomic structure of NN using a combination of x-ray/neutron diffraction and neutron pair-distribution function (PDF) analyses. The Rietveld refinement of the x-ray/neutron-diffraction patterns indicates a coexistence of the FE Q (P2 1 ma) and AFE P (Pbma) phases in the temperature range of 300 K ≤ T ≤ 615K, while PDF analysis indicated that the local structure (r < 8Å) is better described by a P2 1 ma symmetry. Above 615 K, the average structure transitions to an AFE R phase (Pmmn or Pnma), while PDF analysis shows an increased disordering of the octahedral distortions and Na displacements at the local scale. These results indicate that the average P/Q/R phase transitions in NN can be described as a result of complex ordering of distorted octahedral tilts at the nanoscale and off-centered displacements of the Na atoms.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Making sense of vacancy correlations with single-crystal diffuse scattering data

Local ordering of atoms within a crystalline structure is increasingly recognized as essential to understanding the properties of a variety of interesting materials. This is shown by the success of pair distribution function (PDF) analysis of scattering data from powder samples to investigate departures from perfectly crystalline order (Billinge & Kanatzidis, 2004; Egami & Billinge, 2012). Diffuse scattering from single crystals can also be a powerful probe of local order, potentially providing key information that would be difficult to obtain from PDF methods; however, difficulties in both measurement and interpretation of data have too often restricted their use by a larger community. In this issue of IUCrJ, Rothet al.(2020) demonstrate how simple concepts can be applied to better understand single-crystal diffuse scattering from half-Heusler systems.

36 MATERIALS SCIENCE↗