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The atomic pair distribution function (PDF) is a real-space representation of the structure of a material. Experimental PDFs are obtained using a Fourier transform from total scattering data which may or may not have Bragg diffraction peaks. The determination of Bragg peak resolution in scattering data from the fundamental physical parameters of the diffractometer used is well established, but after the Fourier transform from reciprocal to direct space, these contributions are harder to identify. Starting from an existing definition of the resolution function of large-area detectors for X-ray diffraction, this approach is expanded into direct space. The effect of instrumental parameters on PDF peak resolution is developed mathematically, then studied with modelling and comparison with experimental PDFs of LaB6 from measurements made in different-sized capillaries.

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As an important characterization method, pair distribution function (PDF) has been extensively used in structural analysis of nanomaterials, providing key insights into the degree of crystallinity, atomic structure, local disorder etc. The collection of scattering signals with good statistics is necessary for a reliable structural analysis. However, current conventional electron diffraction experiments using PDF (ePDF) are limited in their ability to acquire continuous diffraction rings for large nanoparticles. Herein, a new method - tilt-ePDF - is proposed to improve the data quality and compatibility of ePDF by a combination of electron diffraction and specimen tilting. In the present work, a tilt-series of electron diffraction patterns was collected from gold nanoparticles with three different sizes and a standard sample polycrystalline aluminium film for ePDF analysis. The results show that tilt-ePDF can not only enhance the continuity of diffraction rings, but can also improve the signal-to-noise ratio in the high scattering angle range. As a result, compared with conventional ePDF data, tilt-ePDF data provide structure parameters with a better accuracy and lower residual factors in the refinement against the crystal structure. This method provides a new way of utilizing ePDF to obtain accurate local structure information from nanoparticles.

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Our study compares short-range order parameters refined from the diffuse scattering in single-crystal X-ray and single-crystal electron diffraction data. Nb0.84CoSb was chosen as a reference material. The correlations between neighbouring vacancies and the displacements of Sb and Co atoms were refined from the diffuse scattering using a Monte Carlo refinement in DISCUS. The difference between the Sb and Co displacements refined from the diffuse scattering and the Sb and Co displacements refined from the Bragg reflections in single-crystal X-ray diffraction data is 0.012 (7) Šfor the refinement on diffuse scattering in single-crystal X-ray diffraction data and 0.03 (2) Šfor the refinement on the diffuse scattering in single-crystal electron diffraction data. As electron diffraction requires much smaller crystals than X-ray diffraction, this opens up the possibility of refining short-range order parameters in many technologically relevant materials for which no crystals large enough for single-crystal X-ray diffraction are available.

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The application of grazing-incidence total X-ray scattering (GITXS) for pair distribution function (PDF) analysis using >50 keV X-rays from synchrotron light sources has created new opportunities for structural characterization of supported thin films with high resolution. Compared with grazing-incidence wide-angle X-ray scattering, which is only useful for highly ordered materials, GITXS/PDFs expand such analysis to largely disordered or nanostructured materials by examining the atomic pair correlations dependent on the direction relative to the surface of the supporting substrate. A characterization of nanocrystalline In2O3-derived thin films is presented here with in-plane-isotropic and out-of-plane-anisotropic orientational ordering of the atomic structure, each synthesized using different techniques. The atomic orientations of such films are known to vary based on the synthetic conditions. Here, an azimuthal orientational analysis of these films using GITXS with a single incident angle is shown to resolve the markedly different orientations of the atomic structures with respect to the planar support and the different degrees of long-range order, and hence, the terminal surface chemistries. It is anticipated that orientational analysis of GITXS/PDF data will offer opportunities to extend structural analyses of thin films by providing a means to qualitatively determine the major atomic orientation within nanocrystalline and, eventually, non-crystalline films.

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X-ray structural science is undergoing a revolution driven by the emergence of X-ray Free-electron Laser (XFEL) facilities. The structures of crystalline solids can now be studied on the picosecond time scale relevant to phonons, atomic vibrations which travel at acoustic velocities. In the work presented here, X-ray diffuse scattering is employed to characterize the time dependence of the liquid phase emerging from femtosecond laser-induced melting of polycrystalline gold thin films using an XFEL. In a previous analysis of Bragg peak profiles, we showed the supersonic disappearance of the solid phase and presented a model of pumped hot electrons carrying energy from the gold surface to scatter at internal grain boundaries. This generates melt fronts propagating relatively slowly into the crystal grains. By conversion of diffuse scattering to a partial X-ray pair distribution function, we demonstrate that it has the characteristic shape obtained by Fourier transformation of the measured F(Q). The diffuse signal fraction increases with a characteristic rise-time of 13 ps, roughly independent of the incident pump fluence and consequent final liquid fraction. This suggests the role of further melt-front nucleation processes beyond grain boundaries.

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The structural investigation of amorphous pharmaceuticals is of paramount importance in comprehending their physicochemical stability. However, it has remained a relatively underexplored realm primarily due to the limited availability of high-resolution analytical tools. In this study, we utilized the combined power of X-ray pair distribution functions (PDFs) and solid-state nuclear magnetic resonance (ssNMR) techniques to probe the molecular packing of amorphous posaconazole and its amorphous solid dispersion at the molecular level. Leveraging synchrotron X-ray PDF data and employing the empirical potential structure refinement (EPSR) methodology, we unraveled the existence of a rigid conformation and discerned short-range intermolecular C-F contacts within amorphous posaconazole. Encouragingly, our ssNMR 19F-13C distance measurements offered corroborative evidence supporting these findings. Furthermore, employing principal component analysis on the X-ray PDF and ssNMR data sets enabled us to gain invaluable insights into the chemical nature of the intermolecular interactions governing the drug-polymer interplay. These outcomes not only furnish crucial structural insights facilitating the comprehension of the underlying mechanisms governing the physicochemical stability but also underscore the efficacy of synergistically harnessing X-ray PDF and ssNMR techniques, complemented by robust modeling strategies, to achieve a high-resolution exploration of amorphous structures.

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RESUMEN

The approach based on atomic pair distribution function (PDF) has revolutionized structural investigations by X-ray/electron diffraction of nano or quasi-amorphous materials, opening up the possibility of exploring short-range order. However, the ab initio crystal structural solution by the PDF is far from being achieved due to the difficulty in determining the crystallographic properties of the unit cell. A method for estimating the crystal cell parameters directly from a PDF profile is presented, which is composed of two steps: first, the type of crystal cell is inferred using machine-learning approaches applied to the PDF profile; second, the crystal cell parameters are extracted by means of multivariate analysis combined with vector superposition techniques. The procedure has been validated on a large number of PDF profiles calculated from known crystal structures and on a small number of measured PDF profiles. The lattice determination step has been benchmarked by a comprehensive exploration of different classifiers and different input data. The highest performance is obtained using the k-nearest neighbours classifier applied to whole PDF profiles. Descriptors calculated from the PDF profiles by recurrence quantitative analysis produce results that can be interpreted in terms of PDF properties, and the significance of each descriptor in determining the prediction is evaluated. The cell parameter extraction step depends on the cell metric rather than its type. Monometric, dimetric and trimetric cells have top-1 estimates that are correct 40, 20 and 5% of the time, respectively. Promising results were obtained when analysing real nanocrystals, where unit cells close to the true ones are found within the top-1 ranked solution in the case of monometric cells and within the top-6 ranked solutions in the case of dimetric cells, even in the presence of a crystalline impurity with a weight fraction up to 40%.

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Pair distribution function (PDF) analysis is a powerful technique to understand atomic scale structure in materials science. Unlike X-ray diffraction (XRD)-based PDF analysis, the PDF calculated from electron diffraction patterns (EDPs) using transmission electron microscopy can provide structural information from specific locations with high spatial resolution. The present work describes a new software tool for both periodic and amorphous structures that addresses several practical challenges in calculating the PDF from EDPs. The key features of this program include accurate background subtraction using a nonlinear iterative peak-clipping algorithm and automatic conversion of various types of diffraction intensity profiles into a PDF without requiring external software. The present study also evaluates the effect of background subtraction and the elliptical distortion of EDPs on PDF profiles. The EDP2PDF software is offered as a reliable tool to analyse the atomic structure of crystalline and non-crystalline materials.

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In situ gas-loading sample holders for two-dimensionally arranged detectors in time-of-flight neutron total scattering experiments have been developed to investigate atomic arrangements during deuterium absorption using time and real-space resolution. A single-crystal sapphire container was developed that allows conditions of 473 K and 10 MPa hydrogen gas pressure. High-resolution transient measurements detected deuterium absorption by palladium that proceeded within a few seconds. A double-layered container with thick- and thin-walled vanadium allowed conditions of 423 K and 10 MPa hydrogen gas pressure. The deuterium occupation sites of a lanthanum-nickel-aluminium alloy are discussed in detail on the basis of real-space high-resolution data obtained from in situ neutron scattering measurements and reverse Monte Carlo structural modeling.

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Structural modelling of octahedral tilts in perovskites is typically carried out using the symmetry constraints of the resulting space group. In most cases, this introduces more degrees of freedom than those strictly necessary to describe only the octahedral tilts. It can therefore be a challenge to disentangle the octahedral tilts from other structural distortions such as cation displacements and octahedral distortions. This paper reports the development of constraints for modelling pure octahedral tilts and implementation of the constraints in diffpy-CMI, a powerful package to analyse pair distribution function (PDF) data. The model in the program allows features in the PDF that come from rigid tilts to be separated from non-rigid relaxations, providing an intuitive picture of the tilting. The model has many fewer refinable variables than the unconstrained space group fits and provides robust and stable refinements of the tilt components. It further demonstrates the use of the model on the canonical tilted perovskite CaTiO3 which has the known Glazer tilt system α+ß-ß-. The Glazer model fits comparably to the corresponding space-group model Pnma below r = 14 Šand becomes progressively worse than the space-group model at higher r due to non-rigid distortions in the real material.

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An approach is described for studying texture in nanostructured materials. The approach implements the real-space texture pair distribution function (PDF), txPDF, laid out by Gong & Billinge {(2018 ▸). arXiv:1805.10342 [cond-mat]}. It is demonstrated on a fiber-textured polycrystalline Pt thin film. The approach uses 3D PDF methods to reconstruct the orientation distribution function of the powder crystallites from a set of diffraction patterns, taken at different tilt angles of the substrate with respect to the incident beam, directly from the 3D PDF of the sample. A real-space equivalent of the reciprocal-space pole figure is defined in terms of interatomic vectors in the PDF and computed for various interatomic vectors in the Pt film. Furthermore, it is shown how a valid isotropic PDF may be obtained from a weighted average over the tilt series, including the measurement conditions for the best approximant to the isotropic PDF from a single exposure, which for the case of the fiber-textured film was in a nearly grazing incidence orientation of ∼10°. Finally, an open-source Python software package, FouriGUI, is described that may be used to help in studies of texture from 3D reciprocal-space data, and indeed for Fourier transforming and visualizing 3D PDF data in general.

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Structural characterization of powder samples via total scattering methods, in either real or reciprocal space, must take into account the effect of particle shape. Here, the shape contribution of a set of ideally isolated particles to the small-angle scattering (SAS) component of the intensity profile is modelled using the shape function [Svergun & Koch (2003). Rep. Prog. Phys. 66, 1735-1782]. The shape function is obtained by orientational averaging of common volume functions (CVFs) for a discrete set of directions. The effects of particle size and size dispersity are accounted for via scaling of the CVFs and their convolution with the underlying probability distribution. The method is applied to shapes with CVFs expressed analytically or by using discrete tables. The accurate calculation of SAS particle shape contributions up to large momentum transfer demonstrates the reliability and flexibility of modelling shape functions from sets of CVFs. The algorithm presented here is computationally efficient and can be directly incorporated into existing routines for analysis of powder total scattering data.

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Data-driven approaches in materials science demand the collection of large amounts of data on the target materials at synchrotron beamlines. To accurately gather suitable experimental data, it is essential to establish fully automated measurement systems to reduce the workload of the beamline staff. Moreover, the recent COVID-19 pandemic has further emphasized the necessity of automated and/or remote measurements at synchrotron beamlines. Here, the installation of a new sample changer combined with a high-temperature furnace and a fully automated alignment system on beamline BL04B2 at SPring-8 is reported. The system allows X-ray total scattering measurements of up to 21 samples at different temperatures (from room temperature to 1200°C) to be conducted without any human assistance.

Asunto(s)

RESUMEN

A novel symmetry-adapted pair distribution function analysis (SAPA) method for extracting information on local distortions from pair distribution function data is introduced. The implementation of SAPA is demonstrated in the TOPAS-Academic software using the freely available online software ISODISTORT, and scripts for converting the output from ISODISTORT to a SAPA input file for TOPAS are provided. Finally, two examples are provided to show how SAPA can evaluate the nature of both dynamic distortions in ScF3 and the distortions which act as an order parameter for the phase transitions in BaTiO3.

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An approach for the comparison of pair distribution functions (PDFs) has been developed using a similarity measure based on cross-correlation functions. The PDF is very sensitive to changes in the local structure, i.e. small deviations in the structure can cause large signal shifts and significant discrepancies between the PDFs. Therefore, a comparison based on pointwise differences (e.g. R values and difference curves) may lead to the assumption that the investigated PDFs as well as the corresponding structural models are not in agreement at all, whereas a careful visual inspection of the investigated structural models and corresponding PDFs may reveal a relatively good match. To quantify the agreement of different PDFs for those cases an alternative approach is introduced: the similarity measure based on cross-correlation functions. In this paper, the power of this application of the similarity measure to the analysis of PDFs is highlighted. The similarity measure is compared with the classical R wp values as representative of the comparison based on pointwise differences as well as with the Pearson product-moment correlation coefficient, using polymorph IV of barbituric acid as an example.

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Synchrotron powder X-ray diffraction (PXRD) is a well established technique for investigating the atomic arrangement of crystalline materials. At modern beamlines, X-ray scattering data can be collected in a total-scattering setting, which additionally opens up the opportunity for direct-space structural analysis through the atomic pair distribution function (PDF). Modelling of PXRD and PDF data is typically carried out separately, but employing a concurrent structural model to both direct- and reciprocal-space data has the possibility to enhance total-scattering data analysis. However, total-scattering measurements applicable to such dual-space analyses are technically demanding. Recently, the technical demands have been fulfilled by a MYTHEN microstrip detector system (OHGI), which meets the stringent requirements for both techniques with respect to Q range, Q resolution and dynamic range. In the present study, we evaluate the quality of total-scattering data obtained with OHGI by separate direct- and reciprocal-space analysis of Si. Excellent agreement between structural parameters in both spaces is found, demonstrating that the total-scattering data from OHGI can be utilized in dual-space structural analysis e.g. for in situ and operando measurements.

RESUMEN

Microstructure-based design of materials requires an atomic level understanding of the mechanisms underlying structure-dependent properties. Methods for analyzing either the traditional diffraction profile or the pair distribution function (PDF) differ in how the information is accessed and in the approximations usually applied. Any variation of structural and microstructural features over the whole sample affects the Bragg peaks as well as any diffuse scattering. Accuracy of characterization relies, therefore, on the reliability of the analysis methods. Methods based on Bragg's law investigate the diffraction peaks in the intensity plot as distinct pieces of information. This approach reaches a limitation when dealing with disorder scenarios that do not conform to such a peak-by-peak basis. Methods based on the Debye scattering equation (DSE) are, otherwise, well suited to evaluate the scattering from a disordered phase but the structure information is averaged over short-range distances usually accessed by experiments. Moreover, statistical reliability is usually sacrificed to recover some of the computing-efficiency loss compared with traditional line-profile-analysis methods. Here, models based on Bragg's law are used to facilitate the computation of a whole PDF and then model powder-scattering data via the DSE. Models based on Bragg's law allow the efficient solution of the dispersion of a crystal's properties in a powder sample with statistical reliability, and the PDF provides the flexibility of the DSE. The whole PDF is decomposed into the independent directional components, and the number of atom pairs separated by a given distance is statistically estimated using the common-volume functions. This approach overcomes the need for an atomistic model of the material sample and the computation of billions of pair distances. The results of this combined method are in agreement with the explicit solution of the DSE although the computing efficiency is comparable with that of methods based on Bragg's law. Most importantly, the method exploits the strengths and different sensitivities of the Bragg and Debye theories.

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A novel approach for finding and evaluating structural models of small metallic nanoparticles is presented. Rather than fitting a single model with many degrees of freedom, libraries of clusters from multiple structural motifs are built algorithmically and individually refined against experimental pair distribution functions. Each cluster fit is highly constrained. The approach, called cluster-mining, returns all candidate structure models that are consistent with the data as measured by a goodness of fit. It is highly automated, easy to use, and yields models that are more physically realistic and result in better agreement to the data than models based on cubic close-packed crystallographic cores, often reported in the literature for metallic nanoparticles.

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P2-type Fe- and Mn-based layered sodium transition metal oxides are promising positive electrode materials for sodium batteries due to their high energy density and low costs of the constituting transition metals. However, poor structural reversibility and fast capacity decay have prevented their breakthrough so far. Herein, the real-time dynamic phase transitions and capacity fading mechanism of the P2 Na0.67Fe0.5Mn0.5O2 positive electrode are revealed by operando X-ray diffraction, operando/ex situ X-ray absorption spectroscopy, neutron powder diffraction, and neutron pair distribution functions. Upon the desodiation process, a layered OP4 phase with long-range order is found as an intermediate state. With further deep desodiation, the formation of a Na-depleted ramsdellite phase with a short coherent length of 30 Å is observed for the first time. However, the transition from OP4 to ramsdellite is considered to be irreversible due to the breakdown of the layered structural characteristics, resulting in poor cycling performance in a variety of Fe-based layered sodium transition metal oxides. This work suggests that stabilizing the crystal structure by substitution or chemical modification can be a favorable strategy to avoid the degradation of positive electrodes and thus to improve the cycling performance.

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Porous, high-surface-area electrode architectures are described that allow structural characterization of interfacial amorphous thin films with high spatial resolution under device-relevant functional electrochemical conditions using high-energy X-ray (>50 keV) scattering and pair distribution function (PDF) analysis. Porous electrodes were fabricated from glass-capillary array membranes coated with conformal transparent conductive oxide layers, consisting of either a 40 nm-50 nm crystalline indium tin oxide or a 100 nm-150 nm-thick amorphous indium zinc oxide deposited by atomic layer deposition. These porous electrodes solve the problem of insufficient interaction volumes for catalyst thin films in two-dimensional working electrode designs and provide sufficiently low scattering backgrounds to enable high-resolution signal collection from interfacial thin-film catalysts. For example, PDF measurements were readily obtained with 0.2 Šspatial resolution for amorphous cobalt oxide films with thicknesses down to 60 nm when deposited on a porous electrode with 40 µm-diameter pores. This level of resolution resolves the cobaltate domain size and structure, the presence of defect sites assigned to the domain edges, and the changes in fine structure upon redox state change that are relevant to quantitative structure-function modeling. The results suggest the opportunity to leverage the porous, electrode architectures for PDF analysis of nanometre-scale surface-supported molecular catalysts. In addition, a compact 3D-printed electrochemical cell in a three-electrode configuration is described which is designed to allow for simultaneous X-ray transmission and electrolyte flow through the porous working electrode.