X‐ray pair distribution function analysis of nanostructured materials using a Mythen detector

Total scattering from nanocrystalline materials recorded on the Australian Synchrotron powder diffraction beamline has been analysed to produce atomic pair distribution functions (PDFs) for structural analysis. The capability of this beamline, which uses the massively parallel Mythen II detector, has been quantified with respect to PDF structure analysis. Data were recorded to a wavevector magnitude, Q, of 20.5 Å^?1, with successful PDFs obtained for counting times as short as 10 s for crystalline LaB₆ and 180 s for nanocrystalline (47 Å) anatase. This paper describes the aspects of a PDF experiment that are crucial to its success, with reference to the outcomes of analysis of data collected from nanocrystalline TiO₂ and microcrystalline LaB₆ and IrO₂.     

Data analysis method to achieve sub‐10 pm spatial resolution using extended X‐ray absorption fine‐structure spectroscopy

Obtaining sub‐10 pm spatial resolution by extended X‐ray absorption fine structure (EXAFS) spectroscopy is required in many important fields of research, such as lattice distortion studies in colossal magnetic resistance materials, high‐temperature superconductivity materials etc. However, based on the existing EXAFS data analysis methods, EXAFS has a spatial resolution limit of π/2Δk which is larger than 0.1 Å. In this paper a new data analysis method which can easily achieve sub‐10 pm resolution is introduced. Theoretically, the resolution limit of the method is three times better than that normally available. The method is examined by numerical simulation and experimental data. As a demonstration, the LaFe_1–xCr_xO₃ system (x = 0, 1/3, 2/3) is studied and the structural information of FeO₆ octahedral distortion as a function of Cr doping is resolved directly from EXAFS, where a resolution better than 0.074 Å is achieved.     

Correction method for the self‐absorption effects in fluorescence extended X‐ray absorption fine structure on multilayer samples

A novel correction method for self‐absorption effects is proposed for extended X‐ray absorption fine structure (EXAFS) detected in the fluorescence mode on multilayer samples. The effects of refraction and multiple reflection at the interfaces are fully considered in this correction method. The correction is performed in k‐space before any further data analysis, and it can be applied to single‐layer or multilayer samples with flat surfaces and without thickness limit when the model parameters for the samples are known. The validity of this method is verified by the fluorescence EXAFS data collected for a Cr/C multilayer sample measured at different experimental geometries.     

Pressure study of monoclinic ReO2 up to 1.2 GPa using X‐ray absorption spectroscopy and X‐ray diffraction

The crystal and local atomic structure of monoclinic ReO₂ (α‐ReO₂) under hydrostatic pressure up to 1.2 GPa was investigated for the first time using both X‐ray absorption spectroscopy and high‐resolution synchrotron X‐ray powder diffraction and a home‐built B₄C anvil pressure cell developed for this purpose. Extended X‐ray absorption fine‐structure (EXAFS) data analysis at pressures from ambient up to 1.2 GPa indicates that there are two distinct Re—Re distances and a distorted ReO₆ octahedron in the α‐ReO₂ structure. X‐ray diffraction analysis at ambient pressure revealed an unambiguous solution for the crystal structure of the α‐phase, demonstrating a modulation of the Re—Re distances. The relatively small portion of the diffraction pattern accessed in the pressure‐dependent measurements does not allow for a detailed study of the crystal structure of α‐ReO₂ under pressure. Nonetheless, a shift and reduction in the (011) Bragg peak intensity between 0.4 and 1.2 GPa is observed, with correlation to a decrease in Re—Re distance modulation, as confirmed by EXAFS analysis in the same pressure range. This behavior reveals that α‐ReO₂ is a possible inner pressure gauge for future experiments up to 1.2 GPa.     

Atomic pair distribution function method development at the Shanghai Synchrotron Radiation Facility

The atomic pair distribution function(PDF) reveals the interatomic distance in a material directly in real-space. It is a very powerful method to characterize the local structure of materials. With the help of the third generation synchrotron facility and spallation neutron source worldwide, the PDF method has developed quickly both experimentally and theoretically in recent years. Recently this method was successfully implemented at the Shanghai Synchrotron Radiation Facility(SSRF). The data quality is very high and this ensures the applicability of the method to study the subtle structural changes in complex materials. In this article, we introduce in detail this new method and show some experimental data we collected.     

In situ electrochemical high‐energy X‐ray diffraction using a capillary working electrode cell geometry

The ability to generate new electrochemically active materials for energy generation and storage with improved properties will likely be derived from an understanding of atomic‐scale structure/function relationships during electrochemical events. Here, the design and implementation of a new capillary electrochemical cell designed specifically for in situ high‐energy X‐ray diffraction measurements is described. By increasing the amount of electrochemically active material in the X‐ray path while implementing low‐Z cell materials with anisotropic scattering profiles, an order of magnitude enhancement in diffracted X‐ray signal over traditional cell geometries for multiple electrochemically active materials is demonstrated. This signal improvement is crucial for high‐energy X‐ray diffraction measurements and subsequent Fourier transformation into atomic pair distribution functions for atomic‐scale structural analysis. As an example, clear structural changes in LiCoO₂ under reductive and oxidative conditions using the capillary cell are demonstrated, which agree with prior studies. Accurate modeling of the LiCoO₂ diffraction data using reverse Monte Carlo simulations further verifies accurate background subtraction and strong signal from the electrochemically active material, enabled by the capillary working electrode geometry.     

Oscillation of the radial distribution function

We prove that the radial distribution function oscillates at low density in a system with a short-range nonnegative potential and investigate the branching of the solutions of an approximate equation of state.     

Position and flux stabilization of X‐ray beams produced by double‐crystal monochromators for EXAFS scans at the titanium K‐edge

The simultaneous and active feedback stabilization of X‐ray beam position and monochromatic beam flux during EXAFS scans at the titanium K‐edge as produced by a double‐crystal monochromator beamline is reported. The feedback is generated using two independent feedback loops using separate beam flux and position measurements. The flux is stabilized using a fast extremum‐searching algorithm that is insensitive to changes in the synchrotron ring current and energy‐dependent monochromator output. Corrections of beam height are made using an innovative transmissive beam position monitor instrument. The efficacy of the feedback stabilization method is demonstrated by comparing the measurements of EXAFS spectra on inhomogeneous diluted Ti‐containing samples with and without feedback applied.     

In situ X‐ray absorption spectroscopic studies of copper in a copper‐rich sludge during electrokinetic treatments

Speciation of copper in a copper‐rich chemical‐mechanical polishing sludge during electrokinetic treatment has been studied by in situ extended X‐ray absorption fine structure (EXAFS) and X‐ray absorption near‐edge structure (XANES) spectroscopy. The least‐squares‐fitted XANES spectra indicate that the main copper species in the sludge are Cu(OH)₂ (74%), nanosize CuO (20–60 nm) (13%) and CuO (>100 nm) (13%). The average bond distance and coordination number (CN) of Cu—O are 1.96 Å and 3.5, respectively. Under electrokinetic treatment (5 V cm^?1) for 120 min, about 85% of the copper is dissolved in the electrolyte, 13% of which is migrated and enriched on the cathode. Notably the copper nanoparticles in the sludge can also migrate to the cathode under the electric field. By in situ EXAFS, it is found that during the electrokinetic treatment the bond distance and CN of Cu—O are increased by 0.1 Å and 0.9, respectively.     

Rietveld and pair distribution function study of Hägg carbide using synchrotron X‐ray diffraction

Fischer–Tropsch (FT) synthesis is an important process in the manufacturing of hydrocarbons and oxygenated hydrocarbons from mixtures of carbon monoxide and hydrogen (syngas). The reduced iron catalyst reacts with carbon monoxide and hydrogen to form bulk Fe₅C₂ Hägg carbide (χ‐HC) during FT synthesis. Arguably, χ‐HC is the predominant catalyst phase present in the working iron catalyst. Deactivation of the working catalyst can be due to oxidation of χ‐HC to iron oxide, a step‐wise decarburization to cementite (θ‐Fe₃C), carbon formation or sintering with accompanying loss of catalytic performance. It is therefore critical to determine the precise crystal structure of χ‐HC for the understanding of the synthesis process and for comparison with the first‐principles ab initio modelling. Here the results of high‐resolution synchrotron X‐ray powder diffraction data are reported. The atomic arrangement of χ‐HC was confirmed by Rietveld refinement and subsequent real‐space modelling of the pair distribution function (PDF) obtained from direct Fourier transformation. The Rietveld and PDF results of χ‐HC correspond well with that of a pseudo‐monoclinic phase of space group Pī [a = 11.5661 (6) Å, b = 4.5709 (1) Å, c = 5.0611 (2) Å, α = 89.990 (5)°, β = 97.753 (4)°, γ = 90.195 (4)°], where the Fe atoms are located in three distorted prismatic trigonal and one octahedral arrangement around the central C atoms. The Fe atoms are distorted from the prismatic trigonal arrangement in the monoclinic structure by the change in C atom location in the structure.     

Local structure of NiAl compounds investigated by extended X‐ray absorption fine‐structure spectroscopy

The local structures of pure NiAl and Ti‐, Co‐doped NiAl compounds have been obtained utilizing extended X‐ray absorption fine‐structure (EXAFS) spectroscopy. The results provide experimental evidence that Ni antisite defects exist in the Ni‐rich NiAl compounds. The site preference of Ti and Co has been confirmed. Ti occupies the Al sublattice, while Co occupies the Ni sublattice. The structure parameters obtained by EXAFS were consistent with the X‐ray diffraction results. Owing to the precipitation of α‐Cr, the local structure of NiAl‐Cr has not been obtained, making the site preference of Cr unclear.     

A new integral equation for the radial distribution function of a hard sphere fluid

Based on a proposal by Shinomoto, a new integral equation is derived for the radial distribution function of a hard-sphere fluid using mainly geometric arguments. This integral equation is solved by a perturbation expansion in the density of the fluid, and the results obtained are compared with those from molecular dynamics simulations and from the Born-Green-Yvon (BGY) and Percus-Yevick (PY) theories. The present theory provides results for the radial distribution function which are intermediate in accuracy between those obtained from the BGY and from the PY theories.     

Electron density distribution in Si and Ge using multipole, maximum entropy method and pair distribution function analysis

The local, average and electronic structure of the semiconducting materials Si and Ge has been studied using multipole, maximum entropy method (MEM) and pair distribution function (PDF) analyses, using X-ray powder data. The covalent nature of bonding and the interaction between the atoms are clearly revealed by the two-dimensional MEM maps plotted on (100) and (110) planes and one-dimensional density along [100], [110] and [111] directions. The mid-bond electron densities between the atoms are 0.554 e/?³ and 0.187 e/?³ for Si and Ge respectively. In this work, the local structural information has also been obtained by analyzing the atomic pair distribution function. An attempt has been made in the present work to utilize the X-ray powder data sets to refine the structure and electron density distribution using the currently available versatile methods, MEM, multipole analysis and determination of pair distribution function for these two systems.      

XAS spectroelectrochemistry: reliable measurement of X‐ray absorption spectra from redox manipulated solutions at room temperature

The design and operation of a low‐volume spectroelectrochemical cell for X‐ray absorption spectroscopy (XAS) of solutions at room temperature is described. Fluorescence XAS measurements are obtained from samples contained in the void space of a 50 µL reticulated vitreous carbon (sponge) working electrode. Both rapid electrosynthesis and control of the effects of photoreduction are achieved by control over the flow properties of the solution through the working electrode, where a good balance between the rate of consumption of sample and the minimization of decomposition was obtained by pulsing the flow of the solution by 1–2 µL with duty cycle of ～3 s while maintaining a small net flow rate (26–100 µL h^?1). The performance of the cell in terms of control of the redox state of the sample and minimization of the effects of photoreduction was demonstrated by XAS measurements of aqueous solutions of the photosensitive Fe^III species, [Fe(C₂O₄)₃]^3?, together with that of the electrogenerated [Fe(C₂O₄)₃]^4? product. The current response from the cell during the collection of XAS spectra provides an independent measure of the stability of the sample of the measurement. The suitability of the approach for the study of small volumes of mM concentrations of protein samples was demonstrated by the measurement of the oxidized and electrochemically reduced forms of cytochrome c.     

Improved charge transfer multiplet method to simulate M‐ and L‐edge X‐ray absorption spectra of metal‐centered excited states

Charge transfer multiplet (CTM) theory is a computationally undemanding and highly mature method for simulating the soft X‐ray spectra of first‐row transition metal complexes. However, CTM theory has seldom been applied to the simulation of excited‐state spectra. In this article, the CTM4XAS software package is extended to simulate M_2,3‐ and L_2,3‐edge spectra for the excited states of first‐row transition metals and also interpret CTM eigenfunctions in terms of Russell–Saunders term symbols. These new programs are used to reinterpret the recently reported excited‐state M_2,3‐edge difference spectra of photogenerated ferrocenium cations and to propose alternative assignments for the electronic state of these cations responsible for the spectroscopic features. These new programs were also used to model the L_2,3‐edge spectra of Fe^II compounds during nuclear relaxation following photoinduced spin crossover and to propose spectroscopic signatures for their vibrationally hot states.     

Atomic pair distribution function at the Brazilian Synchrotron Light Laboratory: application to the Pb1–xLaxZr0.40Ti0.60O3 ferroelectric system

This work reports the setting up of the X‐ray diffraction and spectroscopy beamline at the Brazilian Synchrotron Light Laboratory for performing total scattering experiments to be analyzed by atomic pair distribution function (PDF) studies. The results of a PDF refinement for Al₂O₃ standard are presented and compared with data acquired at a beamline of the Advanced Photon Source, where it is common to perform this type of experiment. A preliminary characterization of the Pb_1–xLa_xZr_0.40Ti_0.60O₃ ferroelectric system, with x = 0.11, 0.12 and 0.15, is also shown.     

FDMX: extended X‐ray absorption fine structure calculations using the finite difference method

A new theoretical approach and computational package, FDMX, for general calculations of X‐ray absorption fine structure (XAFS) over an extended energy range within a full‐potential model is presented. The final‐state photoelectron wavefunction is calculated over an energy‐dependent spatial mesh, allowing for a complete representation of all scattering paths. The electronic potentials and corresponding wavefunctions are subject to constraints based on physicality and self‐consistency, allowing for accurate absorption cross sections in the near‐edge region, while higher‐energy results are enabled by the implementation of effective Debye–Waller damping and new implementations of second‐order lifetime broadening. These include inelastic photoelectron scattering and, for the first time, plasmon excitation coupling. This is the first full‐potential package available that can calculate accurate XAFS spectra across a complete energy range within a single framework and without fitted parameters. Example spectra are provided for elemental Sn, rutile TiO₂ and the FeO₆ octahedron.     

Finite lifetime broadening of calculated X‐ray absorption spectra: possible artefacts close to the edge

X‐ray absorption spectra calculated within an effective one‐electron approach have to be broadened to account for the finite lifetime of the core hole. For methods based on Green's function this can be achieved either by adding a small imaginary part to the energy or by convoluting the spectra on the real axis with a Lorentzian. By analyzing the Fe K‐ and L_2,3‐edge spectra it is demonstrated that these procedures lead to identical results only for energies higher than a few core‐level widths above the absorption edge. For energies close to the edge, spurious spectral features may appear if too much weight is put on broadening via the imaginary energy component. Special care should be taken for dichroic spectra at edges which comprise several exchange‐split core levels, such as the L₃‐edge of 3d transition metals.     

Early stages of decomposition in Al alloys investigated by X‐ray absorption

We demonstrate the sensitivity of X‐ray absorption fine‐structure (XAFS) measurements to the earliest stages of decomposition in Al alloys, i.e. just a few minutes after quenching. XAFS is one of the few applicable experimental approaches to this regime. Three different AlCu(Mg) samples were investigated by XAFS at the Cu K edge. Significant changes of the XAFS can be detected in the course of the decomposition in these alloys during the first 15 minutes. Actually, these changes correspond to relaxations of the nearest neighbours towards the absorbing Cu atoms. The Fourier transformation of the XAFS spectra thus leads to a pseudo radial distribution function which reflects this relaxation. In addition, XAFS measurements of the S‐phase of AlCuMg are used to decide in favour of the Perlitz and Westgren model for the S‐phase. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determining the elemental composition of Calotropis procera using X‐ray Analytical Microscopy

Caloptropis procera (Oshar) is a desert plant that did not receive much attention from the science community. The objective of this study was to investigate the elemental composition of the different parts of the plant using an X‐ray analytical microscope, to identify the elements naturally present in the plant and in the future detect the presence of any contaminants absorbed by the plants from the surrounding environment. Stalks, leaves and flowers from three Oshar plants were qualitatively and quantitatively analyzed. Leaves were scanned to establish the elemental spatial distribution within individual leaves. Subsequently, parts of the plants were dried, crushed and pulverized, then analyzed to determine elemental concentrations. The major elements present throughout the plant were Cl, K and Ca with varied concentrations. Other elements (Mg, Si, P, Fe, Sr, Mn and Br) are present in the leaf with various low concentrations of <5%. Major, minor and trace elements present in the various plant parts were determined. The outcome of this study will be used as a pilot for further investigations pertaining to the utilization of the Oshar plant for environmental cleaning purposes. Copyright © 2012 John Wiley & Sons, Ltd.