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Theory of the Extended X-Ray Absorption Fine Structure
Abstract
The extended x-ray absorption fine structure is a consequence of the modification of the photoelectron final state due to scattering by the surrounding atoms. We present a theory of the absorption fine structure starting from theoretically obtained electron-atom scattering phase shifts. The electron scattering is treated using a spherical wave expansion which takes into account the finite size of the atoms. Multiple-scattering effects are included by classifying multiple-scattering paths by their total path lengths. Their effects are quite large but appear to make quantitative but not qualitative changes on the single-scattering contribution. The exceptional case is the fourth shell in fcc or bcc structure, where it is shadowed by the first-shell atom and is profoundly affected by forward scattering due to the first shell. This may account for the anomaly observed experimentally at the fourth-shell radius in metals. A detailed numerical calculation is carried out for copper and is shown to agree quite well with experiment.
... 9 In contrast, Ag nanoclusters are less studied due to their relatively low stability. 10 With the improvement of synthesis methods, synthesizing stable Ag nanoclusters has become easier, and their total structures have been determined such as Ag 25 (SPhMe 2 ) 18 PPh 4 (abbreviated as [Ag 25 (SR) 18 ] − ) and Na 4 Ag 44 (p-MBA) 30 . 11,12 The improvement in their stability could be due to their closed-shell electron configuration like noble gas atoms. ...
... 11,12 The improvement in their stability could be due to their closed-shell electron configuration like noble gas atoms. The [Ag 25 (SR) 18 ] − nanocluster has been found to be the only matching analogue with Au nanoclusters. It has an icosahedron Ag 13 metal core and protected by six Ag 2 S 3 staple motifs. ...
... It has an icosahedron Ag 13 metal core and protected by six Ag 2 S 3 staple motifs. The [Ag 25 (SR) 18 ] − satisfies a quasi-T h symmetry. It has eight free electrons with the electron configuration 1S 2 |1P 6 . ...
Atomically precise metal nanoclusters have attracted significant interest due to their molecule-like properties. [Ag25(SR)18]- is one of the Ag nanoclusters having a unique structure similar to its Au counterpart but different from most other Ag nanoclusters. In this study, a new five-shell fitting method was developed to analyze the extended X-ray absorption fine structure (EXAFS) spectra of [Ag25(SR)18]- to provide more insights into its bonding properties. This new method was successfully applied to compare the bond lengths as the temperature changed from 300 K to 90 K. Interestingly, the metal core of [Ag25(SR)18]- shows negative thermal expansion behaviour that is not observed for Au25(SR)18. These unique bonding properties of [Ag25(SR)18]- could be related to the Ag4 tetrahedral units found in the metal core, which are absent in Au25(SR)18. These new findings about its bonding properties can provide a better understanding of the structure-property relationship of [Ag25(SR)18]-. This new EXAFS analysis method could be applied to gain insights into the bonding properties of other metal nanoclusters.
... 1920年, Friche [14] 和Hertz [15] 从实验上发现了扩展 Pendry [20] 利用EXAFS数据分析中的傅里叶变换, 提出 基于有效路径长度的多重散射EXAFS的理论描述. 后 来Rehr和Albers [21] 发展了基于格林函数传播子的可分 离表示, 获得了XAFS路径展开理论的巨大成功, 解决 了很多计算上的困难. 迄今为止, 各种各样的EXAFS 数据处理软件和XAFS理论模型都已经被发展出来, 如全路径多重散射(full multiple-scattering, FMS) [22] 、 自洽场和完全相对论计算 [23] 等. ...
... (2) 描述, 这时将利用累积量展开法 [25,26] , 或引入一个指 数分布函数来表示结构无序, 通过其与高斯原子分布 函数的卷积来表示非谐性的原子对分布函数 [27,28] . Pendry [20] , 他们把多重散射的贡献按其有效路径长度 进行分类, 这对分析原子间距及其他结构参数非常有 利. Rehr和Albers [21,29] 较深入描述的综述文章或章节 [7,8,30] . ...
... If the shape of RDF is assumed to be Gaussian, Equation 2.7 can be rewritten as Equation 2.9, which is known as the EXAFS equation (139,140). ...
... The EXAFS equation; in the classic form, Equation 2.9 (139,140), which is used for bond length distributions that can be approximated with a Gaussian; and the cumulant expansion version (141,142), used for asymmetric bond length distributions caused by a moderate disorder, have been used for decades to link the observed EXAFS oscillations to the local structure parameters (N, R, and 2 ). Central to the success of the fitting approach is the availably of a code that calculates the backscattering amplitudes ( , ), phase shifts, and photoelectron mean free path. ...
A bottom-up approach for designing heterogeneous catalysts is required to ensure a future with smarter, efficient, and sustainable chemical production. Bimetallic nanomaterial systems are exciting candidates for this purpose, as they demonstrate unique and enhanced catalytic selectivities for various catalytic processes due to structural alterations. With precise knowledge of the nanostructure of bimetallic catalysts, i.e., the identity of the surface species in general and active structures in particular, fundamental structure-property relationships can be developed and exploited for a rational design approach— but this is much easier said than done. Efforts to identify the reactive structures in bimetallic catalysts by typical multimodal operando characterization methods are hampered by their complex heterogeneous nanostructures, which can change dynamically under reaction conditions. The relatively new type of nanoparticle catalyst, the “dilute alloy” catalyst, composed of a minority metal that activates reactants and a majority metal that imparts selectivity, is essentially the epitome of the aforementioned challenges. These catalysts are fascinating because pretreatment and gas conditions result in a dynamic restructuring of the surface, which, if fully understood, could be used as a tuning knob in the design process, effectively tuning the surface composition directly. However, indeed the dynamic nature of the surface and its dilute nature make characterization very difficult. The knowledge of local structural, electronic, and dynamic descriptors of reactivity requires accurate local structure characterization, but the range of available operando methods lack spatial and temporal resolutions required for their quantitative evaluations.
In this thesis, we will present three novel methods, centered around X-ray absorption fine structure, for characterizing the local structure of bimetallic nanomaterials, namely; 1) the detection of local compositional heterogeneities in bimetallic alloys, illustrated on the example of Pd hydride formation, 2) an unsupervised machine-learning-assisted method for analysis of the information contained in the spectroscopy data, illustrated on the example of the X-ray absorption near edge structure (XANES) data, and 3) a supervised machine-learning method for the “inversion” of the XANES spectrum and mapping it onto local structure descriptors. After the development of this toolbox, we demonstrate its utility for solving several representative catalysis problems. We highlight the use of NN-XANES for solving the active site structure in metal ensembles containing 1 to 3 atoms, enabled by a unified approach that combined operando XANES spectra, activity measurements, and microkinetic modeling. These methods can apply to a broad range of mono- and hetero-metallic catalytic materials in a large number of reactions and processes.
... The initial model was in the following further refined and developed by E.A. Stern, D.E. Sayers and F.W. Lytle and coauthors [124][125][126][127][128] and others [129][130][131][132][133]. Inside the sample, the X-ray beam is attenuated according to Beer's law ...
... The initial model was in the following further refined and developed by E.A. Stern, D.E. Sayers and F.W. Lytle and coauthors [124][125][126][127][128] and others [129][130][131][132][133]. ...
Many envisaged applications, such as nanoelectronics, photovoltaics, thermoelectric power generation, light-emission devices, energy storage and biomedicine, necessitate single-walled carbon nanotube (SWCNT) samples with specific uniform electronic properties. The precise investigation of the electronic properties of filled SWCNTs on a qualitative and quantitative level is conducted by optical absorption spectroscopy, Raman spectroscopy, photoemission spectroscopy and X-ray absorption spectroscopy. This review is dedicated to the description of the spectroscopic methods for the analysis of the electronic properties of filled SWCNTs. The basic principle and main features of SWCNTs as well as signatures of doping-induced modifications of the spectra of filled SWCNTs are discussed.
... S 2 0 in Eq. (1) accounts for the inelastic loss process due to multielectron excitations at the absorbing atom. The typical distance that a photoelectron can travel before it scatters inelastically and loses coherence combined with the core-hole lifetime is called the meanfree path, λ(k), and is one of the reasons that EXAFS is a local structure probe, not able to see much further than 5 Å, [33][34][35] ...
High-entropy oxides (HEOs) are single phase solid solutions where five or more metals share the same sublattice, giving rise to unexpected features in various fields of applications. Recently, HEOs have emerged as an alternative conversion electrode anode material for next-generation Li-ion batteries, where the combination of several different elements in a single solid solution can synergistically act to overcome some of its main drawbacks, improving performance. Due to their chemical complexity, x-ray absorption spectroscopy (XAS) emerges as an appropriate technique to study the electronic (x-ray absorption near edge structure, XANES) and local structure (extended x-ray absorption fine structure, EXAFS) of these compounds as a function of cycling. This work aims to highlight the capabilities of XAS as an element-specific probe to understand a material's structure at the atomistic level through EXAFS modeling of (MgFeCoNiCuZn)O high-entropy system and how to extract valuable information about the bond distance, number of near neighbors, and local disorder, which are crucial to a full understanding of the electrochemical reaction mechanisms of such battery electrodes.
... 5), N i is the coordination number, r i is the interatomic distance and s i is the Debye-Waller factor that quantifies the disorder of each i shell. 10,11 In this approximation the photoelectron is viewed as a plane wave and it assumes that the atomic radii is much smaller than the inter-atomic distances. Therefore, the equation is valid only for k values above 3. ...
Extended X-ray Absorption Fine Structure or EXAFS spectroscopy is commonly used to characterize inorganic materials and in particular, those used in heterogeneous catalysis. This chapter begins by introducing the EXAFS technique including a brief history of its development, the theory behind it, sample environments, data analysis routines and limitations. What then follows is the main body of the work where select examples are presented from literature which demonstrate the power of the technique to characterize catalytic active sites comprising single site (ions/atoms), clusters, nanoparticles and even bulk structures in attempt to show the scope of what is possible with the EXAFS technique as far as the determination of catalyst structure-activity relationships where thermal and electrocatalytic reactions are concerned. The chapter concludes with a summary of the current state of the art as well as an outlook of what is on the horizon as far as the technique is concerned.
... where α is the fine structure constant, ψ c is the initial core level, and ψ f is the final state in the continuum part of the spectrum [1]. The dipole approximation for the matter-light coupling is enough for most of the systems, mainly for the K-edges of the elements. ...
In this work, we used, for the first time, a computational Self-Consistent Field procedure based on plane waves to describe the low and high spin conformational states of the complex [Fe(bpy)3]2+. The results obtained in the study of the minimum energy structures of this complex, a prototype of a wide class of compounds called Spin Cross Over, show how the plane wave calculations are in line with the most recent studies based on gaussian basis set functions and, above all, reproduce within acceptable errors the experimental spectra of X-ray absorption near-edge structure spectroscopy (XANES). This preliminary study shows the capabilities of plane wave methods to correctly describe the molecular structures of metal-organic complexes of this type and paves the way for future even complex computational simulations based on the energy gradient, such as Nudge Elastic Band or ab-initio Born-Oppenheimer molecular dynamics.
... In addition, it is worth mentioning that for the MS paths, which are in many cases neglected in the analysis, these functions show a strong nonlinear angular dependence especially in the case of linear atomic chains. 5,8 The first attempt to solve this problem was provided by Frenkel et al. 9−12 In these studies, the authors were able to estimate, from the analysis of certain double and triple forward MS paths, the average buckling angles of some mixed ionic salts . In particular, they demonstrated that it is possible to describe the buckling dependence for angles ≲ 20°by the expansion of the effective backscattering amplitudes factors of these MS paths around the average buckling angles obtained by diffraction techniques. ...
... X-ray absorption spectroscopy (XAS), the general term used to cover extended x-ray absorption fine structure (EXAFS) and x-ray absorption near edge structure (XANES), was one of the very novel techniques that was established as a crucial structural method from the very beginning of the SRS. The technique was only recently established by the pioneering papers of Stern, Lytle and Sayers between 1971 and 1975 [3][4][5] and the refinement of the theoretical basis by Lee and Pendry in 1975 [6]. At the SRS, the XAS measurements were roughly divided into two categories: biological and materials systems, the former under the supervision of Samar Hasnain [1] and the latter by Neville Greaves. ...
We present a personal account of both the developments in technique and instrumentation led by Neville Greaves and the scientific applications which they enabled. We focus on the pioneering period at the Synchrotron Radiation Source (SRS), Daresbury in the 1980s and 90s. We discuss and illustrate the lasting impact of these key developments on chemistry, materials and catalytic science.
... The resulting EXAFS signal could then be directly compared to the experimental one. Additionally, fits were calculated using the standard EXAFS Eq. [46] without cumulants (blue). Four parameters were refined during the fitting process with the standard EXAFS equation: the energy shift from the L 3 edge (ΔE 0 ), Debye-Waller factor (σ 2 ), the expected U\ \F distance E[R U−F ], and the coordination number (CN). ...
LiF-UF4 is a key binary system for molten fluoride reactor technology, which has not been scrutinized as thoroughly as the closely related LiF-ThF4 system. The phase diagram equilibria in the system LiF-UF4 are explored in this work with X-ray diffraction (XRD) and differential scanning calorimetry (DSC). The short-range ordering in the molten salt solution is moreover surveyed with Extended X-ray Absorption Fine Structure spectroscopy (EXAFS) and interpreted using a combination of standard fitting of the EXAFS data and Molecular Dynamics (MD) simulations with a Polarizable Ion Model (PIM) potential. The density, excess molar volume, thermal expansion, heat capacity, and enthalpy of mixing are extracted from the MD simulations across a range of temperatures and compositions; the behavior is non-ideal, with reasonably good agreement with the experimental data. Also calculated is the distribution of heteropolyanions in the liquid solution, and modelled using the quasi-chemical formalism in the quadruplet approximation taking into account the existence of the single-shell complexes [UF7]³⁻, [UF8]⁴⁻, and the dimeric species [U2F14]⁶⁻. Subjecting the optimization of the excess Gibbs energy parameters of the liquid solution to the constraints of the phase diagram data and local structure of the melt as derived from the EXAFS and coupled MD simulations, a CALPHAD-type assessment is proposed, linking structural and thermodynamic properties, with a rigorous physical description of the melt.
... This is the case e.g. of linear triatomic molecules (such as HgBr 2 , HgCl 2 , AuBr 2 − , and CuBr 2 − [346]); of several metal carbonyl complexes [347][348][349][350][351]; of some other organometallic complexes [352][353][354]; of crystalline solids with specific space groups (e.g. Pm-3m for ReO 3 [355] Fm-3m for NiO [356,357] or MgO [358]); of metals [359,360] and metal NPs that crystallize in the fcc or bcc phases [131,[361][362][363][364][365][366] etc … As an example of a case where MS contributions are relevant, Fig. 25a reports for a bulk polycrystalline NiO measured at RT the k 3 χ(k) -weighted, phase uncorrected, modulus of the FT together with the corresponding best fit scattered gray circles and solid black line, respectively [356]. The contributions of the independent scattering paths, as obtained from the fit, are also shown: SS paths are reported in red for oxygen scatterers and in blue for nickel scatterers, while the most relevant MS paths are reported in green. ...
Everybody dreams to have X-ray eyes and discover the most invisible secrets of the world around us. X-rays can probe matter (depth resolved) down to atomic resolution, if relying on diffraction-based techniques. An X-ray diffraction pattern may contain information over many length scales (atomic structure, microstructure, mesostructure). This peculiarity justifies the well-recognized impact of several X-ray diffraction-based techniques to diverse fields of research. On the other hand, X-ray spectroscopies (both in absorption and in emission) provide insights on the electronic structure and, exploiting element selectivity and local environment, can complement or even replace scattering techniques for diluted systems and amorphous materials. Herein, we provide a theoretical foundation which spans from very basic concepts, through well-known techniques, with applications to nanomaterials research. An increasing level of material complexity is explored: size and shape analysis of nanoparticles dispersed in solution or single nanostructures localized onto surfaces; local morphology/strain analysis of nanostructured surfaces; average defects analysis of stacking faulted nanocrystals; regular 2D and 3D lattices of self-assembled nanocrystals; clusters of nanocrystals without any nanoscale lattice order, standing alone as isolated objects or embedded in tenths-of-µm-thick polymers (here coherent and focused X-rays were mandatory to explore the spatial inhomogeneity and lattice (in)coherence of the materials).
... where S 2 0 is a scaling factor; N i is the coordination number; R i is the interatomic distance; λ(k) is the photoelectron MFP; f l eff (k, R) and φ l (k, R) are the photoelectron effective scattering amplitude and phase shift functions (Sayers et al. (1971); Lee and Pendry (1975)). The sum in Eq. (5) is taken over groups of atoms located at different distances from the absorber. ...
The contribution of static and thermal disorder is one of the largest challenges for the accurate determination of the atomic structure from the extended X-ray absorption fine structure (EXAFS). Although there are a number of generally accepted approaches to solve this problem, which are widely used in the EXAFS data analysis, they often provide less accurate results when applied to outer coordination shells around the absorbing atom. In this case, the advanced techniques based on the molecular dynamics and reverse Monte Carlo simulations are known to be more appropriate: their strengths and weaknesses are reviewed here.
... These MS eventsa re intensified duet ot he focusinge ffect, which plays an important role when two atoms in ac oordinatingl igand, or part of a larger ligand, form al inear or close to linear M-L-L's tructural motif with the absorbinga tom. [48,49] The refinedd istances for the Ru···O of the carbonyls are 3.045 . ...
The activation process of a known Ru‐catalyst, dicarbonyl(pentaphenylcyclopentadienyl)ruthenium chloride, has been studied in detail using time resolved in situ X‐ray absorption spectroscopy. The data provide bond lengths of the species involved in the process as well as information about bond formation and bond breaking. On addition of potassium tert‐butoxide, the catalyst is activated and an alkoxide complex is formed. The catalyst activation proceeds via a key acyl intermediate, which gives rise to a complete structural change in the coordination environment around the Ru atom. The rate of activation for the different catalysts was found to be highly dependent on the electronic properties of the cyclopentadienyl ligand. During catalytic racemization of 1‐phenylethanol a fast‐dynamic equilibrium was observed.
... This information is incorporated in the fine structure of the spectrum spanning far more than a hundred electronvolts above the X-ray absorption edge. The length of the bonds, coordination numbers and chemical structure surrounding the investigated atom can be deduced from the spectrum using the theoretical expression for EXAFS [2]. This technique does not rely on long-range order in the material and thus, the material does not need to exhibit a crystalline-like structure. ...
We present results of applying a compact laboratory system based on a laser-plasma soft X-ray (SXR) source to the extended X-ray absorption fine structure (EXAFS) spectroscopy of titanium in the vicinity of the LIII absorption edge. The source, operating with a plasma produced as a result of irradiation a krypton/helium double-stream gas-puff target, was optimized for an intense emission in the spectral range between 200 and 700 eV. A broad SXR spectrum and high photon flux are indispensable in the EXAFS studies. The experimental setup assured the simultaneous acquisition of both the reference and the absorption spectra. A grazing-incidence flat-field spectrometer was used to record the spectra. The absorption spectra of a thin (200-nm thick) titanium sample revealed the features in the EXAFS region allowing for quite accurate determination of the radial distances between the atoms. Results are in good agreement with the output of numerical modeling based on photoelectron wave function scattering and with the data reported for using a synchrotron source. This confirms the suitability of the source for using it in the standard EXAFS method.
... On my return to the UK in October 1978, I took a conscious decision to use my physics and synchrotron radiation background at the interface of chemistry and biomedical science, thus joining an interdisciplinary team at Manchester derived from the Chemistry (Dave Garner, FRS) and Medical Biophysics (David Hukins) Departments who had just started the UK's first biological XAFS project working on metalloenzymes and biological calcification. Again, I decided to locate myself at Daresbury where I had the good fortune of being given a temporary office (which became my office for the next 15 years) that was only two doors away from Sir John Pendry, FRS, who had put forward the most comprehensive modern theory of EXAFS (more of this later) [1]. A year later, in 1979, I joined the national effort of establishing the world's first dedicated synchrotron radiation source (SRS) as a full time scientific staff member of the Daresbury Laboratory where I remained until March 2008, having formed a Molecular Biophysics Group in 1989 after returning from a sabbatical in the protein crystallographic laboratories of Charlie Bugg (Birmingham) and Lyle Jensen (Seattle) during the high brightness lattice shutdown of the SRS. ...
The development of synchrotron science over the last 50 years is reviewed from the perspective of the authors' own scientific programmes.
This article is part of the theme issue ‘Fifty years of synchrotron science: achievements and opportunities’.
... However within the range of energies (10-80 eV) above the absorption edge, the spherical nature of the electron waves can no longer be neglected and the full curved theory must be used which was introduced by Lee and Pendry [Lee 1975]. This theory was later simplified [Gurman 1984]. ...
This thesis consists of three main investigations. The first of these is a study of the magnetic properties of Fe nanoparticles embedded in an Al matrix, with different volume fraction. Both Fe nanoparticles, with a diameter of ̴ 2 nm, and the Al matrix were deposited from the gas phase. The atomic Fe moment of the Fe nanoparticles in Al is much less than the bulk Fe value because of considerable alloying at the Fe nanoparticle and Al matrix interface. Two important parameters, the exchange field (H ex) and random anisotropy field (H r), were investigated using the Random Anisotropy Model (RAM). Fitting the data to this model reveals that with increasing volume filling fraction (VFF) of Fe nanoparticles in Al, both H ex and H r show an increase, with H r showing a more significant increase than for H ex. The second main investigation in this thesis is a study of structure and magnetism in Co nanoparticles embedded in antiferromagnetic Cr. Co K edge and Cr K edge extended x-ray absorption fine structure (EXAFS) experiments were performed in order to investigate atomic structure in the Cr-embedded Co nanoparticles and Cr matrix respectively, whereas magnetism was investigated using a vibrating sample magnetometer (VSM). The atomic structure of the Co nanoparticles is same as the host Cr matrix (bcc), although with a degree of disorder, rather than the bulk Co hcp structure. The net Co moment per atom in the Co/Cr nanocomposite films is significantly lower than bulk Co value, and decreases as the proportion of Co nanoparticles in the film is decreased; for the sample with the most dilute concentration of Co nanoparticles (4.9% by volume), the net Co moment was 0.18 μ B /atom. Both the structural and magnetic results show that there is a degree of alloying at the nanoparticle/matrix interface, leading to a core/shell structure in the embedded nanoparticles consisting of an antiferromagnetic CoCr alloy shell surrounding a reduced ferromagnetic Co core.
... l eff and k R ( , ) l are the photoelectron effective scattering amplitude and phase shift functions (Sayers et al., 1971;Lee and Pendry, 1975). The sum in Eq. (5) is taken over groups of atoms located at different distances from the absorber. ...
The contribution of static and thermal disorder is one of the largest challenges for the accurate determination of the atomic structure from the extended X-ray absorption fine structure (EXAFS). Although there are a number of generally accepted approaches to solve this problem, which are widely used in the EXAFS data analysis, they often provide less accurate results when applied to outer coordination shells around the absorbing atom. In this case, the advanced techniques based on the molecular dynamics and reverse Monte Carlo simulations are known to be more appropriate: their strengths and weaknesses are reviewed here.
... The theoretical spectra are calculated following the photoelectron wave model (Lee & Pendry, 1975;Barton & Shirley, 1985), and expressed as a sum of photoelectron scattering paths through the XAFS equation (Zabinsky et al., 1995;Bunker, 2010), ...
Accurate experimental XAFS (X-ray absorption fine-structure) data including uncertainties are required during analysis for valid comparison of results and conclusions of hypothesis testing on structural determinations. Here an approach is developed to investigate data without standard interpolation of experimental data and with minimal loss of information content in the raw data. Nickel coordination complexes bis(i-n-propylsalicylaldiminato)nickel(II) (i-pr) and bis( N -n-propylsalicylaldiminato)nickel(II) (n-pr) are investigated. The additional physical insight afforded by the correct propagation of experimental uncertainty is used to determine newly refined structures for the innermost co-ordination shell. Two sets of data are investigated for each complex; one optimized for high point accuracy and one optimized for high point density. Clearly both are important and in this investigation the quality of the physical insight from each is directly provided by measured and propagated uncertainties to fairly represent the relevant accuracies. The results provide evidence for an approximate tetrahedral geometry for the i-pr Ni complex that is more symmetric than previously concluded, with our high point accuracy data yielding ligand lengths of 2.017 ± 0.006 Å and 2.022 ∓ 0.006 Å for Ni—N and Ni—O bonds, respectively, and an even more skewed square-planar ( i.e. rhombohedral) arrangement for the n-pr complex with corresponding bond lengths of 2.133 ± 0.004 Å and 1.960 ∓ 0.003 Å. The ability to distinguish using hypothesis testing between the subtle differences in XAFS spectra arising from the approximate local tetrahedral and square-planar geometries of the complexes is also highlighted. The effect of standard interpolation on experimental XAFS spectra prior to fitting with theoretical model structures is investigated. While often performed as a necessary step for Fourier transformation into position space, this will nonetheless skew the fit away from actual data taken, and fails to preserve the information content within the data uncertainty. The artificial effects that interpolation imposes on χ r² are demonstrated. Finally, a method for interpolation is introduced which locally preserves the χ r² and thus information content, when a regular grid is required, e.g for further analysis in r -space.
... L'observation de la partie réelle indique que les ondes responsables des pics 1, 2 et 3 ont le même type d'atome diffuseur : les pics 1 et 3 sont en phase et les maxima des pics de lapartie réelle coïncident avec les maxima des pics de l'amplitude. Le pic 2 est en anti-phase par rapport aux pics 1 et 3, ce qui, d'aprèsLee & Pendry (1975) est causé par la prédominance (« shadowing ») de la première sphère de coordination (pic 1). ...
Les composites organiques-inorganiques avec la zéolithe comme matrice hôte sont de plus en plus étudiés dans le but de concevoir des matériaux multifonctionnels conjuguant les propriétés de la molécule organique et celle de la zéolithe (ex. : élaboration de commutateurs magnétiques/optiques, doubleurs de fréquence). Les propriétés macroscopiques recherchées (SHG, transition de spin) dépendent des interactions entre les espèces organiques invitées et la zéolithe (charpente, cations compensateurs de charge), qui sont encore mal connue, en particulier en raison de l'absence de structures cristallographiques précises. Cette thèse s'est intéressée à deux types de composites principalement : (Co2+(bpy)3-zéolithe X) réputé présenter une transition de spin en température et dmpNA-MORdénite), à propriété potentielle de génération de second harmonique. Dans l'étude du composite magnétique, nous nous sommes particulièrement penché sur l'évolution de la structure de la zéolithe précurseur Na,Co-X dans différents état d'hydratation. Des études complémentaires par diffraction des rayons X sur monocristal, EXAFS et simulations Monte-Carlo ont mis en évidence la forte interaction entre cations cobalt et charpente aluminosilicatée ainsi que la migration des cations Co2+ accompagnant l'hydratation progressive de la zéolithe Na,Co-X. L'étude structurale du composite dmpNA-mordénite par diffraction des rayons X sur poudre (synchrotron SPring-8, Japon) a montré que les canaux droits de la mordénite sont presque totalement occupés par les molécules de dmpNA, qui adoptent un empilement quasi linéaire favorable à la Génération de Seconde Harmonique.
... Extended X-ray absorption fine-structure (EXAFS) is a method, that allows one to study detailed information on the local environment surrounding the atom, through the observation of the fine spectral structure on the high energy side of an X-ray absorption edge. From that information, using the theoretical expression for EXAFS [1] the length of the bonds, coordination numbers and chemical structure surrounding the investigated atom can be deduced. This technique has some advantages over the other methods, for example X-ray crystallography [2], such as it does not rely on long-range order in the material, thus the material does not need to exhibit crystalline-like structure, as well as it is element specific, since the measurements are related to a particular atom present in the investigated molecular structure. ...
We present a compact laboratory system for near edge soft X-ray fine structure (NEXAFS) spectroscopy that was developed using a laser-plasma light source. The source is based on a double stream gas puff target. The plasma is formed by the interaction of a laser beam with the double stream gas puff target approach. The laser plasma source was optimized for efficient soft X-ray emission from a krypton/helium target in the range of 1.5 to 5 nm wavelength. This emission is used to acquire simultaneously the emission and absorption spectra of soft X-ray light from the source and from the investigated sample using a grazing incidence spectrometer. The measurements in the transmission mode reveal the features near the carbon K-α absorption edge of thin PET film. From those features, the composition of the sample was successfully obtained. The data are in agreement with synchrotron measurements. In the paper, the detailed information about the source, its optimization, the system, spectral measurements and the results are presented and discussed.
... The X-ray PDF of Co-0.70 and Co-0.75 and C-S-H ( Figure 5b) bore strong resemblance. According to 504 the literature ( Grangeon et al., 2013;Lequeux et al., 1999;Meral et al., 2011;Skinner et al., 2010;505 White, 2016;White et al., 2015), the correlations peaks might correspond to Si-O distances (r = 1.61 Å 506 M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT and 5.38 Å in the co-precipitated samples were characteristic of Mg-Mg distances observed in M-S-H. 510 ...
Calcium silicate hydrate (C-S-H) and magnesium silicate hydrate (M-S-H) have been described as two separate phases. This work investigates their stability domains and the possible uptake of small amounts of magnesium by C-S-H or, reversely, the uptake of small amounts of calcium by M-S-H. The phases, synthesized by co-precipitation, are characterized using a large panel of techniques (thermogravimetry analysis, X-ray diffraction, X-ray pair distribution function analysis, 29Si MAS-NMR spectroscopy, measurement of zeta potential and cation exchange capacity) while the compositions of the solutions at equilibrium are determined by ion chromatography and pH measurements. Syntheses of C-S-H samples in the presence of magnesium ((Ca+Mg)/Si = 0.80 and Mg/Si = 0.05 or 0.10) yield two separate phases: C-S-H and M-S-H. There is no experimental evidence of any uptake of magnesium by C-S-H. On the contrary, when M-S-H samples are synthesized in the presence of calcium ((Ca+Mg)/Si = 0.80 and Ca/Si = 0.05 or 0.10), the low pH of the suspension (9-10) prevents the formation of C-S-H but favors the precipitation of M-S-H with small amounts of calcium. This latter may be sorbed onto the surface of M-S-H to outbalance its negative charges and/or incorporated into the interlayer, as suggested by small structural changes.
The emerging CdTe-BeTe semiconductor alloy that exhibits a dramatic mismatch in bond covalency / stiffness clarifying its vibrational-mechanical properties is used as a benchmark to test the limits of the percolation model (PM) worked out to explain the complex Raman spectra of the related but less contrasted Zn1‑xBex‑chalcogenides. The test is done by way of experiment (x< 0.11) – combining Raman scattering with X-ray diffraction at high pressure – and ab initio calculations (x~0 – 0.5, x~1). The (macroscopic) bulk modulus B0 drops below the CdTe value on minor Be incorporation, at variance with a linear B0 vs. x increase predicted ab initio, thus hinting at large anharmonic effects in the real crystal. Yet, no anomaly occurs at the microscopic (bond) scale as the regular bimodal PM-type Raman signal predicted ab initio for Be-Te in minority (x~0, 0.5) is (barely) detected experimentally. At large Be content (x~1) the same bimodal signal “relaxes” down to inversion – an unprecedented case. However, specific pressure dependencies of the regular (x~0, 0.5) and inverted (x~1) Be-Te Raman doublets are in line with PM-predictions. Hence, the PM applies as such to Cd1‑xBexTe – albeit in a “relaxed” form, without further refinement. This enhances the model’s validity as a generic descriptor of phonons in alloys.
Here, we present a review of the major achievements in kinetics, electronic properties, and engineering in the Fermi level of single-walled carbon nanotubes (SWCNTs). Firstly, the kinetics of metal-filled SWCNTs were revealed with precision over several minutes. Secondly, the growth rates of nanotubes were calculated. Thirdly, the activation energies of nanotubes were measured. Fourthly, the methods of the quantitative analysis of the doping level were developed. Indeed, only qualitative analysis has been previously performed. The quantitative analysis allowed us to obtain quantitative data on charge transfer. Fifthly, the correlation between the physical properties, chemical properties, electronic properties of SWCNTs was elucidated.
Extended X-ray absorption fine structure (EXAFS) has evolved into an unprecedented local-structure technique that is routinely used to study materials' problems in the biological, chemical, and physical sciences. Like many other experimental techniques, EXAFS also requires that several key atomic parameters must be known a priori before structural information can be quantitatively determined. Utilizing current analytical methods, we revisit the isoelectronic series CuBr, ZnSe, GaAs, and Ge originally studied by Stern et al. during the early development of EXAFS [E. A. Stern et al., Phys. Rev. B: Condens. Matter Mater. Phys., 1980, 21, 5521; B. A. Bunker and E. A. Stern, Phys. Rev. B: Condens. Matter Mater. Phys. 1983, 27, 1017]. We demonstrate that the ab initio EXAFS code FEFF accurately predicts the atomic phase shifts and backscattering amplitudes that are primarily functions of the sum of atomic numbers Z along an EXAFS scattering path. We also investigate quantitative fitting and first- and second-shell phase transferability together with problems that arise if a backscattering atom is identified incorrectly in an EXAFS fitting model. Features in the near-edge region, on the other hand, are shown to require a comprehensive treatment of the band structure and density-of-states, including effects of the screened Coulomb interaction between the photoelectron and core hole. We demonstrate that the Bethe-Salpeter equation (BSE) accurately captures the NEXAFS (or XANES) portion of the spectrum for the isoelectronic series in addition to Si and Ge-Si alloys, including within a few eV of the absorption edge, where band structure and excitonic effects are most important.
The multiple scattering formalism used to describe the primary electron beam scattering events in crystalline solids results in theoretical distributions of elastically backscattered electrons and Auger electrons. In calculations different locations of the monolayer and the resulting intensity distributions are shown. The theoretical formalism concerns the final form of the wave field in a solid and the interference of the primary plane and the scattered spherical electron waves. The explicit form of the wave function at the emitter site, the formula used to calculate the signal of elastically backscattered electrons and Auger electrons as well as parameters involved in simulations are discussed. The results of numerical calculations presented as stereographic distributions reveal characteristic intensity maxima and bands associated with crystalline directions and planes, respectively. The data are discussed in the context of the sample structure within the surface near region, scattering properties of individual atoms, lattice parameters, location of the layer as well as the sample chemical composition. Moreover, a detailed analysis of intensities associated with different atomic directions in the face centred cubic crystals, as well as averaged intensities of whole distributions are shown. The short range order structural information, which concerns the nearest and next nearest neighbours in a three dimensional unit cell, can be applied in the modelling of heterostructures and the calculation of signal distributions with the use of the multiple scattering approach. This can be helpful in the detailed analysis of intensity features observed experimentally.
The development of high-performance and low-cost cathode materials is of great significance for the progress in lithium-ion batteries. The use of Co and even Ni is not conducive to the sustainable and healthy development of the power battery industry owing to their high cost and limited resources. Here, we report LiMn2O4 integrated with coating and doping by Sn self-segregation. Auger electron energy spectrum and soft X-ray absorption spectrum show that the coating is Sn-rich LiMn2O4, with a small Sn doping in the bulk phase. The integration strategy can not only mitigate the Jahn-Teller distortion but also effectively avoid the dissolution of manganese. The as-obtained product demonstrates superior high initial capacities of 124 mAh·g−1 and 120 mAh·g−1 with the capacity retention of 91.1% and 90.2% at 25°C and 55°C after 50 cycles, respectively. This novel material-processing method highlights a new development direction for the progress of cathode materials for lithium-ion batteries.
Nickel based magnetic nanocrystals have been widely applied in magnetic and catalytic facilities. Tunable magnetic properties of nickel can be easily obtained via non-magnetic doping or phase transformation. However, phase transformation from face centered cubic (fcc) to hexagonal close packed (hcp) induced magnetism adjustment of Ni are always confused with nickel carbide (Ni3C), due to the similar atomic structures of hcp-Ni and Ni3C. Here, we present series of Au@Ni-carbide magnetic materials achieved from the controlled carbonation of Au@Ni core-shell structures, whose magnetism is tunable by adjusting the amount of carbon in the Ni layer. Ex-situ hard X-ray absorption spectroscopy (XAS) at the metal K edge and soft XAS at both metal L edge and carbon K edge provide solid evidence for the carbonation process from fcc-Ni to NixC, rather than phase transformation to hcp-Ni. Further investigation reveals that the magnetism of the hybrids is mainly contributed from the residual fcc-Ni. The result represents an accurate and effective way to distinguish hexagonal Ni3C from hcp-Ni, and provides the pathway to control magnetism of Ni-based materials for applications.
Volume 10 addresses materials characterization from an engineering perspective, describing the capabilities and limitations of various analytical tools and what they reveal about the composition, structure, and state of engineering materials. It examines optical metallography, electron microscopy, diffraction, chromatography, spectroscopy, and chemical analysis. It also discusses sample requirements and imaging enhancement techniques and includes glossary and other reference information.
Time-resolved luminescence provides indeed the measure of spectroscopic parameters useful to fully describe the optical cycle excitation/emission. This chapter provides a theoretical background of the luminescence properties related to color centers in wide band-gap insulators. The symmetry property of the Franck–Condon integral applies to the absorption and luminescence lineshapes; as a consequence they are characterized by a mirror symmetry with symmetry plane at the energy of the transition between the lowest vibrational levels. The chapter focuses on specific features arising from the electron–phonon coupling, which are fundamental for the interpretation of luminescence experiments in solids. The use of tunable lasers in the time-resolved luminescence setup is very advantageous to improve the sensitivity in the acquisition of emission spectra. It allows a selective excitation of defects, on which the site-selective luminescence is based. The chapter describes a typical setup that can be conveniently used to perform time-resolved photoluminescence measurements.
X‐ray absorption spectroscopy measures the X‐ray absorption coefficient of a material as a function of incident X‐ray energy. The extended X‐ray absorption fine structure signal emerges from the constructive and destructive interference of the outgoing photoelectron with itself after scattering off of atoms in the immediate environment of the absorber. The X‐ray excited photoelectron can be scattered by two atoms before returning to the absorbing atom. The X‐ray absorption fine structure (XAFS) technique requires the measurement of the X‐ray absorption coefficient as a function of photon energy. Synchrotron radiation is the ideal source for XAFS, thanks to the continuous spectrum of high intensity and strong collimation. The chapter outlines a brief overview of the transmission and fluorescence yield geometry. It discusses the use of X‐ray Raman scattering spectroscopy to alleviate these shortcomings and provides a brief introduction to the underlying theory, instrumentation, and an instructive example.
This book collects several contributions presented at the 2019 meeting of the Italian Synchrotron Radiation Society (SILS), held in Camerino, Italy, from 9 to 11 September 2019.
Topics included are recent developments in synchrotron radiation facilities and instrumentation, novel methods for data analysis, applications in the fields of materials physics and chemistry, Earth and environmental science, coherence in x-ray experiments. The book is intended for advanced students and researchers interested in synchrotron-based techniques and their application in diverse fields.
The occurrence of multiple scattering (MS) phenomena in the extended portion of the X-ray absorption spectrum permits to disclose details of the local atomic structure of the target atom. The high order MS paths become relevant only in peculiar structures, regardless the crystallinity of the investigated sample, such as in metal hexacyanoferrates. General guidelines and prescriptions are presented in order to give the authors a useful guide for a correct interpretation of the EXAFS spectra of this class of compounds, which is characterized by close, but sufficiently separated, discontinuities of the absorption coefficient due to the probed contiguous transition metal K-edges. The large number of experimental points, the occurrence of large four-body MS terms, and the presence of multiple probes are discussed in the frame of the renewed attention of these compounds for their use in the battery community.
We have recently performed accurate constant initial state (CIS) Al 2p photoemission experiments on Al films covered with layers of amorphous Ge of variable thickness, using synchrotron radiation in a variable photon energy range 100–1100 eV at the BEAR beamline at Elettra. Experiments were performed within the framework of a larger research effort aimed to obtain accurate and reliable measurements of the photoelectron mean free path (MFP) at variable kinetic energy and ultimately of the probing depth of the total electron yield and total fluorescence yield (TEY, TFY) techniques. Present MFP results are compared with previous experiments and simulations, improving our present knowledge of the MFP curve in amorphous germanium and opening new experimental possibilities for accurate measurements of the probing depth.
To resolve the fleeting structures of lanthanide Ln3+ aqua ions in solution, we (i) performed the first ab initio molecular dynamics (AIMD) simulations of the entire series of Ln3+ aqua ions in explicit water solvent using pseudopotentials and basis sets recently optimized for lanthanides and (ii) measured the symmetry of the hydrating waters about Ln3+ ions (Nd3+, Dy3+, Er3+, Lu3+) for the first time with extended X-ray absorption fine structure (EXAFS). EXAFS spectra were measured experimentally and generated from AIMD trajectories to directly compare simulation, which concurrently considers the electronic structure and the atomic dynamics in solution, with experiment. We performed a comprehensive evaluation of EXAFS multiple-scattering analysis (up to 6.5 Å) to measure Ln-O distances and angular correlations (i.e., symmetry) and elucidate the molecular geometry of the first hydration shell. This evaluation, in combination with symmetry-dependent L3- and L1-edge spectral analysis, shows that the AIMD simulations remarkably reproduces the experimental EXAFS data. The error in the predicted Ln-O distances is less than 0.07 Å for the later lanthanides, while we observed excellent agreement with predicted distances within experimental uncertainty for the early lanthanides. Our analysis revealed a dynamic, symmetrically disordered first coordination shell, which does not conform to a single molecular geometry for most lanthanides. This work sheds critical light on the highly elusive coordination geometry of the Ln3+ aqua ions.
Measurements of mass attenuation coefficients and X-ray absorption fine structure (XAFS) of zinc selenide (ZnSe) are reported to accuracies typically better than 0.13%. The high accuracy of the results presented here is due to our successful implementation of the X-ray extended range technique, a relatively new methodology, which can be set up on most synchrotron X-ray beamlines. 561 attenuation coefficients were recorded in the energy range 6.8–15 keV with measurements concentrated at the zinc and selenium pre-edge, near-edge and fine-structure absorption edge regions. This accuracy yielded detailed nanostructural analysis of room-temperature ZnSe with full uncertainty propagation. Bond lengths, accurate to 0.003 Å to 0.009 Å, or 0.1% to 0.3%, are plausible and physical. Small variation from a crystalline structure suggests local dynamic motion beyond that of a standard crystal lattice, noting that XAFS is sensitive to dynamic correlated motion. The results obtained in this work are the most accurate to date with comparisons with theoretically determined values of the attenuation showing discrepancies from literature theory of up to 4%, motivating further investigation into the origin of such discrepancies.
The X-ray Absorption Fine Structure (XAFS) with its subregions X-ray Absorption Near-edge Structure (XANES) and Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for the structural analysis of materials, which is nowadays a standard component of research strategies in many fields. This review covers a wide range of topics related to its measurement and use: the origin of the fine structure, its analytical potential, derived from the physical basis, the environment for measuring XAFS at synchrotrons, including different measurement geometries, detection modes, and sample environments, e. g. for in-situ and operando work, the principles of data reduction, analysis, and interpretation, and a perspective on new methods for structure analysis combining X-ray absorption with X-ray emission. Examples for the application of XAFS have been selected from work with heterogeneous catalysts with the intention to demonstrate the strength of the method providing structural information about highly disperse and disordered systems, to illustrate pitfalls in the interpretation of results (e. g. by neglecting the averaged character of the information obtained) and to show how its merits can be further enhanced by combination with other methods of structural analysis and/or spectroscopy.
A review of directional Auger (DAES) and directional elastic peak electron spectroscopy (DEPES) for investigations of the short range order within a near-surface region, similar to XPD, is presented. The application of these techniques requires nothing more than a retarding field analyser (RFA), commonly applied for the observation of low energy electron diffraction (LEED) patterns and Auger electron spectroscopy (AES) measurements, for in depth structural investigations associated with the short range order within a near-surface region. The physical principles, experimental set-up, as well as examples of experimental and theoretical results, the latter obtained with the use of single scattering cluster (SSC) and multiple scattering (MS) calculations adopted for primary electron plane wave, are shown. The scattering geometry and details concerning the scattering events of primary electrons in crystalline solids described by SSC and MS approximations are presented. Furthermore, some issues related to computation parameters such as: maximal scattering order, the maximum radius around the emitter, the number of cluster layers, and the averaging range considered in the calculations are also addressed. The presentation of the data obtained for clean and covered substrates in the form of polar profiles and stereographic intensity distributions enables the straightforward identification of the crystalline structure within the first few sample layers. The data presented in the form of anisotropy maps enable the identification of interatomic axes formed between substrate and adsorbate atoms at the interface. The contribution of different sample layers to the final DEPES signal is discussed. The comparison of DAES results with those obtained by means of x-ray photoelectron diffraction (XPD) is also presented. The qualitative and quantitative data analysis, the latter achieved by the comparison of experimental data with theoretical results by means of an R-factor analysis, is shown. The application of DAES and DEPES enables the characterization of the crystalline structure of adsorption systems from one monolayer (1 ML) up to thicknesses of the adsorbate limited by the inelastic mean free path of the registered electrons. Exemplary results are presented for adsorption systems, where the adsorbate and the substrate crystallize in the same (Ag/Cu, Pt/Cu, Cu/Pt) and in different (Cu/Ru) structures. The influence of the large unit cell of graphene formed on Ru(0001) on measured DEPES intensities is also shown. The detailed analysis of these results enables an identification of the short range order of atoms within the near-surface region, of adsorbate domains exhibiting different orientation with respect to the crystalline substrate, the determination of the domain populations, the relaxation and termination of the surface, the specific adsorption sites of adsorbed atoms, as well as the positions of atoms within a unit cell and their bond lengths (e.g. O/Ru(101¯0)).
Os princípios básicos das espectroscopias de absorção e fotoeletrônica de raios-X (XAS e XPS) e seus principais equipamentos e métodos de tratamento de dados utilizados são introduzidos. É dada ênfase aos estudos das propriedades eletrônica e estrutural de materiais inorgânicos descrevendo alguns exemplos da literatura. Essas técnicas fornecem diferentes informações. A XPS permite a investigação da superfície, sendo principalmente usada na investigação de mudanças química e estrutural dos elementos presentes na superfície do material estudado. Por outro lado, a XAS fornece informações do volume (bulk) da amostra e sonda a ordem a curto alcance ao redor do átomo de interesse. Os exemplos descritos mostram que essas técnicas são complementares na caracterização de materiais.
There are several data reduction and analysis procedures available worldwide. This chapter provides guidance in utilizing X-ray absorption fine structure (XAFS) data for structural, analytical, and physico-chemical information. The data treatment provides the normalized energy-calibrated spectrum, which is the first stage of the background subtraction procedures and can be the basis of compositional analysis and x-ray absorption near-edge structure (XANES) simulations. The most obvious means of mapping heterogeneous samples beyond x-ray absorption contrast is through elemental analysis by x-ray fluorescence, akin to EDX methods in electron microscopy. The chapter further introduces the extended XAFS (EXAFS) phenomenon, and reproduces the standard equation quantifying the event for a randomly oriented sample. As far as structure determination is concerned, the accuracy of the interatomic distance is dependent upon the felicity of the calculated phase shifts. There are two ways in which EXAFS analysis can provide estimates of bond angles, namely multi-edge analysis and multiple scattering.
A general theory of the extended x-ray absorption edge fine structure is
given within the framework of a one-electron approximation. An
approximate evaluation of this theory is proposed which allows a simple
calculation of the spectrum starting from theoretically calculated
electron-atom scattering phase shifts. This is shown to agree quite well
with the observed spectrum for copper in the energy range 200-800 eV
above the K edge without the use of any adjustable parameters. A
qualitative evaluation of multiple scattering effects in the general
theory is made which should be reasonably good below 100 eV. Multiple
scattering corrections are found to be very important in the low-energy
region of the spectrum for close-packed structures. It is shown that
significant cancellation of single scattering amplitudes can occur which
could account for detailed anomalies in the spectrum of Cu found by
Stern, Sayers, and Lytle.
The spatial distribution of electronic charge is calculated exactly for three simple cases. These are the perfect lattice, perfect lattice with a single vacancy and perfect lattice with a single substitutional impurity. The potential is assumed to be of muffin tin form. The results are similar in appearance to the equation's for the Kohn-Rostoker band structure calculations and appear ideally suited to numerical computation. Examples are given to illustrate the results. These are rather simple, but two interesting conclusions can be drawn: the charge at a vacancy is not directly proportional to the density of states of the host lattice and an impurity can cause two bound states to appear from a narrow band.
We have applied Fourier analysis to our point-scattering theory of x-ray absorption fine structure to invert experimental data formally into a radial structure function with determinable structural parameters of distance from the absorbing atom, number of atoms, and widths of coordination shells. The technique is illustrated with a comparison of evaporated and crystalline Ge. We find that the first and second neighbors in amorphous Ge are at the crystalline distance within the accuracy of measurement (1%).
Second-order elliptic differential equations (such as the time-independent single particle Schrödinger equation) may be solved in a finite closed disjoint region of space independently of the rest of space. The solution in all space may then be determined by solving the equations in the exterior region together with boundary conditions at the junction of the two regions. These boundary conditions are determined by the previously found interior solution. This means that such regions may be taken as `black boxes' whose exact details do not matter. The simplest example of this is phase-shift scattering theory from a single scatterer where all the scattering properties are described by the phase shifts, and the exact details of the scattering potential are unimportant. In a macroscopic condensed system, however, there are many core regions and one is really concerned with the multiple scattering which takes place between these different scattering centres. Much of this article is devoted to investigating the formal properties of scattering theory when there are many non-overlapping spherical regions of radius RM, each of which is described by its own scattering matrix, or, equivalently for a spherically symmetric potential, by its phase shifts. Non-spherically symmetric and spin-dependent potentials are permitted, but for simplicity we assume initially that the interstitial region between each disjoint scattering region has zero potential. The generalization of the multiple scattering formalism for non-zero interstitial potential is also given at a later stage.
A new theory of the extended x-ray-absorption fine structure (EXAFS) is
presented which avoids the inaccurate approximations of previous ones.
It is shown that, in addition to structure determination, EXAFS gives
detailed information on the shielding of the singly ionized absorbing
atom. Experimental verification of the theory is obtained from EXAFS
data for Ge and Cu, explicitly showing shielding oscillations for Cu.
The Kronig, Kostarev, Hayasi, and Sawadi theories of extended fine
structure of x-ray absorption edges are discussed. The essential features of
each theory and its success in interpreting experimental curves are outlined.
The shortcomings of each theory are pointed out, and a general evaluation and
comparison with experimental data are made. (C.E.S.)
A general theory of the fine structure observed on the high-energy side of the K-absorption edge (EXAFS) is presented. The form of the theory presented is useful when the excited atom is not too highly ionized and the potential is approximately spherically symmetric. A critical analysis is made of long-range-order theories of EXAFS and it is shown that the coherent effects of the periodic potential are not the dominant mechanism as assumed previously. The dominant mechanism is the scattering in the vicinity of the absorbing atom, and can most naturally be calculated by considering only the immediate environment surrounding the absorbing atom. Fourier-transforming EXAFS data determines the spatial dependence of a scattering matrix. This scattering matrix is expected to peak at the location of surrounding atoms, locating them, and can give information on the type of surrounding atoms and possibly the surrounding valence electron density. Because the K edges of different atoms are separated, such information can be obtained around each atom type separately, making EXAFS a potentially powerful tool for determining the microscopic structure of condensed matter.
Fourier transforms of extended x-ray-absorption fine structure (EXAFS) give structural information in the vicinity of each kind of atom, separately, in a wide variety of gaseous, liquid, and solid systems. A detailed description of the analysis of EXAFS data is presented including details of the Fourier transform of the data and the extraction of structural and other physical parameters from these transforms. Included in this description are the measurement of interatomic distances, coordination numbers, disorder effects (thermal and structural), energy-dependent electron scattering amplitudes, inelastic mean free paths, and phase shifts. EXAFS spectra of Ge, Cu, and GeO2 are analyzed in detail. Multiple-scattering effects between atoms are generally found to be small. There are no multiple-scattering effects in the first shell of the Fourier transform. The phase shifts introduced by both the absorbing and surrounding atoms empirically appear to be characteristic of the particular atoms and independent of the surroundings for a given class of material. This is of great practical importance because it indicates that EXAFS can be calibrated by measuring known structures and then used to determine unknown ones.
The two theoretical approaches to extended x-ray-absorption fine
structure, based on either "long-range order" or "short-range order" are
critically examined within a muffin-tin-scatterer model. It is argued
that the two apparently dissimilar theories will in practice yield
essentially the same results. The argument is based on the implications
of recent multiple scattering calculations on clusters of atoms.
Die in Teil I entwickelte Theorie der Sekundrstruktur in den Rntgenabsorptionsbanden von Kristallen wird weiter ausgearbeitet. Nach dieser Theorie ist die Sekundrstruktur dadurch verursacht, da die von den Rntgenquanten beim Absorptionsproze aus den Atomen losgelsten Elektronen den Kristall in einer gegebenen Richtung nicht mit allen Werten der Energie durchlaufen knnen, sondern ein aus erlaubten und verbotenen Zonen bestehendes Energiespektrum haben. Es wird gezeigt, warum im Absorptionskoeffizienten endliche Schwankungen brig bleiben, trotzdem die Lage dieser Zonen richtungsabhngig ist und die beobachteten Absorptionsbanden einen ber alle Fortpflanzungsrichtungen der Elektronen integrierten Effekt darstellen. Anschlieend wird untersucht, inwieweit es mglich ist, die einzelnen Minima, hnlich wie die Linien eines Debye-Scherrer-Diagramms, den verschiedenen Reflexionen der Elektronen an den Gitterebenen zuzuordnen.
Das Auftreten einer ausgedehnten Sekundrstruktur in den K-Absorptionsbanden von Kristallen und namentlich von Metallen im festen Zustand wird in Verbindung gebracht mit der Tatsache, da das Energiespektrum eines Elektrons, welches sich durch ein periodisches Potentialfeld in einer bestimmten Richtung bewegt, aus erlaubten und verbotenen Zonen endlicher Breite besteht. Man erhlt hiermit auch eine Deutung der von Hanawalt untersuchten Beeinflussung dieser Sekundrstruktur durch Temperaturerhhung. Mit Hilfe eines einfachen Modells wird gezeigt, warum nicht nur bei den aus einer groen Zahl von Atomen bestehenden Kristallen sondern auch schon bei mehratomigen Moleklen hufig eine ausgedehnte Sekundrstruktur auftritt, whrend sie beim isolierten Atom fehlt.
Der schon in Teil I skizzierte Gedankengang zur Deutung der Feinstruktur in den Rntgenabsorptionsbanden molekularer Gase wird weiter ausgearbeitet.
An alumina‐supported CuCr catalyst was examined with the extended x‐ray absorption fine‐structure (EXAFS) technique. This is a new technique which can determine the chemical states and near‐neighbor environments of the separate Cu and Cr atomic species. Cu was found to occupy both tetrahedral and octahedral sites in the supporting alumina lattice while Cr was found only in octahedral sites. The valence state was Cr<sup>+5</sup> in the fresh catalyst which changed to Cr<sup>+6</sup> in the exhaust‐cycled material. Confirmation of the valence state assignment was obtained by EPR. Fourier analysis of the EXAFS produced separate radial structure functions for the Cu and Cr atoms since the experiment measures the properties of the individual atomic species rather than those of the structure as a whole. Significant differences were observed by both techniques between fresh and exhaust‐cycled material.