J. D. Bourke

Electron Energy Loss Spectra and Overestimation of Inelastic Mean Free Paths in Many-Pole Models

We investigate established theoretical approaches for the determination of electron energy loss spectra (EELS) and inelastic mean free paths (IMFPs) in solids. In particular, we investigate effects of alternate descriptions of the many plasmon resonances that define the energy loss function (ELF), and the contribution of lifetime broadening in these resonances to the IMFP. We find that despite previously claimed agreement between approaches, approximations of different models consistently conspire to underestimate electron scattering for energies below 100 eV, leading to significant overestimates of the IMFP in this regime.

Momentum-Dependent Lifetime Broadening of Electron Energy Loss Spectra: A Self-Consistent Coupled-Plasmon Model

The complex dielectric function and associated energy loss spectrum of a condensed matter system is a fundamental material parameter that determines both the optical and electronic scattering behavior of the medium. The common representation of the electron energy loss function (ELF) is interpreted as the susceptibility of a system to a single- or bulk-electron (plasmon) excitation at a given energy and momentum and is commonly derived as a summation of noninteracting free-electron resonances with forms constrained by adherence to some externally determined optical standard. This work introduces a new causally constrained momentum-dependent broadening theory, permitting a more physical representation of optical and electronic resonances that agrees more closely with both optical attenuation and electron scattering data. We demonstrate how the momentum dependence of excitation resonances may be constrained uniquely by utilizing a coupled-plasmon model, in which high-energy excitations are able to relax into lower-energy excitations within the medium. This enables a robust and fully self-consistent theory with no free or fitted parameters that reveals additional physical insight not present in previous work. The new developments are applied to the scattering behavior of solid molybdenum and aluminum. We find that plasmon and single-electron lifetimes are significantly affected by the presence of alternate excitation channels and show for molybdenum that agreement with high-precision electron inelastic mean free path data is dramatically improved for energies above 20 eV.

Structure determination from XAFS using high-accuracy measurements of x-ray mass attenuation coefficients of silver, 11 keV–28 keV, and development of an all-energies approach to local dynamical analysis of bond length, revealing variation of effective thermal contributions across the XAFS spectrum

We use the x-ray extended range technique (XERT) to experimentally determine the mass attenuation coefficient of silver in the x-ray energy range 11 kev-28 kev including the silver K absorption edge. The results are accurate to better than 0.1%, permitting critical tests of atomic and solid state theory. This is one of the most accurate demonstrations of cross-platform accuracy in synchrotron studies thus far. We derive the mass absorption coefficients and the imaginary component of the form factor over this range. We apply conventional XAFS analytic techniques, extended to include error propagation and uncertainty, yielding bond lengths accurate to approximately 0.24% and thermal Debye-Waller parameters accurate to 30%. We then introduce the FDMX technique for accurate analysis of such data across the full XAFS spectrum, built on full-potential theory, yielding a bond length accuracy of order 0.1% and the demonstration that a single Debye parameter is inadequate and inconsistent across the XAFS range. Two effective Debye-Waller parameters are determined: a high-energy value based on the highly-correlated motion of bonded atoms (σ(DW) = 0.1413(21) Å), and an uncorrelated bulk value (σ(DW) = 0.1766(9) Å) in good agreement with that derived from (room-temperature) crystallography.

Full-potential theoretical investigations of electron inelastic mean free paths and extended x-ray absorption fine structure in molybdenum

X-ray absorption fine structure (XAFS) spectroscopy is one of the most robust, adaptable, and widely used structural analysis tools available for a range of material classes from bulk solids to aqueous solutions and active catalytic structures. Recent developments in XAFS theory have enabled high-accuracy calculations of spectra over an extended energy range using full-potential cluster modelling, and have demonstrated particular sensitivity in XAFS to a fundamental electron transport property-the electron inelastic mean free path (IMFP). We develop electron IMFP theory using a unique hybrid model that simultaneously incorporates second-order excitation losses, while precisely accounting for optical transitions dictated by the complex band structure of the solid. These advances are coupled with improved XAFS modelling to determine wide energy-range absorption spectra for molybdenum. This represents a critical test case of the theory, as measurements of molybdenum K-edge XAFS represent the most accurate determinations of XAFS spectra for any material. We find that we are able to reproduce an extended range of oscillatory structure in the absorption spectrum, and demonstrate a first-time theoretical determination of the absorption coefficient of molybdenum over the entire extended XAFS range utilizing a full-potential cluster model.

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.

Conformation Analysis of Ferrocene and Decamethylferrocene via Full-Potential Modeling of XANES and XAFS Spectra

Recent high-accuracy X-ray absorption measurements of the sandwich organometallics ferrocene (Fc) and decamethylferrocene (DmFc) at temperatures close to liquid helium are compared with new full-potential modeling of X-ray absorption fine structure (XAFS) covering the near-edge region (XANES) and above up to k = 7 Å(-1). The implementation of optimized calculations of the oscillatory part of the spectrum from the package FDMX allows detailed study of the spectra in regions of the photoelectron momentum most sensitive to differences in the molecular stereochemistry. For Fc and DmFc, this corresponds to the relative rotation of the cyclopentadienyl rings. When applied to high-accuracy XAFS of Fc and DmFc, the FDMX theory gives clear evidence for the eclipsed conformation for Fc and the staggered conformation for DmFc for frozen solutions at ca. 15 K. This represents the first clear experimental assignment of the solution structures of Fc and DmFc and reveals the potential of high-accuracy XAFS for structural analysis.

New constraints for low-momentum electronic excitations in condensed matter: fundamental consequences from classical and quantum dielectric theory

We present new constraints for the transportation behaviour of low-momentum electronic excitations in condensed matter systems, and demonstrate that these have both a fundamental physical interpretation and a significant impact on the description of low-energy inelastic electron scattering. The dispersion behaviour and characteristic lifetime properties of plasmon and single-electron excitations are investigated using popular classical, semi-classical and quantum dielectric models. We find that, irrespective of constrained agreement to the well known high-momentum and high-energy Bethe ridge limit, standard descriptions of low-momentum electron excitations are inconsistent and unphysical. These observations have direct impact on calculations of transport properties such as inelastic mean free paths, stopping powers and escape depths of charged particles in condensed matter systems.

Novel plasmon-coupling theory for XAFS and diffraction

We present a new self-consistent model of inelastic electron scattering in condensed matter systems for accurate calculations of low-energy electron inelastic mean free paths (IMFPs) for XAFS and low energy diffraction. Our model implements plasmon coupling mechanisms for the first time, in addition to causally-constrained lifetime broadening and highprecision density functional theory, and enables dramatic improvements in the agreement with recent high profile IMFP measurements. The accuracy of theoretical determinations of the electron inelastic mean free path (IMFP) at low energies is one of they key limiting factors in current XAFS modeling and Monte Carlo transport. Recent breakthroughs in XAFS analysis show that there exist significant discrepancies between theoretical and experimental IMFP values [1], and that this can significantly impact upon extraction of other key structural parameters from both XANES and XAFS. Resolution of these discrepancies is required to validate experimental studies of material structures, and is particularly relevant to the characterization of small molecules and organometallic systems for which tabulated electron scattering data is often sparse or highly uncertain. We have devised a new theoretical approach for IMFP determination linking the optical dielectric function and energy loss spectrum of a material with its electron scattering properties and characteristic plasmon excitations. For the first time we present a model inclusive of plasmon coupling, allowing us to move beyond the longstanding statistical approximation and explicitly demonstrate the effects of band structure on the detailed behavior of bulk electron excitations in a solid or small molecule [2]. This is a novel generalization of the optical response of the material, which we obtain using density functional theory [3]. We find that our developments dramatically improve agreement with experimental electron scattering results in the lowenergy region (<~100 eV) where plasmon excitations are dominant. Corresponding improvements are therefore made in theoretical XAFS spectra and detector modelling. [1] Bourke, JD, Chantler, CT (2007) Phys. Lett. A 360, 702; Bourke, JD, Chantler, CT (2010) Phys. Rev. Lett. 104, 206601; Chantler, CT et al. (2012) J. Synch. Rad. 19, 145 [2] Bourke, JD, Chantler, CT (2015) J. Phys. Chem. Lett. 6 314; Chantler, CT, Bourke, JD (2015) J Phys CM 27 455901-1-7 [3] Chantler, CT, Bourke, JD (2014) J. Phys. Chem. A 118 909; Bourke, JD, Chantler, CT, Joly, Y (2016) J Synch Rad 23 551559

DFT and Plasmon-Coupling Models for Optical and Electronic Scattering Properties

We present calculations and applications of optical energy loss data for use in studies of inelastic electron scattering in condensed matter systems. A new model of plasmon coupling and excitation broadening is implemented along with high-precision density functional theory to evaluate fundamental material properties critical to many areas of spectroscopic analysis. Recent developments in x-ray and electron spectroscopies have demonstrated critical dependence on low-energy electron scattering and optical loss properties, and significant discrepancies between theoretical and experimental scattering values [1]. Resolution of these discrepancies is required to validate experimental studies of material structures, and is particularly relevant to the characterization of small molecules and organometallic systems for which electron scattering data is often sparse or highly uncertain [2]. We have devised a new theoretical approach linking the optical dielectric function and energy loss spectrum of a material with its electron scattering properties and characteristic plasmon excitations. For the first time we present a model inclusive of plasmon coupling, allowing us to move beyond the longstanding statistical approximation and explicitly demonstrate the effects of band structure on the detailed behavior of bulk electron excitations in a solid or small molecule. This is a novel generalization of the optical response of the material, which we obtain using density functional theory [3]. We find that our developments improve agreement with experimental electron scattering results in the low-energy region (<~100 eV) where plasmon excitations are dominant; a region that is particularly crucial for structural investigations using x-ray absorption fine structure and electron diffraction. This work is further relevant to several commissions of the IUCr including the commissions on XAFS, International Tables, and Electron Crystallography.

Redox modulation of Low-Volume (100 µL) Solutions for XAFS measurements

A key to the understanding of transition metal catalysis is a detailed knowledge of the changes in coordination environment that accompany a change in redox state. The capacity of a given metal complex to support the high rates of electron transfer needed for effective catalysis is strongly dependent on the magnitude of structural reorganization coupled to the redox step. The ability of the ligand to control the dynamics of electron transfer is beautifully illustrated by copper redox proteins such as plastocyanin.[1] The polypeptide-imposed constraints on the environment at the coordination site of the metal minimize the structural change attendant on interconversion between the CuI and CuII redox states of the metal, facilitating fast electron transfer. Further, unravelling the molecular details of enzyme catalysis often hinges on knowledge of the structural changes attendant on oxidation or reduction. XAFS can provide the key structural information for reactive or unstable redox states of biological and abiological molecules. Our research has mostly centred on the use of a combination of spectroscopic and computational techniques to reveal the chemistry associated with dihydrogen activation in diiron compounds related to [FeFe]-hydrogenases [2], where a combination of XAFS, IR spectroscopy and theory can provide reliable structural information. Sampling of such species can provide a comparable challenge to spectral analysis – an issue made more difficult in cases where the quantity of sample is limited. We have developed low-volume electrosynthesis cells suitable for the study of electrogenerated species where the total volume of solution required for XAS data collection is of order 100 μL [3]. The design and operation of cells designed to allow freeze quenching and tow-temperature spectral collection or RT on-line measurement will be described.