We present a method for determining inelastic mean free paths (IMFPs) in materials using high-accuracy measurements of x-ray absorption fine structure (XAFS). For electron energies below 100 eV, theoretical predictions have large variability and alternate measurement techniques exhibit significant uncertainties. In this regime, the short IMFP makes photoelectrons ideal for structural determination of surfaces and nanostructures, and measurements are valuable for studies of diverse fields such as low-energy electron diffraction and ballistic electron emission microscopy. Our approach, here applied to solid copper, is unique and exhibits enhanced sensitivity at electron energies below 100 eV. Furthermore, it is readily applicable to any material for which sufficiently high accuracy XAFS data can be obtained.
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.
X-ray absorption fine structure (XAFS) of ferrocene (Fc) and Decamethylferrocene (DmFc) have been determined on an absolute scale using transmission measurements of multiple solutions of differing concentrations (15 mM, 3 mM, pure solvent) at operating temperatures of 10–20 K. Mass attenuation coefficients and photoelectric absorption cross sections are measured and tabulated for both molecules for an extended energy range in excess of 1.5 keV from the Fe K-shell absorption edge. At these temperatures, the minimization of of dynamic disorder has enabled a critical determination of the oscillatory absorption structures created by multiple-scattering paths of the excited photoelectron. These oscillatory structures are highly sensitive to the local conformation environment of the iron absorber in organometallic structures. Crystallographic and scattering studies have reported both structures characterized by staggered cyclopentadienyl rings, in contrast with low temperature crystallography and recent density functional theoretical predictions. Phase changes in the crystallographic space groups are reported for Fc at different temperatures, raising the possibility of alternative conformation states. Robust experimental techniques are described which have allowed the measurement of XAFS spectra of dilute systems by transmission at accuracies ranging from 0.2% to 2%, and observe statistically significant fine structure at photoelectron wavenumbers extending to >12 Å–1. The subtle signatures of the conformations are then investigated via extensive analysis of the XAFS spectra using the full multiple scattering theory as implemented by the FEFF package. Results indicate a near-eclipsed D 5h geometry for low-temperature Fc, in contrast with a staggered D 5d geometry observed for DmFc. The ability of this experimental approach and data analysis methodology combined with advanced theory to investigate and observe such subtle conformational differences using XAFS is a powerful tool for future challenges and widens the capacity of advanced XAFS to solve a broad range of challenging systems.
The electron inelastic mean free path (IMFP) of molybdenum is determined experimentally over an energy range of 1−120 eV using analysis of X-ray absorption fine structure (XAFS). This new approach enables accurate measurements of IMFPs in this energy range where direct measurements are often difficult and highly uncertain, and provides a means for studying materials inaccessible through current alternate techniques. This approach can also be used to determine localized IMFPs within complex molecular systems, enabling detailed study of surfaces and nanoenvironments. This information is important for diverse applications in physical chemistry including electron microscopy, spectroscopy, and diffraction (low-energy electron diffraction (LEED) and electron energy loss spectroscopy (EELS) in particular). Here we reveal the accuracy achievable using experimental data of high statistical precision, and critically evaluate the form of the IMFP in the asymptotic region in the low energy limit.
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.
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