Electron inelastic mean free path theory and density functional theory resolving discrepancies for low-energy electrons in copper.

We develop the many-pole dielectric theory of UV plasmon interactions and electron energy losses, and couple our advances with recent developments of Kohn-Sham density functional theory to address observed discrepancies between high-precision measurements and tabulated data for electron inelastic mean free paths (IMFPs). Recent publications have demonstrated that a five standard error difference exists between longstanding theoretical calculations and measurements of electron IMFPs for elemental solids at energies below 120 eV, a critical region for analysis of electron energy loss spectroscopy (EELS), X-ray absorption spectroscopy (XAS), and related technologies. Our implementation of improved optical loss spectra and a physical treatment of second-order excitation lifetimes resolves this problem in copper for the first time for energies in excess of 80 eV and substantially improves agreement for lower energy electrons.

Success and failure of dead-time models as applied to hybrid pixel detectors in high-flux applications.

The performance of a single-photon-counting hybrid pixel detector has been investigated at the Australian Synchrotron. Results are compared with the body of accepted analytical models previously validated with other detectors. Detector functionals are valuable for empirical calibration. It is shown that the matching of the detector dead-time with the temporal synchrotron source structure leads to substantial improvements in count rate and linearity of response. Standard implementations are linear up to ∼0.36 MHz pixel(-1); the optimized linearity in this configuration has an extended range up to ∼0.71 MHz pixel(-1); these are further correctable with a transfer function to ∼1.77 MHz pixel(-1). This new approach has wide application both in high-accuracy fundamental experiments and in standard crystallographic X-ray fluorescence and other X-ray measurements. The explicit use of data variance (rather than N(1/2) noise) and direct measures of goodness-of-fit (χ(r)(2)) are introduced, raising issues not encountered in previous literature for any detector, and suggesting that these inadequacies of models may apply to most detector types. Specifically, parametrization of models with non-physical values can lead to remarkable agreement for a range of count-rate, pulse-frequency and temporal structure. However, especially when the dead-time is near resonant with the temporal structure, limitations of these classical models become apparent. Further, a lack of agreement at extreme count rates was evident.

Testing three-body quantum electrodynamics with trapped Ti20+ ions: evidence for a Z-dependent divergence between experiment and calculation.

We report a new test of quantum electrodynamics (QED) for the w (1s2p(1)P(1)→1s(2)(1)S(0)) x-ray resonance line transition energy in heliumlike titanium. This measurement is one of few sensitive to two-electron QED contributions. Systematic errors such as Doppler shifts are minimized in our experiment by trapping and stripping Ti atoms in an electron beam ion trap and by applying absolute wavelength standards to calibrate the dispersion function of a curved-crystal spectrometer. We also report a more general systematic discrepancy between QED theory and experiment for the w transition energy in heliumlike ions for Z>20. When all of the data available in the literature for Z=16-92 are taken into account, the divergence is seen to grow as approximately Z(3) with a statistical significance on the coefficient that rises to the level of 5 standard deviations. Our result for titanium alone, 4749.85(7) eV for the w line, deviates from the most recent ab initio prediction by 3 times our experimental uncertainty and by more than 10 times the currently estimated uncertainty in the theoretical prediction.

Measurements of electron inelastic mean free paths in materials.

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.

Low-energy electron properties: Electron inelastic mean free path, energy loss function and the dielectric function. Recent measurements, applications, and the plasmon-coupling theory.

We review new self-consistent models 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. The accuracy of theoretical determinations of the electron IMFP at low energies is one of the 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, 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. Novel models implement plasmon coupling mechanisms for the first time, in addition to causally-constrained lifetime broadening and high-precision density functional theory, and enables dramatic improvements in the agreement with recent high profile IMFP measurements. We discuss a 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. We review models inclusive of plasmon coupling, allowing us to move beyond the longstanding statistical approximation and explicitly demonstrate the effects of band structure on the detailed behaviour of bulk electron excitations in a solid or small molecule. This interrogates the optical response of the material, which we obtain using density functional theory. We find that new developments dramatically improve agreement with experimental electron scattering results in the low-energy region (30 eV  → 200 eV) where plasmon excitations are dominant. Corresponding improvements are therefore made in Low Energy Electron Transport, LEEM, theoretical XAFS spectra and detector modelling.

Methods and methodology for FTIR spectral correction of channel spectra and uncertainty, applied to ferrocene.

We present methodology for the first FTIR measurements of ferrocene using dilute wax solutions for dispersion and to preserve non-crystallinity; a new method for removal of channel spectra interference for high quality data; and a consistent approach for the robust estimation of a defined uncertainty for advanced structural χr2 analysis and mathematical hypothesis testing. While some of these issues have been investigated previously, the combination of novel approaches gives markedly improved results. Methods for addressing these in the presence of a modest signal and how to quantify the quality of the data irrespective of preprocessing for subsequent hypothesis testing are applied to the FTIR spectra of Ferrocene (Fc) and deuterated ferrocene (dFc, Fc-d10) collected at the THz/Far-IR beam-line of the Australian Synchrotron at operating temperatures of 7K through 353K.

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.

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.

A curved crystal spectrometer for energy calibration and spectral characterization of mammographic x-ray sources.

Clinical efficacy of diagnostic radiology for mammographic examinations is critically dependent on source characteristics, detection efficiency, image resolution and applied high voltage. In this report we focus on means for evaluation of source-dependent issues including noninvasive determination of the applied high voltage, and characterization of intrinsic spectral distributions which in turn reflect the effects of added filtration and target and window contamination. It is shown that a particular form of x-ray curved crystal spectrometry with electronic imaging can serve to determine all relevant parameters within the confines of a standard clinical exposure.

Flat and curved crystal spectrography for mammographic X-ray sources.

The demand for improved spectral understanding of mammographic X-ray sources and non-invasive voltage calibration of such sources has led to research into applications using curved crystal spectroscopy. Recent developments and the promise of improved precision and control are described. Analytical equations are presented to indicate effects of errors and alignment problems in the flat and curved crystal systems. These are appropriate for all detection systems. Application to and testing of spectrographic detection (using standard X-ray film) is presented. Suitable arrangements exist which can be used to measure X-ray tube voltages well below 1 kV precision in the operating range of 20-35 kV.

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.

New consistency tests for high-accuracy measurements of X-ray mass attenuation coefficients by the X-ray extended-range technique.

An extension of the X-ray extended-range technique is described for measuring X-ray mass attenuation coefficients by introducing absolute measurement of a number of foils - the multiple independent foil technique. Illustrating the technique with the results of measurements for gold in the 38-50 keV energy range, it is shown that its use enables selection of the most uniform and well defined of available foils, leading to more accurate measurements; it allows one to test the consistency of independently measured absolute values of the mass attenuation coefficient with those obtained by the thickness transfer method; and it tests the linearity of the response of the counter and counting chain throughout the range of X-ray intensities encountered in a given experiment. In light of the results for gold, the strategy to be ideally employed in measuring absolute X-ray mass attenuation coefficients, X-ray absorption fine structure and related quantities is discussed.

Theoretical determination of characteristic x-ray lines and the copper K alpha spectrum.

Core excitations above the K edge result in K alpha characteristic x-ray emission. Understanding these spectra is crucial for high accuracies in investigations into QED, near-edge x-ray structure and advanced crystallography. We address unresolved quantitative discrepancies between experiment and theory for copper. These discrepancies arise from an incomplete treatment of electronic interactions. By finding solutions to relativistic multiconfigurational Dirac-Fock equations accounting for correlation and exchange corrections, we obtain an accurate reproduction of the peak energies, excellent agreement of theory with experiment for the line shapes, good convergence between gauges, and account for the K alpha doublet ratio of 0.522 +/- 0.003ratio1.

Photographic response to x-ray irradiation. I: Estimation of the photographic error statistic and development of analytic density-intensity equations.

Formulations for specular optical density as a function of incident x-ray intensity are shown to be inadequate, theoretically and compared with available data. Approximations assuming low intensities, grain densities, or energies yield significant error in typical emulsions. Unjustifiable simplifications limit analysis and consequent results. The avoidance of assumptions leads to models for rough and smooth emulsion surfaces, which correspond to Kodak 101-01 and DEF-392 emulsion types. The self-consistent use of spherical grains yields scaling that is dependent on emulsion roughness. We obtained improvement over standard formulations, avoiding the empirical character of earlier models and associated parameterization. The correlation of grain locations and occluded emulsion area is approximated within monolayer depths but neglected between layers. Effects of the incident angle from a broad source, scattering, and photoelectrons are considered. The models presented herein apply to the vacuum UV and x-ray energies from 9 eV to 20 keV and may be preferred over alternative models at lower energies, densities greater than unity, emulsions with high grain fractions, or where interpolation over energy ranges is desired. Error contributions may be dominated by intensity statistics or densitometry statistics. Both are inadequate in medium-density regimes. We have derived estimates including pseudo-binomial grain development statistics, using a summation over layers.

Photographic response to x-ray irradiation. II: Correlated models.

In this paper models from the first paper are generalized so that they include the correlation of attenuation coefficients and coverages with emulsion depth. They avoid further assumptions and can provide physically meaningful parameters (as opposed to earlier studies); thus closer agreement with experimental measurements is obtained. The difficulty in estimating correlated overlap functions is discussed. Error estimates resulting from grain statistics are generalized and computed in a selfconsistent manner. Contributions to granularity from densitometer and grain statistics have been shown to be significant or dominant in most emulsion types. The formulation derives reliable error estimates. Correlated models are important for thick emulsions such as DEF-392, whereas integral formalisms may be as useful for thin emulsions. In agreement with the first paper, reciprocity failure appears to be negligible for UV or x-ray energies above 9 eV.

Detailed tabulation of atomic form factors, photoelectric absorption and scattering cross section, and mass attenuation coefficients in the vicinity of absorption edges in the soft X-ray (Z = 30-36, Z = 60-89, E = 0.1-10 keV)--addressing convergence issues of earlier work.

A new tabulation of atomic form factors is discussed briefly, extending the validity of the isolated atom approximation and serving as a baseline for near-edge solid-state and XAFS investigations. This is detailed by Chantler [J. Phys. Chem. Ref. Data, (2000), 29, 597-1048] and is the latest component of the FFAST tabulation of NIST.

Photographic response to x-ray irradiation. III: Photographic linearization of beam-foil spectra.

In this paper models for the relation of specular density to incident (x-ray) intensity with uncertainties are applied to experimental data, indicating methods for the correction of additional effects. Linearization and error calculations are simplified by double linear interpolation, and the effect of this is quantified. Relative first-order intensities are determined directly. Secondary linearization or calculation for higher-order lines gives correction factors that yield absolute and relative higher-order intensity ratios. The effects of energy and angle on linearization are included. Densitometry uncertainty is estimated and quantified.