We report calculations of electron inelastic mean free paths (IMFPs) of 50–2000 eV electrons for a group of 14 organic compounds: 26-n-paraffin, adenine, β-carotene, bovine plasma albumin, deoxyribonucleic acid, diphenylhexatriene, guanine, kapton, polyacetylene, poly(butene-1-sulfone), polyethylene, polymethylmethacrylate, polystyrene and poly(2-vinylpyridine). The computed IMFPs for these compounds showed greater similarities in magnitude and in the dependences on electron energy than was found in our previous calculations for groups of elements and inorganic compounds (Papers II and III in this series). Comparison of the IMFPs for the organic compounds with values obtained from our predictive IMFP formula TPP-2 showed systematic differences of ∼40%. These differences are due to the extrapolation of TPP-2 from the regime of mainly high-density elements (from which it had been developed and tested) to the low-density materials such as the organic compounds. We analyzed the IMFP data for the groups of elements and organic compounds together and derived a modified empirical expression for one of the parameters in our predictive IMFP equation. The modified equation, denoted TPP-2M, is believed to be satisfactory for estimating IMFPs in elements, inorganic compounds and organic compounds.

Calculations of electron inelastic mean free paths. III. Data for 15 inorganic compounds over the 50–2000 eV range

A multiplatform code for the analysis of energy-dispersive X-ray fluorescence spectra

We report calculations of electron inelastic mean free paths (IMFPs) for 50–2000 eV electrons in a group of 27 elements (C, Mg, Al, Si, Ti, V, Cr, Fe, Ni, Cu, Y, Zr, Nb, Mo, Ru, Rh, Pd, Ag, Ta, W, Re, Os, Ir, Pt, Au and Bi). This work extends our previous calculations (Surf. Interface Anal. 11, 57 (1988)) for the 200–2000 eV range. Substantial variations were found in the shapes of the IMFP versus energy curves from element to element over the 50–2000 eV range and we attribute these variations to the different inelastic scattering properties of each material. Our calculated IMFPs wee fitted to a modified form of the Bethe equation for inelastic electron scattering in matter; this equation has four parameters. These four parameters could be empirically related to several material parameters for our group of elements (atomic weight, bulk density and number of valence electron per atom). IMFPs and those initially calculated was 13%. The modified Bethe equation and our expressions for the four parameters can therefore be used to estimate IMFPs in other materials. The uncertainties in the algorithm used for our IMFP calculation are difficult to estimate but are believed to be largely systematic. Since the same algorithm has been used for calculating IMFPs, our predictive IMFP formula is considered to be particularly useful for predicting the IMFP dependence on energy in the 50–2000 eV range and the material dependence for a given energy.

Calculations of electorn inelastic mean free paths. II. Data for 27 elements over the 50–2000 eV range

Attenuation lengths of low-energy electrons in solids

After passage through matter, the energy spectrum of a polychromatic beam of x-rays contains valuable information about the elemental composition of the absorber. Conventional x-ray systems or x-ray computed tomography (CT) systems, equipped with scintillator detectors operated in the integrating mode, are largely insensitive to this type of spectral information, since the detector output is proportional to the energy fluence integrated over the whole spectrum. The main purpose of this paper is to investigate to which extent energy-sensitive photon counting devices, operated in the pulse-mode, are capable of revealing quantitative information about the elemental composition of the absorber. We focus on the detection of element-specific, K-edge discontinuities of the photo-electric cross-section. To be specific, we address the question of measuring and imaging the local density of a gadolinium-based contrast agent, in the framework of a generalized dual-energy pre-processing. Our results are very promising and seem to open up new possibilities for the imaging of the distribution of elements with a high atomic number Z in the human body using x-ray attenuation measurements. To demonstrate the usefulness of the detection and the appropriate processing of the spectral information, we present simulated images of an artherosclerotic coronary vessel filled with gadolinium-based contrast agent. While conventional systems, equipped with integrating detectors, often fail to differentiate between contrast filled lumen and artherosclerotic plaque, the use of an energy-selective detection system based on the counting of individual photons reveals a strong contrast between plaque and contrast agent.

https://iopscience.iop.org/article/10.1088/0031-9155/52/15/020/pdf

K-edge imaging in x-ray computed tomography using multi-bin photon counting detectors.

It is shown that calculations of electron attenuation lengths and escape depths would require modification of definitions proposed in the literature, since these definition are not universally applicable. Exemplary experimental arrangements are indicated for which more general definitions are necessary, and such definitions are proposed. A Monte Carlo program has been developed with which it is possible to estimate attenuation lengths and escape depths. A comparison of these parameters is made for photoelectrons arising from s levels.

Comparison of electron attenuation lengths and escape depths with inelastic mean free paths

After a systematic analysis of different databases and a comparison with empirical data, we decided to describe photoelectric absorption coefficients, coherent and incoherent scattering coefficients and mass attenuation coefficients in the energy range from 1 to 300 keV for elements from Z = 1 to 94 by a modified version of Scofield's tables in combination with scattering coefficients from Elam et al. Modifications include check and correction of edge positions, description of M4- and M5-ranges of elements from promethium upwards by sawtooth responses and reduction of data by introduction of least-squares fits of fifth order to Scofield's and Elam et al.'s numerical data. Our database was developed especially for application in fundamental parameter programs for quantitative x-ray analysis (XRFA, EPMA, XPS and TEY). Copyright © 2003 John Wiley & Sons, Ltd.

Numerical description of photoelectric absorption coefficients for fundamental parameter programs

X-ray tube spectra make an essential contribution to the quantitative description of experimental setups or for quantitative x-ray analysis. After an outline of the historical development of the description of tube spectra the approaches given by Wiederschwinger, Ebel et at. Schossmann et al. and Pella et at, are treated in detail. Summarizing the theoretical treatment and the applications, it can be stated that both approaches give comparable results over a certain spectral range. Pella's approach is restricted to electron incidence angles of 90° and application of Pella's spectral responses in the lower keV range should be avoided.

X-ray tube spectra

XPS imaging promises to be a powerful analytic tool because it enables specific information on both elements and bonding to be recorded on a two-dimensional distribution map. As far as the authors are aware, the only scanning XPS method to date which has been found to be practical is essentially a scanned-particle-beam method, like scanning AES, and it is only applicable to thin film specimens. This paper provides the basic ideas of a new imaging XPS technique based on a quite different concept. It will be applicable to any kind of specimen that can be analysed in a conventional XPS system. It makes use of the dispersion properties of a spherical condenser-type spectrometer and applies a two-dimensional electron detection device for decoding the energy and emission position of an analysed photoelectron. Experimental arrangement and theory of operation are presented.

Horst Ebel

Papers

Comparison of electron attenuation lengths and escape depths with inelastic mean free paths

Numerical description of photoelectric absorption coefficients for fundamental parameter programs

X-ray tube spectra

Imaging XPS—A new technique, I—principles

Quantitative XPS — multiline approach