Inner-shell Ionization Cross Sections Research Articles

Statistical Approach of Inner-Shell Ionization in 0.1–1.625 MeV/u Cu + Bi Collisions

Experimental data of inner-shell ionization cross sections and outer-shell ionization probabilities per electron, obtained for the collision system. Cu + Bi in the energy range of 0.1–1.625 MeV/u, are in good agreement with the predictions of the statistical model of Mittleman and Wilets. The found dependence of the diffusion constant determined for different final vacancy states on the excitation (ionization) energy is in fair agreement with the model prediction.

ENERGY-LOSS EFFECT IN K-SHELL IONIZATION

The energy-loss effect of the projectile for direct inner-shell ionization cross sections by charged-particle impact has been examined. The relativistic and nonrelativistic calculations for K-shell ionization with and without the energy-loss effect are made in the plane-wave Born approximation and compared with the Brandt-Lapicki theory for the corrections of the relativistic and energy-loss effect. It is demonstrated that the Brandt-Lapicki method gives a good approximation to both relativistic and nonrelativistic cross sections, which implicitly take into account the energy-loss effect. However, the use of the Brandt-Lapicki relativistic correction method in the nonrelativistic theory with the exact integration limits for energy and momentum transfer overestimates the relativistic calculations for low-energy projectiles. This indicates that the Brandt-Lapicki method for correction of the electronic relativistic effect should be used only with their energy-loss correction method.

Single, double and triple ionization of Ne, Ar, Kr and Xe by 30 - 1000 keV impact

Experimental data for single, double and triple ionization of Ne, Ar, Kr and Xe by 30 - 1000 keV antiproton impact are presented and compared with existing proton data. It is found that the current phenomenological understanding of ionization developed from studies of light targets generally apply to heavy atomic targets as well. Inner-shell ionization followed by Auger decay is found to be an important channel for multiple ionization of the heaviest targets, and the projectile charge dependence of their multiple ionization cross sections must be understood as stemming from the underlying inner-shell ionization cross sections.

Quantitative chemical phase imaging by means of energy filtering transmission electron microscopy

Electron spectroscopic imaging (ESI) in the transmission electron microscope (TEM) is a powerful method to produce 2-dimensional elemental distribution maps. These maps show in a clear way the chemical situation of a small specimen region. In this work we used a Gatan Imaging Filter (GIF) attached to a 200 kV TEM to investigate a Ba-Nd-titanate ceramic. The three phases occuring in this material could be visualized using inner-shell ionization edges (Ba M45, Nd M45 and Ti L23). We applied different image correlation techniques to the ESI elemental maps for direct visualization of the chemical phases. First we simply overlaid the elemental maps assigning each element one colour to form an RGB image. Secondly we used the technique of scatter diagrams to classify the different phases. Finally we quantified the elemental maps by dividing them and multiplying them by the appropriate inner-shell ionization cross-sections which gave atomic ratio images. By using these methods we could clearly identify and quantify the various phases in the Ba-Nd-titanate specimen.

Dynamical diffraction in electron-energy-loss spectrometry: The independent Bloch-wave model.

The double-differential cross section for inner-shell ionization in a crystal by fast electrons is calculated within the theory of dynamical electron diffraction. Bloch waves are used for the incident and the emerging electrons. We show that interference terms are still present in the independent Bloch-wave model. In the two-beam case, the cross section contains but six terms, three of them caused by interference. From the six terms, three are identified as the Kikuchi excess and defect lines and the Kikuchi band. The remaining three terms have not yet been described explicitly. As an example, the Si K-shell ionization cross section is calculated for a (220) two-beam case, in a dipole approximation for the mixed dynamic form factor. It is shown that in electron spectroscopic diffraction the maximum of the fundamental Lorentzian can be significantly shifted with respect to the direction of incidence, and that the interpeak minimum between the fundamental and the Bragg-excited Lorentzians is depressed relative to the kinematical case. \textcopyright{} 1996 The American Physical Society.

Ionization cross-sections for the L 23-edges of the elements Sr to Mo for quantitative EELS analysis

Quantitative microanalysis by electron energy-loss spectrometry requires knowledge of partial inner-shell ionization cross-sections. Data for the L 23-edges of the elements strontium to molybdenum are not well known. We have therefore measured cross-section ratios ( k-factors) for the L 23-edges of the elements Sr to Mo using thin film oxide-standards. The experimental values are compared with calculations derived from a modified hydrogenic and a Hartree-Slater model. The results are presented in terms of an integrated dipole oscillator strength to facilitate both comparisons between theory and experiment, and calculations of cross-sections for particular experimental conditions. While hydrogenic theory oscillatorstrength values deviate from the experimental ones by more than 30%, there is good agreement between Hartree-Slater theory and experiment. We have also compared the relative microanalytical sensitivities for the M 45- and L 23-ionization edges of these elements.

An accelerator based multi-coincidence electron-photon spectrometer for the measurement of bremsstrahlung and inner-shell ionization cross-sections

A new system for the measurement of coincidences between electrons and photons has been devised. This system, which is coupled with a 300 keV electron accelerator, will allow the user to measure electron-electron and electron-photon coincidences between any number of detectors simultaneously. Advantages of such a setup include the ability to carry out multiple scattering experiments simultaneously with just one beam. Also, provided enough detectors are available, coincidence measurements can be made at various angles simultaneously in one run. Details on the implementation of this system are presented.

A semi-empirical approach to the calculation of absolute inner-shell electron impact ionization cross sections

Extending a recently developed semiclassical approach, we report the development of a formula which allows the satisfactory description and prediction of absolute electron impact ionization cross sections for K, L, and M inner-shell ionization in the energy range from threshold up to 109 eV for all elements. The present formulation also allows to derive and extend a previously noted scaling law for K-shell ionization. The present results are compared with previous theoretical and experimental determinations where available.

Recent experiments at the Giessen slow positron source TEPOS

Recent results for the K- and L-shell ionization of silver and gold, respectively, by positron and electron impact and for the energy loss of 6–20 keV positrons in thin foils obtained at the Giessen slow positron source TEPOS will be discussed. The measured cross section for inner-shell ionization by positron impact decreases more rapidly towards threshold compared to electron impact. This behaviour is confirmed by theoretical calculations performed in the plane wave Born approximation which include an electron exchange term and take the deceleration or acceleration of the incident positron or electron, respectively, in the target nuclear field into account.

Evaluation of particle effects in bremsstrahlung and in quantitative energy-dispersive x-ray microanalysis

The magnitude and the spectral form of bremsstrahlung signal contains much information about the target and is significantly influenced by the surface irregularities. By computer modelling, it is possible to extract the information to perform more accurate quantitative x-ray microanalysis for specimens with special geometries. In this research, bremsstrahlung spectra obtained from electron beams striking at selected locations of spherical particles were investigated by Monte Carlo simulations and experimental observations. The effects of surface geometries and the x-ray path lengths in the specimens on the variation of bremsstrahlung spectra and peak-to-background ratios were studied.The Monte Carlo electron trajectory calculations were determined with a screened Rutherford cross-section and a plural scattering model. The continuum x-ray depth profile is computed using Kramer's bremmstrahlung cross-section. The cross-section for inner shell ionization proposed by Green and Cosslett were employed for calculating characteristic x-rays. Bethe stopping power was determined by using the Luo-Joy modification at low energies. The mass absorption coefficient was calculated using Heinrich expression. The detector efficiency was determined experimentally.

Coulomb-Born calculation of the triple-differential cross section for inner-shell electron-impact ionization of carbon.

A Coulomb-Born approximation is used to compute the triple-differential cross section for electron-impact inner-shell (1s) ionization of carbon. We employ a perturbation series that allows the use of Coulomb waves with arbitrary ${\mathit{Z}}_{\mathrm{eff}}$ for the incoming, scattered, and ejected electrons. Most of the features of the triple-differential cross section observed experimentally are reproduced, even though these wave functions are distorted by an effective Coulomb potential and therefore do not satisfy the plane-wave boundary conditions at infinity. In order to explain some features that appear in the cross section, and in order to probe the validity of a dipole approximation, we make a multipole expansion of the transition matrix and show that the amplitudes of the multipole components are similar to those obtained in the Born approximation, while the relative phases of the multipoles differ greatly.

X-RAY PRODUCTION, INNER SHELL IONIZATION AND READING’S THEOREM IN ION · ATOM COLLISIONS

When a solid or gaseous target is bombarded with heavy charged particles, inner shell electrons of target atoms are ionized and characteristic x rays are produced. We can easily observe these x rays with a Si(Li) detector and derive inner-shell ionization cross section from the x-ray production cross sections. In this paper, we make a review of x-ray production, inner shell ionization and Reading’s theorem in light ion·atom collisions. This theorem is one of the most important ones in the ion·atom collision physics and permits precise discussion on comparison between experimental inner-shell ionization cross sections obtained with a Si(Li) detector and the calculations based on usual theories where the incident particle is assumed to interact with only one electron in an atom and the presence of other electrons is ignored.

INNER-SHELL IONIZATION BY LIGHT-ION IMPACT

The ECPSSR theory to calculate the inner-shell ionization cross sections by light-ion impact is studied. Starting from the general formulation of the plane-wave Born approximation, the corrections for the energy-loss effect (E) and the Coulomb-deflection effect (C) of the projectile, and for the binding-polarization effect in the perturbed-stationary-state approach (PSS) and the electronic relativistic effect (R) of the target electron are described. The calculated values in the ECPSSR theory are compared with the experimental data. In general, agreement is good, but there are systematic deviations for low-energy projectiles. The comparison with other theoretical treatments for the inner-shell ionization is discussed.

Inner-Shell Ionization Cross Sections

Values of cross sections for ionization of inner-shell electrons by electron impact are required for electron probe microanalysis, Auger-electron spectroscopy, and electron energy-loss spectroscopy. The present author has reviewed measurements and calculations of inner-shell ionization cross sections. This paper is an update and summary of these previous reviews.It is convenient to start with the Bethe equation for inner-shell ionization cross sections which is frequently used (and misused) in x-ray microanalysis:(1)where σnℓ is the cross section for ionization of the nℓ shell with binding energy Enℓ by incident electrons of energy E. The terms bnℓ and cnℓ are the Bethe parameters discussed further below. It has been assumed in the derivation of Eq. (1) that E ≫ Enℓ ; this requirement will also be discussed. Finally, it has been assumed here that E is low enough (≲50 keV) so that a relativistic correction is unnecessary.The extent to which a given set of measured or calculated cross-section data is consistent with Eq. (1) can be determined from a Fano plot in which σnℓE is plotted versus ℓnE; if such a plot is linear, Eq. (1) is consistent with the data and values of the Bethe parameters can be easily derived.

A Simulation of Electron Scattering in Metals and its Application for Scanning Electron Microscopy

In a recent research, the scanning electron microscope(SEM) has been shown to provide spatial resolution of less than 0.5nm. With the knowledge of the ultimate resolution or the factor which controls the resolution, it is possible to optimize the specimen preparation method and the choice of various electron beam parameters (eg. acceleration voltage etc.) For a precise discussion of the SEM image, it is necessary to take into account not only the signal (electron) production and the propagation in a specimen and its emission from the surface, but also electron trajectories in vacuum toward the detector. However, electron scattering process in the specimen does not depend on the detection system, and the resolution is mainly attributed to the spatial distribution of the electron emission from the specimen surface. Here, we focused on the electron scattering mechanisms in metals and developed a Monte Carlo simulation model of electron trajectories. Also, this simulation is applied to evaluate a compositional contrast in the SEM.In the present study electron interactions with atomic potential, inner-shell electrons, conduction electrons are taken into account. Cross sections calculated by the present model are shown in Fig.1 for [l]elastic scattering, [2]inner-shell (1s, 2s, 2p for Al) electron ionization, [3]conduction electron ionization through non-radiative plasmon decay, and [4] stable plasmon excitation in the conduction band electrons for Al. For the elastic scattering, the Mott cross section is used. For inner-shell electron ionizations by an electron collision, the Gryzinski equation is used. In order to express the plasmon-electron interaction in a free electron gas at the conduction band, the Lindhard treatment is used. This treatment is based on the random phase approximation in the dielectric response function of metals. The cross section is shown in a unit of the inverse mean free path. The cross sections for conduction electron ionization and the plasmon excitation agree with the data of Tung, Ashley, and Ritchie. Cross sections for inner-shell electron ionization, which Tung et al. have derived using the generalized oscillator strength, are also shown in Fig.1 for a comparison.

Impact-parameter dependence of inner-shell ionization cross sections induced by protons and He ions in the energy range 0.4-2.0 MeV/u.

The impact-parameter dependence of the K-shell ionization cross section has been measured for protons and $^{3}\mathrm{He}$ ions incident on thin-foil targets of Ti, Ni, and Cu at selected energies in the region from 0.4 to 2.0 MeV/u. Comparison is made of these experimentally determined values with the results of a recently developed theoretical model in which the electron binding energy and initial-state wave function are allowed to respond in a time-dependent fashion to the field of the projectile as a function of its position along a hyperbolic Coulomb trajectory. Generally good agreement between the theoretical and experimental values is obtained. A comparison between the results of this theoretical model and two other published theoretical results and with experimental data for 0.5-MeV p in Cu is also shown. Remarkably close agreement is seen, particularly between the predictions of the rather disparate theoretical models. Measurements for a single system, 2.0-MeV p in Sm, involving ionization from the L shell, are also reported.

Low- Z inner-shell ionization cross sections for 0.5–1.5 MeV H and He ions

K and L cross sections for inner-shell ionization of low- Z elements by 0.5–1.5 MeV protons and helium ions were determined from the experimental X-ray production data. Proton K X-ray production cross sections were measured for NaCl, Mg, Al, SiO, GaP, CaF 2, Ti, V, Cr, Fe, Co, Ni and Cu targets and the corresponding L data were obtained for NaCl, Al, SiO, GaP, CaF 2, Ti, V, Cr, Fe, Co, Ni, Cu, Zn and As targets. Sample thicknesses were in the range of 30–60 μg/cm 2 but thick-target effects were also taken into account. Special care was given to the incident particle dose and the X-ray detector efficiency determination. Measured inner-shell ionization cross sections were compared with the results of the ECPSSR calculations.

Cross sections for inelastic electron scattering in solids

An overview is given of available information on cross-sections for inelastic electron scattering in solids with emphasis on the need for cross-section data in electron energy-loss spectroscopy (EELS), X-ray emission spectroscopy (XES), and Auger-electron spectroscopy (AES). After a brief survey of the relevant theory, information is given on inelastic mean free paths of 200–2000 eV electrons in solids (AES), total inner-shell ionization cross sections (AES and XES), partial inner-shell ionization cross section (EELS), and electron-beam-induced damage.

Quantitative analysis of electron-energy-loss spectra

Numerical procedures are described for removing plural scattering from a transmitted electron-energy-loss spectrum, for calculation of the energy-dependent dielectric function, for the measurement of specimen thickness and for elemental microanalysis. A formula is proposed for rapidly calculating inner-shell ionization cross-sections, making use of X-ray absorption data, energy-loss measurements and atomic scattering theory.

Finite-base-set expansion method for inner-shell ionization in ion-atom collisions

The inner-shell ionization cross sections in ion-atom collisions have been calculated with the finite-base-set expansion method, using expansion into atomic orbitals and pseudostates. The calculations have been made within the framework of the impact-parameter formalism and the distortion approximation has been used. The obtained cross sections are in good agreement with the experimental results. The extension of the method to the relativistic case has been attempted and good agreement with the measured results is achieved.