Evaluation of elastic‐scattering cross sections for electrons and positrons over a wide energy range

Quantification of surface‐ and bulk‐analytical methods, e.g. Auger‐electron spectroscopy (AES), X‐ray photoelectron spectroscopy (XPS), electron‐probe microanalysis (EPMA), and analytical electron microscopy (AEM), requires knowledge of reliable elastic‐scattering cross sections for describing electron transport in solids. Cross sections for elastic scattering of electrons and positrons by atoms, ions, and molecules can be calculated with the recently developed code ELSEPA (Elastic Scattering of Electrons and Positrons by Atoms) for kinetic energies of the projectile from 10 eV to 50 eV. These calculations can be made after appropriate selection of the basic input parameters: electron‐density distribution, a model for the nuclear‐charge distribution, and a model for the electron‐exchange potential (the latter option applies only to scattering of electrons). Additionally, the correlation‐polarization potential and an imaginary absorption potential can be considered in the calculations. We report comparisons of calculated differential elastic‐scattering cross sections (DCSs) for silicon and gold at selected energies (500 eV, 5 keV, 30 keV) relevant to AES, XPS, EPMA, and AEM, and at 100 MeV as a limiting case. The DCSs for electrons and positrons differ considerably, particularly for medium‐ and high‐atomic‐number elements and for kinetic energies below about 5 keV. The DCSs for positrons are always monotonically decreasing functions of the scattering angle, while the DCSs for electrons have a diffraction‐like structure with several minima and maxima. A significant influence of the electron‐exchange correction is observed at 500 eV. The correlation‐polarization correction is significant for small scattering angles at 500 eV, while the absorption correction is important at energies below about 10 keV. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiple scattering of light from polymer dispersed liquid crystal material

Light scattering from polymer dispersed liquid crystal (PDLC) material has been studied experimentally and by Monte Carlo simulation. Light scattering was measured as a function of both scattering angle and cell thickness. The cell thicknesses of practical interest are in an intermediate regime where neither single scattering nor light diffusion applies. Both the angular and the thickness dependence of the scattering intensity can be described accurately by a Monte Carlo simulation of multiple scattering from a homogeneous distribution of independent scatterers. The model smoothly interpolates between the single scattering limit for thin cells and the diffusion limit for thick cells. It can easily be extended to include any specific feature of a scattering display system.     

Energy loss of scattered ions at glancing-angle incidence on the crystal surface

Experimental findings of glancing-angle scattering of energetic ions are reviewed with particular emphasis on the energy loss of ion during scattering. The position-dependent stopping power of the surface which is derived from the angular dependence of observed energy loss is explained in terms of single and distance electron excitations of surface electrons. For the ions with velocities less than the Fermi velocity of target valence electrons, it is shown that the stopping power of a surface is determined only by the elastic collisions of the ion with valence electrons. From the analysis of the energy losses of 12–30 keV He ions reflected from the (001) surface of SnTe, a method is proposed to derive the electron density distribution averaged over the plane parallel to the surface from this position-dependent stopping power.     

Interlaboratory study comparing analyses of simulated angle‐resolved X‐ray photoelectron spectroscopy data

An interlaboratory study has been conducted to determine the following: (i) the similarities and differences of film thicknesses and composition profiles obtained from analyses of simulated angle‐resolved X‐ray photoelectron spectroscopy (ARXPS) data by different analysts using different algorithms for data analysis, and (ii) the effects of two assumptions commonly made in data‐analysis algorithms for ARXPS on derived film thicknesses and composition profiles. The analyzed data were generated by the National Institute of Standards and Technology Database for the Simulation of Electron Spectra for Surface Analysis, (SESSA) which provides a simple way to study the influence of the aforementioned effects on compositional depth profile reconstruction. Sets of simulated ARXPS data were produced for thin films of SiO₂, SiON, HfO₂, and HfON of varying thicknesses on a Si substrate. For some HfON films, the N concentration varied with depth. Eleven groups participated in the round robin study. The majority (eight) employed a commercial ARXPS instrument in which the angular distribution is measured for a fixed sample geometry, in contrast to conventional ARXPS in which the sample is tilted for angular variation. The average deviations between the reported average depth, film thickness, and amount of material typically varied between 20% and 30% but were considerably larger, between 30% and 80%, for some cases. The average errors were generally larger for simulations that included elastic scattering and the finite analyzer‐acceptance angle (realistic conditions) than those for simulations that neglected elastic scattering and the finite analyzer‐acceptance angle (simplified conditions). The retrieved N depth profiles were quantitatively different from the true depth profiles and showed substantial variability among the group of members who used the same instrument and analysis software. Copyright © 2014 John Wiley & Sons, Ltd.     

Depth and angular profiles of inelastic low-energy electron scattering in condensed molecular samples

Angular distributions of electrons scattered elastically and inelastically from cold solid molecular films of ethylene and nitrogen in various proportions, grown from the gas phase at different temperatures, have been studied by high-resolution electron energy loss spectroscopy. The probing depth of dipole and impact scattering has been investigated by covering the sample by overlayers of argon of increasing thickness. The angular distribution measured for elastically and inelastically dipole-scattered electrons was found to be peaked about the specular direction for all surface conditions studied, while a diffuse angular distribution was possible for electrons that underwent dipole-forbidden scattering. These results allow us to identify favorable conditions for monitoring the composition of a solid sample during the course of reactions occurring under exposure to low-energy electrons.     

New developments in theory of fast electron scattering in solids: Applications to microbeam analysis

The study of fast electron interaction with solids in the energy range from 100 eV to several tens of keV is prompted by quickly developing microbeam analysis techniques such as electron probe microanalysis, scanning electron microscopy, electron energy loss spectroscopy and so on. It turned out that for random solids the electron transport problem might be solved on the basis of the generalized radiative field similarity principle. The latter states that the exact differential elastic cross section in the kinetic equation may be replaced by an approximate one provided the conditions of radiative field similarity are fulfilled. Application of the generalized similarity principle to electron scattering in solids has revealed many interesting features of electron transport. Easy to use and effective formulae have been obtained for the angular and energy distribution of electrons leaving a target, total yields of characteristic photons and slow electrons escaping from a sample bombarded by fast primaries, escape probability of Auger electrons as a function of depth etc. The analytical results have been compared with Monte Carlo calculations and experiments in a broad range of electron energies and scattering properties of solids and good agreement has been observed.     

Monte Carlo simulation of full energy spectrum of electrons emitted from silicon in Auger electron spectroscopy

A Monte Carlo simulation including surface excitation, Auger electron‐ and secondary electron production has been performed to calculate the energy spectrum of electrons emitted from silicon in Auger electron spectroscopy (AES), covering the full energy range from the elastic peak down to the true‐secondary‐electron peak. The work aims to provide a more comprehensive understanding of the experimental AES spectrum by integrating the up‐to‐date knowledge of electron scattering and electronic excitation near the solid surface region. The Monte Carlo simulation model of beam–sample interaction includes the atomic ionization and relaxation for Auger electron production with Casnati's ionization cross section, surface plasmon excitation and bulk plasmon excitation as well as other bulk electronic excitation for inelastic scattering of electrons (including primary electrons, Auger electrons and secondary electrons) through a dielectric functional approach, cascade secondary electron production in electron inelastic scattering events, and electron elastic scattering with use of Mott's cross section. The simulated energy spectrum for Si sample describes very well the experimental AES EN(E) spectrum measured with a cylindrical mirror analyzer for primary energies ranging from 500 eV to 3000 eV. Surface excitation is found to affect strongly the loss peak shape and the intensities of the elastic peak and Auger peak, and weakly the low energy backscattering background, but it has less effect to high energy backscattering background and the Auger electron peak shape. Copyright © 2014 John Wiley & Sons, Ltd.     

Microheterogeneity in mixtures of benzene with alcohols and hydrocarbons: Positron annihilation and molecular light scattering

Experimentally measured concentration dependences of the probability of positronium formation and the intensity of molecular light scattering in binary benzene-ethanol and benzene-cyclohexane mixtures were analyzed. The observed behavior was explained by association of molecules. Arguments are presented in favor of the formation in benzene-ethanol mixtures of alcohol associates capable of capturing and solvating quasi-free electrons formed in the tracks of high-energy positrons during their passage through the mixture. As the concentration of associates rises, the positronium formation rate decreases while the intensity of the light scattered by them increases. The mean size and lifetime of the associates were evaluated. It was established that, in benzene-ethanol and benzene-cyclohexane mixtures at temperatures below room temperature, benzene associates are formed.     

Monte Carlo simulation of bremsstrahlung emission by electrons

The basic components of Monte Carlo simulation of bremsstrahlung emission by electrons are presented. Various theoretical cross-sections that have been used in Monte Carlo codes are described and the emphasis is on the more accurate partial-wave cross-sections for which numerical databases are available. Sampling algorithms for a combination of numerical scaled energy-loss cross-sections and various analytical approximations to the intrinsic angular distribution are presented. Analogue simulation of the energy spectra and angular distribution of X rays from targets irradiated by electron beams is very inefficient and a simple variance-reduction technique, which is easy to implement and has proven to be particularly effective in speeding up these simulations, is described. Results from simulations of X-ray spectra with the general-purpose Monte Carlo code penelope are compared with experimental data for different materials and incident electrons with energies in the 20 keV to 1 GeV energy range.     

Particle size analysis of polymer latexes by light scattering. V. The significance of an assumed distribution in the analysis of angular scattering data

In the analysis of light scattering data from polymer latex systems or other systems of spherical particles, it is necessary to assume a particle size distribution function. Theoretical angular scattering functions based on the assumed distribution and representing a wide range of size distribution parameters are compared to experimental data in order to obtain a best fit. In previous work, it has been shown that as the polydispersity increases beyond certain limits the uncertainty in the assignment of the size distribution parameters (i.e., the best fit) increases. This report is concerned with the analysis of angular scattering from unimodal systems and simulated cases where theoretical scattering functions for wide, negatively skewed distributions are used as “experimental data,” are analyzed by utilizing four different distribution functions. These functions represent different degrees of skewness and include negatively, positively, and normally skewed distributions. The results from the use of the various distribution functions are discussed with respect to the uncertainly in the assignment of distribution parameters resulting from the loss of structure in the angular scattering pattern due to increased polydispersity. Scattering data from the bimodal distribution are analyzed by assuming a unimodel distribution, and the consequences of this assumption are assessed.     

Electron scattering in Pt(PF3)4: elastic scattering, vibrational, and electronic excitation

Experimental absolute differential cross sections for elastic scattering, and for vibrational and electronic excitation of Pt(PF(3))(4) by low-energy electrons are presented. The elastic cross sections have a deep angle-dependent Ramsauer-Townsend minimum (E(min) = 0.26 eV at θ = 135°). The angular distributions of the elastic cross section at and above 6.5 eV show an unusually narrow peak at an angle which decreases with increasing energy (it is at 40° at 20 eV). Wavy structure is observed at higher angles at 15 and 20 eV. Vibrational excitation cross sections reveal five shape resonances, at 0.84, 1.75, 3.3, 6.6, and 8.5 eV. The angular distributions of the vibrational cross sections have a strong forward peak and are nearly isotropic above about 60°. Electronically excited states are characterized by electron energy-loss spectra. They show a number of unstructured bands, the lowest at 5.8 eV. They are assigned to Rydberg states converging to the 1st and 2nd ionization energies. The cross sections for electronic excitation have very high forward peaks, reaching the value of 50 A?(2) at 50 eV and 0° scattering angle. Purity of the sample was monitored by the very low frequency (26 meV) Pt-P stretch vibration in the energy-loss spectra.     

Investigations on the melting behaviour of triglyceride nanoparticles

Suspensions of triglyceride nanoparticles have been proposed as carrier systems for intravenous administration of poorly water soluble drugs. Such nanosuspensions can easily be produced by homogenization of the melted triglyceride in an aqueous phase. Using special emulsifier blends it is possible to obtain suspensions with an average size of the recrystallized particles below 100 nm (photon correlation spectroscopy z-average). As can be observed by transmission electron microscopy the particles are very thin platelets with thicknesses in the range of only a few molecular layers. Nanoparticles of saturated monoacid triglycerides (smaller than 200 nm) exhibit uncommon melting behaviour, which is expressed in their differential scanning calorimetry curve by multiple endothermal peaks over a temperature range of about 10 °C. This effect was attributed earlier to the particle thickness distribution in the suspension rather than to polymorphic transitions since all the material exists in the stable β modification. Here we present experimental investigations on the correlation between the melting behaviour of trilaurin nanosuspensions and the particle thickness distribution determined by analysis of difference X-ray diffraction patterns recorded at progressively higher temperatures in the melting range of the particles. Because of the weak X-ray scattering of the systems investigated synchrotron radiation was used besides conventional sources. The Fourier analysis of the difference diffraction patterns is described in detail and the advantages and difficulties in using this method are discussed. It was observed that the melting temperatures of the nanoparticles increase with increasing particle thicknesses. Simultaneously a decrease in the interplanar (001) spacing with increasing particle thickness was found. Received: 27 July 1999 Accepted: 5 October 2000     

Electron Transmission Through Thin Organized Organic Films

The interaction between electrons and organized organic thin films was investigated by measuring the energy distribution of photoelectrons injected from a thin silver film coated with thin organic layers. Electrons with energy above ∽0.8 eV were transmitted ballistically through an organic layer that contains up to five monolayers, each ∽2 nm thick. Elastic scattering processes contribute significantly to the electron energy distribution only for thicker layers. The transmission of low-energy electrons is controlled mainly by an electrostatic barrier perpendicular to the surface. A signature of a band structure in the organic layer was observed when the electrons were transmitted through 13 layers. © 1997 by John Wiley & Sons, Ltd.     

Low energye ± — Li2 scattering using LFCC method

The scattering of slow electrons and positrons by lithium metal dimer has been studied in the laboratory frame close coupling method. The effect of polarization is included through the parameter free model correlation potential given by Perdew and Zunger. In the case of electron, the exchange kernel is replaced by a local model exchange potential as used by Sur and Ghosh. To have a convergent result seven rotational states (j=0, 2, 4, 6, 8, 10, 12) are retained in the coupling scheme. The results for elastic, rotational and total cross sections fore ^? — Li₂ ande ⁺ — Li₂ are reported. The electron results are in fair agreement with measured values and existing theoretical predictions.     

Model for the capture of secondary electrons by a fast ion

A capture process is discussed which is strongly assisted by the relaxation of energetic secondary electrons inside a solid target. The following processes are incorporated into the model (in a simplified form): — the production of secondary electrons by a fast projectile inside the target (in binary encounter approximation of the projectile with free target electrons), — the dynamics of the secondary electrons (in continuously slowing down approximation without elastic scattering), — the reduction of the screening of the projectile charge at the exit surface (in sudden approximation and neglecting the image charge). The capture efficiently populates Rydberg states with high angular momenta and gives high coherences between Rydberg states. The application to convoy electrons gives contributions only to the innermost part of the cusp shaped velocity spectra which is possibly caused by the neglect of elastic scattering of the secondary electrons.     

Structure of atoms and fields

In a previous paper the theory of the toroidal spiral field was employed to derive equations for the stationary orbits of particles that belong to both the atomic nucleus and electrons orbiting the nucleus. This theory offered new relativistic relationships for both the mass and electrical charges, leading to the existence inside the nucleus of particles with not only opposite electrical charges in comparison with the electrons, but also with the masses of opposite sign. In this paper, this theory was applied to create a model of the atom that consists of positive and negative muons, positrons and electrons. The two methods that are used to determine the stationary orbits of particles are: (1) quantizing the particle angular momentum, and (2) quantizing the particle relative electrical charge. The existence of particles with the charges 1/3 and 2/3 is explained by the relativistic dependence of the electrical charges on the particle velocity and also by the quantum character of these charges. Creation of the particles and their distribution in the orbits follows the proposed rule of duality and the rule of stability. The theory describes the processes of creation, excitation and annihilation of the positron-electron pairs inside the atoms. In addition, it explains the nature of the self-sustaining movement of particles inside the atom and illustrates the similarity between the propagation of the positron--electron pair inside the atom and the propagation of electromagnetic waves in a free space. It gives a novel interpretation of the physical meaning of Maxwell's displacement current and demonstrates that electromagnetic fields are intimately associated with electrical charges.     

Investigation of thin surface films by microprobe analysis

The electron microprobe has been applied to study thin films on metallic substrates. The intensities of the characteristic X-rays emitted by thin films of various elements and thicknesses on sublayers of different materials were measured. Two different theoretical approaches (Bishop and Poole, as well as Yakowitz and Newbury) were applied to interpet the X-ray intensities and to determine the film thickness from the intensity measurements. The effect of backscattering from the substrate, resulting in an increase of the intensity of characteristic X-rays of the film, is being described on the basis of a theory given by Hutchins. The corresponding equation for the backscattering factor has been modified to take into account the transmission of the electrons through the film, depending on the mass thickness of the film and the electron energy. The results obtained from theory and experiment are in good agreement for the different experimental parameters applied, except for very thick layers of high atomic numbers measured at low energies where the absorption of electrons in the film plays a dominant role.     

Ion induced ridge electrons and their diffraction in solid foil targets

We present detailed double differential distributions of electrons emitted downstream when 100 and 170 keV protons interact with thin carbon, gold and aluminuum foils and compare them to those obtained with protons and neutral hydrogen projectiles interacting with helium gas. The distributions obtained with the gas target show, besides the well known convoy electron peak produced by capture or loss of electrons into the continuum of the emerging ion, a narrow ridge that is aligned with the beam direction. This ridge, which is attributed to electrons moving in the two Coulomb center potential saddle determined by the target and projectile ions, also appears in the ion-solid electron distributions. A typical solid state effect consists in the appearance of two strong lateral humps which are explained as due to diffraction of the ridge electrons in the three dimensional lattice of the polycrystalline foil material. Contrarily the diffraction of convoy electrons is impeded by their strong correlation to the moving ions. In the case of the Aluminuun target the observed diffraction is typical for Al₂O₃. This indicates that the observed electrons originate from a thin polycrystalline oxyde layer close to the downstream surface of emission.