Xavier Llovet

Monte Carlo simulation of x-ray spectra generated by kilo-electron-volt electrons

We present a general algorithm for the simulation of x-ray spectra emitted from targets of arbitrary composition bombarded with kilovolt electron beams. Electron and photon transport is simulated by means of the general-purpose Monte Carlo code PENELOPE, using the standard, detailed simulation scheme. Bremsstrahlung emission is described by using a recently proposed algorithm, in which the energy of emitted photons is sampled from numerical cross-section tables, while the angular distribution of the photons is represented by an analytical expression with parameters determined by fitting benchmark shape functions obtained from partial-wave calculations. Ionization of K and L shells by electron impact is accounted for by means of ionization cross sections calculated from the distorted-wave Born approximation. The relaxation of the excited atoms following the ionization of an inner shell, which proceeds through emission of characteristic x rays and Auger electrons, is simulated until all vacancies have migra...

Monte Carlo simulation of bremsstrahlung emission by electrons

An algorithm for the simulation of bremsstrahlung emission by fast electrons using numerical cross sections is described. It is based on natural factorization of the double-differential cross section and on the fact that the intrinsic angular distribution of photons with a given energy can be very closely approximated by a Lorentz-boosted dipole distribution. The parameters of this angular distribution vary smoothly with the atomic number of the target atom and with the energies of the projectile’s electron and the photon emitted. Results from simulations of thick-target bremsstrahlung are compared with experimental data.

Cross Sections for Inner-Shell Ionization by Electron Impact

An analysis is presented of measured and calculated cross sections for inner-shell ionization by electron impact. We describe the essentials of classical and semiclassical models and of quantum approximations for computing ionization cross sections. The emphasis is on the recent formulation of the distorted-wave Born approximation by Bote and Salvat [Phys. Rev. A 77, 042701 (2008)] that has been used to generate an extensive database of cross sections for the ionization of the K shell and the L and M subshells of all elements from hydrogen to einsteinium (Z = 1 to Z = 99) by electrons and positrons with kinetic energies up to 1 GeV. We describe a systematic method for evaluating cross sections for emission of x rays and Auger electrons based on atomic transition probabilities from the Evaluated Atomic Data Library of Perkins et al. [Lawrence Livermore National Laboratory, UCRL-ID-50400, 1991]. We made an extensive comparison of measured K-shell, L-subshell, and M-subshell ionization cross sections and of ...

Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

A physical model for the simulation of x-ray emission spectra from samples irradiated with kilovolt electron beams is proposed. Inner shell ionization by electron impact is described by means of total cross sections evaluated from an optical-data model. A double differential cross section is proposed for bremsstrahlung emission, which reproduces the radiative stopping powers derived from the partial wave calculations of Kissel, Quarles and Pratt [At. Data Nucl. Data Tables 28, 381 (1983)]. These ionization and radiative cross sections have been introduced into a general-purpose Monte Carlo code, which performs simulation of coupled electron and photon transport for arbitrary materials. To improve the efficiency of the simulation, interaction forcing, a variance reduction technique, has been applied for both ionizing collisions and radiative events. The reliability of simulated x-ray spectra is analyzed by comparing simulation results with electron probe measurements.

Measurements of K-shell ionization cross sections of Cr, Ni and Cu by impact of 6.5-40 keV electrons

Results from measurements of K-shell ionization cross sections of the elements Cr, Ni and Cu by electron impact with energies in the range 6.5-40 keV are presented. Cross sections were obtained by measuring characteristic x-rays emitted from (1-6 nm thick) films of the studied elements deposited on self-supporting carbon backing films. The procedure yields relative cross sections with uncertainties of the order of 2%. Transformation to absolute units increases the uncertainties to about 10%. Our results are compared with those from other groups and with two calculations based on the first Born approximation, which include corrections for exchange, Coulomb and relativistic effects. A simple empirical formula that accurately describes the energy dependence of the measured cross sections is provided.

Correction of secondary X-ray fluorescence near grain boundaries in electron microprobe analysis; application to thermobarometry of spinel lherzolites

Abstract A correction procedure is proposed to account for the effect of secondary X-ray fluorescence near grain boundaries in electron microprobe analysis. The procedure is based on the Monte Carlo simulation method, which is used to calculate the X-ray spectrum emitted by the mineral couple (i.e., the mineral of interest with the neighboring mineral). The contribution of secondary fluorescence from the neighboring mineral, which appears in the simulated spectrum in a natural way, is then subtracted from the measured k-ratio and thereafter conventional matrix corrections are applied. The Monte Carlo simulation algorithm used is largely based on the general-purpose simulation package PENELOPE. In order to assess the reliability of this code, simulated “apparent” element profiles are compared with electron microprobe measurements found in the literature, in which the effect of secondary fluorescence was characterized and the reliability of the different assumptions underlying the proposed procedure is discussed. Finally, the procedure is used to assess data from the olivine-clinopyroxene thermobarometer in a spinel lherzolite xenolith. The application of the secondary fluorescence correction leads to: (1) higher systematic pressure estimations than those obtained from uncorrected data, with lower uncertainties; and (2) a better agreement between the olivine-clinopyroxene temperature estimations and those estimated using the two-pyroxene thermometer. Estimated P-T conditions indicate a decompressional path with a slight decrease in temperature from core to crystal rim. However, if the effect of secondary fluorescence is not taken into account, an apparent heating event is observed.

Monte Carlo Simulation of Secondary Fluorescence in Small Particles and at Phase Boundaries

Abstract. Results from Monte Carlo simulations and experimental measurements of X-ray spectra of small Cu-particles in Fe-containing slags are presented. The analyzed Cu-particles remain suspended in flash smelting and Cu converter slags, which contain Fe up to about 33 wt%, and have diameters ranging from 5 up to 100 μm. Conventional standardless analysis of measured X-ray spectra gives an apparent Fe content of ∼ 1–5 wt%, depending on the particle diameter, which cannot be explained in terms of the thermodynamic solubility of Fe in solid Cu. In order to study the influence of the Fe-containing slag to the apparent Fe content in the particles, X-ray spectra have been computed by means of Monte Carlo simulation of the coupled electron and photon transport. The simulation code used is largely based on the general-purpose simulation package PENELOPE and it incorporates ionization cross sections evaluated from an optical-data model and bremsstrahlung cross sections that reproduce radiative stopping power derived from partial wave calculations. Simulated Fe k-ratios, for different experimental situations, have been found to be in satisfactory agreement with measurements. The apparent Fe content is explained in terms of secondary fluorescence of Fe Kα by Cu Kα X-rays.

Measurements of absolute L- and M-subshell x-ray production cross sections of Pb by electron impact

Absolute L- and M-subshell x-ray production cross sections of Pb have been measured for incident electron energies ranging from 3 to 38 keV. The experimental cross sections were obtained by measuring Lα, Lβ, Mα, Mβ and Mγ x-ray intensities emitted from ultrathin Pb films deposited onto self-supporting thin C films. Measurements were performed on two electron microprobes using wavelength-dispersive spectrometers. X-ray intensities were converted into x-ray production cross sections by using estimated values of the number of incident electrons, target thickness and spectrometer efficiency. Experimental results are compared with calculated cross sections obtained using different predictive formulae, and, whenever possible, with experimental data from the literature.

Monte Carlo simulation of characteristic x-ray emission from thick samples bombarded by kiloelectronvolt electrons

We describe systematic Monte Carlo (MC) calculations of characteristic K and L x-ray emission from thick samples bombarded by kiloelectronvolt electrons. The simulations were performed using the general-purpose MC code PENELOPE, which was modified by introducing a new database of electron-impact ionization cross sections calculated from the distorted-wave Born approximation (DWBA). The calculated yields, defined as the number of photons emerging from the target per unit solid angle and per incident electron, are compared with experimental measurements available from the literature, which pertain to single-element materials with atomic numbers ranging from Z = 6 up to Z = 82 and electron beam energies from a few kiloelectronvolts up to 40 keV. To reveal the dependence of the characteristic x-ray yields on the adopted ionization cross sections, simulations were also performed using cross sections based on the plane-wave Born approximation (PWBA). Our calculations confirm that, in the considered energy range, the DWBA is considerably more accurate than the PWBA.

Low-Voltage Electron-Probe Microanalysis of Fe–Si Compounds Using Soft X-Rays

Conventional electron-probe microanalysis has an X-ray analytical spatial resolution on the order of 1-4 μm width/depth. Many of the naturally occurring Fe-Si compounds analyzed in this study are smaller than 1 μm in size, requiring the use of lower accelerating potentials and nonstandard X-ray lines for analysis. Problems with the use of low-energy X-ray lines (soft X-rays) of iron for quantitative analyses are discussed and a review is given of the alternative X-ray lines that may be used for iron at or below 5 keV (i.e., accelerating voltage that allows analysis of areas of interest <1 μm). Problems include increased sensitivity to surface effects for soft X-rays, peak shifts (induced by chemical bonding, differential self-absorption, and/or buildup of carbon contamination), uncertainties in the mass attenuation coefficient for X-ray lines near absorption edges, and issues with spectral resolution and count rates from the available Bragg diffractors. In addition to the results from the traditionally used Fe Lα line, alternative approaches, utilizing Fe Lβ, and Fe Ll-η lines, are discussed.