Quantitative X-Ray Microanalysis of Heterogeneous Materials Using Monte Carlo Simulations

Monte Carlo simulations are used to obtain new results of x-ray microanalysis of sample types frequently encountered in practical analytical situations such as a vertical layer embedded in a homogeneous matrix and a spherical particulate deposited on a substrate. The simulations show that a 10-nm layer of boron in a steel matrix can be imaged using backscattered electrons and detected using x-ray microanalysis with a field emission scanning electron microscope even with an electron beam energy equals to 20 keV and also that these simulations can be useful to estimate the optimum acceleration voltage to perform such analyses. For a carbon spherical particulate located on the top of a gold substrate, it is shown that x-ray emission and electron backscattering are a strong function of the diameter of the particulate and also of the electron beam energy. Finally, a new method to determine the thickness of a thin film deposited on a substrate is proposed that does not require the measurement of the beam current. That technique can also be used for a spherical particulate deposited on a substrate.     

Assessment of the suitability of Monte Carlo simulation for activity measurements of extended sources

Monte Carlo simulations can be a powerful tool in calibrating high-resolution gamma-ray spectrometry based on high pure germanium (HPGe) detectors. The purpose of this work is to examine the applicability of Monte Carlo simulations for the computation of the efficiency transfer in various measurement geometries on the basis of the detected efficiency for point source geometry. For this, GEANT4 code was applied for the computation of the detection efficiency for incident gamma energy of radionuclide placed at different distances from HPGe detector from 50 to 2,000 keV in addition for volume sources of different compositions and densities. The experimental efficiency curves were compared with the prediction of the GEANT4 code. Efficiency is computed at discrete values of point and volume sources in different distances to derive new efficiencies values for other distances.     

Win X-ray: a new Monte Carlo program that computes X-ray spectra obtained with a scanning electron microscope.

A new Monte Carlo program, Win X-ray, is presented that predicts X-ray spectra measured with an energy dispersive spectrometer (EDS) attached to a scanning electron microscope (SEM) operating between 10 and 40 keV. All the underlying equations of the Monte Carlo simulation model are included. By simulating X-ray spectra, it is possible to establish the optimum conditions to perform a specific analysis as well as establish detection limits or explore possible peak overlaps. Examples of simulations are also presented to demonstrate the utility of this new program. Although this article concentrates on the simulation of spectra obtained from what are considered conventional thick samples routinely explored by conventional microanalysis techniques, its real power will be in future refinements to address the analysis of sample classifications that include rough surfaces, fine structures, thin films, and inclined surfaces because many of these can be best characterized by Monte Carlo methods. The first step, however, is to develop, refine, and validate a viable Monte Carlo program for simulating spectra from conventional samples.     

Characterization of HPGe gamma spectrometers by geant4 Monte Carlo simulations

Two coaxial and a low-energy HPGe detector were characterized with Monte Carlo simulations, using the geant4 toolkit. The geometry of the detectors, including the dimensions of the crystal and the internal structural parts, were initially taken from the factory specifications and from X-ray radiographies, and were later fine-tuned. The detector response functions, with special emphasis on the absolute full-energy peak efficiencies and peak-to-total ratios, were calculated and compared to experimental data taken at different measurement geometries. Between 150 keV and 11 MeV an agreement within 1–2 standard deviation has been achieved, whereas systematic deviations were experienced at lower energies.     

Optimization of electron beam crosslinking of wire and cable insulation

The computer simulations based on Monte Carlo (MC) method and the ModeCEB software were carried out in connection with electron beam (EB) radiation set-up for crosslinking of electric wire and cable insulation. The theoretical predictions for absorbed dose distribution in irradiated electric insulation induced by scanned EB were compared to the experimental results of irradiation that was carried out in the experimental set-up based on ILU 6 electron accelerator with electron energy 0.5–2.0 MeV.The computer simulation of the dose distributions in two-sided irradiation system by a scanned electron beam in multilayer circular objects was performed for various process parameters, namely electric wire and cable geometry (thickness of insulation layers and copper wire diameter), type of polymer insulation, electron energy, energy spread and geometry of electron beam, electric wire and cable layout in irradiation zone. The geometry of electron beam distribution in the irradiation zone was measured using CTA and PVC foil dosimeters for available electron energy range. The temperature rise of the irradiated electric wire and irradiation homogeneity were evaluated for different experimental conditions to optimize technological process parameters. The results of computer simulation are consistent with the experimental data of dose distribution evaluated by gel-fraction measurements. Such conformity indicates that ModeCEB computer simulation is reliable and sufficient for optimization absorbed dose distribution in the multi-layer circular objects irradiated with scanned electron beams.     

Low Voltage Contrast with an SEM Transmission Electron Detector

The images obtained with a transmission electron detector in low voltage SEM show an evolution of the well known dark field and bright field contrast with the accelerating voltage. Monte Carlo simulations explain these contrasts by the evolution of the electron scattering angle and stopping power of the thin foil with the accelerating voltage.     

Transmission probability and energy distribution of electrons impinging on indium thin film targets

Based on a home‐made Monte Carlo simulation, the electron backscattering coefficient, mean penetration depth, transmission probability, and transmission energy distribution of 1–5 keV electron normally incident penetrating in indium thin film targets have been computed. The trend of all features of interest as a function of the indium film thickness at both nanometric scale region and bulk material region has been examined and discussed. The present predictions may be seen as the first investigation regarding 1–5 keV electrons impinging on indium thin film targets. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterisation of 13C implantations in silicon by NRA [13C(p,γ)14N] and RBS

SiC_X layers close to the surface have been produced by implanting 40 keV ¹³C ions into silicon with a fluence of 6×10¹⁷ at./cm² (j=12 μA/cm²) at room temperature (RT). Depth distributions and areal densities (doses) of the implanted carbon have been analysed by the nuclear reaction ¹³C(p,γ)¹⁴N (NRA) which shows a sharp resonance in the excitation function at a proton energy of 1748 keV (Γ=75 eV FWHM). The depth resolution at the surface amounts to 31 nm due to energy spread of the proton beam (1.2 keV FWHM) and resonance width. The surface resolution of the NRA can be increased up to 8 nm when tilting the sample (surface normal) to an angle of 75° with respect to the proton beam direction. Using a NaI detector the detection limit of ¹³C in silicon is approximately 1 at.%. Comparative elastic backscattering measurements with ⁴He⁺ projectiles were performed at 2 MeV (Rutherford backscattering spectroscopy, RBS) and 3.45 MeV (high energy backscattering, HEBS) at a backscattering angle of 171°. The measured ¹³C depth distributions have been compared with a distribution calculated by the Monte Carlo algorithm T-DYN.     

Virtual point detector for HPGe detectors for 26.6–1332 keV photon energies by experiment and Monte Carlo simulation

Variation of virtual point detector (VPD) position inside HPGe detector as a function of source photon energy for the energy range from 26.6 to 1,332 keV was investigated. Although VPD concept was well established for HPGe detectors from 59.5 to 10 MeV, a new attempt was made to obtain VPD positions for photon energies below 59.5 keV. It was found that VPD position shows different functional behavior for the energy ranges 26.6–59.5 keV and 59.5–1,332 keV. The VPD position decreases with increasing energy for 26.6, 31.7, 36.4, and 37.3 keV and increases with the energy until it reaches a plateau. The functional behavior of VPD position for the energy range 26.6–59.5 keV was attributed to the dead layer thickness of the Ge crystal. Monte Carlo simulations were performed to investigate the behavior of VPD position with various dead layer thickness ranging from 100 to 800 μm. It was seen that VPD position increases with increasing energy for 31.7, 59.5, and 80.1 keV more significant at relatively lower energies, but constant for the energies 661–1,332 keV.     

Relative Cross Sections for L- and M-Shell Ionization by Electron Impact

 Results from measurements and calculations of relative L- and M-shell ionization cross sections by electron impact are presented. Measurements were performed for elements Te, Au and Bi on an electron microprobe with specimens consisting of extremely thin films of the studied element deposited on thin, self-supporting, carbon layers. The relative variation of the ionization cross section was obtained by counting the number of characteristic X-rays from the considered element and shell, for varying incident electron energies, from the ionization energy up to 40 keV. Measured data were corrected to account for the energy-dependent spread of the electron beam within the active film and for the ionization due to the electrons backscattered from the carbon layer, using Monte Carlo simulation. Cross sections were evaluated in the Born approximation using an optical-data model with numerically evaluated dipole photoelectric cross sections. Calculated ionization cross section were converted to vacancy production cross sections, which can be directly compared with our experimental data.     

Monte Carlo simulation of low–medium energy electrons backscattered from C/Al double layer thin films

The backscattering coefficient of low–medium energy electron beams (from 250 to 10 000 eV) impinging on C/Al double layered thin films was investigated by a Monte Carlo simulation. The aim of the research was to study the behaviour of the backscattering coefficient as a function of the beam primary energy and the thicknesses of the two layers. The backscattering coefficient as a function of the primary energy presents features that can be used to evaluate the thicknesses of the two layers. Copyright © 2006 John Wiley & Sons, Ltd.     

Light Element Analysis of Individual Microparticles Using Thin-Window EPMA

 The determination of the concentration of light elements, such as carbon, nitrogen and oxygen, in e.g. atmospheric aerosol particles is important to study the chemical behaviour of atmospheric pollution. The knowledge of low-Z element concentrations gives us information on the speciation of nutrients (species having nutritional value for plants) and toxic heavy metals in the particles. The capability of the conventional energy-dispersive EPMA is strongly limited for the analysis of low-Z elements, mainly because the Be window in the EDX detector hinders the detection of characteristic X-rays of light elements such as C, N, O and Na. WDS is suitable for analysis of light elements, but the measurement of beam sensitive microparticles requires the minimisation of the beam current and the measurement time. A semi-quantitative analytical method based on EPMA using an ultra-thin window EDX detector was developed. It was found that the matrix and geometric effects that are important for low-energy X-rays can be reliably evaluated by Monte Carlo calculations. Therefore, the quantification part of the method contains reverse Monte Carlo calculation done by iterative simulations. The method was standardised and tested by measurements on single particles with known chemical compositions. Beam-sensitive particles such as ammonium-sulphate and ammonium-nitrate were analysed using a liquid nitrogen cooled sample stage. The shape and size of the particles, which are important for the simulations, were determined using a high-magnification secondary electron image. Individual marine aerosol particles collected over the North Sea by a nine-stage Berner cascade impactor were analysed using this new method. Preliminary results on five samples and 4500 particles show that the method can be used to study the modification of sea-salt particles in the troposphere.     

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.     

Effects of physics change in Monte Carlo code on electron pencil beam dose distributions

Pencil beam algorithms used in computerized electron beam dose planning are usually described using the small angle multiple scattering theory. Alternatively, the pencil beams can be generated by Monte Carlo simulation of electron transport. In a previous work, the 4th version of the Electron Gamma Shower (EGS) Monte Carlo code was used to obtain dose distributions from monoenergetic electron pencil beam, with incident energy between 1 MeV and 50 MeV, interacting at the surface of a large cylindrical homogeneous water phantom. In 2000, a new version of this Monte Carlo code has been made available by the National Research Council of Canada (NRC), which includes various improvements in its electron-transport algorithms. In the present work, we were interested to see if the new physics in this version produces pencil beam dose distributions very different from those calculated with oldest one. The purpose of this study is to quantify as well as to understand these differences. We have compared a series of pencil beam dose distributions scored in cylindrical geometry, for electron energies between 1 MeV and 50 MeV calculated with two versions of the Electron Gamma Shower Monte Carlo Code. Data calculated and compared include isodose distributions, radial dose distributions and fractions of energy deposition. Our results for radial dose distributions show agreement within 10% between doses calculated by the two codes for voxels closer to the pencil beam central axis, while the differences are up to 30% for longer distances. For fractions of energy deposition, the results of the EGS4 are in good agreement (within 2%) with those calculated by EGSnrc at shallow depths for all energies, whereas a slightly worse agreement (15%) is observed at deeper distances. These differences may be mainly attributed to the different multiple scattering for electron transport adopted in these two codes and the inclusion of spin effect, which produces an increase of the effective range of electrons.     

Applicability of the condensed-random-walk Monte Carlo method at low energies in high-Z materials

The predictions of several Monte Carlo codes were compared with each other and with experimental results pertaining to the penetration of through gold foils of electrons incident with energies from 128 to 8 keV. The main purpose was to demonstrate that reflection and transmission coefficients, for number and energy, can be estimated reliably with a simple Monte Carlo code based on the condensed-random-walk and continuous-slowing-down approximations.     

Monte Carlo simulation of X-ray fluorescence spectra: Part 4. Photon scattering at high X-ray energies

The photon scattering model of a Monte Carlo simulation code for synchrotron radiation X-ray fluorescence (SRXRF) spectrometers is evaluated at high X-ray energies (60–100 keV) by means of a series of validation experiments performed at Beamline BW5 of HASYLAB. Using monochromatic X-rays, Compton/Rayleigh multiple scattering experiments were performed on polypropylene, Al and Cu samples. Especially in the case of the first two matrices multiple Compton scattering occurs with high probability. This work demonstrates that the simulation model provides a reliable estimate of the spectral distribution of the multiply scattered linearly polarized photon beam as observed by an HPGe detector. Next to variations in sample composition and thickness, the ability of the code to simulate various detection geometries has also been verified. As an application of the code, the achievable detection limits of SRXRF for rare earth elements as obtained with white beam and monochromatic (80 keV) excitation are compared.     

Radial dose profiles for pencil electron beams

The relationship between the Boltzmann and Fermi-Eyges-Yang equations governing electron transport is examined. Radial dose profiles for a pencil beam obtained by numerical solution of the Boltzmann equation in the small angle approximation are compared with both the Gaussian approximation and with Monte Carlo simulations for a carbon medium. For energies ranging from 5 to 20 MeV and penetration depths up to 75% of the range the numerical results are within 10% of the Monte Carlo results for the radial distance encompassing 63% of the energy deposition.