Monte Carlo simulation of the backscatter region in photon-excited energy dispersive X-ray fluorescence spectra

The backscatter region of energy-dispersive X-ray fluorescence spectra obtained by a typical radioisotope system is examined in detail. A Monte Carlo simulation program which incorporates all the information on photon scattering processes including electron momentum distributions in target atoms, form factors and scattering factors for the cross-sections is presented. The program uses extensive variance reduction techniques and has the option of simulating any type of either single or any specified combination of multiple scatters or the complete process as appears in a real detector response spectrum. Based on several simulated spectra various conclusions are reached including that the energy spread of Compton peaks depends mainly on the broadening effect of electron momenta together with detection system resolution, and that the intensity of double scatters is roughly an order of magnitude lower than that of single scatters for thick targets.     

Calculation of the surface excitation parameter for Si and Ge from measured electron backscattered spectra by means of a Monte-Carlo simulation.

A new Monte Carlo method has been developed for simulating backscattered electron spectra, and this was applied for determining the surface excitation parameter (SEP). The simulation is based on direct tracking of electron trajectories in the solid, taking into account elastic and inelastic events. The elastic scattering cross sections are taken from literature, while inelastic cross section data are obtained by a fitting procedure. After some iterations, the program produces electron spectra fitting well to the experimental ones. Si and Ge electron spectra were simulated and SEP values were calculated. The SEP values are compared to other ones from literature.     

Status of the Monte Carlo library least-squares (MCLLS) approach for non-linear radiation analyzer problems

The Center for Engineering Applications of Radioisotopes (CEAR) has been working for over a decade on the Monte Carlo library least-squares (MCLLS) approach for treating non-linear radiation analyzer problems including: (1) prompt gamma-ray neutron activation analysis (PGNAA) for bulk analysis, (2) energy-dispersive X-ray fluorescence (EDXRF) analyzers, and (3) carbon/oxygen tool analysis in oil well logging. This approach essentially consists of using Monte Carlo simulation to generate the libraries of all the elements to be analyzed plus any other required background libraries. These libraries are then used in the linear library least-squares (LLS) approach with unknown sample spectra to analyze for all elements in the sample. Iterations of this are used until the LLS values agree with the composition used to generate the libraries. The current status of the methods (and topics) necessary to implement the MCLLS approach is reported. This includes: (1) the Monte Carlo codes such as CEARXRF, CEARCPG, and CEARCO for forward generation of the necessary elemental library spectra for the LLS calculation for X-ray fluorescence, neutron capture prompt gamma-ray analyzers, and carbon/oxygen tools; (2) the correction of spectral pulse pile-up (PPU) distortion by Monte Carlo simulation with the code CEARIPPU; (3) generation of detector response functions (DRF) for detectors with linear and non-linear responses for Monte Carlo simulation of pulse-height spectra; and (4) the use of the differential operator (DO) technique to make the necessary iterations for non-linear responses practical. In addition to commonly analyzed single spectra, coincidence spectra or even two-dimensional (2-D) coincidence spectra can also be used in the MCLLS approach and may provide more accurate results.     

Calculation of Surface Excitation Parameters by a Monte Carlo Method

Electron inelastic mean free path (IMFP) is an important parameter for surface chemical quantification by surface electron spectroscopy techniques. It can be obtained from analysis of elastic peak electron spectroscopy (EPES) spectra measured on samples and a Monte Carlo simulation method. To obtain IMFP parameters with high accuracy, the surface excitation effect on the measured EPES spectra has to be quantified as a surface excitation parameter (SEP), which can be calculated via a dielectric response theory. However, such calculated SEP does not include influence of elastic scattering of electrons inside samples during their incidence and emission processes, which should not be neglected simply in determining IMFP by an EPES method. In this work a Monte Carlo simulation method is employed to determine surface excitation parameter by taking account of the elastic scattering effect. The simulated SEPs for different primary energies are found to be in good agreement with the experiments particularly for larger incident or emission angles above 60° where the elastic scattering effect plays a more important role than those in smaller incident or emission angles. Based on these new SEPs, the IMFP measurement by EPES technique can provide more accurate data.     

A high-performance X-ray system for medical device irradiation

A new concept of X-ray irradiator for low-density products on pallets is proposed. Monte Carlo simulations are applied to predict the performance of this system. The Monte Carlo predictions reveal in good agreement with experimental data obtained using products of different densities.     

Three-dimensional modeling of EXAFS spectral mixtures by combining Monte Carlo simulations and target transformation factor analysis

We have developed a new method for the three-dimensional modeling of extended X-ray absorption fine structure (EXAFS) spectra which enables the extraction of the local structure of aqueous metal complexes from spectral mixtures of several components. The new method combines two techniques: Monte Carlo simulation and target transformation factor analysis (TFA). Monte Carlo simulation is used to create random arrangements between the X-ray absorbing metal ion and the ligand atoms, and to calculate the theoretical EXAFS spectrum of each arrangement. The theoretical EXAFS spectrum is then introduced as test spectrum in the TFA procedure, to test whether or not the test spectrum is likely to be a component of the spectral mixtures. This coupled procedure is repeated until the error in the test spectrum is minimized. The new method can thus be used to isolate and refine the structure of complexes from spectral mixtures and to determine their relative concentrations, solely on the basis of an estimate of a ligand structure. The performance of the proposed method is validated using uranium Liii-edge EXAFS spectra of binary mixtures of two uranium(VI) 3,4-dihydroxybenzoic acid complexes.     

Monte Carlo studies of a novel X-ray tube anode design

When energetic electrons are incident on high atomic number absorbers, a substantial fraction is back-scattered. This phenomenon is responsible for several undesirable effects in X-ray tubes, in particular a reduction in the X-ray output. The extent of this shortfall has been estimated by using Monte Carlo simulation to start electrons at increasing depth inside the anode, the results indicating that an output enhancement of nearly 50% could be achieved in principle if the electrons wasted in back-scatter events could be trapped inside a tungsten anode. To test this idea a further set of simulations were done for a novel anode geometry. Results showed that X-ray tube efficiencies might be substantially enhanced by this approach.     

Voxel-based Monte Carlo simulation of X-ray imaging and spectroscopy experiments

A Monte Carlo code for the simulation of X-ray imaging and spectroscopy experiments in heterogeneous samples is presented. The energy spectrum, polarization and profile of the incident beam can be defined so that X-ray tube systems as well as synchrotron sources can be simulated. The sample is modeled as a 3D regular grid. The chemical composition and density is given at each point of the grid. Photoelectric absorption, fluorescent emission, elastic and inelastic scattering are included in the simulation. The core of the simulation is a fast routine for the calculation of the path lengths of the photon trajectory intersections with the grid voxels. The voxel representation is particularly useful for samples that cannot be well described by a small set of polyhedra. This is the case of most naturally occurring samples. In such cases, voxel-based simulations are much less expensive in terms of computational cost than simulations on a polygonal representation. The efficient scheme used for calculating the path lengths in the voxels and the use of variance reduction techniques make the code suitable for the detailed simulation of complex experiments on generic samples in a relatively short time. Examples of applications to X-ray imaging and spectroscopy experiments are discussed.     

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.     

X-ray treatment at 5 MeV and above

There is agreement in the scientific community that X-ray treatment of food at 7.5 MeV can be safe. Possible process improvements for treating at higher than 5 MeV X-rays have been re-visited. Monte Carlo methods have been applied to simulate the X-ray conversion process and to calculate dose distributions in homogeneous phantoms. Experimental data obtained using X-rays produced with a Rhodotron TT200 at 5 and 10 MeV verifies a representative set of data which is calculated with the presented method.

With this qualified Monte Carlo tool, calculations at 7.5 MeV incident electron energy were performed. The analysis gives special attention to higher photon yield, improved product penetration, as well as surface and edge effects.     

Flexible polyelectrolyte simulations at the Poisson-Boltzmann level: a comparison of the kink-jump and multigrid configurational-bias Monte Carlo methods

We present a new approach for simulating the motions of flexible polyelectrolyte chains based on the continuous kink-jump Monte Carlo technique coupled to a lattice field theory based calculation of the Poisson-Boltzmann (PB) electrostatic free energy "on the fly." This approach is compared to the configurational-bias Monte Carlo technique, in which the chains are grown on a lattice and the PB equation is solved for each configuration with a linear scaling multigrid method to obtain the many-body free energy. The two approaches are used to calculate end-to-end distances of charged polymer chains in solutions with varying ionic strengths and give similar numerical results. The configurational-bias Monte Carlo/multigrid PB method is found to be more efficient, while the kink-jump Monte Carlo method shows potential utility for simulating nonequilibrium polyelectrolyte dynamics.     

Monte Carlo Simulation in Electron Probe Microanalysis. Comparison of Different Simulation Algorithms

Practical aspects of Monte Carlo simulation of EPMA experiments are considered. Simulations are performed using the general-purpose Monte Carlo code system Penelope, which is briefly described. This code includes geometry tools and variance reduction methods that allow the practical simulation of x-ray spectra from samples with complex geometries in moderate computing times. The reliability of simple interaction models and approximations, which have been frequently used in EPMA studies, is analyzed by studying their effects on the simulated x-ray spectra.     

A general Monte Carlo simulation of ED-XRF spectrometers. II: Polarized monochromatic radiation,homogeneous samples

A general Monte Carlo code for the simulation of X-ray fluorescence spectrometers, described in a previous paper is extended to predict the spectral response of instruments employing polarized exciting radiation. Details of the calculation method specific for the correct simulation of photon-matter scatter interactions in case of polarized X-ray beams are presented. Comparisons are made with experimentally collected spectral data obtained from a monochromatic X-ray fluorescence setup installed at a synchrotron radiation source. The use of the simulation code for quantitative analysis of intermediate and massive samples is also demonstrated.     

The influence of defects on the morphology of Si (111) etched in NH4F

We have implemented a kinetic Monte Carlo (KMC) simulation to study the effects of wafer miscut and wafer defects on the morphologies of Si (111) surfaces etched in NH4F. Although a conventional KMC simulation reproduced previously published results, it failed to produce the morphologies observed in our experiments. By introducing both dopant sites and lattice defect sites into the model, we are able to simulate samples having different dopant elements and densities as well as different defect concentrations. Using the modified KMC simulation, the simulated surface morphologies agree well with the morphologies observed in our experiments. The enhanced model also gives insights to the formation mechanism for multiple level stacking pits, a notable morphology on the etched surfaces of samples with very small miscut angles.     

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.     

Modified Monte Carlo simulation of adsorption in a spatially inhomogeneous porous system

A modified Monte Carlo method in conjunction with the canonical and grand canonical ensembles is proposed for simulating adsorption in spatially inhomogeneous porous systems. Unlike the traditional Monte Carlo simulation in terms of the grand canonical ensemble, the simulation for the regions of pore space having no direct communication with the bulk phase is performed in local conditions of the canonical ensemble.     

Backscattered electron images,X-ray maps and Monte Carlo simulations applied to the study of plagioclase composition in volcanic rocks

Zoning patterns in plagioclases are related to abrupt changes in the anorthite content along the crystal growing direction. Accurate characterization of these patterns by electron microprobe is useful to identify magma chamber processes such as recharge, mingling and whole-chamber overturn events.In this work, a new procedure to obtain high resolution quantitative maps of anorthite concentration in single plagioclase crystals is developed. The methodology consists of performing a calibration of backscattered electron images using quantitative X-ray maps. The ultimate resolution of characteristic X-rays and backscattered electron signals is studied by Monte Carlo simulation. The method is applied to characterize the chemical composition of a volcanic plagioclase from the Cerro Vilama, Argentina. The results obtained are more precise than the values given by the methods commonly used in the study of plagioclase composition, i.e. the classical profiling by electron microprobe point analysis or the modern backscattered electron image calibration by means of quantitative energy or wavelength dispersive X-ray analysis at a few selected points.