In electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

Accurate elemental quantification of materials by X-ray detection techniques in electron microscopes or microprobes can only be carried out if the appropriate mass absorption coefficients (MACs) are known. With continuous advancements in experimental techniques, databases of MACs must be expanded in order to account for new detection limits. Soft X-ray emission spectroscopy (SXES) is a characterization technique that can detect emitted X-rays whose energies are in the range of 10 eV to 2 keV by using a varied-line-spaced grating. Transitions producing soft X-rays can be detected and accurate MACs are required for use in quantification. This work uses Monte Carlo modeling coupled with multivoltage SXES measurements in an electron probe micro-analyzer (EPMA) to compute MACs for the L2,3-M and Li Kα transitions in a variety of aluminum alloys. Electron depth distribution curves obtained by the software MC X-ray are used in a parametrized fitting equation. The MACs are calculated using a least-squares regression analysis. It is shown that X-ray distribution cross-sections at such low energies need to take into account additional contributions, such as Coster–Kronig transitions, Auger yields, and wave function effects in order to be accurate.

A technique to characterize the native passivation layer (NPL) on pure lithium metal foils in a scanning electron microscope (SEM) is described in this paper. Lithium is a very reactive metal, and consequently, observing and quantifying its properties in a SEM is often compromised by rapid oxidation. In this work, a pure lithium energy-dispersive x-ray spectrum is obtained for the first time in a high vacuum SEM using a cold stage/cold trap with liquid nitrogen reservoir outside the SEM chamber. A nanomanipulator (OmniProbe 400) inside the microscope combined with x-ray microanalysis and windowless energy dispersive spectrometer is used to fully characterize the NPL of lithium metal and some of its alloys by a mechanical removal procedure. The results show that the native films of pure lithium and its alloys are composed of a thin (25 nm) outer layer that is carbon-rich and an inner layer containing a significant amount of oxygen. Differences in thickness between laminated and extruded samples are observed and vary depending on the alloy composition.

Due to recent advances in modeling the production of characteristic X-rays, Monte Carlo simulation of electron–solid interactions can provide improved quantitative estimates of X-ray intensities for both homogeneous and heterogeneous interaction volumes. In the case of homogeneous materials, these modeled X-ray intensities can predict with excellent accuracy, matrix corrections for arbitrary compositions, arbitrary emission lines, and electron energies. By pre-calculating these Monte Carlo X-ray intensities for pure element standards and a range of compositions of binary systems, we can derive matrix corrections for complex compositions in real-time by parameterizing these k-ratios as the so-called alpha factors. This method allows one to perform Monte Carlo-based bulk matrix corrections in seconds for arbitrary and complex compositions (with two or more elements), by combining these binary alpha factors using the so-called beta expression. We are systematically calculating X-ray intensities for 11 compositions from 1 to 99 wt% for binary pairs of all emitters and absorbers in the periodic table, for the main emission lines (Kα, Kβ, Lα, Lβ, Mα, and Mβ) at beam energies from 5 to 50 keV, using Monte Carlo calculations based on a modified PENELOPE electron-photon transport code, although any other Monte Carlo software could also be utilized. Comparison of k-ratios calculated with the proposed method and experimental k-ratios from the Pouchou and Pichoir database suggest improvements over typical φ(ρz) methods. Additional comparisons with k-ratio measurements from more complex compositions would be ideal, but our testing of the additivity of the beta equation suggests that arbitrary compositions can be handled as well, except in cases of extreme fluorescence or absorption.

The f-ratio quantitative X-ray microanalysis method has been recently developed for binary systems based on a scanning electron microscope/energy dispersive spectroscopy (SEM/EDS) system. This method incorporates traditional EDS experiments and Monte Carlo simulations, and calibration factors are calculated with standard samples to evaluate the differences between them. In this work, the f-ratio method was extended to Mg–Al–Zn multi-element systems using a cold field emission SEM and a tungsten emission SEM. Results show that the stability of the beam current does not influence the f-ratio quantification accuracy. Thus, the f-ratio method is suitable for quantitative X-ray mapping with a long-time acquisition or even an unstable beam current. Comparing with other quantitative techniques including the routine standardless analysis and the standard-based k-ratio method, the f-ratio method is a simple and accurate quantification method.

Secondary fluorescence effects are important sources of characteristic X-ray emissions, especially for materials with complicated geometries. Currently, three approaches are used to calculate fluorescence X-ray intensities. One is using Monte Carlo simulations, which are accurate but have drawbacks such as long computation times. The second one is to use analytical models, which are computationally efficient, but limited to specific geometries. The last approach is a hybrid model, which combines Monte Carlo simulations and analytical calculations. In this article, a program is developed by combining Monte Carlo simulations for X-ray depth distributions and an analytical model to calculate the secondary fluorescence. The X-ray depth distribution curves of both the characteristic and bremsstrahlung X-rays obtained from Monte Carlo program MC X-ray allow us to quickly calculate the total fluorescence X-ray intensities. The fluorescence correction program can be applied to both bulk and multilayer materials. Examples for both cases are shown. Simulated results of our program are compared with both experimental data from the literature and simulation data from PENEPMA and DTSA-II. The practical application of the hybrid model is presented by comparing with the complete Monte Carlo program.

A number of techniques for the characterization of rare earth minerals (REM) have been developed and are widely applied in the mining industry. However, most of them are limited to a global analysis due to their low spatial resolution. In this work, phase map analyses were performed on REM with an annular silicon drift detector (aSDD) attached to a field emission scanning electron microscope. The optimal conditions for the aSDD were explored, and the high-resolution phase maps generated at a low accelerating voltage identify phases at the micron scale. In comparisons between an annular and a conventional SDD, the aSDD performed at optimized conditions, making the phase map a practical solution for choosing an appropriate grinding size, judging the efficiency of different separation processes, and optimizing a REM beneficiation flowsheet.

The spatial resolution of aberration-corrected annular dark field scanning transmission electron microscopy was studied as function of the vertical position z within a sample. The samples consisted of gold nanoparticles (AuNPs) positioned in different horizontal layers within aluminum matrices of 0.6 and 1.0 µm thickness. The highest resolution was achieved in the top layer, whereas the resolution was reduced by beam broadening for AuNPs deeper in the sample. To examine the influence of the beam broadening, the intensity profiles of line scans over nanoparticles at a certain vertical location were analyzed. The experimental data were compared with Monte Carlo simulations that accurately matched the data. The spatial resolution was also calculated using three different theoretical models of the beam blurring as function of the vertical position within the sample. One model considered beam blurring to occur as a single scattering event but was found to be inaccurate for larger depths of the AuNPs in the sample. Two models were adapted and evaluated that include estimates for multiple scattering, and these described the data with sufficient accuracy to be able to predict the resolution. The beam broadening depended on z1.5 in all three models.