Secondary Fluorescence Correction for Characteristic and Bremsstrahlung X-Rays Using Monte Carlo X-ray Depth Distributions Applied to Bulk and Multilayer Materials

Abstract

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.

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

“…The analytical model used to perform the SF correction of voxels is an extension of the model used for multilayers (Yuan et al, 2019), which is based on analytical models from previous research (Cox et al, 1979; Armigliato et al, 1982; Armstrong & Buseck, 1985; Youhua et al, 1988; Waldo, 1991; Pfeiffer et al, 1996). The derivation of the model is discussed below.…”

“…However, for materials with complex structures, it can be important (Cox et al, 1979). Although SF corrections of bulk and multilayer materials for MC X-ray have been implemented (Yuan et al, 2019), it has not been formulated or applied to materials with arbitrarily complex structures. This paper provides an accurate solution to this widely appreciated problem.…”

“…They obtained physical interaction parameters from PENELOPE and calculated SF using an analytical model. Following Llovet et al (2012), Yuan et al (2019) proposed a hybrid model which used MC X-ray to calculate the depth distribution of X-ray intensity and adopted an analytical model to calculate both characteristic and bremsstrahlung fluorescence. It can be applied to any bulk or multilayer materials.…”

Growth of Molybdenum Trioxide Nanoribbons on Oriented Ag and Au Nanostructures: A Scanning Electron Microscopy (SEM) Study

“…There is no preferred growth on Ag microstructures whereas the density of MoO 3 NRs varies from Au NSs to the Si substrate. For further confirmation, we have simulated the Mo X-ray intensity using CASINO (Huvington et al, 1997; Yuan et al, 2019) software for both MoO 3 /Ag/Si and MoO 3 /Au/SiO 2 /Si systems to check if there is any contribution of backscattered electrons from Au to the Mo signal. We have found almost the same Mo intensity for both the cases [ I Mo (MoO 3 /Au/SiO 2 /Si)/ I Mo (MoO 3 /Ag/Si) = 1.06].…”

Correction of Secondary Fluorescence Across Phase Boundaries in Electron Probe Microanalysis of Mineral Inclusions

“…The advantage of the Monte Carlo method is that it can be applied to samples with relatively complex geometries (see, e.g., Jennings et al, 2019aJennings et al, , 2019b. Its main drawback is that results are affected by statistical uncertainties, which in principle can only be reduced by increasing the simulation time, but recent progress in variance reduction techniques along with the increasing availability of fast computers have enhanced the attractiveness of this method for SF calculations (Llovet & Salvat, 2017;Ritchie, 2017;Yuan et al, 2019). The Monte Carlo simulation program PENEPMA (Llovet & Salvat, 2017) has the advantage over other existing codes that it simulates not only the transport of primary and secondary electrons but also that of generated X-rays, thus providing the SF contribution without any further calculation.…”