The calculation equations of characteristic fluorescence for multi-layer films

Hu, Youhua; Yuencai, He; Jiaguang, Chen

doi:10.1088/0022-3727/21/7/026

Cited by 6 publications

(5 citation statements)

References 1 publication

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“…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.…”

Section: Methodsmentioning

confidence: 99%

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

Yuan

Demers²,

Wang

et al. 2020

Microsc Microanal

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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.

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Section: Methodsmentioning

confidence: 99%

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

Yuan

Demers²,

Wang

et al. 2020

Microsc Microanal

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“…The generated primary X-ray intensity of X b in slice B is known as . Thus, the fluorescence X-ray intensity of X a , which is generated in slice A and excited by X-ray X b in slice B , , is expressed as (Cox et al, 1979; Armigliato et al, 1982; Armstrong & Buseck, 1985; Youhua et al, 1988; Waldo, 1991; Pfeiffer et al, 1996): where is the weight fraction of element E a in layer m , d ( ρz ) A is the mass thickness of slice A , is the jump ratio of X-ray line X a , is the fluorescence yield of X-ray line X a , is the relative intensity, ( ρs ) i is the mass distance during which X-ray X b travels in layer i , ( μ / ρ ) i is the mass absorption coefficient of X-ray X b absorbed by layer i , and E 1 ( t ) is the exponential integral (Geller & Ng, 1969) whose value can be directly obtained through the C++ library boost (Maddock & Cleary, 2000).…”

Section: Methodsmentioning

confidence: 99%

“…The derivation of the fluorescence correction equation has been mentioned numerous times in the literature, but not all the details are given (Cox et al, 1979; Armigliato et al, 1982; Armstrong & Buseck, 1985; Youhua et al, 1988; Waldo, 1991; Pfeiffer et al, 1996). In this appendix, all the details of the derivation are explained.…”

Section: Appendixmentioning

confidence: 99%

“…Benhayoune calculated the characteristic and bremsstrahlung fluorescence at oblique incidence based on Cox et al’s equation (Benhayoune, 1996). Later, Youhua et al derived an equation, which allows the computation for both thin and thick films (Youhua et al, 1988). However, they assumed characteristic X-rays in certain films were emitted from the mid-point of the films.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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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.

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“…Although the effective electron range is relatively small (of the order of a few µm), characteristic primary x-rays penetrate much deeper into the specimen and can ionize atoms at much larger distances, thus degrading the spatial resolution of the technique as well as the accuracy of evaluated chemical compositions (Reed and Long 1963). Analytical formulae to account for secondary fluorescence corrections in simple geometries have been proposed for homogeneous specimens (Reed 1965), for material couples (Hénoc et al 1969, Maurice et al 1965, Bastin et al 1983, for thin films on substrates (Cox et al 1979) and for multilayers (Youhua et al 1988). Usually, these formulae only account for fluorescence from characteristic x-rays, the contribution from the bremsstrahlung continuum has only been considered for homogeneous samples.…”

Section: Introductionmentioning

confidence: 99%

Secondary fluorescence in electron probe microanalysis of material couples

Llovet¹,

Pinard²,

Donovan³

et al. 2012

J. Phys. D: Appl. Phys.

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We describe a semi-analytical method for the fast calculation of secondary fluorescence in electron probe microanalysis of material couples. The calculation includes contributions from primary K-, Land M-shell characteristic x-rays and bremsstrahlung photons. The required physical interaction parameters (subshell partial cross sections, attenuation coefficients, etc) are extracted from the database of the Monte Carlo simulation code system PENELOPE. The calculation makes use of the intensities of primary photons released in interactions of beam electrons and secondary electrons. Since these intensities are not readily available and do not allow analytical calculation, they are generated from short Monte Carlo simulation runs. The reliability of the proposed calculation method has been assessed by comparing calculated, distance-dependent k-ratios with experimental data available in the literature and with results from simulations with PENELOPE. Numerical results are found to be in close agreement with both simulated and experimental data.

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The calculation equations of characteristic fluorescence for multi-layer films

Cited by 6 publications

References 1 publication

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

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

Secondary fluorescence in electron probe microanalysis of material couples

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