Quantitative x‐ray microanalysis of spherical inclusions embedded in a matrix using a SEM and Monte Carlo simulations

Gauvin, Raynald; L’Éspérance, Gilles; St-Laurent, Sylvain

doi:10.1002/sca.4950140107

Cited by 16 publications

(12 citation statements)

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“…Simulations of the continuous component of x-ray spectra have been carried out by Statham 4 and Heckel and Jugelt, 5 and more recently by Ding et al 6 Similar Monte Carlo simulations have been reported by Araki et al,7 who included characteristic lines. Gauvin et al 8 have used Monte Carlo simulation results to derive calibration curves for quantitative analysis of particulate matter. In these cases, only the transport of electrons was considered.…”

Section: Introductionmentioning

confidence: 99%

“…X-ray absorption and secondary x-ray fluorescence were taken into account by simply assuming exponential attenuation inside the sample. This procedure is only approximate and, moreover, it is difficult to generalize to complex geometries ͑e.g., samples with inclusions and particulate materials.͒ 8 This difficulty is overcome here by simulating the transport of both electrons and photons, in such a way that complex geometries can be handled easily and accurately with the aid of available geometry packages.…”

Section: Introductionmentioning

confidence: 99%

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Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

Acosta

Llovet

Coleoni

et al. 1998

Journal of Applied Physics

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A physical model for the simulation of x-ray emission spectra from samples irradiated with kilovolt electron beams is proposed. Inner shell ionization by electron impact is described by means of total cross sections evaluated from an optical-data model. A double differential cross section is proposed for bremsstrahlung emission, which reproduces the radiative stopping powers derived from the partial wave calculations of Kissel, Quarles and Pratt ͓At. Data Nucl. Data Tables 28, 381 ͑1983͔͒. These ionization and radiative cross sections have been introduced into a general-purpose Monte Carlo code, which performs simulation of coupled electron and photon transport for arbitrary materials. To improve the efficiency of the simulation, interaction forcing, a variance reduction technique, has been applied for both ionizing collisions and radiative events. The reliability of simulated x-ray spectra is analyzed by comparing simulation results with electron probe measurements.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

Acosta

Llovet

Coleoni

et al. 1998

Journal of Applied Physics

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“…The regions can be defined as horizontal (i.e., layered samples) or vertical (i.e., grain boundary). In addition, based on the results of Gauvin et al (1992), spherical inclusions can also be modeled.…”

Section: Development Of a Monte Carlo Program For Low-energy Workmentioning

confidence: 99%

“…By combining polynomial a-factors with Monte Carlo-based algorithms in an iterative correction scheme, it is now possible with a fast desktop, PCtype computer to perform practical, online, Monte Carlo data processing. Gauvin et al (1992) have shown that spherical inclusions embedded in a matrix can be chemically quantified by x-ray IV-1 …”

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confidence: 99%

Proceedings of SCANNING 94/SEEMS 94 Charleston, South Carolina, USA

1994

Scanning

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Monte Carlo techniques have long been employed to simulate the nature of electron scattering in solid materials. These simulations, in turn, have been used to predict parameters for electron microscopy and x-ray microanalysis such as electron and x-ray ranges and backscattered electron yields. Monte Carlo techniques have also been used to predict analytical behavior in unconventional specimens, such as thin films and particles (e.g., relative intensity as a function of particle size). However, because of limitations in the physical models and lengthy calculations involved, Monte Carlo techniques have only very rarely been applied to actually correct quantitative analysis data.We have explored the practicality of developing a Monte Carlo technique-based correction procedure for microbeam analysis and the current state of accuracy of Monte Carlobased corrections versus "conventional" corrections. By using a simple but accurate numerical approximation for the relative elastic scattering cross section as a function of Z and E, it is possible to develop Monte Carlo procedures to calculate trajectories in multiple-element samples with the same speed as for single element standards. Modern expressions for the ionization cross section and the electron energy loss (particularly at low energies) have significantly improved the agreement between Monte Carlo calculations and experimentally-measured data. Monte Carlo algorithms that produce the same level of accuracy in correcting conventional electron microbeam analyses of thick, polished specimens and thin films are the best of the currently used correction procedures, and are of superior accuracy in the analysis of small particles and samples at multiple accelerating potentials. By combining polynomial a-factors with Monte Carlo-based algorithms in an iterative correction scheme, it is now possible with a fast desktop, PCtype computer to perform practical, online, Monte Carlo data processing. Gauvin et al. (1992) have shown that spherical inclusions embedded in a matrix can be chemically quantified by x-ray IV-1 Proceedings of SCANNING 94/SEEMS 94Charleston, South Carolina, USA microanalysis in the scanning electron microscope using a quantitative procedure similar to that developed by Kyser and Murata (1976) for the quantitative analysis of thin films deposited on a substrate. These quantitative procedures are based on calibration curves obtained from Monte Carlo simulations. A generalized Monte Carlo code allows quantitative analysis of spherical inclusions as well as elliptic inclusions embedded in a metallic matrix, simulations of emitted x-rays and backscattered electrons from these materials, including line scans and images, and a consideration of the effects of inclusion size, shape, composition, matrix composition, and the fractal behavior of electron trajectories in these materials. ReferencesGauvin R, L'Espérance G, St-Laurent S: Quantitative x-ray microanalysis of spherical inclusions embedded in a matrix using an SEM and Monte Carlo simulations. Scanning 14, ...

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“…3,4 These schemes inspired a new quantitative method for the microanalysis of spherical inclusions or second phase embedded in a matrix. 5,6 It is important to note that these schemes are based on Monte Carlo simulations of electron trajectories in solids since they allow the incorporation of complex geometries for the computation of X-ray emission. Also, the accuracy of the peak to background method for performing quantitative X-ray analysis of rough surfaces was evaluated using Monte Carlo simulations and it was found that significant deviations are found in the case where the surface roughness is about the same size as that of the electron range.…”

Section: Introductionmentioning

confidence: 99%

X‐ray microanalysis of real materials using Monte Carlo simulations

Gauvin

2005

Surface & Interface Analysis

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In this paper, new results of Monte Carlo simulations are presented in the context of X-ray microanalysis in the scanning electron microscope and the variable pressure scanning electron microscope. For the analysis of bulk samples in the scanning electron microscope, the simulation of X rays emitted from porous materials is covered. Modeling of electron scattering in gases is also presented in the context of X-ray microanalysis in variable pressure scanning electron microscopy. Finally, characterization of electron trajectories from the results of Monte Carlo simulations using the concepts of fractal geometry is described with their implications for quantitative X-ray microanalysis.

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Quantitative x‐ray microanalysis of spherical inclusions embedded in a matrix using a SEM and Monte Carlo simulations

Cited by 16 publications

References 12 publications

Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

Monte Carlo simulation of x-ray emission by kilovolt electron bombardment

Proceedings of SCANNING 94/SEEMS 94 Charleston, South Carolina, USA

X‐ray microanalysis of real materials using Monte Carlo simulations

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