The results of a numerical simulation of natural convection due to concentration gradients during dissolution of silicon in an indium solution in a horizontal substrate-solution-substrate system are presented. The Chebyshev-Tau spectral method has been used for the simulations. The results are in very good agreement with the experimental data available in the literature. It is concluded that the discrepancies in the dissolution depths between the previous simulations and experimental data, especially at the earlier stages of the process, are mostly due to combined effects of uncertainties in the predicted properties and insufficient numerical accuracy.
The least-squares method with complete component library spectra is applied to the quantitative analysis of X-ray fluorescence spectral intensities. An approach is outlined for application to the general case of thick homogeneous samples at high counting rates, A simplified approach can be taken with the more specific case represented, by atmospheric particulates collected on filters. The details and sample results of this approach for this specific case are given for an energy dispersive X-ray fluorescence analyzer. The results indicate that the least-squares method as developed and applied here is valid and should prove generally useful to X-ray analysts.
The backscatter region of an energy‐dispersive x‐ray fluorescence spectrum obtained by radioisotope photon excitation of a homogeneous, multi‐element sample of any thickness is considered to be made up of a linear summation of several backscatter response spectra, each due to a constituent in the sample. A Monte Carlo computer program already developed for pure samples has been modified to generate these spectra and the results are compared with real spectra. The characteristic data used for each constituent in mixture and alloy samples, such as scattering cross‐sections and Compton profiles, are those of pure elements. As for chemical‐compound samples, an effective Compton profile is determined from a calibration graph and is used for all the constituent elements. It is shown that, for samples with unknown weight fractions, it is possible to generate the Ag Kα backscatter peaks dependent on such sample characteristics as density, thickness, approximate total cross‐section determined from another calibration graph at the scattered photon energy and effective Compton profile. The unknown weight fractions for all the constituents, including those with very low atomic numbers, are then calculated by using the computer‐simulated Ag Kα peaks for each constituent and a background spectrum as the standard library spectra of a linear least‐squares program. The advantages and drawbacks of such a qualitative analysis together with future improvements are discussed.
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