EDS PhiRhoZ (PhiRhoZ) Quantification Mode  Practical Electron Microscopy and Database   An Online Book  

Microanalysis  EM Book https://www.globalsino.com/EM/  


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Between the 1970s and early 1980s, there was little work in the field of EDS quantitative analysis on bulk samples. However, there has been an increased interest in improvement of the accuracy of Xray microanalysis since Packwood and Brown proposed “PhiRhoZ” methods [1]. Overall, during the 1980s, PhiRhoZ models had been introduced using varous mathematical functions including parabolic expressions [2], modified Gaussian function [1], exponentials [3], and quadrilateral function [4]. These correction procedures are general models for calculating the Xray intensities and can be used for a wide range of Xray energies from 100 eV to >10 keV and accelerating voltages between 1 keV and 40 keV. In fact, the PhiRhoZ mode is an evolution from ZAF methods. EDS quantification in PhiRhoZ mode is an elemental quantification method based on the matrix correction with the depth distribution function (Phi), mass density (Rho) and mean atomic number (Z). Modern PhiRhoZ methods include fluorescence correction. The common PhiRhoZ analysis is not selfcalibrating and depends on standardization or reference measurements. The depth distribution function is used to evaluate Xray generation and selfabsorption. To evaluate the absorption correction, it is also necessary to know the depth distribution of Xray production in the specimen, which is given by the PhiRhoZ curve, Figure 1745a shows the PhiRhoZ function in depth distribution of Xray production. However, the exact shape of the curve is dependent on the atomic number Z and the depth scale is mainly determined by the accelerating voltage. Figure 1745a. PhiRhoZ function in depth distribution of Xray production. Several models have been proposed for the procedures of absorption and atomic number corrections in PhiRhoZ mode. Different EDS software uses different models that have their own advantages but also have their own inaccuracies. Comparing with the ZAF methods, the PhiRhoZ methods have improved the accuracy of Xray microanalysis and perform much better for light element analysis, but are computationally complex. When the Xray absorption is significant, especially for SEMEDS measurements on bulk samples, the shape of the depth distribution of Xray production is crucial, and thus ZAF and Phi–Rho–Z models should be used. However, the mass absorption coefficients are still problematic because significant uncertainties exist even in absorptioncorrected ZAF and Phi–Rho–Z models. Figure 1745b shows the physical and mathematical fits of background of an EDX spectrum, taken from an alloy with P 49.29 at.% and In 50.71 at.%, in Bruker software. Both the fit methods can be applied to the PhiRhoZ case.
[1] Packwood, R. H. and J. D. Brown, Xray Spectrometry, 10, 138, (1981).


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