EDS PhiRhoZ (Phi-Rho-Z) Quantification Mode
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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 X-ray microanalysis since Packwood and Brown proposed “Phi-Rho-Z” methods [1]. Overall, during the 1980s, Phi-Rho-Z 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 X-ray intensities and can be used for a wide range of X-ray energies from 100 eV to >10 keV and accelerating voltages between 1 keV and 40 keV. In fact, the Phi-Rho-Z mode is an evolution from ZAF methods.

EDS quantification in Phi-Rho-Z 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 Phi-Rho-Z methods include fluorescence correction. The common Phi-Rho-Z analysis is not self-calibrating and depends on standardization or reference measurements.

The depth distribution function is used to evaluate X-ray generation and self-absorption. To evaluate the absorption correction, it is also necessary to know the depth distribution of X-ray production in the specimen, which is given by the Phi-Rho-Z curve,
φ = f (ρz) --------------- [1745]
where,
φ -- The ionization distribution.
ρ -- The mass density.
z -- The depth.

Figure 1745a shows the Phi-Rho-Z function in depth distribution of X-ray 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. Phi-Rho-Z function in depth distribution of X-ray production.

Several models have been proposed for the procedures of absorption and atomic number corrections in Phi-Rho-Z mode. Different EDS software uses different models that have their own advantages but also have their own inaccuracies. Comparing with the ZAF methods, the Phi-Rho-Z methods have improved the accuracy of X-ray microanalysis and perform much better for light element analysis, but are computationally complex.

When the X-ray absorption is significant, especially for SEM-EDS measurements on bulk samples, the shape of the depth distribution of X-ray 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 absorption-corrected 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 Phi-Rho-Z case.

 (a) (b)
 Figure 1745b. 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. [5]

[1] Packwood, R. H. and J. D. Brown, X-ray Spectrometry, 10, 138, (1981).
[2] Jean-Louis Pouchou and Francoise Pichoir, Quantitative Analysis of Homogeneous or Stratified Microvolumes Applying the Model “PAP”, Electron Probe Quantitation, 31-75, 1987.
[3] Jean-Louis Pouchou and F. Pichoir, Microbeam Analysis, San Francisco Press, 319, 1988.
[4] G. Love, D.A. Sewell and V.D. Scott, J. de Physique, 45 C2,21, 1984.
[5] Quantification of EDS spectra, Bruker.

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