Quantitative X-Ray Analysis. Introduction: It is extremely important to grasp the underlying physical principles to become a sophisticated analyst rather than a mere user.
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Some key points :
4. Perform quanta calibration: This procedure is to develop the x-ray intensity ratios using the specimen intensity and the standard intensity for each element present in the sample and carry out matrix corrections to obtain quantitative concentration values.
i.e. Ci/C(i) = Ii/I(i) = k
Deviations between the Ratio of
Measured Intensities and the Ratio of Concentrations
Using these matrix effects, the most common form of the correction equation is
Ci/C(i) = [ZAF]i Ii/I(i) = [ZAF]i ki
Where Ci is the weight fraction of the element I of interest in
the sample and C(i) is the weight fraction of i in the standard.
This equation must be applied separately for each element
present in the sample. The Z. A. and F effects must therefore
be calculated separately for each element.
Above equation is used to express the matrix effects and is the common basis for x-ray microanalysis in the SEM.
Effect of Atomic Number
The following figure shows that Cu characteristic x-rays are generated deeper in the specimen and the x-ray generation volume is larger as Eo increases. This is because the energy of the backscattered electrons increases with higher values of Eo.
In specimens of high atomic number, the electrons undergo more elastic scattering per unit distance and the average scattering angle is greater, as compared to low-atomic-number materials. The electron trajectories in high-atomic-number materials thus tend to deviate out of the initial direction of travel more quickly and reduce the penetration into the solid.
The shape of the interaction volume also changes significantly as a function of atomic number.
As the angle of tilt of a specimen surface increases (i.e., the angle of the beam relative to the surface decreases), the interaction volume becomes smaller and asymmetric.
Interaction Volumes of Materials with Different Density
Quantitative x-ray analysis of the low-energy (<0.7 keV) K lines of the light elements is difficult in the SEM. The following table lists the low-atomic-number elements considered in this section along with the energies and wavelengths of the K lines. X-ray analysis in this energy range is a real challenge for the correction models developed for quantitative analysis since a large absorption correction is usually necessary. Unfortunately, the mass absorption coefficients for low-energy x-rays are very large and the values of many of these coefficients are still not well known. The low-energy x-rays are measured using large d spacing crystals in a WDS system or thin-window or windowless EDS detector.