k-Factor Determination & EDS Calibration
- Practical Electron Microscopy and Database -
- An Online Book -



This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.



The accuracy of EDS quantification is mainly limited by the counting statistics for the collection of X-rays not only in the determination of the kAB factors but also in the acquisition of the intensities IA,B. Therefore, the total percentage error in concentration is determined by the percentage errors of kAB and counts. In other words, the total error will be higher than the error in kAB alone or the error in counts alone.

It is necessary to highlight that except for the random errors from counting statistics, some factors, however, will contribute systematic errors. Those factors are mainly:
         i) The accuracy of the chemical composition of the standard (if calibration or correction of kAB factors is applied).
         ii) The presence of spurious X-rays.
         iii) The inaccuracy of evaluation of the specimen thickness.
         iv) The deconvolution of overlapping peaks.
         v) Thee background-fitting routine.  

The elemental concentration quantification in EDS measurements can be done with reasonable accuracy by comparing the peak intensities with k-factors (Cliff–Lorimer factors) in EDS spectra. These k-factors are a combination of specimen and detector properties. For instance, if a thin TEM specimen is used, the kAB factor for Kα X-ray emission from elements A and B can be given by,
         k-Factor Determination ------------------------------ [4373]
          AA and AB -- The atomic weights of elements A and B, respectively.
          aA and aB -- The fractions of Kα emissions of elements A and B, respectively.
          ϖA and ϖB -- The X-ray yields of elements A and B, respectively.
          μA and μB -- The effective mass-absorption coefficients (from the window of the EDS detector) for the X-rays from elements A and B, respectively.
          QK,A and QK,B -- The K-shell ionization cross-sections of elements A and B, respectively.
          t -- The effective thickness of the window of the EDS detector.
Three methods are mainly used to determine the k-factors (kAB):
          i) The most reliable way is to determine it by experimental calibration with a standard. A similar structure with “similar” elemental concentrations should be used if it is available. These similarities can also ensure that the effects on X-ray signals, from the scatterings of electrons and X-rays, for both the standard and unknown specimens are “identical”. The quantification will be more accurate if a more similar standard to the unknown specimen is used. In this method, the effects from the specific microscope, EDS detector, operating conditions and even the absorptions of X-rays in the specimen itself are included. Furthermore, with this calibration method, the ZAF correction also can iteratively be applied until proper Z, A, and F correction factors that are consistent with the composition in the specimen are found. In extremely accurate EDS quantifications, elemental detection is possible down to a few % wt. for elements with atomic numbers Z << 11 and down to 0.1 - 0.5 wt. % for elements with Z >1.
          ii) Calculate it from first principles.
          ii) Use the values in the existing database which are collected from the literature.

In general, the quantification errors with methods ii) and iii) are higher than that with method i), as specific differences of the characteristics of the specimens, and the properties of the microscopes and detectors, and experimental geometries cannot be accurately considered. The offset of the experimental kAB factor from the calculated values can be ~5% for Z >14. However, the offset for low Z elements may be not only due to the factors mentioned in method i) above but also due to the absorption of low-energy X-rays within the specimens and contamination on the detector windows. For modern EDS systems, kAB databases obtained from a combination of methods ii) and iii) are normally stored in the software of EDS data acquisition and support computers as default.






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