Electron microscopy
EDS Quantification with k-factors (Cliff-Lorimer Factors)
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For a thin specimen, the absorption of the emitted X-ray is negligible so that the Cliff-Lorimer equation with kAB factor can be used and corrected, which depends only on the measurement conditions and on both the elements A and B, but not on the composition of the specimen. In this case, quantitative analysis based on EDS method can be done by the following procedure:
        i) Measure the characteristic line energies corresponding to the pre-selected elements for both specimens and standards under known operating conditions.
        ii) Measure the intensity of the spectral peaks (accurate to at least 1% level in order to have ~1% of accuracy of quantification). To measure the intensity of an X-ray line, the line must be separated from other lines and from the continuum background. The separation relies on accurate modeling of the shape of individual peaks.
        iii) Accurately measure the background, especially for the analysis of low concentrations (because the peak-to-background ratios are small). For instance, a 1% error is induced for a 100% error in a background measurement with a peak 100 times larger than the background, while the same error with a peak twice background introduces a ~50% error!
        iv) Calculate the intensity ratios (k values).
        v) Convert the values into chemical concentration.

Note that for qualitative analysis, only steps i) and ii) are needed.

In EDS analysis, elemental concentrations in materials can be quantified, without standards, by using theoretical and experimental Cliff-Lorimer-factors (k-factors). However, the accurate quantification can be done with experimental k-factors obtained from standard specimens.

For thick TEM samples, k-factor correction due to X-ray absorption is needed in order to accurately quantify EDS measurements. Table 1748 lists examples of thicknesses at which the thin-film approximation is no longer valid due to X-ray absorption effects in specific materials.

Table 1748. Examples of limits to the thin-film approximation caused by X-ray absorption: Maximum thicknesses of thin specimens for which the absorption correction (or error) is less than ±10% and ±3%.


10% error in kAB
3% error in kAB
Absorbed X-ray lines
Primary X-ray lines
Thickness (nm)
Al-7% Zn
336 94 Al Kα Al Kα (1.486 keV) and Zn Kα(8.63 keV)
40 12 Al Kα Al Kα (1.486 keV) and Cu Kα (8.04 keV)
  11 Cu Kα and Au Mα Cu Kα (8.027) and Au Lα (9.628 keV)
32 9 Al Kα Al Kα (1.486 keV) and Ni Kα (7.471 keV)
33 10 Al Kα and Ag Lα Al Kα (1.486 keV) and Ag Lα (2.984 keV)
31 9 Al Kα and Ag Lα Al Kα (1.486 keV) and Ag Lα (2.984 keV)
  89 Ni Kα Fe Kα (6.391 keV) and Ni Kα (7.461 keV)
  34 P Kα Fe Kα (6.391 keV) and P Kα (2.014 keV)
  22 P Kα Fe Kα (6.391 keV) and P Kα (2.014 keV)
180 50 S Kα Fe Kα (6.398 keV) and S Kα (2.307 keV)
113 14 Al Kα and O Kα Al Kα (1.486 keV) and O Kα (0.525 keV)
  25 Mg Kα, O Kα Mg Kα (1.253 keV) and O Kα (0.525 keV)
167 14 Si Kα and O Kα Si Kα (1.739 keV) and O Kα (0.525 keV)
413 6 Si Kα and N Kα Si Kα (1.739 keV) and N Kα (0.392 keV)
13 3 Si Kα and C Kα Si Kα (1.739 keV) and C Kα (0.277 keV)