Quantitative X-rays Analysis

If the X-ray spectrum was measured on a TEM, the Cliff-Lorimer ratio technique can be applied for the quantification:

$$ \frac{N_A}{N_B} = k_{AB} \cdot \frac{ I_A}{I_B}$$

\(N_A, N_B\): atomic % of elements \(A, B\)
\(I_A, I_B\): measured intensities of elements \(A, B\)
\(k_{AB}\): Cliff-Lorimer factor

The Cliff-Lorimer factor is NOT a constant but depends on the TEM voltage, on the detector efficiency and several other parameters. Thus, accurate results can only be obtained if a standard containing the elements A and B in a well-defined ratio is used to determine k_AB. Calculated values of k_AB, which are given by the various programs used for X-ray spectroscopy, are only raw approximations and can only be used for quick and rather inaccurate analyses. Although the program output for the composition is a seemingly accurate value with a rather small error bar, the actual error might be much higher because of the k_AB problem.
In all cases, the background ("bremsstrahlung") has to be subtracted first. The accuracy of the quantification is additionally reduced by statistical errors of the measurement, absorption, fluorescence, and electron channeling, just to mention the most important effects.

Electron-matter interactions | Generation of X-rays | X-ray spectroscopy