Cliff-Lorime (k-) Sensitivity Factors in EDS
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If the TEM sample is infinitely thin, then the absorption and fluorescence effects are negligible in Equation . Therefore, the X-ray intensity collected by the EDS detector should equal to the X-ray intensity generated from the sample by the electron beam. This is normally not true because of X-ray absorption within the sample and due to absorption in the X-ray detector. However, the discussion below simply ignores the effects of the absorption and fluorescence effects.
Quantitative X-ray measurements, e.g. EDS, in analytical electron microscopy involves the use of Cliff-Lorimer kAB factors  to relate the measured X-ray intensities from elements A and B to their composition. Here, the subscript of kAB indicates that the values of the k factors for the intensity of each element A is ratioed to the intensity of element B. The selection of element B has to reduce the uncertainty of k factors due to the variations in the efficiency of individual energy dispersive spectrometers, and thus makes the values of k-factors more universally applicable. Here, kAB is given by,
Note kAB is a factor that accounts for the relative efficiency of production and detection of the X-rays. Therefore, kAB is a constant for a given accelerating voltage and the efficiency of a specific EDS spectrometer at the relevant x-ray energies, and is independent of specimen thickness and composition, which is so-called 'thin-film criterion'. This criterion assumes that the X-rays are neither absorbed nor fluoresced in the specimen. The kAB factors for the Kα X-ray peaks of the elements from about Mg (Z=12) to Zn (Z=30) is about 1. However, below or above this range of atomic numbers the kAB factor gradually increases as shown in Tables 4624a and 4624c.
The kAB factors are experimentally determined from well-investigate, homogeneous standards and are normally stored in a look-up table in EDS software. The quality of EDS analyses depends significantly on the accuracy of the kAB values so that it is very important these values are carefully quantified using several standards for each element. For the elements with atomic numbers greater than 12, the kAB factors can now be determined with an error in the range of 1 to 4%, while the determination of kAB factors for light elements is normally less accurate.
For a system with many elements, the elemental concentrations can be evaluated with a set of equations. For instance, in a ternary system with three elements A, B and C, the elemental concentration can be evaluated with the following equations:
K-factors vary from instrument to instrument significantly as shown in Tables 4624a-4624d and the excel file. The kASi factors listed in Tables 4624a and 4624b are most useful to geologists and semiconducting engineers where silicon is often the major component element after oxygen, while for metallurgists it is often more useful to display kAFe factors where element B is iron as listed in Tables 4624c and 4624d.
Figure 4624 shows the plots of KASi Factors listed in Table 4624a. From the figures, we can know that the K-factors for a specific element are not constant even though at the same accelerating voltage (e.g. 100 keV) because the K-factors are not only determined by the relevant elements but also affected by the characteristics of the EDS systems. Those differences will affect quantification if no calibration was done on the particular EDS system.
Furthermore, it is better to use the k factors with Fe as the standard, namely kAFe, instead of kASi, for elemental evaluations because of two reasons. Firstly, the error of the detected Si x-ray intensity, due to Si Kα absorption in the specimen, is larger than that of Fe Kα. Secondly, the EDS detector is almost 100% efficient for the detection of Fe Kα X-ray, while for Si Kα x-ray the detection efficiency is significantly degraded due to x-ray absorption in the detector itself. If a proper standard containing the two elements (A and B) of interest cannot be found, kAB factors can be obtained from two standards,
kASi = kAB * kBSi ------------------------------------ [4624f]
In Equation 4624h, it is most difficult to accurately calculate Q and ε. The extraction of the kAB values for K lines above 1.5 eV in energy is in error of ~10 to 15% mainly due to the inaccurate estimation of Q. For the same reason, it is not recommended to calculate the kAB values for light elements Z < 11 or for L lines.
Note that at a constant accelerating voltage of a given incident beam the k-factors are independent of specimen thickness and the complexity of compositions in a thin specimen. If the peaks of many elements are measured simultaneously, the measurements are independent of variations in the probe current.
The kAB factors depend upon the composition of the specimen and the thickness of the detector window, and change if contamination builds up on the window of the detector, so that they are not constants. However, kAB values for a particular EDS instrument can be stored in a computer and used for a long time. Therefore, no standardization of kAB factors is normally needed at the time of analysis.
Table 4624e lists the KMoO factors for Mo Lα1 and O K X-rays at accelerating voltages from 15 keV to 30 keV. The X-rays are collected from a bulk sample in an SEM system. At the lower voltage 15 keV, both intensities of Mo Lα1 and O K X-rays are higher and the KMoO factor is lower.
Note that, in general, k-factors obtained by experimental methods are normally more accurate than those determined by theoretical calculation:
 Lorimer, GW, Al-Salman, SA and Cliff, G 1977 The Quantitative Analysis of Thin Specimens: Effects of
Absorption, Fluorescence and Beam Spreading in Developments in Electron Microscopy and Analysis
369–371 Ed. DL Misell The Institute of Physics Bristol and London.