Cliff-Lorime (k-) Sensitivity Factors in EDS
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The Cliff-Lorime sensitivity factors in EDS measurements can be in form of kAB. Here, kAB is given by,

           Cliff-Lorime sensitivity factors ------------------------------------ [4624a]

where,
           CA – The concentration of element A,
           CB – The concentration of element B,
           IA – The intensity from element A,
           IB – The intensity from element B.

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. 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:
           in a ternary system with three elements A, B and C --------------------------------------- [4624b]
           in a ternary system with three elements A, B and C --------------------------------------- [4624c]            
           in a ternary system with three elements A, B and C --------------------------------------- [4624d]            
            kAB = kAC kCB --------------------------------------- [4624e]

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.

Table 4624a. KASi Factors for Kα X-rays at various accelerating voltages of electron beams. The number in [] gives the reference.
Atomic number (Z) Symbol 80 kV 100 kV 100 kV 100 kV 120 kV 200 kV 200 kV
11 Na 2.8 [2] 5.77 [8] 3.2 [9] 2.17 [3] 3.57 [1] 2.42 [3] 3.97±2.32 [5]
12 Mg 1.7 [2] 2.07 [8] 1.6 [9] 1.44 [3] 1.49 [1] 1.43 [3] 1.81 [5]
13 Al 1.15 [2] 1.42 [8] 1.2 [9]   1.12 [1]   1.25 [5]
15 P         0.99 [1]   1.04 [5]
16 S       1.008 [3] 1.08 [1] 0.989 [3] 1.06 [5]
17 Cl       0.994 [3]   0.964 [3] 1.06±0.3 [5]
19 K 1.14 [2]   1.03 [9]   1.12±0.27 [1]   1.21±0.2 [5]
20 Ca 1.13 [2] 1.0 [8] 1.06 [9]   1.15 [1]   1.05 [5]
22 Ti   1.08 [8] 1.12 [9]   1.12 [1]   1.14 [5]
23 V 1.3 [2] 1.13 [8]         1.16 [5]
24 Cr   1.17 [8] 1.18 [9]   1.46 [1]    
25 Mn   1.22 [8] 1.24 [9]   1.34 [1]   1.24 [5]
26 Fe 1.48 [2] 1.27 [8] 1.3 [9]   1.3 [1]   1.35 [5]
27 Co             1.41 [5]
28 Ni   1.47 [8] 1.48 [9]   1.67 [1]    
29 Cu   1.58 [8] 1.6 [9] 1.72 [3] 1.59 [1] 1.5 [3] 1.51 [5]
30 Zn   1.68 [8]   1.74 [3]   1.55 [3] 1.63 [5]
32 Ge   1.92 [8]         1.91±0.54 [5]
40 Zr             3.62±0.56 [5]
42 Mo   4.3 [8]     4.95 [1]    
47 Ag   8.49 [8]     12.4 [1]   6.26±1.5 [5]
48 Cd   10.6 [8]   9.47 [3]   6.2 [3]  
49 In             7.99±1.8 [5]
50 Sn   10.6 [8]         8.98±1.48 [5]
56 Ba       29.3 [3]   17.6 [3] 21.6±2.6 [5]

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.

KASi Factors
KASi Factors
(a)
(b)
Figure 4624. Plots of KASi Factors in Table 4624a: (a) At all the accelerating voltages and (b) At the accelerating voltage of 100 keV only.

 

Table 4624b. KASi Factors for L X-rays at various accelerating voltages of electron beams. The number in [] gives the reference.
Atomic number (Z) Symbol
100 keV [7]
100 keV [6]
100 keV [4]
200 keV [5]
200 keV [3]
29 Cu     8.76   12.2
30 Zn     6.53 8.09±0.8 6.5
32 Ge       4.22±1.48  
33 As       3.6±0.72  
34 Se       3.47±1.11  
38 Sr          
40 Zr       2.85±0.4  
42 Mo 2.0        
47 Ag   2.32   2.8±1.19  
49 In       2.86±0.71  
48 Cd     2.92   2.75
50 Sn 1.3 3.09      
56 Ba     3.38 3.36±0.58 2.94
58 Ce 1.4        
74 W 1.8 3.11   3.97±1.12  
79 Au   4.19 4.64 4.93±2.03 3.93
82 Pb 2.8 5.3 4.85 5.14±0.89 4.24

 

Table 4624c. KAFe Factors for Kα X-rays at accelerating voltages of 100 keV and 120 keV. The number in [] gives the reference.
Atomic number (Z)
Symbol
100 keV [1,10]
100 keV [11]
120 kV [4]
11 Na 2.46    
12 Mg 1.23 1.16 1.02
13 Al 0.92 0.8 0.86
14 Si 0.76 0.71 0.76
15 P     0.77
16 S     0.83
19 K 0.79 0.77 0.86
20 Ca 0.81 0.75 0.88
22 Ti 0.86   0.86
24 Cr 0.91   0.9
25 Mn 0.95   1.04
27 Co 1.05   0.98
28 Ni 1.14   1.07
29 Cu 1.23   1.17
30 Zn 1.24   1.19
41 Nb     2.14
42 Mo 3.38   3.8
47 Ag 6.65   9.52

 

Table 4624d. KAFe Factors for L X-rays at accelerating voltages of 100 keV and 120 keV. The number in [] gives the reference.
Atomic number (Z)
Symbol
100 keV [6] 
120 keV [4]
38 Sr   1.21
40 Zr   1.35
41 Nb   0.9
47 Ag 1.04 1.18
49 In   2.21
50 Sn 2.39  
56 Ba 2.18  
74 W 2.43  
79 Au 3.27 3.1
82 Pb 4.14  

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]
Or,
           kAFe = kAB * kBFe ------------------------------------ [4624g]
If neither a proper database nor standards are available, the kAB factors can be theoretically calculated,
           Cliff-Lorime sensitivity factors ----------------------------- [4624h]
where,
          QA and QB -- The ionization cross-sections for the X-rays of elements A and B, respectively,
          wA and wB -- The fluorescence yields for elements A and B, respectively,
          aA and aB -- The relative transition probabilities for elements A and B, respectively,
          AA and AB -- The atomic weights for elements A and B, respectively,
          εA and εB -- The detection efficiencies of the EDS detector for the X-rays from elements A and B, respectively.

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.

 

 

 

 

[1] 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.
[2] McGill, R. and Hubbard, FH 1981 Quantitative Analysis with High Spatial Resolution p30 Eds. GW Lorimer, MH Jacobs and P Doig The Metals Society London.
[3] Schreiber, TP and Wims, AM 1981 Quantitative Analysis of Thin Specimens in the TEM Using a f(rz) Model Ultramicrosc. 6 323–334.
[4] Wood, JE, Williams, DB and Goldstein, JI 1984 An Experimental and Theoretical Determination of kAFe Factors for Quantitative X-ray Microanalysis in the Analytical Electron Microscope J. Microsc. 133 255–274.
[5] Sheridan, PJ 1989 Determination of Experimental and Theoretical kASi Factors for a 200-kV Analytical Electron Microscope J. Electr. Microsc. Tech. 11 41–61.
[6] Goldstein, JI, Costley, JL, Lorimer, G, and Reed, SJB 1977 Quantitative X-ray Microanalysis in the Electron Microscope SEM 1977 1 315–325 Ed.O Johari IITRI Chicago IL.
[7] Sprys, JW and Short,MA1976 Quantitative Elemental Analysis of ‘Transparent’ Particles in theTEM Proc. 34th EMSA Meeting Ed. GW Bailey Claitors Baton Rouge LA 416–7
[8] Cliff, G and Lorimer, GW 1975 The Quantitative Analysis of Thin Specimens J. Microsc. 103 203–207. The original paper based on crushed mineral standards (all borrowed from the desk drawer of Pam Champness, Lorimer’s wife, who is a well-known mineralogist).
[9] Wood, JE, Williams, DB and Goldstein, JI 1981 Determination of Cliff-Lorimer k Factors for a Philips EM 400T in Quantitative Analysis with High Spatial Resolution 24–30 Eds.GWLorimer,MHJacobs and P Doig The Metals Society London. kFe factors.
[10] Lorimer GW, Cliff G, Clark JN. In: Venables JA, ed. Developments in Electron Microscopy and Analysis. London: Academic Press, 1976, p 153.
[11] McGill RL, Hubbard FH. In: Quantitative Microanalysis with High Spatial Resolution. London: The Metals Society of London, 1981, p 30.

 

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