Secondary Electrons
X- Ray Intensity Emitted from Thick, Solid Specimens
4.5 X-Ray Fluorescence
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s d= cscψ (4.15)
Normalizing by the intensity generated in each layer, the ϕ(ρz) histogram gives the probability, with a value between 0 and 1, that a photon generated in that layer and emitted into the solid angle of the EDS detector will escape and reach the detector, as shown in . Fig. 4.16b for each histogram bin of the silicon ϕ(ρz) distribution. The escape probability of X-rays integrated over the complete ϕ(ρz) histogram gives the parameter designated “f(χ),” which is the overall escape probability, between 0 and 1, for an X-ray generated any- where in the ϕ(ρz) distribution.
. Figure 4.21b shows a sequence of calculations of the C K ϕ(ρz) distribution and subsequent absorption as a func- tion of incident beam energy. As the incident beam energy increases, the depth of electron penetration increases so that carbon characteristic X-rays are produced deeper in the tar- get. For pure carbon with E0 = 5 keV, the cumulative value of f(χ) = 0.867; that is, 86.7 % of all carbon X-rays that are gener- ated escape, while 13.3 % are absorbed. As the C X-rays are produced deeper with increasing beam energy, the total X-ray absorption increases so that the value of f(χ) for C K decreases sharply with increasing beam energy, as shown in . Fig. 4.21b and in . Table 4.3.
Thus, with E0 = 2 keV, 97.4 % of the carbon X-rays escape the specimen, while at E0 = 30 keV, nearly 90 % of the carbon X-rays generated in pure carbon are absorbed before they can exit the specimen.
When the parameter f(χ) is plotted at every photon energy from the threshold of 100 eV up to the Duane–Hunt limit of the incident beam energy E0, X-ray absorption is seen to sharply modify the X-ray spectrum that is emitted from the target, as illustrated for carbon (. Fig. 4.22), copper (. Fig. 4.23), and gold (. Fig. 4.24). The high relative intensity of the X-ray continuum at low photon energies compared to higher photon energies in the generated spectrum is greatly diminished in the emitted spectrum because of the higher absorption suffered by low energy photons. Discontinuities
in f(χ) are seen at the critical ionization energy of the K-shell in carbon, the K- and L-shells in copper, and the M- and L-shells in gold, corresponding to the sharp increase in μ/ρ just above the critical ionization energy. Because the X-ray continuum is generated at all photon energies, the continuum is affected by every ionization edge represented by the atomic species present, resulting in abrupt steps in the background.
An abrupt decrease in X-ray continuum intensity is observed just above the absorption edge energy due to the increase in the mass absorption coefficient. The characteristic peaks in these spectra are also diminished by absorption, but because a characteristic X-ray is always lower in energy than the ion- ization edge energy from which it originated, the mass absorption coefficient for characteristic X-rays is lower than that for photons with energies just above the shell ionization energies. Thus an element is relatively transparent to its own characteristic X-rays because of the decrease in X-ray absorp- tion below the ionization edge energy.
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.Fig. 4.22 a Absorption parameter f(χ) as a function of photon energy for carbon and an incident beam energy of E0 = 20 keV. Note the abrupt decrease for photons just above the ionization energy of carbon at 0.284 keV.
b Expansion of the region from 0 to 5 keV. Note the abrupt decrease for photons just above the ionization energy of carbon at 0.284 keV. c Comparison of the generated (black) and emitted (red) X-ray spectra for carbon with an incident beam energy of E0 = 20 keV
1.0 a
0.8
0.6
0.4
0.2
0.0 5 10
Photon energy (keV) 15 20
Absorption parameter f(χ) for C, E0 = 20 keV
f(χ)
Absorption parameter f(χ) for C, E0 = 20 keV
1.0
0.8
0.6
0.4
0.2
0.0
f(χ)
1 0
0
2 3
Photon energy (keV) 4 5
b
c1e+8 Generated and emitted X-ray spectra for carbon E0 = 20 keV
1e+7 1e+6 1e+5 1e+4 1e+3
Intensity
1e+2 1e+1
1e+00 5 10
X-ray photon energy (keV)15 20 Generated
Emitted Chapter 4 · X-Rays
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.Fig. 4.23 a Absorption parameter f(χ) as a function of photon energy for copper and an incident beam energy of E0 = 20 keV. Note the abrupt decrease just above the ionization energies of the three L-shells near 0.930 keV and the K-shell ionization energy at 8.98 keV.
b Comparison of the generated (red) and emitted (blue) X-ray spectra for copper with an incident beam energy of E0 = 20 keV. c Comparison of the generated and emitted X-ray spectra for copper with an incident beam energy of E0 = 20 keV; expanded to show the region of the Cu L-shell and Cu K-shell ionization energies
Absorption parameter f(χ) for copper, E0 = 20 keV
Photon energy (keV)
f(χ)
1.0 a
0.8
0.6
0.4
0.2
0.00 5 10 15 20
c 1e+7
1e+6
1e+5
Emitted Copper, E0 = 20 keV
Generated
1e+4
1e+3
1e+20 2
Photon energy (keV)
X-ray intensity
4 6 8 10
1e+8 1e+7 1e+6
1e+5 Emitted
Generated Copper, E0 = 20 keV
1e+4 X-ray intensity 1e+3
1e+2 1e+1
1e+00 5 10
Photon energy (keV) 15 20
b 4.5 · X-Ray Fluorescence
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1.0
0.8
0.6
0.4
0.2
0.00 5 10
Photon energy (keV)
Absorption parameter f(c) for gold, E0 = 20 keV a
15 20
f(c)
0 5 10
Photon energy (keV) Gold, E0 = 20 keV b 1e+8
1e+7 1e+6 1e+5 1e+4 1e+3 1e+2
1e+0 1e+1
X-ray intensity
15 20
Emitted Generated
0 1 2
Photon energy (keV) Gold, E0 = 20 keV c 1e+8
1e+7
1e+6
1e+5
1e+4
1e+3
1e+2
X-ray intensity
3 4 5
Emitted Generated
Emitted Generated
.Fig. 4.24 a Absorption parameter f(χ) as a function of photon energy for gold and an incident beam energy of E0 = 20 keV. Note the abrupt decrease in f(χ) for photons just above the ionization energies of the gold M-shell and gold L-shell. b Comparison of the generated (red) and emitted (blue) X-ray spectra for gold with an incident beam energy of E0 = 20 keV. c Comparison of the generated (red) and emitted (blue) X-ray spectra for gold with an incident beam energy of E0 = 20 keV; expansion of the region around the gold M-shell ionization edges
Chapter 4 · X-Rays
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90%
99%
10 µm Ni-10% Fe E0 = 20 keV
.Fig. 4.25 Range of secondary fluorescence of Fe K-L3 (EK = 7.07 keV) by Ni K-L3 X-rays (7.47 keV). Red arc = extent of direct electron excita- tion of Ni K-L3 and Fe K-L3. Blue arc = range for 50 % of total secondary fluorescence of Fe K-L3 by Ni K-L3; green arc = 90 %; magenta arc = 99 % References
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