The characteristic line spectrum

Arndt, U. W.

doi:10.1107/97809553602060000592

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 191-192

Section 4.2.1.1. The characteristic line spectrum

U. W. Arndt^a ^‡

4.2.1.1. The characteristic line spectrum

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Characteristic X-ray emission originates from the radiative decay of electronically highly excited states of matter. We are concerned mostly with excitation by electron bombardment of a target that results in the emission of spectral lines characteristic of the target elements. The electronic states occurring as initial and final states of a process involving the absorption of emission of X-rays are called X-ray levels. Levels involving the removal of one electron from the configuration of the neutral ground state are called normal X-ray levels or diagram levels.

Table 4.2.1.1 shows the relation between diagram levels and electron configurations. The notation used here is the IUPAC notation (Jenkins, Manne, Robin & Senemaud, 1991), which uses arabic instead of the former roman subscripts for the levels. The IUPAC recommendations are to refer to X-ray lines by writing the initial and final levels separated by a hyphen, e.g. Cu K-L₃ and to abandon the Siegbahn (1925) notation, e.g. Cu Kα₁, which is based on the relative intensities of the lines. The correspondence between the two notations is shown in Table 4.2.1.2. Because this substitution has not yet become common practice, however, the Siegbahn notation is retained in Section 4.2.2, in which the wavelengths of the characteristic emission lines and absorption edges are discussed.

Table 4.2.1.1| top | pdf |
Correspondence between X-ray diagram levels and electron configurations; from Jenkins, Manne, Robin & Senemaud (1991), courtesy of IUPAC

Level	Electron configuration	Level	Electron configuration	Electron configuration
K	$[1s^{-1}]$	N₁	$[4s^{-1}]$	$[5s^{-1}]$
L₁	$[2s^{-1}]$	N₂	$[4p^{-1}_{1/2}]$	$[5p^{-1}_{1/2}]$
L₂	$[2p^{-1}_{1/2}]$	N₃	$[4p^{-1}_{3/2}]$	$[5p^{-1}_{3/2}]$
L₃	$[2p^{-1}_{3/2}]$	N₄	$[4d^{-1}_{3/2}]$	$[5d^{-1}_{3/2}]$
M₁	$[3s^{-1}]$	N₅	$[4d^{-1}_{5/2}]$	$[5d^{-1}_{5/2}]$
M₂	$[3p^{-1}_{1/2}]$	N₆	$[4f^{-1}_{5/2}]$	$[5f^{-1}_{5/2}]$
M₃	$[3p^{-1}_{3/2}]$	N₇	$[4f^{-1}_{7/2}]$	$[5f^{-1}_{7/2}]$
M₄	$[3d^{-1}_{3/2}]$
M₅	$[3d^{-1}_{5/2}]$

Table 4.2.1.2| top | pdf |
Correspondence between IUPAC and Siegbahn notations for X-ray diagram lines; from Jenkins, Manne, Robin & Senemaud (1991), courtesy of IUPAC

Siegbahn	IUPAC	Siegbahn	IUPAC	Siegbahn	IUPAC
$[K\alpha_1]$	$[K\hbox{-}L_3]$	$[L\alpha_1]$	$[L_3\hbox{-}M_5]$	$[L\gamma_1]$	$[L_2\hbox{-}N_4]$
$[K\alpha_2]$	$[K\hbox{-}L_2]$	$[L\alpha_2]$	$[L_3\hbox{-}M_4]$	$[L\gamma_2]$	$[L_1\hbox{-}N_2]$
$[K\beta_1]$	$[K\hbox{-}M_3]$	$[L\beta_1]$	$[L_2\hbox{-}M_4]$	$[L\gamma_3]$	$[L_1\hbox{-}N_3]$
$[K\beta^1_2]$	$[K\hbox{-}N_3]$	$[L\beta_2]$	$[L_3\hbox{-}N_5]$	$[L\gamma_4]$	$[L_1\hbox{-}O_3]$
$[K\beta^{11}_2]$	$[K\hbox{-}N_2]$	$[L\beta_3]$	$[L_1\hbox{-}M_3]$	$[L\gamma'_4]$	$[L_1\hbox{-}O_2]$
$[K\beta_3]$	$[K\hbox{-}M_2]$	$[L\beta_4]$	$[L_1\hbox{-}M_2]$	$[L\gamma_5]$	$[L_2\hbox{-}N_1]$
$[K\beta^1_4]$	$[K\hbox{-}N_5]$	$[L\beta_5]$	$[L_3\hbox{-}O_{4,5}]$	$[L\gamma_6]$	$[L_2\hbox{-}O_4]$
$[K\beta^{11}_4]$	$[K\hbox{-}N_4]$	$[L\beta_6]$	$[L_3\hbox{-}N_1]$	$[L\gamma_8]$	$[L_2\hbox{-}O_1]$
$[K\beta_{4x}]$	$[K\hbox{-}N_4]$	$[L\beta_7]$	$[L_3\hbox{-}O_1]$	$[L\gamma'_8]$	$[L_2\hbox{-}N_{6(7)}]$
$[K\beta^1_5]$	$[K\hbox{-}M_5]$	$[L\beta'_7]$	$[L_3\hbox{-}N_{6,7}]$	$[L_\eta]$	$[L_2\hbox{-}M_1]$
$[K\beta^{11}_5]$	$[K\hbox{-}M_4]$	$[L\beta_9]$	$[L_1\hbox{-}M_5]$		$[L_3\hbox{-}M_1]$
		$[L\beta_{10}]$	$[L_1\hbox{-}M_4]$		$[L_3\hbox{-}M_3]$
		$[L\beta_{15}]$	$[L_3\hbox{-}N_4]$		$[L_3\hbox{-}M_2]$
		$[L\beta_{17}]$	$[L_2\hbox{-}M_3]$		$[L_3\hbox{-}N_{6,7}]$
					$[L_2\hbox{-}N_{6(7)}]$

Siegbahn	IUPAC
$[M\alpha_1]$	$[M_5\hbox{-}N_7]$
$[M\alpha_2]$	$[M_5\hbox{-}N_6]$
$[M\beta]$	$[M_4\hbox{-}N_6]$
$[M\gamma]$	$[M_3\hbox{-}N_5]$
$[M\zeta]$	$[M_{4,5}\hbox{-}N_{2,3}]$

In the case of unresolved lines, such as $[K\hbox{-}L_2]$ and $[K\hbox{-}L_3]$ , the recommended IUPAC notation is $[K\hbox{-}L_{2,3}]$ .

4.2.1.1.1. The intensity of characteristic lines

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The efficiency of the production of characteristic radiation has been calculated by a number of authors (see, for example, Dyson, 1973, Chap. 3). For a particular line, it depends on the fluorescence yield, that is the probability that the decay of an excited state leads to the emission of a photon, on the statistical weights of the X-ray levels involved, on the effects of the penetration and slowing down of the bombarding electrons in the target, on the fraction of electrons back-scattered out of the target, and on the contribution caused by fluorescent X-rays produced indirectly by the continuous spectrum. The emerging X-ray intensity is further affected by the partial absorption of the generated X-rays in the target .

Dyson (1973) has also reviewed calculations and measurements made of the relative intensities of different lines in the K spectrum. The ratio of the $[K\alpha_2]$ to $[K\alpha_3]$ intensities is very close to 0.5 for Z between 23 and 48. The ratio of $[K\beta_3]$ to $[K\alpha_2]$ rises fairly linearly with Z from 0.2 at Z = 20 to 0.4 at Z = 80 and that of $[K\beta_1]$ to $[K\alpha_2]$ is near zero at Z = 29 and rises linearly with Z to about 0.1 at Z = 80. Relative intensities of lines in the L spectrum are given by Goldberg (1961).

Green & Cosslett (1968) have made extensive measurements of the efficiency of the production of characteristic radiation for a number of targets and for a range of electron accelerating voltages. Their results can be expressed empirically in the form $[N_K/4\pi=N_0/4\pi(E_0-E_K-1){}^{1.63},\eqno (4.2.1.1)]$ where $[N_K/4\pi]$ is the generated number of Kα photons per steradian per incident electron, N₀ is a function of the atomic number of the target, E₀ is the electron energy in keV and [E_K] is the excitation potential in keV. It should be noted that $[N_K/4\pi]$ decreases with increasing Z.

For a copper target, this expression becomes $[N_K/4\pi=1.8\times10^{-6}\,(E_0 - 8.9){}^{1.63}\eqno (4.2.1.2)]$ or $[N'_K/4\pi=1.1\times10^{10}\,(E_0 - 8.9){}^{1.63},\eqno (4.2.1.3)]$ where $[N'_K/4\pi]$ is the number of Kα photons per steradian per second per milliampere of tube current.

These expressions are probably accurate to within a factor of 2 up to values of [E_0/E_K] of about 10. Guo & Wu (1985) found a linear relationship for the emerging number of photons with electron energy in the range $[2\lt E_0/E_K\lt 5]$ .

To obtain the number of photons that emerge from the target, the above expressions have to be corrected for absorption of the generated radiation in the target. The number of photons emerging at an angle $[\varphi]$ to the surface, for normal electron incidence, is usually written $[N_\varphi/4\pi=f(\chi)N/4\pi,\eqno (4.2.1.4)]$ where $[\chi=(\mu/\rho)\hbox{ cosec }\varphi]$ (Castaing & Descamps, 1955). Green (1963) gives experimental values of the correction factor f(χ) for a series of targets over a range of electron energies. His curves for a copper target are given in Fig. 4.2.1.1 . It will be noticed that the correction factor increases with increasing electron energy since the effective depth of X-ray generation increases with voltage. As a result, curves of $[N_\varphi]$ as a function of [E_0] have a broad maximum that is displaced towards lower voltages as $[\varphi]$ decreases, as shown in the experimental curves for copper K radiation due to Metchnik & Tomlin (1963) (Fig. 4.2.1.2 ). For very small take-off angles, therefore, X-ray tubes should be operated at lower than customary voltages. Note that the values in Fig. 4.2.1.2 agree to within ∼40% with those of Green & Cosslett. f(χ) at constant [E_0/E_K] increases with increasing Z, thus partly compensating for the decrease in [N_K] , especially at small values of $[\varphi]$ . A recent re-examination of the characteristic X-ray flux from Cr, Cu, Mo, Ag and W targets has been carried out by Honkimaki, Sleight & Suortti (1990).

Figure 4.2.1.1| top | pdf |

f(χ) curves for Cu K-L₃ at a series of different accelerating voltages (in kV). From Green (1963).

Figure 4.2.1.2| top | pdf |

Experimental measurements of $[N_\varphi]$ for Cu K-L₃ as functions of the accelerating voltage for different take-off angles. From Metchnik & Tomlin (1963).

References

Castaing, R. & Descamps, J. (1955). Sur les bases physiques de l'analyse ponctuelle par spectrographie X. J. Phys. Radium, 16, 304–317.Google Scholar

Dyson, N. A. (1973). X-rays in atomic and nuclear physics. London: Longman.Google Scholar

Goldberg, M. (1961). Intensités relatives des raies X du spectre L excité par bombardement électronique des éléments lourds. J. Phys. Radium, 22, 743–748.Google Scholar

Green, M. (1963). The target absorption correction in X-ray microanalysis. X-ray optics and X-ray microanalysis, edited by H. Pattee, V. E. Cosslett & A. Engstrom, pp. 361–377. London: Academic Press.Google Scholar

Green, M. & Cosslett, V. E. (1968). Measurement of K, L and M shell X-ray production efficiencies. Br. J. Appl. Phys. Ser. 2, 1, 425–436.Google Scholar

Guo, C.-L. & Wu, Y.-Q. (1985). Empirical relationship between the characteristic X-ray intensity and the incident electron energy. Kexue Tongbao, 30, 1621–1627.Google Scholar

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, pp. 191-192