After an electron transition, the released energy is emitted. This is possible by the emission of characteristic radiation, which is due to the large energy differences of the involved electron levels in the range of X-ray radiation. Another possibility is the transfer of the energy to an outer electron of the atom under consideration and its emission. This process is called Auger effect. The probability for the emission of an X-ray photon again depends on the atomic number and is called fluorescence yield ωfluo. This probability is shown in Figure 2.4; more precise values for the fluorescence yield of the individual elements can be taken from Table A.11. Since an ionized atom always goes into the stable basic state,
Figure 2.4 Fluorescence yield as a function of the atomic number.
The relation shows that the fluorescence yields are very small for elements with low atomic numbers. Most of the atoms then emit the energy released by the transition to the ground state as Auger electron and only very few as X-ray photons. This is the main reason for the low sensitivity of X-ray spectrometry for light elements. For higher radiation energies, the fluorescence yield increases significantly.
2.2.3 Nomenclature of X-ray Lines
Two nomenclatures are used to designate the X-ray lines. The older is based on the fixed intensity ratios of the individual lines and was introduced by Siegbahn (1923). It also shows the development of the performance of X-ray spectrometers, in particular their energy resolution. For the first instruments, only the distinction between K-, L-, and M-lines was possible. With the improvement of the resolution, a splitting of these lines was then discovered, i.e. α-, β-, and γ-lines could be distinguished. Later, further splittings were detected, which are denoted by indices.
There is also the nomenclature introduced by the IUPAC, which is based on an exact designation of the respective electron levels from which the X-ray lines are generated. A comparison of the designations for the most important X-ray lines can be found in Table 2.2.
2.2.4 Interaction of X-rays with Matter
X-radiation interacts with matter – it will be scattered and absorbed. This process is described by Lambert–Beer's law.
(2.5)
with
| I | intensity after absorption in a layer |
| D | thickness of the layer |
| P | density of the layer |
| M | mass attenuation coefficient of the layer material |
| I 0 | primary intensity |
The mass attenuation coefficient μ has several contributions. At low energies, the absorption described by the photoionization coefficient τ is dominant; the influence of the scattering characterized by the scattering coefficient σ increases with energy, and in the case of energies >1.2 MeV the electron pair production described by κ gains importance. However, this is outside the range of energy that is of interest for X-radiation.
(2.6)
All these interactions depend on both the analyzed material and the energy of the radiation, as shown in the diagrams in Figure 2.5 for the elements (a) carbon and (b) lead. They show that in the energy range of about 0.5–40 keV, absorption dominates. Rayleigh scattering contributes a fraction of less than 1% for low energies. At higher energies, Compton scattering dominates the radiation attenuation coefficient.
2.2.4.1 Absorption
Absorption will be understood merely as the attenuation of the incident X-ray radiation by the ionization of atoms. This process is described by the element- and energy-dependent photoionization coefficient. It increases with higher atomic number and decreases with increasing energy as can be seen in Figure 2.5. This energy dependence can be approximated by τ ≈ E−3. The curve does show discontinuities that manifest themselves as jumps. They occur when the energy of the absorbed radiation is sufficient to ionize a new electron shell, i.e. a new interaction mechanism is added. In the diagrams in Figure 2.5, this applies to Pb for the excitation of M, L, and K radiation at energies of approximately 3, 15, and 88 keV, respectively. The energy of the K-absorption edge of C, on the other hand, is 0.283 keV and is therefore not displayed in the diagram.
Table 2.2 Comparison