If this process is carried out in an X-ray tube, the generated radiation must be directed at the sample through an exit window. The exit window of the tube absorbs the low-energy parts of the primary spectrum. This process is described by the following addition to Kramers' law, in which μ is the mass attenuation coefficient, ρ is the density, and d is the thickness of the tube window:
(2.3)
The proportions of this relation are shown in Figure 2.1. It shows the continuous spectrum (emission) generated at the target, the low transmission through the tube window in the low-energy range (transmission) as well as the resulting radiation emitted by the tube (tube output).
In addition to the continuous radiation, there are also line-like spectral components in the energy range of X-rays, which are generated by electron transitions in an atom. For this purpose, an internal electron level must be ionized by an energy input, which is higher than the binding energy of the electron. This excitation is possible by radiation, i.e. electron, proton, or even X-rays themselves or by the generation of a high-energy plasma. The resulting electron vacancy in an inner shell is filled by electrons of outer shells, in order to transfer the atom to a stable state again. These transitions can occur from different electron levels, resulting in a series of X-ray lines being emitted. The energy level differences depend on the type of the emitting atom; therefore, this radiation is called the characteristic radiation. The labeling of these lines starts with the designation of the primary vacancy, i.e. when the innermost K-shell is ionized it is K-radiation, when the L-shell is primarily ionized it is L-radiation, etc.
Figure 2.1 Parts of the continuous spectrum of an X-ray tube.
Figure 2.2 Line energy as a function of the atomic number.
The energies of the electron levels depend mainly on the number of protons of the atom, i.e. on the atomic number. This means that the energy differences depend on the type of the atoms. These energy differences are described by Moseley's law.
with
| E | = | energy difference between the electron levels |
| Z | = | atomic number of the atom |
| C1, C2 | = | constants |
This relation is shown for different lines as a function of the atomic number in Figure 2.2. Detailed information can be found in Tables A.4–A.9.
Figure 2.2 shows that the energy of the characteristic radiation increases with the atomic number; it also shows that the line energies of an element decrease from the K series over the L series to the M series, and that in the energy range of approximately 1–40 keV, which is commonly used for X-ray spectrometry, almost all elements emit their characteristic radiation. Exceptions are only elements with very low atomic numbers (Z ≤ 7).
2.2.2 Intensity of the Characteristic Radiation
The intensity of the characteristic radiation is determined by the number and type of the atoms in the excited volume; in other words, the intensity depends on their mass fraction w. It is further influenced by the intensity I0 of the primary radiation. The photo-absorption coefficient τ(E) describes the probability for the excitation of an atom by X-rays with energy E. If an inner electron shell is ionized, the transition from an outer electron shell is described by the transition probability p. For shells that are close together, p has the greatest value; therefore, the α-lines are the most intense within a series. For energy levels with a larger difference the transition probabilities are smaller, i.e. the intensities of the β-lines are correspondingly lower; however, their energies are higher. Special electron transitions can be excluded as a result of quantum selection rules; for these transitions, the transition probabilities are p = 0. For the main electron transitions, the labels of the corresponding X-ray lines are shown in Figure 2.3.
Figure 2.3 Electron transitions with the corresponding line names.
The approximate intensity ratios within a series as well as between the main lines of the different series (dependent on the excitation conditions) are shown in Table 2.1.
Table 2.1 Approximate relative line intensities of main X-ray lines.
| K-series | L-series | M-series | ||||||
|---|---|---|---|---|---|---|---|---|
| 100 | Approx. 5–10 | Approx. 1 | ||||||
| Kα1 | K–L3 | 100 | Lα1 | L3–M5 | 100 | Mα1 | M5–N7 | 100 |
| Kα2 | K–L2 | 50 | Lβ1 | L2–M4 | 50 | Mα2 | M5–N6 | 100 |
| Kα1,2 | K–L23 | 150 | Lβ2 |