During XRF, an electron is ejected from the K or L electron orbital of the elements to be analyzed. The vacancy is filled with an electron from an outer orbital. The energy difference between the two orbitals is emitted as a characteristic X-ray pho­ton. The energy of the X-ray photons relates to the elements, thus providing quali­tative analysis. The intensity of the X-ray photons provides quantitative analytical information.

The X-ray photons can be produced by the excitation with charged particles (electron microprobe, discussed in Section 10.2.4.2, and proton-induced X-ray emission, discussed in Section 10.2.5.1) or by electromagnetic radiation. Electromagnetic radiation is produced in an X-ray tube, or it may be the gamma radiation emitted by a radioactive isotope. In an X-ray tube, the photocathode emits X-ray radiation. During isotopic excitation, 55Fe (5.9 keV), 109Cd (22—25 keV), 125I (27—31 keV), and 241Am (60 keV gamma energy) are used as exciting sources.

The initial process of excitation with electromagnetic radiation is the photoelec­tric effect. The excitation takes place if the energy of the exciting particle exceeds the binding energy of the electron. The exciting photons transfer their energy to the orbital electron. The energy equal to the binding energy ejects the electron, and the residual part of the energy becomes the kinetic energy of the ejected electron:

Ek = hv0 — Eb (10.35)

where Ek is the kinetic energy of the emitted electron, Eb is the binding energy of the electron, and hv0 is the energy of the exciting photon before the photoelectric effect. This process occurs if the energy of the exciting photon is close to the bind­ing energy of the electron. This means that the electrons are ejected from the K and L orbitals.

As discussed previously, the excited state can be relaxed by the emission of characteristic X-ray photons. The wave number of the X-ray photons is expressed by Moseley’s law (Eq. (5.88)). The wave number (i. e., the energy of the character­istic X-ray photons) increases along with the increase of the atomic number, pro­viding information for qualitative analysis. As seen in Figure 4.12, the light elements practically do not emit characteristic X-ray photons, XRF is useful for the elements Z > 20. For the elements 10 < Z < 19, the X-ray photons are absorbed in air and thus can only be measured in a vacuum.

In Figure 10.16, the energy of characteristic X-ray photons emitted by the differ­ent elements is shown as a function of the atomic number. K and L mean the orbi­tals where the vacancies are formed under the excitation, and а, в, and y mean the outer orbitals from which the vacancy is filled. For instance, Ka means that a vacancy on the K orbital is filled with an electron from the next orbital, L.

The sensitivity of X-ray fluorescence spectrometry is influenced by two factors, both of which relate to excitation: the energy of the exciting photons should be higher than the binding energy but not by too much. The excitation is optimal if the energies exciting and the emitted photons are close, but not identical, so they can be separated spectroscopically in the given measuring system. For this reason, the excitation source and the element to be analyzed should be correlated. Practically, the “light” (Z > 20) elements are excited by low energy, and the K lines are measured. The heavy elements are analyzed using the L lines.

The X-ray fluorescence spectrum of a mixture of Fe2O3, ZnO, KBr, Sr(NO3)2, MoO3, AgNO3, CsNO3, and Nd2O3 is shown in Figure 10.17. The exciting source was the gamma radiation of the 241Am isotope, and the detector is SiLi semiconduc­tor detector (as discussed in Section 14.3). The concentrations of the elements in the mixture are Fe: 0.012523 mol/g; Zn: 0.01229 mol/g; K and Br: 0.008403 mol/g; Sr: 0.004725 mol/g; Mo: 0.006947 mol/g; Ag: 0.005887 mol/g; Cs: 0.005131 mol/g; and Nd: 0.005944 mol/g. Since the exciting energy is about 60 keV, the K lines of all elements are detected. As seen, the light elements (nitrogen and oxygen) do not have lines in the spectrum.

Energy (keV)

As in most spectroscopic methods, the intensity of the emitted X-ray photons provides quantitative analytical information. This intensity is expressed by the fol­lowing formula:

_d + *Si

1 _ e srn Фієд sin Ф2єй

MS,£0 1 Ms, i

sin Ф^ sin Ф2єГГ where Si is the sensitivity for the ith element expressed in the mass unit of the pure element; C, is the concentration of the ith element; d is the surface density of the sam­ple (g/cm2); ^S£o and ^s,; are the mass absorption coefficient of the sample for the exciting radiation and the characteristic X-ray photons of the ith element (cm2/g), respectively; and Ф1б(ї and Ф2б(ї are the angles of irradiation and detection related to the surface of the sample.

Equation (10.36) shows that the intensity versus concentration function should be linear. In most cases, the intensity of the characteristic X-ray and the concentra­tion are not in linear relation because the sample contains other elements (such as a
matrix) which are also excited. This effect is called the “matrix effect.” The matrix effect can influence the intensity—concentration relation in two ways:

1. The intensity is smaller than expected from linear intensity—concentration plot. This is the case if the mass absorption coefficient of the matrix is greater than the mass absorp­tion coefficient of the element to be analyzed. The mean atomic number (Eq. (5.74)) of the matrix exceeds the atomic number of the element.

2. The intensity is higher than expected from the linear intensity—concentration plot. This is the case if the mass absorption coefficient of the matrix is smaller than the mass absorp­tion coefficient of the element to be analyzed. The mean atomic number (Eq. (5.74)) of the matrix is less than the atomic number of the element.

Besides the matrix effect, the intensity—concentration plot is influenced by the so-called internal excitation effect. This means that the studied element is excited not only by the exciting radiation but also by the characteristic X-ray photons of elements with higher atomic numbers. As a result, the intensity increases.

In conclusion, we can say that the matrix effect is significant in XRF. This effect is corrected in different experimental and theoretical ways, as summarized in Table 10.6.

In Figure 10.18, the calibration curves for the X-ray fluorescence spectrum of iron is shown when the mean atomic number of the matrix is smaller (boric acid matrix) or larger (barium nitrate matrix), respectively, than the atomic number of the element in question (iron).

The X-ray fluorescence method is used for the direct analysis of samples without any chemical pretreatment, or after chemical preparations (e. g., separation and enrichment). As mentioned previously in this chapter, all elements from calcium to uranium can be analyzed, or, using a vacuum, even the elements that are heavier than sodium can be measured. The concentration range is from about 1 ppm to 100%.

The arrangement of an XRF is shown in Figure 10.19. The excitation source is a gamma emitter radioactive isotope. The characteristic X-ray photons induced in the sample are detected by a SiLi semiconductor detector (as described in Section 14.3).