An Overview of XRF Basics

1. Fundamental Principles

1.4 Excitation of Characteristic Radiation in Sample Material

The Bremsspektrum and the characteristic radiation of the X-ray tube's anode material are used to excite the characteristic radiation of the elements in the sample material. It is very important to know that an element in the sample can only be made to emit X-rays when the energy of the incident X-ray quanta is higher than the binding energy (absorption edge) of the element's inner electrons. If the sample is irradiated with a tube high-voltage of 20 kV, the maximum energy of the quanta emitted from the tube is 20 keV. Hence, it is impossible, for example, to excite the K radiation of the elements that have an atomic number Z ≥ 43 as their K binding energy is greater than 20 keV. Excitation of the K radiation of heavier elements is achieved with a generator setting of 60 kV.

All spectrometer manufacturers use rhodium (Rh) as the standard anode material because the characteristic energies of this element are simultaneously suitable for exciting both heavy and light elements.

Energies and wavelengths of rhodium's characteristic lines, and the heaviest element that can be excited with the appropriate line in each case, are listed in Table 2.

Table 2: Rhodium's characteristic lines
Line	Energy	Wavelength	Heaviest Element
Rh Kα₁	20.214 keV	0.0613 nm	Molybdenum (Mo)
Rh Kα₂	20.072 keV	0.0617 nm	Molybdenum (Mo)
Rh Kα₁	22.721 keV	0.0546 nm	Ruthenium (Ru)
Rh Lα_1,2	2.694 keV	0.4601 nm	Sulpher (S)
Rh Lα₂	2.834 keV	0.4374 nm	Chlorine (Cl)

The following can be extracted from Table 2:

The K lines of the heavy elements from rhodium to tantalum (Ta) can, in principle, only be excited with the Bremsspektrum of the rhodium tube because the energy of the rhodium lines is insufficient to do it. A generator setting of 60 kV is recommended for such cases.
Elements up to molybdenum are excited by the Rh K radiation. The Rh-Kβ₁ radiation can even excite the element ruthenium but it is of lower intensity than the K-alpha radiation.
The light elements up to sulphur are excited very effectively by the Rh L radiation.
The Rh-Lβ₁ radiation can excite the element chlorine but is of a lower intensity. The available intensity of the Rh L radiation depends on the thickness of the tube's beryllium exit window.

Instead of rhodium, other elements can be used as an anode material for special applications. Tungsten (W) and gold (Au) are particularly suitable for exciting heavier elements with the Bremsspektrum. Chromium (Cr) is often used in side-window tubes for exciting lighter elements. Molybdenum (Mo) is frequently used for the interference-free measurement of rhodium and, for example, cadmium.

The use of the rhodium end-window tube as a "universal tube" is justified because the light elements can be excited far more effectively with the Rh L radiation than with the K radiation of a chromium anode. Moreover, instrument technology is so advanced nowadays that measuring rhodium itself (or cadmium) presents no problem.

Absorption, the Mass Attenuation Coefficient

Passing through matter weakens the intensity of X-rays. The degree of this weakening depends on both the radiation energy and the chemical composition of the absorbing material (e.g. the sample). Heavier elements absorb better than light ones: 1 mm of lead absorbs practically all of the higher-energy radiation occurring during X-ray fluorescence, whereas 1 mm of polypropylene is more or less permeable to X-rays. Low-energy X-ray quanta are absorbed more readily than quanta with higher energy (= short wavelengths): the quanta emitted by the element boron, for example, have a very low energy of 0.185 keV (= 67 nm) and are almost completely absorbed by even 6 µm of polypropylene foil.

If an X-ray with quanta of energy E and an intensity of I_O pass through a layer of material, e.g. 1 mm sheet of pure iron (Fe), the ray emerging from behind the iron layer will only be left with the intensity I < I_O as a result of the absorption. The relationship between I and I_O after the transition through the layer thickness x is described by the law of absorption:

I = I_Oe^-µx

µ = linear absorption coefficient

The linear absorption coefficient has the dimension [1/cm] and is dependent on the energy or the wavelength of the X-ray quanta and the special density ρ (in [g/cm³]) of the material that was passed through.

If the iron sheet in the above example is replaced by a 1 mm layer of iron powder, the absorption is less because the density of the absorber is lower. Therefore, it is not the linear absorption coefficient that is specific to the absorptive properties of the element iron, but the coefficient applicable to the density r of the material that was passed through

µ / ρ = mass attenuation coefficient

The mass attenuation coefficient has the dimension [cm²/g] and only depends on the atomic number of the absorber element and the energy, or wavelength, of the X-ray quanta.

Fig. 6 illustrates the schematic progression of the mass attenuation coefficients depending on the energy or wavelength.

Fig. 6: Schematic progression of the mass attenuation coefficient of energy or wavelength

As shown in Fig. 6:

The overall progression of the coefficient decreases as energy increases, i.e. the higher the energy of the X-ray quanta, the less they are absorbed.
The rapid changes in the mass attenuation coefficient reveal the binding energies of the electrons in the appropriate shells. If an X-ray quanta has a level of energy that is equivalent to the binding energy of an atomic shell electron in an appropriate shell, it is then able to transfer all its energy to this electron and displace it from the atom. In this case, absorption increases sharply. Quanta whose energy is only slightly below the absorption edge are absorbed far less readily.

Example:
The K radiation of iron (Fe) is absorbed less by its neighbouring element manganese (Mn) than by the element chromium (Cr) as Fe Ka1,2 is below the absorption edge of Mn but above that of Cr.

1.4.1 Layer Thickness, Saturation Thickness

The more readily the radiation of an element in the sample material is absorbed, the smaller is the layer of the sample from which the measurable radiation comes. A K-alpha quantum from the element molybdenum (Mo Kα₁, 17.5 keV) has a far greater chance of being measured at a depth of 0.5 mm from the analysis surface of a steel sample than a quantum from carbon (C Kα_1,2, 0.282 keV). As a consequence, a specific layer thickness is analyzed for each element, which depends on the specific energy of the used element line. The analysis of very light elements e.g. in solids (such as Be, B, C, N and O) is comparable with a plain surface analysis as their radiation originates from a few atomic layers. Practically all the radiation from deeper layers is fully absorbed within the sample.

A sample is referred to as being infinitely thick for a radiation component if it is sufficiently thick to completely absorb the radiation from the rear. Thus, a 1mm thick sample of cement is infinitely thick for Fe Kα_1,2 radiation as the radiation from the rear of the sample is almost fully absorbed in the sample material. The thickness of a sample that is sufficient to absorb the radiation of an element line to a high degree (e.g. 90%) is called the saturation thickness.

Caution is advised with sample materials that are composed of light elements such as liquids or plastics (hydrocarbons). Here, for the high-energy radiation of heavier elements, high saturation thicknesses that cannot be used in practice (e.g. 10 cm) are easily attainable. Hence, where these material groups are concerned, it must be ensured that identical sample quantities are used for quantitative analysis as the measured intensity may depend on the thickness of the sample.

Applying liquid sample materials to filter paper is a method of almost completely preventing the effects of absorption. The term for this is infinitely thin samples.

Nowadays, the calculation of those layer thicknesses in defined samples that contribute to the analysis is integrated into modern software packages.

1.4.2 Secondary Enhancement

Secondary enhancement, i.e. those X-ray quanta that are produced as a result of the effect of the sample elements' absorbed radiation, is closely linked to produced X-rays' absorption in the sample.

Example:
A Si Kα₁ quantum is produced in a sample by the effect of an X-ray tube's radiation. Inside the sample, it can be absorbed again by transferring its energy to an Al K electron. This can then emit an X-ray quantum itself. The silicon radiation thus contributes to the X-ray emission of the aluminium. This is referred to as secondary enhancement (Fig. 7).

In quantitative analyses, the effects of absorption and secondary enhancement may have to be corrected. Modern software packages offer a selection of correction models (matrix correction or inter-element correction) for this purpose.

Fig. 7: Secondary enhancement

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