Читать книгу X-Ray Fluorescence Spectroscopy for Laboratory Applications - Michael Haschke, Jörg Flock - Страница 30

The information depth is an important parameter for the assessment of sample preparation. It depends on the energy of the fluorescence radiation of the elements of interest as well as on the matrix of the sample. In the case of XRF, the incident radiation penetrates into the material, is absorbed on its way through the sample, and thereby generates fluorescent radiation. The radiation must reach the sample surface in order to be detected by the spectrometer. On its way, the fluorescence radiation is attenuated, i.e. only the radiation from a well-defined sample layer reaches the sample surface. This is referred to as the information depth.

Table 3.1 Preparation technologies for solid samples.

Sample type	Compact and homogeneous	Compact and inhomogeneous	Powder-like	Liquid
Example	Metals, glasses	Minerals (ores, rocks, etc.), glasses, metal alloys, metal swarfs	Minerals (ores, slags, soil, sludge, etc.) powder, dust	Solutions, melts
Homogenization	Usually not necessary, where appropriate remelting	Metals, glasses: remelting ⟹ transfer into compact homogeneous material (from here see compact and homogeneous) Minerals: crushing, grinding ⟹ transfer into powder-like material or direct analysis ⟹ position-sensitive analysis (see Chapter 13)	Grinding, digestion, melting, solution	Stirring, shaking, where appropriate, filtering of solid components (as powder-like material)
Shaping	Sawing, cutting, turning, drilling, milling		Pouring of the powder in sample cups, pressing of disks, preparation of melted disks	Pouring in sample cups
Surface preparation	Polishing or milling with a roughness adapted to the elements to be analyzed		Realized with shaping	Given by covering of the sample cup

Figure 3.1 Information depth of fluorescence radiation.

Because the energy of the primary radiation must be higher than that of the fluorescence radiation, the penetration depth is always greater than the information depth. These geometric relations are shown in Figure 3.1.

The information depth d_information of the radiation can be estimated from Lambert–Beer's law (2.5), as well as from the measurement geometry shown in Figure 3.1. If it is assumed that about 95% of the fluorescence radiation comes from this layer, the information depth is calculated as

(3.1)

This relation for a few different matrices and ψ = 90° is shown in Figure 3.2.

For the fluorescence energy of a specific element, the information depth is shown here for different matrices. Since the information depth is only an approximate measure of the layer thicknesses contributing to the measurement signal, this representation is sufficient for an estimation. For other matrix compositions, it is possible to interpolate between these relations. It should also be taken into account that the information depth in Figure 3.2 is given for a perpendicular incidence. Usually however, there is an incident angle close to 45°, which reduces the information depth according to (3.1) by a factor of about 1.4.

Figure 3.2 Information depth for different matrices.

Table 3.2 Information depth for different fluorescence lines in various materials.

Fluorescence line	Energy (keV)	Graphite (μm)	Silicon oxide (μm)	Steel (μm)	Lead (μm)
B-Kα1	0.18	4	0.13	0.01	0.01
F-Kα1,2	0.68	3.7	1.7	0.4	0.3
Mg-Kα1	1.25	20	7	2	1
S-Kα1	2.31	116	15	10	5
Cr-Kα1	5.41	1 600	100	104	7
Ni-Kα1	7.48	4 000	300	30	17
Cd-Kα1	23.17	14 500	8 000	700	77

Table 3.3 Information depth and accumulated intensity in the case of 10 wt% Ni in different matrices.

Matrix	Mass absorption coefficient (g/cm2)	Information depth (μm)	Count rate in case of 10 wt% (cps)
Steel	333	10.3	6 000
Aluminum	60	170	35 000
Polyethylene	15	1 300	170 000

Table 3.2 gives an overview of the information depth of different fluorescence lines in various materials. It shows, the information depth covers 6 orders of magnitude for these materials. This has to be considered for the sample preparation. The surface layer of the material to be analyzed needs to be homogeneous and representative of the corresponding fluorescence line in this material.

The influence of a different absorption of fluorescence radiation in the matrix on the information depth and the measured intensity is demonstrated in Table 3.3 for the element Ni. It shows very strong changes not only in information depth but also in accumulated intensity depending on the matrix. A factor of almost 30 is observed for the same content of Ni in different matrices. These changes must be considered in case of quantification.

Considering these information depths, the volume contributing to the measurement signal as well as the corresponding sample mass can be estimated depending on the excited sample surface, the sample matrix, and the element under consideration. Table 3.4 summarizes the volume and the analyzed mass in metallic and mineral matrices for different spot diameters. These volumes and masses are very small in metallic or mineral matrices, i.e. only a few mm³; or mg contribute to the measurement signal, but in the case of light matrices such as aqueous solutions or polymers they can be relatively large.

Table 3.4 Estimations of the sample volume and mass that contribute to the measured signal.

Excited area (mm)	Volume/analyzed mass for
Si in SiO2	Si in steel	Fe in SiO2	Fe in steel	Cd in aqueous solution
∅ 20	6 mm3	0.6 mm3	72 mm3	23 mm3	7500 mm3
16 mg	5 mg	190 mg	175 mg	7.5 g
∅ 0.3	0.001 mm3	0.0001 mm3	0.005 mm3	0.0015 mm3	1.7 mm3
0.003 mg	0.0016 mg	0.015 mg	0.04 mg	1.7 mg

The sample preparation must therefore guarantee that the material of this surface layer within its information depth sufficiently characterizes the material to be analyzed. This means

 that in the case of surface contamination it is important to ensure that their thicknesses are small compared to the information depth and thus cannot influence the analytical result too much;

 that the surface roughness should be small against the information depth so that the absorption lengths of the fluorescence radiation are not influenced by topological effects – this influence can be reduced by rotating the sample during the measurement; or

 that for light matrices and high fluorescence energies, the information depth can exceed the sample thickness. Then the measured fluorescence intensity depends not only on the concentration of the analyte but also on the sample thickness. This is shown in Figure 3.3 for the intensities of Cd in polymer samples of different thicknesses. This problem can be solved by using the same amount of sample material for all analyzed samples, i.e. both measured and reference samples.

However, this problem is somewhat mitigated because both the incident and the fluorescence radiation hit the sample at an angle less than 90° and, therefore, the analyzed volume is limited (see Figure 3.4). This means that the sample thickness does not have to be greater than the saturation thickness and in the case of the detection of heavy elements in light matrices, sample thicknesses that are less than the information depth can also generate sample-independent fluorescence intensities in case of an appropriate excitation geometry. Nevertheless, this analyzed sample volume defined by the excitation geometry must also be considered during quantification.