PERFORMANCE OF TXRF and GI-XRF ANALYSES - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 242

individual elements. The finally applied standard solutions should have a
volume of about 1 ml and should contain two to six different elements. One
element, for example, cobalt or copper, which is chosen as reference element,
must be present in all standard solutions.
A droplet of each solution with a volume of about 1-10 μ l (possibly 100 nl) is
pipetted onto a cleaned carrier and dried by evaporation. From the residues,
spectra are recorded in one or several definite excitation modes, as demon-
strated in Figure 4.13a-c. The net intensity for the individual elements is
determined and the relative sensitivities are calculated by the formula

N j = c j S j

N ref = c ref S ref

(4.6)

where S is the relative sensitivity, N is the net intensity, and c is the concentra-
tion of either the different elements j or the reference element ref as indicated.
The quantity S ref can generally be set to 1 because only relative sensitivities
have to be determined. Actually, a single determination per element is suffi-
cient. However, it is preferable to apply several solutions with different
concentrations and to repeat the measurements. The averaged values of
each element should have a coefficient of variation < 5%.
Figure 4.14 provides an overview of relative sensitivities of detectable
elements, determined for the three excitation modes defined in Section
4.2.1. The semilogarithmic plot describes their dependence on the atomic
number of the elements, detected by either their K or their L peaks. The
six curves span three orders of magnitude with a steady course. Each curve
shows a maximum sensitivity reached for a particular element in accordance
with Figure 4.11.
Above all, it should be emphasized distinctly that the relative sensitivities
are independent of the matrix of the applied samples. For the case just
described, the matrix water was separated by evaporation and only oxides,
hydroxides, and further light compounds of the analyte elements remained as
residues. If the original solution, however, is a saline or a gelatinous solution, a
mineral or an organic matrix, respectively, will form the residue. Nevertheless,
the relative sensitivities of elements determined with these matrices correspond
to each other with a deviation of < 8% [51].
Relative sensitivities can even be calculated from theory, which is excep-
tional. According to Equation 2.37, the sensitivity can be expressed by

S j Kg j ω j f j τ = ρ (4.7)

j ; E 0

where S j is the sensitivity of the analyte, g is the relative emission rate of the
respective element peak in its series, ω is the fluorescent yield of the selected K
or L peaks, f is the jump factor of the respective absorption edge, and

E 0 is
the photoelectric absorption coefficient for the primary beam with a photon

τ = ρ