PERFORMANCE OF TXRF and GI-XRF ANALYSES - Total-Reflection X-Ray Fluorescence Analysis and Related Methods - page 238

metal filings of the pure elements or even by pure gases pouring into the sample
chamber. If a complete library of (nearly) all the elements is available, this
technique can provide a qualitative analysis. To this end, the presence of all
these elements has to be checked one after the other.
In most cases, however, the presence of only a few elements is confirmed and
even their approximate concentrations are estimated. Usually, the spectra of
the specimen in question and of a specimen defined as the reference are
compared. Equality of the spectra indicates the identity of both specimens;
dissimilarity means just the opposite. Such fingerprint analyses are useful for
some typical applications. They are used to prevent a mix-up of alloys before
processing, to distinguish between genuine art objects and fakes, and to
scrutinize suspect materials in forensics.

4.4QUANTITATIVEMICRO-ANDTRACEANALYSES

Intensity calculations for a thin homogeneous layer on a substrate have been
carried out in Section 2.4.2 using the complex Fresnel formalism. However, a
simpler approximation for the excitation of a specific element x with mono-
chromatic radiation of energy E 0 can be derived [50]. It leads to the background
corrected fluorescence intensity or net intensity N x , which is dependent on the
mass fraction or concentration c x of the relevant element in the layer:

1 exp μ = ρ

matrix ρ d

N x c x S x N 0 (4.1)

μ = ρ

matrix

S x is the so-called sensitivity of the element according to Equation 2.37 for the
mentioned excitation. ( μ / ρ ) matrix is the mass-absorption coefficient of the layer
matrix with respect to the excitation energy E 0 . The energy of a principal
element peak is E x , the density of the layer matrix is ρ , its thickness is d ,and N 0
is the intensity of the exciting monochromatic beam. The fraction of
Equation 4.1 represents the mass attenuation effect of the layer matrix. For
photon energies below 20 keV, it is mainly determined by mass-absorption and
not by scattering.
The quantity ( μ / ρ ) matrix includes the mass-attenuation of the primary incom-
ing beam and of the secondary emerging beam, corrected for geometry. It can
be calculated from

X

μ = ρ c i μ = ρ

i ; E 0 = sin α

μ = ρ

i ; E i = sin β

(4.2)

matrix

where c i is the mass fraction of the different elements i in the layer matrix, ( μ / ρ )
is its tabulated mass-absorption coefficient for photon energy E 0 and E i ,
respectively, α is the glancing angle of the exciting beam, and β is the respective
take-off angle of the fluorescence radiation.