X-Ray Fluorescence Analytical Techniques - CNSTN : Centre ...

A widely used method is non-linear least squares fitting of the spectral data with an
analytical function. This algebraic function, including all important parameters, such as the
net areas of the fluorescent lines, their energy, resolution, etc., is used as a model for the
measured spectrum. It will consist of the contribution from all peaks (modified Gaussian
peaks, with corrections for low-energy tailing, escape peaks, etc.) within a certain region of
interest and the background (described by, for example, linear or exponential polynomials).
The optimum values of the parameters are those for which the difference between the model
and the measured spectrum is minimal. Unfortunately some of these parameters are nonlinear,
which places some importance on the minimization procedure (usually the Marquardt
algorithm is used).
In another frequently used approach the discrete deconvolutions of a spectrum with a
so-called top-hat filter suppresses the low-frequency component, i.e. the slowly varying
background. A severe distortion of the peaks is introduced. But applying this filter to both the
unknown spectrum and well defined, experimentally obtained, reference spectra, a multiple
linear least-squares fitting to the filtered spectra will result in the net peak areas of interest. A
disadvantage of this method is that reference and unknown spectra should be acquired under
preferably identical conditions; especially, energy calibration changes of
more than only few e can generate large systematic errors.
IV. Detector Artefacts
IV.1 Escape Peaks
A photon is detected in the Si(Li) diode primarily by ionizing the K-shell of a Si atom
besides the interaction of elastic and inelastic scattering. Subsequently a Si-Kα photon is
produced. If the Si-Kα is absorbed within the active volume of the detector, the resulting
amplitude pulse will have the amplitude which is proportional to the original photon energy.
If the Si-Kα photon escapes the active volume of the detector, the event will be recorded at an
energy which is too low by an amount equal to the energy of the escaping photon. Thus, a
peak with an energy E-E(Si-Kα) will occur in the spectrum. Figure II.8 shows this
schematically.