Evaluation of effects of irregular shape on quantitative XRF analysis of metal objects

Quantitative XRF analysis of metal alloys can be obtained by using the general fundamental parameter method based on the comparison of x-ray line fluorescence intensities with those obtained from reference standard pellets in identical experimental conditions. Corrections for auto absorption and secondary excitation effects are fundamental to obtaining quantitative results. When analyzing a real object with irregular, or at least nonpellet-shaped, geometry and/or of incorrect positioning, an additional correction factor for x-ray fluorescence line intensities must be entered. In this paper we review the problem of the contributions to the error specific to an irregular surface or incorrect positioning intrinsic to the fundamental parameter method, in the more enlarged context of considering a real experimental setup in which irradiation and detection angles are not exactly constant, as assumed in the fundamental parameter method. They are accounted for by the corrective irregular shape factors. In principle, these factors must be separately calculated for each value of excitation and characteristic x-ray energies, and the relative precision in the quantitative determination of elemental concentrations with the fundamental parameter method can be estimated from the relative amplitude of the variation of shape factor values depending on the exciting energy spectrum. One obtains the result that the correction due to irregular shape or incorrect positioning of the object under examination tends to the limit 1, or, more generally, to a constant value independent of the excitation and emission x-ray energies in the limiting case where the direction of the exciting radiation coincides with that of the detected fluorescence x-rays. The results of calculations of the relative precision of XRF quantitative analysis are shown for gold-based alloy objects in some specific cases of surface roughness and positioning of the object. Dispersion around the nominal values for the angles of incoming and outgoing x-ray directions is assumed as determined by the geometric conditions in two selected instrumental setups. A nominal value of 45 degrees was assumed for both the angles in the first case. In the second case, we considered an irradiation setup where the condition of coincidence for incoming and outgoing x-ray directions is nearly achieved by employing an annular silicon drift detector (SDD) with a central hole, which allows the passage of the exciting x-rays. An interesting result obtained in the latter case is that, looking only at the dependence on the irregular shape, an attainable precision on the order of < 1%o can be achieved. In view of the possible applications of quantitative XRF analysis to jewellery, employing SDD detectors capable of very high counting rates should allow a statistical error under the above-mentioned limit in a reasonably short measuring time. However, concerning the error deriving from intrinsic x-ray tube instability, an investigation aimed at achieving a stable enough system is still needed.