Calibration inter-elemental correction

Related to the above-described inter-elemental correction method, the need for a proxy element can be obviated at the expense of resorting to sequential analysis of the sample and the calibrator, that is, with external gravimetric calibration. Although this technique is not favored by all, it has played a major role, for example, in the recent re-evaluation of the atomic weight of zinc [13]. 

For complicated samples where matrix or interelement effects are present, a linear calibration curve may not be valid, and one should consider using an empirical model for concentration correction. This usually requires a large set of standards of similar composition to the unknown, which generally makes analysis rather impractical. Inter-element effects can be calculated from a basic knowledge of physical parameters in combination with the appropriate use of samples of known composition, pure elemental standards or composite standards. 

XRF nowadays provides accurate concentration data at major and low trace levels for nearly all the elements in a wide variety of materials. Hardware and software advances enable on-line application of the fundamental approach in either classical or influence coefficient algorithms for the correction of absorption and enhancement effects. Vendors software packages, such as QuantAS (ARL), SSQ (Siemens), X40, IQ+ and SuperQ (Philips), are precalibrated analytical programs, allowing semiquantitative to quantitative analysis for elements in any type of (unknown) material measured on a specific X-ray spectrometer without standards or specific calibrations. The basis is the fundamental parameter method for calculation of correction coefficients for matrix elements (inter-element influences) from fundamental physical values such as absorption and secondary fluorescence. UniQuant (ODS) calibrates instrumental sensitivity factors (k values) for 79 elements with a set of standards of the pure element. In this approach to inter-element effects, it is not necessary to determine a calibration curve for each element in a matrix. Calibration of k values with pure standards may still lead to systematic errors for unknown polymer samples. UniQuant provides semiquantitative XRF analysis [242]. 

Wang et al proposed a multivariate dominant factor based non-linearized PLS model for LIBS measurements. In constructing such a multivariate model, non-linear transformation of multi-characteristic line intensities according to the physical mechanisms of a laser-induced plasma spectrum were made, combined with a linear-correlation-based PLS method, to model the non-linear self-absorption and inter-element interference effects. Moreover, a secondary PLS was applied, utilizing information from the whole spectrum to correct the model results further. The proposed method showed a significant improvement when compared with a conventional PLS model. Even compared with the already improved baseline dominant-factor-based PLS model, the PLS model based on the multivariate dominant factor yielded the same calibration quality while decreasing the RMSEP. 

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