Concerning the obtaining of effective influence coefficients for X‐ray spectrometric analysis

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A thorough theoretical study of the typical iron–nickel–chromium ternary system confirms the essential variability of influence coefficients with composition, thus accounting for the limited validity of empirical coefficient procedures. The origin and mechanisms of coefficient variation are accurately described, namely by distinguishing between binary or ‘longitudinal’ variation, it being related to either an enhancement effect or the use of polychromatic excitation or possibly both, and ‘transverse’ variations resulting from fluorescence crossed effects as well as tertiary fluorescence if represented. As a consequence a general mathematical expression, including all these effects and exactly matching the theoretical intensity equations, is assigned to the coefficients for the entire range of compositions. On a practical basis, precision considerations allow to simplify these relationships considerably and reduce them to a fairly simple, flexible system of ‘crossed’ influence coefficients. Since it closely conforms to the fundamental principles of fluorescent emission, this new scheme should prove effective for determining multicomponent systems, namely by allowing accurate analysis to be performed over a wide range of compositions ‘without standards’.

Crossed influence coefficients for accurate X‐ray fluorescence analysis of multicomponent systems

Tertian¹,

Sage

1977

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A practical relation between atomic numbers and alpha coefficients

Lachance¹

1980

A first approximation indicates that fundamental alpha coefficients for a given analyte vary as a function of the ratio of their respective atomic number raised to a power. This simple rule applies mainly at the limits (i.e., when the weight fraction of analytei, wi is of the order of 0.0 or 1.0) in cases of absorption and weak enhancement. The relation thus provides a means of generating coefficients for the system i‐k from experimental data obtained on system i‐j and a means of verifying experimental alphas, since arrays of coefficients must show a high degree of concordance.

Mathematical matrix correction procedures for x‐ray fluorescence analysis. A critical survey

Tertian¹

1986

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The complexity of the intensity–concentration relationship in x‐ray fluorescence analysis as well as new requirements for speed and accuracy will induce analysts to resort more and more to mathematical methods for effecting matrix correction. A thorough study of Lachance–Traill coefficients, based on theoretically calculated fluorescence intensities, shows that all ‘binary’ coefficients vary systematically with composition under the usual working conditions with polychromatic excitation, while ‘multicomponent’ coefficients can no longer be represented (i.e. in the form of curves or diagrams) owing to the intricacy of third element effects. For these reasons, we are compelled to turn to a fundamental approach, where two methods are now competing: on the one hand, the classical fundamental parameter method, which permitted the abovementioned investigation, but does not in itself offer a sufficiently coherent solution to the problem of matrix correction; on the other, the new fundamental coefficient method, which accounts for all theoretical implications, but preserves the flexibility and adaptability of the older influence coefficient procedures. Utilizing such effective coefficients in a comparison standard correction algorithm allows one to solve any analytical problem, from the most complicated to the simpler ones, through a kind of ‘à la carte’ procedure. The so‐called empirical algorithms are in principle ineffective for treating the complex corrections which belong to the analysis of compact specimens (e.g. metal alloys). They must be reserved for simpler problems, notably the study of diluted specimens where an experimental calibration remains feasible.