Particle size effects in X‐Ray emission analysis: Simplified formulae for certain practical cases

Abstract

The Berry-Furuta-Rhodes model is used to derive formulae for the characteristic X-ray intensity in specimens of 'non-infinite' thickness, as a function of particle size both for discrete values and for continuous distributions, including the Junge distribution for aerosols. Significant simplifications in otherwise complex formulae are obtained for a number of cases of practical importance, namely, thin specimens, monolayers and low or high packing fractions. The simplified working formulae consist of the equation for a thin, homogeneous specimen, multiplied by a grain size dependent factor. This factor is a function of fluorescent grain size only, so eliminating most inter-element effects. Practical applications of these formulae are discussed, with special reference to energy dispersive X-ray fluorescence analysis of thin briquetted specimens and of aerosols collected on filters.

Source apportionment of particulate matter in Europe: A review of methods and results

“…Even though these tracers may be determined in parallel using correction factors or by additional techniques (in the case of Na, Maenhaut & Cafmeyer, 1998;Rhodes & Hunter, 1972), this might introduce a bias in the analysis. Sensitivity studies on the influence of the uncertainty on model results are rarely mentioned in the literature even though often studied to ensure the robustness of results.…”

Measurement Methods to Determine Compliance with Ambient Air Quality Standards for Suspended Particles

“…Particles larger than ~3 urn absorb some of the emitted x-rays for light elements such as sodium, magnesium, aluminum, silicon, phosphorus, sulfur, chlorine, and potassium. Methods 647 ' 652674 - 681 have been developed to compensate for this absorption; these methods involve assumptions about particle size and composition that are accurate for most, but not all, cases of ambient air sampling. Deposits on fiber filters experience x-ray absorption biases for light elements because the particles penetrate deep into the filter, and the intervening filter material attenuates the emitted x-rays.…”

Radiometric diameter concept and exact intensities for spherical particles in x‐ray fluorescence analysis

“…x 100 I(Eqn 6 ) (7) This error, identical for a single particle and for a particle monolayer sample (Eqn 7), is reasonably small for most of the ptR values, but peaks at 5.2% for a ptR value of 1.55. Still, in practice, for semiquantitative estimations of the particle size effect, the error seems acceptable.…”