About the assessment of sampling error and representative sample in X-ray fluorescence analysis of mineral powders

Abstract

The assessment of laboratory sampling errors in X-ray fluorescence analysis (XRF) of mineral powders ground to a particle size less than 75 μm is important when analyzing specimen portions less than 100–300 mg. The sampling error can be found from Poisson statistics, which allows one to estimate the variations in the number of mineral grains containing an analyte in a powder sample of a fixed mass. However, the absorption of X-ray radiation in the sample imposes a limitation on the analyzed mass due to the low penetration depth of X-rays, especially in the energy region below 4 keV.In this paper, we propose the sampling error estimation based on Poisson statistics taking into account the size of powder particles in comparison with the penetration depth of X-rays. Two limiting cases are considered, when the penetration depth is greater or less than the size of the grains containing the analyte. Zircon, ilmenite, and quartz were considered as grains containing the analyte, and boric acid and clay were taken as matrices. Measurements were carried out with wavelength dispersive XRF spectrometer. It was shown that the sampling errors obtained experimentally for different model mixtures are close to the sampling errors calculated using Poisson statistics. The described model of quartz inclusions in clay matrix was used to explain the relatively low sampling error in determining the main components Al2O3, SiO2, K2O in course-grain Neolithic ceramics.