A distance correction method for improving the accuracy of particle coal online X-ray fluorescence analysis - Part 1: Theoretical dependence of XRF intensity on the distance

During online X-ray fluorescence (XRF) measurement, the distance from XRF spectrometer to the sample surface always changes due to the rough surface textures of pulverized coal, resulting in changes in the X-ray fluorescent intensity and inaccuracy of online XRF measurement. To solve the impact of the sample's rough surface textures on the measurement accuracy, the theory and validity details of the dependence of XRF intensity on the distance as well as the comparison of the formula derivation and experimental verification were elaborated in the present research. A typical XRF calculation model has been built for theoretical derivation. The expression of the relationship between the XRF intensity and the distance from XRF spectrometer to sample surface was derived, where the variation of the distance influenced five physical phenomena: (1) absorption of X-rays by the air, (2) irradiated surface area of the samples, (3) changes in exit angle, (4) changes in solid angle and (5) absorption of X-ray fluorescence by the air. The intensities of the Fe Kα spectral lines in iron were calculated and agreed with the experiments very well, indicating that the expression of the dependence was accurate. The dependence of X-ray fluorescence intensity on the distance is the theoretical basis of the distance correction method to improve the accuracy of online XRF analysis techniques in industrial processes.