ZAFG Method for Quantitative Characterization of Spherical Particles: Deriving a Universal Equation for Geometrical Correction

Abstract

This study introduces a universal equation to calculate the geometrical correction factor (G) as the fourth factor in the conventional ZAF method for quantifying spherical particles (specifically, NIST-K411 glass microspheres mounted on bulk carbon substrate). Note that the fluorescence correction factor (F) is not considered in this study. Our findings demonstrate that the G factor, as a function of the particle diameter (D) and the range of emitted X-rays in a bulk sample (Xe), provides the best model. Xe depends on the chemical composition and accelerating voltage. We observed excellent agreement between the G factor predicted by our model and experimental data obtained from NIST-K411 standard particles. Our results show that when Xe is greater than D, the G factor decays exponentially, independent of the incident electron energy, X-ray lines, and chemical composition of the particles. We also found that when DXe > 1, the particle behaves as a bulk sample, and G = 1. Notably, our data indicate that the G factor depends only on DXe, not on the chemical composition or beam energy.