A simple equation to determine the shell thicknesses of core–shell nanoparticles based on XPS data of their elemental composition

Abstract

A simple analytical expression is obtained relating the radius of the core, the thickness of the shell of nanoparticles, and the intensities of X-ray photoelectron lines from the core and shell, recorded during one experiment. The effective evaluation of the proposed equation was verified by comparison with the results of calculations of the parameters of core–shell nanoparticles (NPs) using known methods, as well as by comparing the results of ratios between the radius and thickness of the shell of specific NPs and their evaluations using the transmission electron microscopy method. The formula proposed in this work also allows using EDS data to estimate the core–shell parameters of nanoparticles. It is shown that the equation obtained in this work is not inferior to the solutions of the already existing approximate equations in terms of the accuracy of the determined parameters, but it is more convenient to use, since the data of one experiment are sufficient for its application. A simple approach to determine the thickness of a shell of NPs based on information about the elemental composition of the core–shell of NPs measured by X-ray photoelectron spectroscopy is developed.