A theoretical characterization method for non-spherical core-shell nanoparticles by XPS.

Core-shell nanoparticles (NPs) are active research areas for their unique properties and wide applications. By changing the elemental composition in the core and shell, a series of core-shell NPs with specific functions can be obtained, where the sizes of the core and shell also influence the properties. X-ray photoelectron spectroscopy (XPS) is useful in this context as a means of quantitatively analyzing such NPs. The empirical formula proposed by Shard [, 2012, (31), 16806-16813] for calculating the shell thickness of the spherical core-shell NPs has been verified by Powell [, 2016, (39), 22730-22738] through a simulation of XPS with Simulation of Electron Spectra for Surface Analysis (SESSA) software. However, real core-shell NPs are not necessarily ideal spheres; such NPs can have rich shapes and uneven thicknesses. This work aims to extend the Shard formula to non-ideal core-shell NPs. We have used a Monte Carlo simulation method to study the XPS signal variation with the shell thickness for several modeled non-spherical shapes of core-shell NPs including some complex geometric structures which are numerically constructed with finite-element triangular meshes. Five types of non-spherical shapes, egg, ellipsoid, rod, rough-surface, and star shapes, are considered, while the size parameters are varied over a wide range. The equivalent radius and equivalent thickness are defined to characterize the average size of the nanoparticles for the use of the Shard formula. We have thus derived an extended Shard formula for the specific core-shell NPs, with which the relative error between the predicted shell thickness and the real thickness can be reduced to less than 10%.