Calculation of catalyst crust thickness from full elemental laser-induced breakdown spectroscopy images

We propose a methodology to compute the crust thickness of an element in an egg-shell catalyst from a two-dimensional elemental map. The methodology handles two important catalyst shapes: infinite extrudates of arbitrary section and spheres. The methodology is validated with synthetic analytical profiles on simple shapes (cylinder and sphere). Its relative accuracy is shown close to few percent with a decrease inversely proportional to the square root of the number of sampled pixels. The crust thickness obtained by this method from quantitative Pd maps acquired by laser-induced breakdown spectroscopy are comparable with values obtained from electron-probe microanalysis profiles. Some discrepancies are found and are explained by the heterogeneity of the crust thickness within a grain. As a full map is more representative than a single profile, fast mapping and the methodology exposed in this paper are expected to become valuable tools for the development of new generations of egg-shell deposited catalysts.