Geometrical Determination of Surface Atom Diffusion Paths

Abstract

Identification of surface atom diffusion paths, as well as their activation energies, is important when analyzing the kinetics of surface phenomena, such as spillover in heterogeneous catalysis. This study developed a geometrical algorithm, using Voronoi tessellation, to derive diffusion paths connecting already identified reasonable adsorption sites. Existence of a diffusion path is presumed when the Voronoi cells of two reasonable adsorption sites share a Voronoi ridge and the line segment connecting the two adsorption sites intersect with the corresponding Voronoi ridge. The algorithm was applied on the rutile TiO₂ (110) and reconstructed CeO₂ (001) surfaces. Nudged elastic band calculations on the obtained paths showed that the activation energy required for hydrogen spillover was 1.2 and 0.6 eV for TiO₂ and CeO₂, respectively. The algorithm is, in principle, applicable to any type of surface and adsorbing atom species. Its ability to systematically obtain reasonable surface diffusion paths without eyeballing is valuable when studying the plausibility of surface diffusion in hydrogen spillover, and other situations, on both simple and complicated surfaces.