Relation between crystallite size and dispersion on supported metal catalysts

Universal mathematical relations between the mean relative size of metallic crystallites (d(rel(VS))) and their dispersion (FE) in supported metal catalysts have been developed. The relations are: d(rel)(VS) = 5.01/FE for FE < 0.2, and d(rel(VS)) = 3.32/FE1.23 for 0.2 equal to or less than FE equal to or less than 0.92, where d(rel(VS)) = d(VS)/d(at), (d(VS)) is the volume-surface mean diameter of an assembly of particles of different sizes, and d(at) is the atomic diameter of a given metal. It is shown that for FE > 0.2 the commonly used definition of d(VS) should be modified. The developed relations apply well to various thermodynamically probable crystallite shapes including fee cubooctahedra of varying geometry, icosahedra, surface-reconstructed cubooctahedra, bcc rhombic dodecahedra, and hcp truncated bipyramids. The new relations are more precise than the commonly used equation d(VS) = a/FE, where a is a constant specific to a given metal.