Relation between Crystallite Size and Dispersion on Supported Metal Catalysts

Abstract

Universal mathematical relations between the mean relative size of metallic crystallites (drel(VS)) and their dispersion (FE) in supported metal catalysts have been developed. The relations are: drel(VS) = 5.01/FE for FE < 0.2, and drel(VS) = 3.32/FE1.23 for 0.2 ≤ FE ≤ 0.92, where drel(VS) = dVS/dat, (dVS) is the volume-surface mean diameter of an assembly of particles of different sizes, and dat is the atomic diameter of a given metal. It is shown that for FE > 0.2 the commonly used definition of dVS should be modified. The developed relations apply well to various thermodynamically probable crystallite shapes including fcc 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 dVS = a/FE, where a is a constant specific to a given metal.