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/FE 1.23 for 0.2 ≤ FE ≤ 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 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 d VS = a /FE, where a is a constant specific to a given metal.