On the statistics of adsorption: Active clusters in alloy catalysts

Abstract

The dependence of the sticking coefficient S on the surface coverage θ like S ∼ (1 − θ) n is well known. A similar formula holds for the dependence of the sticking coefficient on the surface concentration of an active species of atoms, x s (diluted by some inactive species) S ∼ x n s. Here n denotes the number of active atoms per adsorption site ( n = 2 for bridge sites, n = 4 for fourfold hollow sites and so on). This formula is especially useful in showing the strong influence of small amounts of inactive atoms on the catalytic activity involving the adsorption of large molecules, e.g. C x H y . Its validity however is limited to the case of a purely statistical mixture of active and inactive atoms. If there is an interaction between the surface atoms, e.g. a tendency towards clustering of inactive atoms, the local probabilities of active clusters are changed forcing a corrective factor in the above equation. This factor is calculated for the simple quadratic and the plane triangular lattices using the method of Kikuchi for the cases: (a) pair. square (= fourfold hollow adsorption site), two squares, square of four squares, on the sq lattice; (b) triangle (= threefold hollow site), adjacent pair of triangles, hexagon (six triangles), on the pt lattice. It can be shown that especially an attraction between active and inactive atoms leads to strong deviations from the simple formula even at moderate interaction enthalpies.