Stochastic model for complex surface-reaction systems with application toNH3formation

A stochastic model is introduced that is appropriate to describe surface-reaction systems. These reaction systems are well suited for the description via master equations using their Markovian behavior. In this representation an infinite chain of master equations for the distribution functions of the state of the surface, of pairs of surface sites, etc., arises. This hierarchy is truncated by a superposition approximation. The resulting lattice equations are solved in a small region which contains all of the structure-sensitive aspects and can be connected to continuous functions which represent the behavior of the system for large distances from a reference point. In the present paper, we focus our interest on the development of the formalism and its use when applied to the formation of ${\mathrm{NH}}_3$. The results obtained (phase-transition points and densities of particles on the surface) are in agreement with Monte Carlo and cellular-automata simulations. The stochastic model can easily be extended to other reaction systems and is therefore an elegant alternative to the description via Monte Carlo and cellular-automata simulations.