STOCHASTIC-MODEL FOR THE A-REACTION - ISLAND FORMATION AND COMPLETE SEGREGATION(B2 SURFACE)

In this paper we introduce a stochastic model for the A + 1/2B2 --> 0 reaction on a square lattice. Reaction between an A and a B particle o ccurs if they are nearest neighbors on the lattice. To this system whi ch includes adsorption and reaction steps we add the effect of A-diffu sion and A-desorption. We describe the model in terms of master equati ons using the Markovian behavior of the system. The equations are trun cated at a certain level via a modified Kirkwood approximation. The re action is in this paper introduced between particles which are nearest neighbors on the lattice. This approach which is different from a pre vious article [J. Mai et al, J. Chem. Phys. 98, 10017 (1993)] requires a special treatment of the stochastic equations and the correlation f unctions. In particular the Kirkwood superposition approximation, whic h is used to truncate the hierarchy of equations, has to be modified. The resulting system of lattice equations is solved in a small region around a reference point. The solution is connected to continuous func tions which describe the system behavior for larger distances. This sy stem shows kinetic phase transitions which separate the reactive regim e from two nonreactive states where the lattice is completely covered by A or B. We study the location and the character of the phase transi tions in detail. With the help of correlation functions we identify th e different phases of particles on the lattice. Island formation and s egregation of the particles on the lattice are found to be dominant pr ocesses. It is established that finite lattices which have to be used in simulations can be seriously inadequate and miss physical processes . This problem does not appear in the ansatz presented here.