A stochastic model of nucleation and subsequent growth of new phase is
lands on solid surfaces is proposed and expressions for the mean induc
tion time and its variance are obtained in an explicit form. The inter
mediate stage of the new surface phase evolution is studied under cond
itions of the supersaturation gradually decreasing as a result of the
growth of the islands. The island size distribution as well as the sup
ersaturation and the fraction of the surface area covered with the new
phase are found as functions of time. It is proved that both the indu
ction period and decrease in surface metastability must be taken into
account when trying to treat the surface reaction kinetics, and some c
onclusions of conventional models with no allowance for the aforementi
oned factors have certainly to be revised.