SATURATION DENSITY OF NUCLEI ON A SURFACE FROM MICROSCOPIC RATE EQUATIONS

Values for the saturation density of nuclei on a surface are obtained from an approximate analysis of the rate equations describing the formation and decay of nuclei of all sizes. The rate equations are reduced to a simplified dimensionless form for each of the following cases: (1) two atoms in the smallest stable nucleus (pairs stable) with possible desorption of single atoms from the surface; (2) three atoms in the smallest stable nucleus with no desorption from the surface. The rate equations do not in fact lead to a strict saturation value of the total number of nuclei, but in practice a convenient saturation point can be defined. In certain limiting conditions expressions are obtained for this saturation density which are similar in their dependence on the incident rate of single atoms and the surface temperature to corresponding expressions which have been derived elsewhere in the literature by other methods. Expressions for the time required for saturation to occur are also derived. No assumptions of thermal equilibrium among the clusters of various sizes are made, and assumptions of a steady-state situation made only where they can be justified from the form of the equations. © 1969.