Bond energy formulations of heterogeneous nucleation theory

Abstract

Condensation of a vapour beam on s substrate depends on the formation and growth of stable nuclei. By expressing the volume and surface energies of the capillarity model and also the cluster energies of the atomistic model in terms of nearest-neighbour bond energies, these two approaches to nucleation theory have been put into forms which may be directly compared. This has revealed that their differences are confined to: (i) continuous and discontinuous variation of critical sizes; (ii) a numerical difference in the value of supersaturation for small nuclei which has the effect in the capillarity model of predicting a larger size for the critical nucleus and a lower nucleation rate; (iii) a compensating numerical difference which is revealed in a comparison of cluster energies, using the bond energy formulation, in which the idealized shapes of the capillarity model give higher cluster energies, smaller critical nuclei and a higher nucleation rate. It is shown that under nucleation conditions the capture rate of single atoms is independent of the sizes of the growing nuclei. In practical cases the critical nucleus is seldom larger than two atoms, and the atomistic model is preferred. Calculated values of nucleation rate are given in terms of incidence rate, substrate temperature, condensate bond strength and adsorption energy. The analysis of experimental data to derive material constants is discussed.