Nucleation is generally understood to refer to the initial process of creating a new phase, for example, liquid water, from another phase, water vapor, as a result of a temperature excursion which carries the system through some critical temperature (in the case at hand, at normal atmospheric pressure, 100°C). The processes involved in such transformations have been the object of careful observations for a long time, at least two centuries; a very good historical perspective on this subject is found at the beginning of Ref. 1. The special case of metal vapors condensing on substrates in order to form thin films is considered in all texts dealing with thin film preparation . The precipitation of a new phase, such as CuAl2, from a supersaturated solution (of copper in aluminum) has immense technological importance which motivates the attention being paid to nucleation phenomena in all metallurgical treatises [3,4].(A particularly thorough discussion is found in Ref. 5.) In all cases, nucleation phenomena are controlled by the necessity of creating an interface between the nucleated phase and the original matrix. The energy of the interface imposes special thermodynamic constraints on the evolution of the system.