In order to arrive at a model for nucleation in the reaction of polycrystalline thin films, we have made use of a transport model that combines atom transport across interface reaction barriers with transport along grain boundaries. Through this transport model, the boundary chemical potential, µIi, and a characteristic length Li, for each specie are defined. Li and the ratio of grain size to Li determine the spatial variation and the time evolution of the boundary chemical potential respectively. Nucleation of the product phase is modeled as a process whose driving force is determined by these position dependent (and time dependent) boundary chemical potentials. Thus thin film reactions become similar to precipitation from bulk homogeneous supersaturated solid solutions. Numerical calculations, however, show that boundary diffusion results in low “effective” driving forces for nucleation which can lead to heterogeneous nucleation of even the first phase. The model provides a new approach to phase selection by re-evaluation of the driving force and considers the effect of product and reactant grain structure to be fundamental to the reaction process.
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Barmak, K., Coffey, K. Grain Boundary Diffusion Controlled Precipitation as a Model For thin Film Reactions. MRS Online Proceedings Library 311, 51–56 (1993). https://doi.org/10.1557/PROC-311-51