Using a new approach, Stauffer's expression for the rate of steady state binary nucleation and Trinkaus's expression for the steady state cluster concentrations f are derived directly from the diffusion equation that governs the evolution of f in composition space. The behavior of φ (≡f/N, where N is the equilibrium cluster concentration) is explored since this function provides a characterization of the nucleating binary system that, to lowest order, is independent of the actual composition of the mother phase. The angle ω that describes the direction of ▽ φ at the saddle point differs, in general, from the angle φ found by Stauffer for the direction of the nucleation current at the saddle point. These two angles are related by the formula: tan φ=r tan ω, where r is the ratio of impingement frequencies defined by Stauffer. In general, at the saddle point, ▽ φ also fails to lie in the direction of steepest descent on the free energy surface.



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© 1999 American Institute of Physics (AIP), All rights reserved.

Publication Date

01 Apr 1999

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