Binary nucleation kinetics. IV. Directional properties and cluster concentrations at the saddle point

Using a new approach, Stauffer close-quote s expression for the rate of steady state binary nucleation and Trinkaus close-quote 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 ampersand hthinsp;φ=r ampersand hthinsp;tan ampersand hthinsp;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. copyright 1999 American Institute of Physics