Journal of Crystal Growth, Vol.377, 118-122, 2013
Volume term of work of critical nucleus formation in terms of chemical potential difference relative to equilibrium one
The work of formation of a critical nucleus is sometimes written as W = n Delta mu + gamma A. The first term W-vol = n Delta mu is called the volume term and the second term gamma A the surface term with gamma being the interfacial tension and A the area of the nucleus. Nishioka and Kusaka [J. Chem. Phys. 96 (1992) 5370] derived W-vol = n Delta mu with n = V-beta/v(beta) and Delta mu = mu(beta)(T, p(alpha))-mu(alpha)(T, p(alpha)) by rewriting W-vol = -(p(beta) - p(alpha))V-beta by integrating the isothermal Gibbs-Duhem relation for an incompressible beta phase, where alpha and beta represent the parent and nucleating phases, V-beta is the volume of the nucleus, v(beta), which is constant, the molecular volume of the beta phase, mu, T, and p denote the chemical potential, the temperature, and the pressure, respectively. We note here that Delta mu = mu(beta)(T,p(alpha))-mu(alpha)(T,p(alpha)) is, in general, not a directly measurable quantity. In this paper, we have rewritten W-vol = -(p(beta)-p(alpha))V-beta in terms of mu(re)-mu(eq), where mu(re) and mu(eq) are the chemical potential of the reservoir (equaling that of the real system, common to the alpha and beta phases) and that at equilibrium. Here, the quantity mu(re)-mu(eq) is the directly measurable supersaturation. The obtained form is similar to but slightly different from W-vol = n Delta mu. (C) 2013 Elsevier B.V. All rights reserved.