Number of clusters formed in nucleation-growth processes

Abstract

The number of clusters, N, formed in nucleation-growth processes in first-order phase transformations, and their average size, 〈R〉, at the end of the stage of independent growth of the supercritical clusters are determined analytically. It is shown that the number of clusters, N, depends only on the thermodynamic parameters like initial supersaturation, specific interfacial energy etc. but not on the values of kinetic parameters like the diffusion coefficient. In addition, estimates are given for the duration of the different stages of the nucleation-growth process. In this way, a complete quantitative description of the basic characteristics of first-order phase transformations (e.g., segregation in solid or liquid solutions, vapor condensation, etc.) is established. The results are in excellent agreement both with experimental results as well as with computer calculations modelling nucleation and growth based on the numerical solution of the set of kinetic equations describing this process in the framework of classical nucleation theory.

Multiphase solidification in multicomponent alloys

“…The classical kinetic model has been extended to nucleation in binary and multi-component systems by several authors: Kozisek and Demo [210], Wilemski and Wyslouzil [211], Slezov et al [212], Kozisek et al [213], Slezov and Schmelzer [214] and Schmelzer et al [215]. A general theory, which includes coagulation/splitting has been worked out for phase separation by Binder and Stauffer [216].…”

Kinetics of Nucleation at Increasing Supersaturation

“…[16], the limit v p 3 0 has to be excluded in Eq. [30] from the considerations. In this limit, the method of analysis employed here is not applicable.…”

“…[1]- [3] and [9], respectively. Based on the knowledge of these quantities, the maximum number of clusters, which may be formed in the system under stationary external conditions, can be determined via the relation N ϭ J N (9,30,31).…”

“…For time-independent boundary conditions, the kinetics of segregation processes was analyzed in detail in preceding papers (9,30,31) (see also the references cited therein). It was assumed in the respective analysis (as it is done also generally in the majority of investigations of the kinetics of phase formation processes) that the initial supersaturation is established suddenly by some appropriate mechanism.…”

“…Since the nucleation process is terminated once the volume of the new phase has reached a certain well-defined value (cf. (9,30,31,36)), immediately the origin of the occurrence of the factor 1 4 in the expression for N for kinetic limited growth becomes clear. For diffusion limited growth this factor has to be replaced by 2 5 , while for growth governed by Rayleigh's equation N is linearly connected with the work of critical cluster formation.…”