Classical nucleation theory for solute precipitation amended with diffusion and reaction processes near the interface

Abstract

During the processes of nucleation and growth of a precipitate cluster from a supersaturated solution, the diffusion flux between the cluster and the solution changes the solute concentration near the cluster-solution interface from its average bulk value. This feature affects the rates of attachment and detachment of solute atoms at the interface, and, therefore, the entire nucleation-growth kinetics is altered. Unless quite obvious, this effect has been ignored in classical nucleation theory. To illustrate the results of this approach, for the case of homogeneous nucleation, we calculate the total solubility and the nucleation rate as functions of two parameters of the model (the reduced interface energy and the inverse second Damköhler number), and we compare these results to the classical ones. One can conclude that discrepancies with classical nucleation theory are great in the diffusion-limited regime, when the rate of bulk diffusion is small compared to the rate of interface reactions, while in the opposite interface-limited case they vanish.

Nominal vs. actual supersaturation of solutions

“…Recent studies demonstrate, that HF in solutions play an important role in the nucleation kinetics [14,15,16,17,18,19]. Here we reveal a crucial role of HF in the thermodynamic treatment of supersaturated metastable solutions.…”

Theoretical Evidence for Stationary Size Distribution Of Oxide Nanoparticles in Dispersion Strengthened Steel Under Cascade Producing Irradiation

“…( 25) one can change from the discrete variable n to the continuous one z and expand its right-hand side into the Taylor series up to the second order to obtain the second order differential equation: Taking into account that , from Eqs. ( 12) and ( 17), one can derive (see also [5,6]): ,…”

“…When irradiation is absent and the solute concentration is undersaturated , Eq. ( 44) reduces to the equilibrium distribution function of subcritical nanoparticles (heterophase fluctuations) (see also [5,6]).…”