Abstract
The kinetics of precipitate nucleation under time-dependent supersaturation is studied on the basis of a Fokker-Planck equation with time-dependent coefficients. Clustering of non-conservative particles for which the monomer concentration is controlled by an external field parameter is considered in detail. The problem is treated with the aid of the Green's function approach, which is introduced in connection with a new analysis of the transient to steady-state nucleation. It is explored under conditions in which the Green's function for a time-dependent infinite parabolic barrier (i.e. the Ornstein-Uhlenbeck process for a time-dependent inverted harmonic potential) may be used as an approximation for the correct Green's function. The former is then used to study the nucleation yield of a supersaturation pulse described by a simple time-dependent model barrier. From this, the conditions for quasi-steady-state nucleation are deduced, and it is shown that in the non-steady-state region the nucleation yield decreases drastically with the reciprocal pulse duration. The quasi-steady-state approximation is applied to derive more general asymptotic expressions for the nucleation yield of a supersaturation pulse and for the average (quasi-continuous) nucleation rate under a randomly fluctuating supersaturation.
