Speaker
Jonas Johansson
(Lund University)
Description
Nucleation is the first step in the formation of a new
thermodynamic phase, either during a spontaneously occurring
phase transition or under more controlled circumstances,
such as in crystal growth processes. In this presentation, I
start by introducing the Becker-Döring rate equations and
classical nucleation theory. I show an alternative way to
approximate the Becker-Döring equations underlying the
nucleation process using a Fokker-Planck equation, based on
stochastic calculus. The derivation proceeds via a Langevin
equation with multiplicative noise. Because of the
Ito-Stratonovich dilemma this leads to a family of possible
Fokker-Planck equations. The purpose of this investigation
is to find out which of the Fokker-Planck equations gives
the best approximation to the nucleation rate. For a simple
and general set of attachment and detachment rates, I
compare the equilibrium cluster sizes and the nucleation
rates resulting from the various interpretations of the
noise term (Ito, Stratonovich, and anti-Ito) with the exact
nucleation rate. I find that the Ito choice provides the
best approximations and the Fokker-Planck equation
corresponding to this choice coincides with the
Fokker-Planck equation resulting from the common way to
Taylor expand the original set of rate equations.
