A statistical theory of nucleation in the presence of uncharacterised impurities

TL;DR

This paper develops a statistical model for nucleation in systems with poorly characterized impurities, revealing how impurity interactions cause the nucleation rate to fluctuate significantly, especially in the non-self-averaging regime.

Contribution

It introduces a novel theoretical framework modeling impurity effects on nucleation as random variables, connecting to Derrida's Random Energy Model and analyzing the transition between self-averaging and non-self-averaging behaviors.

Findings

Derived analytic expressions for the crossover between self-averaging and non-self-averaging nucleation rates.

Demonstrated that impurity interactions can cause significant variability in nucleation rates.

Identified regimes where nucleation rate fluctuations are dominant.

Abstract

First order phase transitions proceed via nucleation. The rate of nucleation varies exponentially with the free-energy barrier to nucleation, and so is highly sensitive to variations in this barrier. In practice, very few systems are absolutely pure, there are typically some impurities present which are rather poorly characterised. These interact with the nucleus, causing the barrier to vary, and so must be taken into account. Here the impurity-nucleus interactions are modelled by random variables. The rate then has the same form as the partition function of Derrida's Random Energy Model, and as in this model there is a regime in which the behaviour is non-self-averaging. Non-self-averaging nucleation is nucleation with a rate that varies significantly from one realisation of the random variables to another. In experiment this corresponds to variation in the nucleation rate from one sample to another. General analytic expressions are obtained for the crossover from a self-averaging to a non-self-averaging rate of nucleation.