The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit

Abstract

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters (the chemical potential, the interfacial free energy, and a Tolman correction) of a model based on classical nucleation theory can be fit using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the chemical potentials and the interface energy are pinned to their planar-interface values, more precise estimates for the Tolman length are obtained. Extrapolating the free energy profile obtained from small simulation boxes to larger nuclei is thus more reliable.

Classical nucleation theory predicts the shape of the nucleus in homogeneous solidification

“…We find a level of quantitative agreement between the shapes extracted using these two methods that indicates that it is appropriate to use classical nucleation to describe this particular system. We furthermore argue that similar comparisons of the shapes extracted using the methods that we have introduced in this work and our previous works 8,12 can now be used to check if the nucleation mechanisms observed in other physical systems follow the classical theory.…”

“…This approach thus takes account of material-specific information and generates atomistic insight. When this method is applied, however, a vast amount of information including all atomic coordinates is typically generated, and sophisticated data a) Electronic mail: bc509@cam.ac.uk analysis methods are therefore required to interpret the results [7][8][9] .…”

“…12 and Ref. 8 describe a thermodynamic framework that uses a Gibbs dividing surface construction to extract interfacial free energies for planar and curved solid-liquid arXiv:1910.13481v2 [cond-mat.stat-mech] 28 Dec 2019 interfaces from MD simulations that can be used in expressions based on classical nucleation theory. In using these methods, however, one must assume that the nucleus has a spherical shape or -alternatively -that the interfacial free energy γ for planar interfaces oriented along high-symmetry directions provide sufficient information to approximate the anisotropy of γ and, by extension, to estimate the shape of the nucleus through a Wulff construction.…”

“…In this paper, we, therefore, extend the construction in Refs. 8,12 and extract the average shape of the nucleus from a molecular dynamics simulation directly. In Ref.…”

“…In Ref. 8 we extracted this shape by performing a Wulff construction using values for the surface tensions that were extracted from simulations of planar interfaces. We thus finish this work by performing a quantitative comparison between the shape we extract from our simulations of a three-dimensional nucleus and the shape that was predicted using the Wulff construction.…”