A fingerprint of surface-tension anisotropy in the free-energy cost of nucleation

TL;DR

This paper extends a field theory of nucleation to include surface-tension anisotropy, revealing that anisotropy introduces a sign change in the logarithmic term of the free energy, which influences the preferred shape of nucleating droplets.

Contribution

The study introduces the effect of surface-tension anisotropy into the nucleation free energy theory, showing a sign change in the logarithmic correction term compared to isotropic cases.

Findings

Anisotropy causes the logarithmic term in $G(V)$ to change sign.

Large solid nuclei likely adopt shapes inferred from the logarithmic term's prefactor.

The extended theory accounts for microscopic interface fuzziness and shape fluctuations.

Abstract

We focus on the Gibbs free energy $\Delta G$ for nucleating a droplet of the stable phase (e.g. solid) inside the metastable parent phase (e.g. liquid), close to the first-order transition temperature. This quantity is central to the theory of homogeneous nucleation, since it superintends the nucleation rate. We recently introduced a field theory describing the dependence of $\Delta G$ on the droplet volume $V$, taking into account besides the microscopic fuzziness of the droplet-parent interface, also small fluctuations around the spherical shape whose effect, assuming isotropy, was found to be a characteristic logarithmic term. Here we extend this theory, introducing the effect of anisotropy in the surface tension, and show that in the limit of strong anisotropy $\Delta G(V)$ once more develops a term logarithmic on $V$, now with a prefactor of opposite sign with respect to the isotropic case. Based on this result, we argue that the geometrical shape that large solid nuclei mostly prefer could be inferred from the prefactor of the logarithmic term in the droplet free energy, as determined from the optimization of its near-coexistence profile.