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

Abstract

Macroscopic models of nucleation provide powerful tools for understanding activated phase transition processes. These models do not provide atomistic insights and can thus sometimes lack material-specific descriptions. Here we provide a comprehensive framework for constructing a continuum picture from an atomistic simulation of homogeneous nucleation. We use this framework to determine the equilibrium shape of the solid nucleus that forms inside bulk liquid for a Lennard-Jones potential. From this shape, we then extract the anisotropy of the solid-liquid interfacial free energy, by performing a reverse Wulff construction in the space of spherical harmonic expansions. We find that the shape of the nucleus is nearly spherical and that its anisotropy can be perfectly described using classical models.

Approaches to modelling the shape of nanocrystals

“…The phrase inverse Wulff construction [ 140 , 141 ] or reverse Wulff construction [ 142 , 143 ] refers to the use of experimentally determined equilibrium shapes to obtain the ratio of facet-dependent surface energies, as shown in Fig. 7 .…”

Out-of-Equilibrium Polymorph Selection in Nanoparticle Freezing

“…In this kind of simulation, the choice of the collective variable (CV) is crucial . In general, traditional CVs include the size of the largest crystalline cluster and Steinhardt’s parameters, which tend to bias the system toward a specific crystal structure. As an alternative, CVs defined from the structure of the initial and final states of the system were proposed on the basis of the permutation-invariant vectors or specific peaks of the X-ray diffractogram. , In the case of polymorph selection, it becomes convenient to employ structurally agnostic collective variables to avoid any constraint on the crystal structure.…”

Out-of-equilibrium Polymorph Selection in Nanoparticle Freezing

“…In this kind of simulations, the choice of the collective variable (CV) is crucial [81]. In general, traditional CVs include the size of the biggest crystalline cluster [82] and Steinhardt's parameters [83], which tend to bias the system towards a specific crystal structure. As an alternative, CVs defined from the structure of the initial and final states of the system were proposed, based on permutation invariant vectors [4] or on specific peaks of the X-ray diffractogram [28,84].…”