Solid-phase nucleation free-energy barriers in truncated cubes: interplay of localized orientational order and facet alignment

Abstract

The nucleation of ordered phases from the bulk isotropic phase of octahedron-like particles has been studied via Monte Carlo simulations and umbrella sampling. In particular, selected shapes that form ordered (plastic) phases with various symmetries (cubic and tetragonal) are chosen to unveil trends in the free-energy barrier heights (ΔG*'s) associated with disorder to order transitions. The shapes studied in this work have truncation parameter (s) values of 0.58, 0.75, 0.8 and 1. The case of octahedra (s = 1.0) is studied to provide a counter-example where the isotropic phase nucleates directly into a (Minkowski) crystal phase rather than a rotator phase. The simulated ΔG*'s for these systems are compared with those previously reported for hard spheres and truncated cubes with s = 0.5 (cuboctahedra, CO) and s = 2/3 (truncated octahedra, TO). The comparison shows that, for comparable degrees of supersaturation, all rotator phases nucleate with smaller ΔG*'s than that of the hard sphere crystal, whereas the octahedral crystal nucleates with a larger ΔG*. Our analysis of near-critical translationally ordered nuclei of octahedra shows a strong bias towards an orientational alignment which is incompatible with the tendency to form facet-to-facet contacts in the disordered phase, thus creating an additional entropic penalty for crystallization. For rotator phases of octahedra-like particles, we observe that the strength of the localized orientational order correlates inversely with ΔG*. We also observe that for s > 0.66 shapes and similar to octahedra, configurations with high facet alignment do not favor high orientational order, and thus ΔG*'s increase with truncation.