  The nucleation of crystals from the liquid melt is often characterized by a
competition between different crystalline structures or polymorphs, and can
result in nuclei with heterogeneous compositions. These mixed-phase nuclei can
display nontrivial spatial arrangements, such as layered and onion-like
structures, whose composition varies according to the radial distance, and
which so far have been explained on the basis of bulk and surface free-energy
differences between the competing phases. Here we extend the generality of
these non-classical nucleation processes, showing that layered and onion-like
structures can emerge solely based on structural fluctuations even in absence
of free-energy differences. We consider two examples of competing crystalline
structures, hcp and fcc forming in hard spheres, relevant for repulsive
colloids and dense liquids, and the cubic and hexagonal diamond forming in
water, relevant also for other group 14 elements such as carbon and silicon. We
introduce a novel structural order parameter that combined with a neural
network classification scheme allows us to study the properties of the growing
nucleus from the early stages of nucleation. We find that small nuclei have
distinct size fluctuations and compositions from the nuclei that emerge from
the growth stage. The transition between these two regimes is characterized by
the formation of onion-like structures, in which the composition changes with
the distance from the center of the nucleus, similarly to what seen in two-step
nucleation process.

Soft Condensed Matter