Abstract
The nucleation of crystals from 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 onionlike 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 nonclassical nucleation processes, showing that layered and onionlike structures can emerge solely based on structural fluctuations even in the 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 onionlike structures, in which the composition changes with the distance from the center of the nucleus, similar to what is seen in the two-step nucleation process.
- Received 24 June 2020
- Revised 28 January 2021
- Accepted 23 April 2021
DOI:https://doi.org/10.1103/PhysRevX.11.031006
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
When a solid phase emerges from a liquid melt, such as during the formation of nanometer-sized ice crystallites in clouds, protein crystallization, or drug molecules synthesis, it can comprise different competing crystalline phases, or polymorphs. This competition among polymorphs is driven by thermodynamic and dynamic factors whose understanding is crucial for predicting the physical and chemical properties of the growing nuclei. Despite the complex nature of this competition, the resulting nuclei often display regular spatial arrangements, such as layered and onionlike structures, which are still not completely understood. We observe for the first time the appearance of these heterogeneous structures in systems where the thermodynamic difference between the competing polymorphs is negligible, thus showing that nonclassical nucleation pathways can be driven exclusively by finite-size structural fluctuations.
We numerically investigate models that are representative of a wide class of materials such as repulsive colloids and dense liquids as well as tetrahedrally bonded materials, such as water and group-14 elements such as carbon and silicon. The key to the characterization of the onionlike structures lies in the development of a novel mathematical parameter for crystal identification that harnesses the power of neural networks to classify each crystalline particle as belonging to a specific polymorph, with resolutions that exceed what was previously possible.
The generality of the neural-network method makes it suitable for application to big data sets from systems showing characteristic ordered or disordered signatures, such as defects or interfaces in crystalline or amorphous materials.
