Unsupervised topological learning approach of crystal nucleation

TL;DR

This paper introduces an unsupervised topological learning method using persistent homology to analyze atomic-scale crystal nucleation mechanisms in metals, revealing complex structural features and pathways beyond classical theories.

Contribution

It presents a novel unsupervised topological approach for studying crystal nucleation at the atomic level without prior assumptions, applicable to monatomic metals.

Findings

Simultaneous translational and orientational ordering during nucleation.

Nucleation pathways vary depending on the element.

Features observed go beyond classical nucleation theory.

Abstract

Nucleation phenomena commonly observed in our every day life are of fundamental, technological and societal importance in many areas, but some of their most intimate mechanisms remain however to be unravelled. Crystal nucleation, the early stages where the liquid-to-solid transition occurs upon undercooling, initiates at the atomic level on nanometre length and sub-picoseconds time scales and involves complex multidimensional mechanisms with local symmetry breaking that can hardly be observed experimentally in the very details. To reveal their structural features in simulations without a priori, an unsupervised learning approach founded on topological descriptors loaned from persistent homology concepts is proposed. Applied here to monatomic metals, it shows that both translational and orientational ordering always come into play simultaneously when homogeneous nucleation starts in regions with low five-fold symmetry. It also reveals the specificity of the nucleation pathways depending on the element considered, with features beyond the hypothesis of Classical Nucleation Theory.