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Nucleation phenomena commonly observed in our every day life are offundamental, technological and societal importance in many areas, but some oftheir most intimate mechanisms remain however to be unraveled. Crystalnucleation, the early stages where the liquid-to-solid transition occurs uponundercooling, initiates at the atomic level on nanometer length andsub-picoseconds time scales and involves complex multidimensional mechanismswith local symmetry breaking that can hardly be observed experimentally in thevery details. To reveal their structural features in simulations without apriori, an unsupervised learning approach founded on topological descriptorsloaned from persistent homology concepts is proposed. Applied here to amonatomic metal, namely Tantalum (Ta), it shows that both translational andorientational ordering always come into play simultaneously when homogeneousnucleation starts in regions with low five-fold symmetry.

Unsupervised topological learning approach of crystal nucleation in pure Tantalum