Machine Learning to Predict Quasicrystals from Chemical Compositions

Quasicrystals have emerged as a new class of solid-state materials that have long-range order without periodicity, exhibiting rotational symmetries that are disallowed for periodic crystals in most cases. To date, hundreds of new quasicrystals have been found, leading to the discovery of many new and exciting phenomena. However, the pace of the discovery of new quasicrystals has slowed in recent years, largely owing to the lack of clear guiding principles for the synthesis of new quasicrystals. Here, we show that the discovery of new quasicrystals can be accelerated with a simple machine learning workflow. With a list of the chemical compositions of known quasicrystals, approximant crystals, and ordinary crystals, we trained a prediction model to solve the three-class classification task and evaluated its predictability compared to the observed phase diagrams of ternary aluminum systems. The validation experiments strongly support the superior predictive power of machine learning, with the precision and recall of the phase prediction task reaching approximately 0.793 and 0.714, respectively. Furthermore, analyzing the input--output relationships black-boxed into the model, we identified nontrivial empirical equations interpretable by humans that describe conditions necessary for quasicrystal formation.