Machine Learning to Predict Quasicrystals from Chemical Compositions

Quasicrystals have emerged as the third class of solid-state materials, distinguished from periodic crystals and amorphous solids, which have long-range order without periodicity exhibiting rotational symmetries that are disallowed for periodic crystals in most cases. To date, more than one hundred stable quasicrystals have been reported, leading to the discovery of many new and exciting phenomena. However, the pace of the discovery of new quasicrystals has lowered in recent years, largely owing to the lack of clear guiding principles for the synthesis of new quasicrystals. Here, it is shown that the discovery of new quasicrystals can be accelerated with a simple machine-learning workflow. With a list of the chemical compositions of known stable quasicrystals, approximant crystals, and ordinary crystals, a prediction model is trained to solve the three-class classification task and its predictability compared to the observed phase diagrams of ternary aluminum systems is evaluated. The validation experiments strongly support the superior predictive power of machine learning, with the overall prediction accuracy of the phase prediction task reaching ≈0.728. Furthermore, analyzing the input-output relationships black-boxed into the model, nontrivial empirical equations interpretable by humans that describe conditions necessary for stable quasicrystal formation are identified.