Predicting colloidal crystals from shapes via inverse design and machine learning

A fundamental challenge in materials design is linking building block attributes to crystal structure. Addressing this challenge is particularly difficult for systems that exhibit emergent order, such as entropy-stabilized colloidal crystals. We combine recently developed techniques in inverse design with machine learning to construct a model that correctly classifies the crystals of more than ten thousand polyhedral shapes into 13 different structures with a predictive accuracy of 96% using only two geometric shape measures. With three measures, 98% accuracy is achieved. We test our model on previously reported colloidal crystal structures for 71 symmetric polyhedra and obtain 92% accuracy. Our findings (1) demonstrate that entropic colloidal crystals are controlled by surprisingly few parameters, (2) provide a quantitative model to predict these crystals solely from the geometry of their building blocks, and (3) suggest a prediction paradigm that easily generalizes to other self-assembled materials.