Chemical-motif characterization of short-range order with E(3)-equivariant graph neural networks

Crystalline materials have atomic-scale fluctuations in their chemical composition that modulate various mesoscale properties. Establishing chemistry–microstructure relationships in such materials requires proper characterization of these chemical fluctuations. Yet, current characterization approaches (e.g., Warren–Cowley parameters) make only partial use of the complete chemical and structural information contained in local chemical motifs. Here we introduce a framework based on E(3)-equivariant graph neural networks that is capable of completely identifying chemical motifs in arbitrary crystalline structures with any number of chemical elements. This approach naturally leads to a proper information-theoretic measure for quantifying chemical short-range order (SRO) in chemically complex materials and a reduced representation of the chemical motif space. Our framework enables the correlation of any per-atom property with their corresponding local chemical motif, thereby enabling the exploration of structure–property relationships in chemically complex materials. Using the MoTaNbTi high-entropy alloy as a test system, we demonstrate the versatility of this approach by evaluating the lattice strain associated with each chemical motif, and computing the temperature dependence of chemical-fluctuations length scale.