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.

晶体材料的化学成分具有原子尺度的波动，可以调节各种介观性质。在此类材料中建立化学-微观结构关系需要对这些化学波动进行适当的表征。然而，当前的表征方法（例如，Warren-Cowley 参数）仅部分利用了局部化学基序中包含的完整化学和结构信息。在这里，我们介绍一个基于 E(3) 等变图神经网络的框架，该框架能够完全识别具有任意数量化学元素的任意晶体结构中的化学基序。这种方法自然会导致适当的信息论测量，用于量化化学复杂材料中的化学短程有序（SRO），并减少化学基序空间的表示。我们的框架能够将任何每原子特性与其相应的局部化学基序相关联，从而能够探索化学复杂材料中的结构-特性关系。使用 MoTaNbTi 高熵合金作为测试系统，我们通过评估与每个化学基序相关的晶格应变并计算化学涨落长度尺度的温度依赖性来证明该方法的多功能性。