Although a number of methods have been proposed to characterize local atomic environments, these methods are often not optimized to magnify the subtle differences present in disordered environments. However, quantifying local atomic disorder in a physically motivated way in practice is extraordinarily difficult 19, 20. Examples include temperature-dependent microstructure evolution 13, 14, hotspot formation 15, 16, and the nucleation and growth of new material phases 17, 18. These processes, in turn, are intricately connected to performance-durability trade-offs in both functional 11 and structural 12 materials. For instance, transport, chemical reactivity, and phase nucleation are all profoundly affected by the presence of interfaces, interphases, and grain boundaries 5, 6, 7, 8, 9, 10. Complicating this endeavor is the fact that the long-range features often depend on structurally disordered atomic environments, which tend to dictate materials functionality 4. Characterizing the nature and propagation of these local environments is therefore vital to understanding macroscale structure-property relationships and their evolution 3. At the center of this paradigm is the fact that macroscopic material’s behavior begins at the atomic scale, with local atomic arrangements ultimately coming together to form structural features observed at larger length scales 1, 2. Understanding how a material’s structure affects its properties is one of the most fundamental principles in materials science. Overall, our framework provides a simple and generalizable pathway to quantify the relationship between complex local atomic structure and coarse-grained materials phenomena. We further show how to extract physics-preserved gradients from our continuous disorder fields, which may be used to understand and predict materials performance and failure. Using elemental aluminum as a case study, we show how our paradigm can track the spatio-temporal evolution of interfaces, incorporating a mathematically defined description of the spatial boundary between order and disorder. We also compare SODAS to several commonly used methods. We apply this methodology to four prototypical examples with varying levels of disorder: (1) grain boundaries, (2) solid-liquid interfaces, (3) polycrystalline microstructures, and (4) tensile failure/fracture. This metric encodes the diversity of the local atomic configurations as a continuous spectrum between the solid and liquid phases, quantified against a distribution of thermal perturbations. Here, we leverage graph neural networks to define a physically interpretable metric for local disorder, called SODAS. Quantifying the level of atomic disorder within materials is critical to understanding how evolving local structural environments dictate performance and durability.
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