Title: Neural Network Kinetics for Exploring Diffusion Multiplicity and Chemical Ordering in Compositionally Complex Materials

Abstract: Diffusion involving atom transport from one location to another governs many important processes and behaviors such as precipitation and phase nucleation. Local chemical complexity in compositionally complex alloys poses challenges for modeling atomic diffusion and the resulting formation of chemically ordered structures. Here, we introduce a neural network kinetics (NNK) scheme that predicts and simulates diffusion-induced chemical and structural evolution in complex concentrated chemical environments. The framework is grounded on efficient on-lattice structure and chemistry representation combined with neural networks, enabling precise prediction of all path-dependent migration barriers and individual atom jumps. Using this method, we study the temperature-dependent local chemical ordering in a refractory Nb-Mo-Ta alloy and reveal a critical temperature at which the B2 order reaches a maximum. Our atomic jump randomness map exhibits the highest diffusion heterogeneity (multiplicity) in the vicinity of this characteristic temperature, which is closely related to chemical ordering and B2 structure formation. The scalable NNK framework provides a promising new avenue to exploring diffusion-related properties in the vast compositional space within which extraordinary properties are hidden.