Abstract
Hard carbon (HC) has attracted considerable interest as a promising anode material for sodium-ion batteries (SIBs) due to its high specific capacity, excellent cycling stability, and cost-effectiveness. Nevertheless, the sodium storage mechanism in HC remains poorly understood owing to challenges in precisely characterizing its structural disorder, complexity, and intricate interatomic interactions. In this work, we investigate the sodium storage behavior in HC anodes using a machine learning potential (MLP) integrated with a random forest-based sodium insertion site identification framework. The trained MLP accurately captures both the structural features of HC and the sodium insertion behavior. HC comprises an amorphous network of defects, edges, graphitic domains, and nanopores, primarily interconnected through sp/sp(2)/sp(3)-hybridized carbon bonds. For the first time, we simulate the continuous voltage profile associated with the stepwise sodium insertion during both the charging and overcharging states. This voltage profile reproduces experimental observations and disentangles the contributions of adsorption, intercalation, and pore filling, offering a pathway to elucidate the storage mechanisms across different systems and rationalize the discrepancies observed in experiments. During the overcharging stage, excessively short Na-Na distances enhance repulsion, leading to negative voltages. Besides, the formation of sodium clusters was observed, which pose a safety risk to the battery. Our findings demonstrate that machine learning-based simulations constitute a powerful and emerging approach for investigating sodium storage mechanisms and offer valuable guidance for the experimental optimization of HC anodes. Moreover, this strategy can be extended to other electrodes, electrolytes in SIBs, and even alternative battery systems.