Upscaling from <i>Ab Initio</i> Atomistic Simulations to Electrode Scale: The Case of Manganese Hexacyanoferrate, a Cathode Material for Na-Ion Batteries

We present a generalizable scale-bridging computational framework that enables predictive modeling of insertion-type electrode materials from atomistic to device scales. Applied to sodium manganese hexacyanoferrate, a promising cathode material for grid-scale sodium-ion batteries, our methodology employs an active-learning strategy to train a moment tensor potential through iterative hybrid grand-canonical Monte Carlo-molecular dynamics sampling, robustly capturing configuration spaces at all sodiation levels. The resulting machine learning interatomic potential accurately reproduces experimental properties, including volume expansion, operating voltage, and sodium concentration-dependent structural transformations, while revealing a four-order-of-magnitude difference in sodium diffusivity between the rhombohedral (sodium-rich) and tetragonal (sodium-poor) phases at 300 K. We directly compute all critical parameters—temperature- and concentration-dependent diffusivities, interfacial and strain energies, and complete free-energy landscapes—to feed them into pseudo-2D phase-field simulations that predict phase-boundary propagation and rate-dependent performances across electrode length scales. This multiscale workflow establishes a blueprint for rational computational design of next-generation insertion-type materials, such as battery electrode materials, demonstrating how atomistic insights can be systematically translated into continuum-scale predictions.