Upscaling from ab initio atomistic simulations to electrode scale: The case of manganese hexacyanoferrate, a cathode material for Na-ion batteries

TL;DR

This work addresses the challenge of predicting electrode performance for insertion-type materials by bridging atomistic and device scales. It develops a generalizable workflow that trains a Moment Tensor Potential (MTP) using active learning with hybrid Grand Canonical Monte Carlo–Molecular Dynamics (GCMC–MD) sampling to cover the full sodium composition space in MnFePBA. By extracting diffusivities D(T), activation energies E_a, interfacial energy γ, and complete free-energy landscapes G(N_Na) from atomistic simulations, it feeds these inputs into a pseudo-2D phase-field model to predict phase-boundary dynamics and rate-dependent behavior across an electrode. The study reveals a four-orders-of-magnitude diffusion contrast between rhombohedral and tetragonal phases, a coherent but highly strained interface, and a biphasic desodiation mechanism at the device scale, establishing a blueprint for first-principles–driven design of next-generation insertion-type batteries.

Abstract

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.

Figures (14)

• Figure 1: Schematic representation of the three phases in the machine-learning interatomic potential (MLIP) training workflow. Phase one involves performing convergence tests on the density functional theory (DFT) parameters required for subsequent phases. In the second phase, machine-learning force field (MLFF) assisted active learning within ab initio molecular dynamics (AIMD) is performed on structures with various sodium concentrations to efficiently acquire a diverse pre-training dataset. In the third phase, the Moment Tensor Potential (MTP) model is first trained on this pre-training dataset. Subsequently, active learning is performed during grand-canonical Monte Carlo--molecular dynamics (GCMC-MD) simulations at different temperatures and chemical potentials for multiple iterations until the MTP no longer selects new structures, which serves as the criterion for convergence. The final trained MTP-MLIP is then utilized to perform production runs on large-scale atomistic systems to calculate the physical properties of MnFePBA.
• Figure 2: Schematic representation of the pseudo two-dimensional domain of active material in the porous electrode model of Doyle-Fuller-Newman. A porous electrode with current collector and separator is displayed on top. A spherical particle of average particle size is placed at each position in the electrode depth to model sodium transport inside the active material. The pseudo two-dimensional domain (bottom) with the horizontal dimension being the electrode width and the vertical dimension being the particles average radius is the continuous limit with an infinite number of identical representative particles.
• Figure 3: (a) presents the distribution of configurations as a histogram plotted against sodium concentration, where the pre-training data (orange) from ab initio molecular dynamics (AIMD) is distinguished from the GCMC-MD generated structures, which show dominant sampling at x = 0 and x=2 (b) illustrates the wide energy dispersion of the training structures. (c) and (d) show the scatter plots comparing the MTP-predicted forces and energies, respectively, against the DFT-calculated reference values.
• Figure 4: The crystal structure of the MnFePBA at (a) x = 0.02 in tetragonal symmetry and (b) x = 1.756 in rhombohedral symmetry. (c) Bond angle distribution for the sodium-poor (x=0.02) and sodium-rich (x=1.756) structures at 300 K. (d) Radial distribution functions (RDFs) for various atom pairs in the sodium-poor (dashed lines) and sodium-rich (solid lines) structures at 300 K.
• Figure 5: (a) Four snapshots of the simulated system at different sodium concentrations. When fully sodiated, the structure contains 4096 sodium atoms. (b) The evolution of system energy (blue), volume (orange), and sodium concentration (green) profiles during GCMC-MD simulation at 300 K and at µ =-5. During the simulation, for every 4000 NPT timesteps, 2000 sodium insertion/deletion (GC moves) and 2000 sodium translation (MC moves) were performed. The four red dashed lines indicate the time points at which system snapshots were recorded. (c) The evolution of the coordination number of sodium (purple)-—defined as the number of N atoms within a 3.5 Å radius-—and the standard distribution (purple shade), the N-Mn (blue) and N-Na (green) bond distance.