The research of new electrode materials such as sodium intercalation compounds is key to meet the challenges of future demands of sustainable energy storage. For these batteries, the intercalation behavior on the micro-scale is governed by a complex interplay of chemical, electrical and mechanical forces strongly influencing the overall cell performance. The multiphase-field method is a suitable tool to study these multi-physics and bridge the scale from ab-initio methods to the cell level. In this work, we follow a combined approach of experiments, density functional theory (DFT) calculations and multiphase-field simulations to predict thermodynamic and kinetic properties for the P2-type Na_XNi_1/3Mn_2/3O₂ sodium-ion cathode material. Experimentally, we obtain the thermodynamic potential and diffusion coefficients at various sodium contents using electrochemical techniques and discuss limitations of the experimentally applied methods. DFT is used to identify stable phases by calculating an energy hull curve. Then, the influence of long-range dispersion interactions and the exchange-correlation functional on the voltage curve is investigated by comparison with experimental results. Finally, multiphase-field simulations are performed based on inputs from experiments and DFT. The fitting of phase-specific chemical free energies from DFT calculations and experimental data is discussed. Our results highlight the thermodynamic consistency of all three approaches close to thermodynamic equilibrium. Furthermore, the phase-field method accurately describes the kinetics of the system including multiple phase transitions, by which we unravel the mechanism of the P2-O2 phase transition in a single crystal under the influence of intercalation reaction, bulk diffusion and elastic deformation. The model is able to predict the kinetic capacity loss depending on charging rate in agreement with C-rate experiments.

Owing to its unique thermodynamical description, phase separation has largely been modeled in the Cahn-Hilliard framework. In the present work, as a computationally efficient alternative, a multicomponent, multiphase-field model operating in Allen-Cahn framework is presented and subsequently employed to simulate spinodal decomposition. Stability analysis shows that the formulation can cover the effect of phase separation while simplifying the extension to multiple phases and incorporation of additional driving forces. Computational efficiency of the proposed approach is compared with the conventional technique by modeling intercalation in a representative one-dimensional domain. Moreover, intercalation within a multigrain system involving multiparticle interaction is studied. Our results suggest initiation of phase transformation at higher order junctions as well as a grain-by-grain intercalation behavior in a two-phase cathode material such as the well-studied ${\text{LiFePO}}_4$.

Hierarchical structures of many agglomerated primary crystals are often employed as cathode materials, especially for layered-oxide compounds. The anisotropic nature of these materials results in a strong correlation between particle morphology and ion transport. In this work, we present a multiphase-field framework that is able to account for strongly anisotropic diffusion in polycrystalline materials. Various secondary particle structures with random grain orientation as well as strongly textured samples are investigated. The observed ion distributions match well with the experimental observations. Furthermore, we show how these simulations can be used to mimic potentiostatic intermittent titration technique (PITT) measurements and compute effective diffusion coefficients for secondary particles. The results unravel the intrinsic relation between particle microstructure and the apparent diffusivity. Consequently, the modeling framework can be employed to guide the microstructure design of secondary battery particles. Furthermore, the phase-field method closes the gap between computation of diffusivities on the atomistic scale and the effective properties of secondary particles, which are a necessary input for Newman-type cell models.