Modeling battery intercalation materials with the multiphase-field method

The multiphase field method holds great potential to accelerate future materials research through simulation studies - for example in the field of battery materials. Through appropriate modeling, fundamental mechanisms of diffusion, phase transformation and reaction kinetics can be investigated, thus providing insight into possible kinetic limitations or degradation mechanisms. In the last decade, the phase-field method has been increasingly used to simulate phase transformations in the active material on the electrode level. However, these studies are mostly limited to single crystals with one coherent phase transformation. A consistent description of materials with multiple phase transformations and polycrystalline morphology has not yet been developed. In the introduction of this work, relevant mechanisms that significantly influence the kinetics of charging and discharging at the particle level are discussed. Based on this, a multiphase-field model for intercalation materials is formulated, which includes phase transformations coupled with ion diffusion and an elastic deformation of the crystal lattice. The intercalation reaction is applied as a boundary condition and correlates with the local chemical potential of sodium at the particle surface. ... mehrAssuming a globally constant charge rate, the effective overpotential can be determined and compared with experiments. Polycrystalline agglomerates can be described in a natural way including the effects of grain boundaries by the underlying multiphase-field formulation. Since this model formulation has not yet been applied to battery materials modeling, this work investigates and validates individual energy contributions in detail. New implementations are tested numerically and build upon previous developments of the simulation software PACE3D, which has been developed for more than 20 years at the chair of Prof. Britta Nestler. Additionally, the detailed discussion in the validation chapters is intended to facilitate the implementation of the same model or similar formulations in other research codes.

In the second part of this work, the versatile capabilities and potentials of the developed model are tested and discussed on the basis of several examples. First, based on the well-researched cathode material lithium iron phosphate, a comparison of the model with an established approach based on the Cahn-Hilliard model is drawn. Furthermore, the underlying assumptions of the simulations are discussed in detail. The results confirm previous research findings and, more-over, show the influence of polycrystals on the intercalation behavior. While the phase transformation occurs preferentially grain by grain at slow charge rates, simultaneous transformation of many grains is enforced at high rates. In addition, high tensile stresses can be observed at grain boundaries of randomly oriented polycrystals, which contribute to mechanical degradation. The final two use cases illustrate new directions in the field of battery modeling. The cathode material NaX Ni1/3 Mn2/3 O2 is a promising candidate for future sodium-ion batteries. However, it exhibits poor cycling stability which is partially attributed to a phase transformation at high potentials associated with a highly anisotropic deformation of the crystal lattice. The simulations provide insight into the interplay between phase transformation, mechanical deformation and diffusion. They reveal that mechanics contributes significantly to the effective capacity at slow to moderate charge rates. High tensile stresses, however, are indicative of cracking in the material. The study on polycrystalline NMC agglomerates emphasizes the influence of microstructure on the overall battery charging behavior. Directional grain structures can improve ion transport and contribute to a more homogeneous concentration distribution in the particle, which positively affects the cycle and rate stability of the material. Future research could investigate the potential of similar microstructures for other cathode materials to accelerate materials research with respect to batteries.