Numerical Modeling of Lithium-ion Battery Electrode Materials with Phase Interfaces.

Abstract

Intercalation processes occur in a single crystallite of many electrode materials for a certain period of charging and discharging processes of primary or secondary batteries. These intercalation processes involve both phase transformation and diffusion. As Li atoms are added to or taken out of the crystallite during the (de)intercalation process, the crystallite relaxes to achieve minimum energy morphology while often having sharp interfaces between two dissimilar phases. Since the two phases have different mechanical properties, especially different lattice parameters, this discrepancy in the lattice parameters near the phase-interfaces causes coherency strain. The resulting coherency strain affects thermodynamic potentials. Conversely the changed thermodynamic potentials vary solubility limits of Lithium, voltage profile, and phase stability. Although the importance of coherency strain has been noticed by many authors, the effect of coherency strain on two-phase equilibrium has not been modeled to satisfactory degrees for the Li_xFePO₄ crystallite. We analytically derived chemical and mechanical equilibrium criteria for 2-phase morphology of the Li_xFePO₄ crystallites in the quasi-static analysis. We checked the effect of coherency strain on the voltage profile and on the optimal shape of the crystallites. Quasi-static FEA showed that needle-shape crystallite along the a-axis of the Li_xFePO₄ crystallite minimized the coherency strain energy density. For olivine Li_xFePO₄ (0 ≤ x ≤ 1) crystallite, by adding the coherency strain energy term to the total free energy, we confirmed that the total energy is minimized when the phase interface parallels the bc-plane, although the Li ions diffuse along the b-axis of the crystallite. In the time dependent analysis, not only the anisotropy of the elastic moduli, but also the anisotropy of the diffusivity was considered. The evolution of the two-phase interface was modeled with the Level set method, one of most accurate and efficient methods to track a surface evolution. We showed a general time-dependent finite element approach for Li-ion battery electrode materials demonstrating Li intercalation processes with the phase interfaces.