A scaling law to determine phase morphologies during ion intercalation

Driven phase separation in ion intercalation materials is known to result in different non-equilibrium phase morphologies, such as intercalation waves and shrinking-core structures, but the mechanisms of pattern selection are poorly understood. Here, based on the idea that the coarsening of the slowest phase is the rate limiting step, we introduce a scaling law that quantifies the transition from quasi-equilibrium intercalation-wave to diffusion-limited shrinking-core behavior. The scaling law is validated by phase-field simulations of single Li(x)CoO(2)particles,in situoptical imaging of single Li(x)C(6)particles undergoing transitions between stage 1 (x= 1) and 2 (x= 0.5) at different rates, and all the available literature data for single-particle imaging of LixCoO2, Li(x)C(6)and LixFePO4. The results are summarized in operational phase diagrams to guide simulations, experiments, and engineering applications of phase-separating active materials. Implications for Li-ion battery performance and degradation are discussed.