Phase-field modeling and simulations for dendrite growth in electrodeposition

This work presents a phase-field differential model for simulating dendritic growth during metal electrodeposition, of special relevance to the operation of rechargeable batteries with metal anodes, such as: lithium, sodium and zinc. The model modifies the well-assessed phase-field model for dendritic crystal growth by Kobayashi, replacing the thermal field by a concentration field for the electroactive species in the electrolyte, that couples electrochemically to the local potential difference across the electrode-electrolyte interface. Such concentration is governed by a mass transport equation that accounts for electrochemical effects. The resulting nonlinear system of PDEs is spatially discretized using finite differences and integrated explicitly in time. Numerical simulations illustrate how the kinetic coefficient, anisotropy mode number, and dimensionless current density influence the evolution and morphology of dendritic structures. We introduce morphological indicators to quantitatively analyze the simulated dendrites: fractal dimension, skeleton-based metrics, and the inverse isoperimetric quotient (IIQ). Based on the IIQ analysis, we provide a segmentation of the parameter space to reproduce key features of electrochemical dendrite formation. We present comparisons with micrographs of experimental dendrites to validate our results.