This paper presents a detailed description of phase-field models of electrodeposition in lithium-anode batteries, along with underlying assumptions and parameters commonly employed. We simulate the coupled electrochemical interactions during a battery charge cycle using finite elements on open-source packages, allowing for parallel computation and time step adaptivity. We compare conventional free energy and grand canonical formulations. We obtain agreement between 1D phase-field simulations and the theoretical Faradic reaction kinetics. We study the mesh-induced errors through spatial convergence analysis. These simulations results set the groundwork for 2D and 3D simulations of dendritic metal electrodeposition in batteries.

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