Perspective—Does the Sand Equation Reliably Predict the Onset of Morphological Evolution in Lithium Electrodeposition?

Abstract

For galvanostatic metal electrodeposition under diffusion-limited conditions, the Sand’s equation provides the time at which the concentration of the cation being reduced reaches zero at the electrode-electrolyte interface. Such a condition causes amplification of the electrodeposit roughness and triggers dendritic growth during electrodeposition. In this perspective article, the question of whether the classical Sand equation reliably predicts the onset of morphological evolution in lithium electrodeposition is addressed and answered in the negative. A comparison of Sand’s times ( t Sand ) with experimentally observed lithium dendrite onset times reveals significant discrepancies over a wide range of Li electrodeposition current densities. Specifically, it is shown that morphology evolution in lithium electrodeposition from organic liquid electrolytes commences at time-scales that are at least 1–2 orders of magnitude lower than Sand’s time. To explain this discrepancy, we present a modified Sand’s approach in which transient multi-phase diffusion through the liquid electrolyte as well as through the solid-electrolyte-interphase (SEI) layer is considered. The proposed approach leads to increased accuracy in the prediction of the morphology onset time in lithium electrodeposition. We hope that this perspective helps researchers circumvent the erroneous application of the classical Sand’s equation for lithium electrodeposition, and stimulates experimental and theoretical research into the complex multi-phase transport processes relevant to morphology evolution in lithium electrodeposition.