Morphological stability during electrodeposition
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esearch Letter
Morphological stability during electrodeposition Raúl A. Enrique, Stephen DeWitt, and Katsuyo Thornton, Joint Center for Energy Research Storage, and Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA Address all Correspondence to Katsuyo Thornton at [email protected] (Received 23 January 2017; accepted 31 May 2017)
Abstract The uniform electrodeposition of certain materials, such as Li metal, remains elusive because the mechanisms controlling growth instability are not fully understood. To determine the conditions that lead to either stable or unstable deposition, we develop a phase-field model for the growth of multiple deposits in a binary electrolyte and examine the behavior as the kinetic parameters are varied. We find that the second Damköhler number, defined as the ratio between the reaction and the mass transfer fluxes, is an indicator of deposition instability. Our results suggest that controlling reaction kinetics and initial roughness are essential in achieving stable electrodeposition.
Electrodeposition is a synthesis method with numerous applications, such as surface coating and plating and fabrication of microelectronics.[1] It also occurs during operation in some systems such as rechargeable batteries. Electrodeposition often results in the formation of unstable morphologies such as dendrites, with characteristic length scales ranging from tens of nanometers to tens of microns. While these instabilities can be exploited to synthesize nanostructures, in many applications including batteries, dendrite formation must be avoided. In fact, dendrite formation during charging remains one of the major hurdles for the development of lithium metal batteries. Solidification and electrodeposition share one common feature: in both cases, the growth of the crystal is influenced by diffusion (of solute or latent heat in solidification and ions in electrodeposition). Therefore, models developed for solidification have been applied to describe unstable electrodeposition. For example, Barton and Bockris[2] introduced a model of dendritic growth based on the difference between the diffusion fluxes associated with planar and spherical geometries. Although this is a valuable first approximation,[3,4] this type of analysis does not rigorously incorporate the coupling between ionic diffusion, electrostatics, and the kinetics of electrochemical reactions. In addition to the growth instabilities that arise from diffusion, the electrostatic potential, which is also governed by a Laplace-type equation, has been identified as a possible source of unstable deposition.[5] According to electrostatics, an equipotential surface induces a localized enhancement of the electric field around protuberances inversely proportional to the local radius of curvature.[6] This local enhancement, called the ‘lightning rod’ effect, has been used to explain the preferred growth at dendrite tips.[5]
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The deposition flux during electrodeposition is governed by the electrochemical reaction
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