Modeling of lithium-whisker growth: Effect of mass transport into grain boundary

Understanding the growth of lithium whiskers is of paramount importance in improving the reliability of lithium-ion batteries. In this work, we consider the effect of the mass transport across the interface between adjacent grain and grain boundary into the grain boundary on the root growth of a lithium whisker in the framework of viscous flow of grain boundary fluid in a circular grain boundary. Closed-form solutions are obtained for the growth rate of the lithium whisker and the temporal evolution of the whisker length. The characteristic time for the growth of the lithium whisker is derived. The numerical results illustrate that increasing the mass transport across the interface between adjacent grain and grain boundary into the grain boundary increases the growth rate of the lithium whisker, which depends on the nominal diffusivity of lithium diffusion for the mass transport across the interface and the viscosity of the grain boundary fluid (the diffusivity of grain boundary diffusion).