General method to predict voltage-dependent ionic conduction in a solid electrolyte coating on electrodes

Understanding the ionic conduction in solid electrolytes in contact with electrodes is vitally important to many applications, such as lithium ion batteries. The problem is complex because both the internal properties of the materials (e.g., electronic structure) and the characteristics of the externally contacting phases (e.g., voltage of the electrode) affect defect formation and transport. In this paper, we developed a method based on density functional theory to study the physics of defects in a solid electrolyte in equilibrium with an external environment. This method was then applied to predict the ionic conduction in lithium fluoride (LiF), in contact with different electrodes which serve as reservoirs with adjustable Li chemical potential $({\ensuremath{\mu}}_{\mathrm{Li}})$ for defect formation. LiF was chosen because it is a major component in the solid electrolyte interphase (SEI) formed on lithium ion battery electrodes. Seventeen possible native defects with their relevant charge states in LiF were investigated to determine the dominant defect types on various electrodes. The diffusion barrier of dominant defects was calculated by the climbed nudged elastic band method. The ionic conductivity was then obtained from the concentration and mobility of defects using the Nernst-Einstein relationship. Three regions for defect formation were identified as a function of ${\ensuremath{\mu}}_{\mathrm{Li}}$: (1) intrinsic, (2) transitional, and (3) $p$-type region. In the intrinsic region (high ${\ensuremath{\mu}}_{\mathrm{Li}}$, typical for LiF on the negative electrode), the main defects are Schottky pairs and in the $p$-type region (low ${\ensuremath{\mu}}_{\mathrm{Li}}$, typical for LiF on the positive electrode) are Li ion vacancies. The ionic conductivity is calculated to be approximately ${10}^{\ensuremath{-}31}\phantom{\rule{4pt}{0ex}}\text{S}\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ when LiF is in contact with a negative electrode but it can increase to ${10}^{\ensuremath{-}12}\phantom{\rule{4pt}{0ex}}\text{S}\phantom{\rule{0.16em}{0ex}}{\text{cm}}^{\ensuremath{-}1}$ on a positive electrode. This insight suggests that divalent cation (e.g., ${\text{Mg}}^{2+}$) doping is necessary to improve Li ion transport through the engineered LiF coating, especially for LiF on negative electrodes. Our results provide an understanding of the influence of the environment on defect formation and demonstrate a linkage between defect concentration in a solid electrolyte and the voltage of the electrode.