Transport of secondary carriers in a solid lithium-ion conductor

Inorganic-solid lithium electrolytes are typically thought of as single-ion conductors, but the presence of secondary carriers can strongly affect their performance. Conventional descriptions of multi-carrier transport neglect both interactions between mobile species and stress diffusion — phenomena which can markedly impact the electrical response. We apply irreversible thermodynamics to develop a chemomechanical transport model for elastic-solid ionic conductors containing two mobile ions. We simulate lithium-ion conducting Li5La3Nb2O12 (LLNO) garnet oxide, a material within which experiments have shown that mobile protons can be freely substituted for lithium to form Li5(1−y)H5yLa3Nb2O12. When subjected to a current, we find that proton-substituted LLNO exhibits bulk lithium polarization, whose extent is partially controlled by cation/cation interactions. Secondary carriers segregate naturally if their global concentration is low, accumulating in a thin boundary layer near the cathode. We quantify the limiting current and Sand's time, and analyze experimental data to show how competitive proton transport affects LLNO performance.