Transport of secondary carriers in a solid lithium-ion conductor

Guanchen Li,Charles W Monroe

doi:10.1016/j.electacta.2021.138563

Abstract

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.

Highlights

Inorganic-solid lithium electrolytes are typically thought of as single-ion conductors, but the presence of secondary carriers can strongly affect their performance
When subjected to a current, we find that proton-substituted LLNO exhibits bulk lithium polarization, whose extent is partially controlled by cation/cation interactions
Interfacial double layers in such materials screen most of the external electric field; the concomitant steep field gradients can lead to surface stresses that are much higher than the bulk, [9]

Summary

Model formulation

The system of Eqs. 1 to 6 is closed by defining the lattice occupancy and stating constitutive laws for the thermodynamic material properties χk j,. Since the ideal-solid-solution assumption requires that configurational entropy accounts entirely for the composition dependence of free energy, L1−yHyLNO must exhibit a compositionindependent bulk modulus K. One can combine Eqs. 1 and 3, integrate to produce an equation for local pressure in terms of E, the x-component of the electric field, p(x) − p(0) = 6 E2(x) − E2(0) This result neglects inertial contributions to momentum, which are very small at practical current densities. If the carrier/carrier interaction strength is zero, the two carrier ions move independently; diffusional drag on them is controlled only by their interactions with the crystal lattice, as is assumed when electrolytes are described by Poisson–Nernst–Planck theory. This can occur via collective transport modes such as the formation of ion pairs, as has been suggested to explain ionomers that exhibit negative transference numbers [31]

Double-layer effects

Steady-state polarization

Conclusions

Declaration of Competing Interest