Phase-Field Based Multiscale Modeling of Heterogeneous Solid Electrolytes: Applications to Nanoporous Li₃PS₄

Modeling the effective ion conductivities of heterogeneous solid electrolytes typically involves the use of a computer-generated microstructure consisting of randomly or uniformly oriented fillers in a matrix. However, the structural features of the filler/matrix interface, which critically determine the interface ion conductivity and the microstructure morphology, have not been considered during the microstructure generation. Using nanoporous β-Li₃PS₄ electrolyte as an example, we develop a phase-field model that enables generating nanoporous microstructures of different porosities and connectivity patterns based on the depth and the energy of the surface (pore/electrolyte interface), both of which are predicted through density functional theory (DFT) calculations. Room-temperature effective ion conductivities of the generated microstructures are then calculated numerically, using DFT-estimated surface Li-ion conductivity (3.14 × 10^-3 S/cm) and experimentally measured bulk Li-ion conductivity (8.93 × 10^-7 S/cm) of β-Li₃PS₄ as the inputs. We also use the generated microstructures to inform effective medium theories to rapidly predict the effective ion conductivity via analytical calculations. When porosity approaches the percolation threshold, both the numerical and analytical methods predict a significantly enhanced Li-ion conductivity (1.74 × 10^-4 S/cm) that is in good agreement with experimental data (1.64 × 10^-4 S/cm). The present phase-field based multiscale model is generally applicable to predict both the microstructure patterns and the effective properties of heterogeneous solid electrolytes.