Computational study of Na diffusion and conduction in P2- and O3-Na2x[NixTi1-x]O2 materials with machine-learning interatomic potentials

Abstract

Sodium-ion batteries (SIBs) provide a feasible solution for large-scale energy storage applications of sustainable energy resources like wind and solar energy. Layered sodium nickel titanates (Na2x[NixTi1-x]O2) (SNTL) are considered a promising electrode material for SIBs since they can function as either a positive or negative electrode due to the coexistence of high redox potential element Ni (V = 3.7 V vs. Na/Na+) and low redox potential element Ti (V = 0.7 V vs. Na/Na+). There have been both experimental and computational studies on the family of Na2x[NixTi1-x]O2 materials, investigating their structures, electrochemical performance, electronic and ionic conductivity, etc. However, the current understanding of the Na migration mechanism is still very limited at an atomic level because of the restrictions of simulation methods: density-functional theory (DFT) simulation is restricted to a small length and time scale, whereas the conventional empirical interatomic potential (IP) is restricted by a limited accuracy. To solve this efficiency-versus-accuracy dilemma, herein we developed a neural network (NN)-based machine-learning interatomic potential (MLIP), which is trained using DFT data. Our MLIP demonstrates a DFT-approaching accuracy in terms of atomic forces. Moreover, the extracted Na self-diffusivity, ionic conductivity, and activation energy values from MLIP-MD simulation agree well with experimental data. In general, P2-SNTL demonstrates a higher Na self-diffusivity and ionic conductivity than O3-SNTL, mainly due to the larger bottleneck size through which Na ions migrate. We also employed the incoherent density correlation function to study the Na migration mechanism. The Singwi-Sjölander (SS) model and Chudley-Elliot (CE) model were used to fit the jump-diffusion behavior in P2- and O3-SNTL, respectively. The obtained jump distance values match well with the typical distance between the nearest Na sites in P2- and O3-SNTL, confirming that the hopping events happen mostly between neighboring Na sites in SNTL. The decrease of residence time and jump distance values with temperature is a result of higher ion mobility and level of delocalization, as validated by the nuclear density maps. In addition, our study also confirmed that both the “straight” and “curved” Na migration paths exist in O3-SNTL, in contrast to previous studies which only mention the “curved” migration path. In the end, our calculated Haven ratios have a value <1, indicating that it is more likely for the Na hopping events to occur via a concerted migration of several atoms other than the jump of an isolated atom.