Study of Li atom diffusion in amorphous Li₃PO₄ with neural network potential

To clarify atomic diffusion in amorphous materials, which is important in novel information and energy devices, theoretical methods having both reliability and computational speed are eagerly anticipated. In the present study, we applied neural network (NN) potentials, a recently developed machine learning technique, to the study of atom diffusion in amorphous materials, using Li₃PO₄ as a benchmark material. The NN potential was used together with the nudged elastic band, kinetic Monte Carlo, and molecular dynamics methods to characterize Li vacancy diffusion behavior in the amorphous Li₃PO₄ model. By comparing these results with corresponding DFT calculations, we found that the average error of the NN potential is 0.048 eV in calculating energy barriers of diffusion paths, and 0.041 eV in diffusion activation energy. Moreover, the diffusion coefficients obtained from molecular dynamics are always consistent with those from ab initio molecular dynamics simulation, while the computation speed of the NN potential is 3-4 orders of magnitude faster than DFT. Lastly, the structure of amorphous Li₃PO₄ and the ion transport properties in it were studied with the NN potential using a large supercell model containing more than 1000 atoms. The formation of P₂O₇ units was observed, which is consistent with the experimental characterization. The Li diffusion activation energy was estimated to be 0.55 eV, which agrees well with the experimental measurements.