Hybrid Functional Study on Small Polaron Formation and Ion Diffusion in the Cathode Material Na₂Mn₃(SO₄)₄

The crystal structure, electronic structure, and diffusion mechanism of Na ions in the cathode material Na₂Mn₃(SO₄)₄ are investigated based on the Heyd-Scuseria-Ernzerhof hybrid density functional method. The simultaneous motion model of polaron-sodium vacancy complexes was used to reveal the diffusion mechanism of Na ions in this material. Polaron formation at the Mn third-nearest neighbor to the Na vacancy was found. Two crossing and two parallel elementary diffusion processes of the polaron-Na vacancy complex were explored. The most preferable elementary diffusion process has an activation energy of 852 meV, which generates a zigzag-like pathway of Na-ion diffusion along the [001] direction in the whole material. Possessing a voltage of 4.4 V and an activation energy of 852 meV, Na₂Mn₃(SO₄)₄ is expected to be a good cathode material for rechargeable sodium ions.