Insight into Diffusion Mechanism in Cathode Materials NaVPO5 and NaVFPO4 for Sodium Ion Batteries: DFT Investigation
Authors: Luong Huu Duc Duc , Dinh Van An , Momida Hiroyoshi , Oguchi Tamio 
Published: December 2020

In transition metal-based cathode materials, the oxidation and reduction of transition metal ions cause local distortion in the crystal structure during intercalation and de-intercalation, resulting in the formation of a quasiparticle, named small polaron. Since a strong binding energy of 500 meV between an alkali ion and a small polaron was reported[1], the polaron would migrate simultaneously with the diffusion of the alkali ions[2]. Using the density functional method, we investigate the crystal, electronic structure, and electrochemical properties of orthorhombic NaxVPO5 and NaxVPO4F, focusing on the diffusion mechanism of a Na ion accompanied with polaron. The diffusion of Na ions can be described as a process of the complex of the Na vacancy and accompanying positive polaron at high Na concentrations and as that of the Na ion and negative polaron at low Na concentrations. When a Na vacancy is introduced to fully occupied structure (x=1), the positive small polaron prefers locating at one of the two first nearest neighbour (1NN) vanadium sites V1NN to the Na vacancy. Similarly, after a Na ion is inserted to fully unoccupied structures (x=0), the negative polaron is formed at a V1NN site of Na ion. Three elementary diffusion processes (EPDs), including the single, crossing,and parallel diffusion processes are explored. The single process occurs when the polaron that strongly binding with the Na vacancy stays at the same position during the Na vacancy diffusion. On the other hand, the parallel (crossing) diffusion process takes place when polaron hops from a V1NN site to the adjacent V1NN site along the direction paralleled (crossed) to Na diffusion path. It is found that the [010] direction is preferable for Na ions diffusing during charging or discharging processes. At a high Na concentration regime, the activation energy E
a gains approximately 400 meV on all three EPDs in NaVPO5, whereas it lowers to 190 meV, 320 meV and 345 meV for single, crossing and parallel EDPs, respectively, in NaVPO4F. These values of E
a indicate that the effect of polaron migration is negligibly weak in NaVPO5 at high Na concentrations. At low Na concentrations, such a effect of negative polaron migration on Na ion diffusion is considerably substantial in both materials. While the parallel diffusion process is less preferred (Ea
= 830 meV and 570 meV for VPO5 and VPO4F, respectively), the single and crossing processes can occur with same activation energy of about 630 meV and 530 meV for VPO5 and VPO4F, respectively. In general, energy barriers required for diffusion in NaVPO4F are notably lower than those in NaVPO5. Compared with some common cathode materials such as the olivines, it is expected that NaVOPO4 and NaVPO5 perform as good as LiFePO4 for LIBs.
Figure 1: Diffusion pathway of Na vacancy–positive polaron complex along the [010] direction in de-intercalation. The brown and green octahedra indicate the 1NN and 2NN VO6 groups relative to the Na vacancy, respectively. The red, green and blue balls illustrate the trace of the crossing, single and parallel diffusion processes, respectively. Curved arrows illustrate the migration directions of the polaron in each EDP.

[1]T. Maxisch, F. Zhou and G. Ceder, Phys. Rev. B: Condens. Matter Mater. Phys., 73, 104301 (2006).

[2]V. A. Dinh, J. Nara, and T. Ohno, Appl. Phys. Express,
5,045801(2012).

Figure 1