Sodium-ion batteries with their abundant resource availability and low cost, show a tremendous potential in energy storage. Sodium-ion batteries emerge as a more economical alternative to lithium-ion batteries, making it highly attractive for large-scale grid energy storage applications. To enhance the competitiveness of sodium-ion batteries, the development of high-energy cathode materials is crucial. As a result, recent efforts are made to explore sodium-ion cathode materials, particularly sodium layered oxides and polyanion compounds. The most extensively studied polyanion sodium-ion cathode materials are vanadium phosphates (i.e., Na₃V₂(PO₄)₃ or NVP) and fluorophosphates (i.e., Na₃V₂(PO₄)₂F₃ or NVPF). NVP with its sodium fast ion conductor (Na-superionic conductor, NASICON) structure is considered as a high-performance sodium-storage cathode material. The related experimental results indicate that the actual specific capacity of pure-phase NVP is lower than theoretical expectations, and its cycling stability is generally poor. Adjusting the composition and structure of NVP through elemental doping is an effective strategy to enhance its cycling reversibility, increase reversible capacity, and improve sodium ion diffusion kinetics. However, some challenges exist in accurately measuring the properties of sodium-ion cathode materials during experiments coupled with high trial-and-error costs and the lack of scientific theoretical guidance. This study was to utilize first-principles calculations to investigate the electronic structure characteristics of mixed polyanions doped with different transition metals, aiming to elucidate the conductivity mechanisms within polyanion systems. In addition, the microscopic processes of sodium ion insertion/extraction during the charge and discharge cycles of polyanion cathode materials were also analyzed via simulating all possible sodium ion migration pathways and calculating the corresponding energy barriers and voltage platforms in an ideally conductive polyanion system.

Spin-polarized DFT calculations were used within the Vienna ab initio simulation package. The projector-augmented wave (PAW) method was applied to solve the ion-electron interactions in a periodic system. The generalized gradient approximation (GGA) with Perdew−Burke−Ernzerhof (PBE) functionals was used to take into consideration of the exchange-correlation interactions in the Kohn−Sham equations. A plane-wave basis set with a cutoff energy of 400 eV was used to expand the Kohn–Sham valence states. A k-point mesh of dimensions of 3 × 3 × 1 was employed for the Brillouin zone integration. For calculating the electronic structure, a Monkhorst-Pack grid of 5 × 5 × 1 was sampled. The self-consistent field convergence criteria were set at 1 ×10^–6 eV. All the structures were sufficiently relaxed until the force at each atom was less than 0.02 eV∙Å^–1. The climbing-image nudged elastic band (CI-NEB) was used to calculate the migration energy barrier corresponding to the migration path of Na ions. This is an effective way to find the saddle points of the ion diffusion energy. Five intermediate images were constructed between the initial and final states along the sodium ion diffusion path. The calculation formula of charge and discharge voltage is: V = (E(Na_xMP) + (y–x)E(Na)–E(Na_yMP))/(y–x), where E(Na_yMP), E(Na_xMP) and E(Na) indicate the discharge completion state, charging completion state and the energy of Na atoms, respectively.

The results show that Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃ have more abundant electronic state near the Fermi level, compared to the original Na₃V₂(PO₄)₃. The conductivity of Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃ is better than that of the original Na₃V₂(PO₄)₃, accelerating the kinetic process of electron transfer and ion extraction. The electronic structure characteristics of mixed polanion based on iron and manganese are analyzed, and the conductive mechanism of polyanionic system is proved via the first-principles calculations, which is helpful to screen the polanion cathode materials with an ideal conductivity.

The CI-NEB method is used to calculate the three diffusion paths and energy barriers in polanionic cathode materials (i.e., Na₃TiMn(PO₄)₃, Na₃TiFe(PO₄)₃ and Na₃V₂(PO₄)₃). The energy barriers for diffusion paths 1 and 3 of the primitive Na₃V₂(PO₄)₃ are both 0.12 eV. The energy barrier of diffusion path 2 is 0.11 eV, which is better than that of diffusion path 1 and 3. For Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃, the energy difference between the initial and final state structures is too large (i.e., 0.6 eV) although the energy barrier of the diffusion path 1 is extremely low (i.e., only 0.04 eV), which is not conducive to the cyclic diffusion of sodium ions in the cathode material from the thermodynamic perspective. Sodium at Na1 is not conducive to prolapse, and sodium at Na2 is easier to prolapse during diffusion. The structural characteristics of Na₃MM'(PO₄)₃ and experimental studies both thus indicate that sodium prolapsed at different positions has different effects on the structure. In terms of diffusion paths 2 and 3, the energy difference between the initial and final structures is close to 0, and the corresponding diffusion energy barrier is between 0.12 eV and 0.18 eV, favoring the diffusive transport of sodium ions both thermodynamically and kinetically.

As the charging process proceeds, the voltage gradually increases, while desodium and sodium value decreases. The Na2 position is the first sodium ion effluent, which is consistent with that of the experimental studies. The theoretical calculation shows that the voltage platform of Na₃V₂(PO₄)₃ changes, the structure of Na₃V₂(PO₄)₃ changes in the process of sodium extraction, and the voltage platform of Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃ is more stable than the voltage platform of original Na₃V₂(PO₄)₃.

The structure and electronic characteristics of Na₃V₂(PO₄)₃, Ti, Cr, Mn, Fe and other transition group metals were investigated. The density of state electronic structure of Ti, Mn and Ti and Fe substituted Na₃MM′(PO₄)₃ polyanionic sodium ion battery cathode material. The results showed that Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃ had more abundant electronic states near the Fermi level, the conductivity of Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃ was better than that of the original Na₃V₂(PO₄)₃, which could effectively enhance the conductivity and accelerate the kinetic process of electron transfer and ion extraction. We calculated three sodium ion diffusion paths, analyzed the three diffusion paths of sodium ion in polyanionic cathode materials (i.e., Na₃TiMn(PO₄)₃, Na₃TiFe(PO₄)₃ and Na₃V₂(PO₄)₃) and the corresponding energy barriers of 0.12–0.18 eV, and explained that the materials Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃ were thermodynamically and kinetically beneficial. The theoretical calculation further studied the influence of voltage platforms on cathode materials. Based on the electronic structure and ion diffusion path results, Na₃TiMn(PO₄)₃ and Na₃TiFe(PO₄)₃ were selected as NASICON sodium ion cathode materials with a superior comprehensive performance.