Ab initio study of Na$M$Fe(MoO$_4$)$_3$ ($M$ = Mn, Fe, Co, Ni, Zn): electron structure, sodium diffusion and potentials

The electronic structures of Na$M$Fe(MoO$_4$)$_3$ ($M$ = Mn, Fe, Co, Ni, Zn) molybdates isostructural to $\alpha$-NaFe$_2$(MoO$_4$)$_3$ or $\beta$-NaFe$_2$(MoO$_4$)$_3$ is studied. Taking into account the electronic correlation in the Hubbard model, it is shown that these compounds are semiconductors with the band gap of 1.2–2.6 eV. The sodium diffusion pathways in the $\alpha$-NaFe$_2$(MoO$_4$)$_3$ and $\beta$-NaFe$_2$(MoO$_4$)$_3$ structures are determined, and it is shown that the energy barrier in the compounds with the $\beta$-NaFe$_2$(MoO$_4$)$_3$ structure is almost twice lower. The simulation of sodium extraction shows that these molybdates must have a high potential from 3 to 5 V and insignificant changes in the volume and the formation enthalpy depend on the sodium content. According to the obtained data, low-symmetry Na$M$Fe(MoO$_4$)$_3$ ($M$ = Mn, Fe, Co, Ni, Zn) molybdates exhibit diffusion properties and cathode voltage similar to those in the compounds of the NASICON structural type and also can be promising materials for sodium-ion batteries.