Fig. 1. Energy versus volume using PBEsol-GGA, and the optimized cubic structure (inset) using the Xcrysden software^[29] for NaVO₃, KVO₃, and RbVO₃.

Fig. 2. (a) The calculated specific heat capacity and (b) the number electron density of NaVO₃, KVO₃, and RbVO₃ plotted against temperature.

Fig. 3. Electronic band structures of NaVO₃, KVO₃, and RbVO₃ using mBJ.

Fig. 4. The total density of states (TDOS) along with partial density of states (PDOS) calculated for NaVO₃, KVO₃ and RbVO₃ by using the mBJ potential.

Fig. 5. The electrical and thermal conductivities of NaVO₃, KVO₃ and RbVO₃ against [(a), (c)] chemical potential and [(b), (d)] temperature, respectively.

Fig. 6. The Seebeck coefficients S of NaVO₃, KVO₃, and RbVO₃ against (a) chemical potential and (b) temperature.

Fig. 7. The power factors σ S²/τ of NaVO₃, KVO₃, and RbVO₃ against (a) chemical potential and (b) temperature.

Table 1. The calculated lattice constant a₀ (Å), bulk modulus B₀ (GPa), tolerance factor t, enthalpy of formation Δ H (eV), elastic constant (C₁₁ (GPa), C₁₂ (GPa), C₄₄ (GPa)), Shear modulus G (GPa), Young modulus Y (GPa), Pugh ratio B/G, and θ_D (K) of NaVO₃, KVO₃ and RbVO₃ in cubic phase by using the PBEsol-GGA approximation. TF(t_g): compatibility of an ion with perovskite crystal structure, with t_g being the Goldsmidth tolerance factor.

Table 2. The calculated indirect bandgap E_g (eV) and room-temperature values of electrical conductivity σ, thermal conductivity κ and Seebeck coefficient S and power factor σ S² of NaVO₃, KVO₃ and RbVO₃ perovskites.