Electronic band structures of the scheelite materials CaMoO4, CaWO4, PbMoO4, and PbWO4

Abstract

Density-functional calculations using the linearized-augmented-plane-wave method were carried out for the scheelite materials ${\mathrm{CaMoO}}_4,$ ${\mathrm{CaWO}}_4,$ ${\mathrm{PbMoO}}_4,$ and ${\mathrm{PbWO}}_4$ in order to determine their ground-state electronic properties. The results indicate that ${\mathrm{CaMoO}}_4$ and ${\mathrm{CaWO}}_4$ have direct band gaps at the center of the Brillouin zone, while ${\mathrm{PbMoO}}_4$ and ${\mathrm{PbWO}}_4$ have band extrema at wave vectors away from the zone center with possibly indirect band gaps. The magnitudes of the band gaps increase in the order ${\mathrm{PbMoO}}_4{<\mathrm{PbWO}}_4{<\mathrm{CaMoO}}_4{<\mathrm{CaWO}}_4.$ The valence and conduction bands near the band gap are dominated by molecular orbitals associated with the ${\mathrm{MoO}}_4^{\mathrm{-}\mathrm{\alpha }}$ and ${\mathrm{WO}}_4^{\mathrm{-}\mathrm{\alpha }}$ ions, where $\alpha \approx 2.$ The valence-band widths are 5 and 5.5 eV for the Ca and Pb materials, respectively. In the Pb materials, the Pb $6s$ states form narrow bands 1 eV below the bottom of the valence bands, and also hybridize with states throughout the valence bands, while the Pb $6p$ states hybridize with states throughout the conduction bands. In the Ca materials, the Ca $3d$ states contribute to a high density of states 3–4 eV above the bottom of the conduction bands.