xdependence of the electronic properties of cubicNaxWO3

Analysis of a variety of experimental data for cubic ${\mathrm{Na}}_{\mathrm{x}}$ ${\mathrm{WO}}_3$ (0.5≤x≤1) indicates that the electronic structure changes significantly with composition x. The lower–conduction-band width decreases and the band gap increases with increasing x. A simple theoretical model is developed which describes the x dependence of the electronic properties of cubic ${\mathrm{Na}}_{\mathrm{x}}$ ${\mathrm{WO}}_3$. The model provides closed-form analytical expressions for the energy bands, and the total and partial density-of-states functions. Results are obtained for the electronic specific heat, effective mass, magnetic susceptibility, and photoemission energy distribution curves of ${\mathrm{Na}}_{\mathrm{x}}$ ${\mathrm{WO}}_3$. These results are shown to agree with experimental data much better than the results of the rigid-band model.