High-energy electron-energy-loss study of sodium-tungsten bronzes.

Abstract

Single-crystal metallic cubic sodium-tungsten bronzes ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{WO}}_{3}$ (x\ensuremath{\ge}0.25) and ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{Ta}}_{\mathit{y}}$${\mathrm{W}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$${\mathrm{O}}_{3}$ (x-y=0.42) and monoclinic reduced ${\mathrm{WO}}_{3\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ have been investigated by high-energy electron-energy-loss spectroscopy (EELS) in transmission. For all electron densities the volume plasmon dispersion appears to be positive quadratic in momentum transfer q. The dispersion coefficient is much smaller than that predicted from the random-phase approximation for one isotropic parabolic band. This deviation can be reduced by recognizing the threefold degeneracy of the conduction-band ${\mathit{t}}_{2\mathit{g}}$ states in an octahedral field and narrowing of these bands with increasing sodium content. Anisotropy of the dispersion between the (100) and (110) direction is not observed. Optical effective masses ${\mathit{m}}^{\mathrm{*}}$(x) of the conduction electrons and background dielectric constants ${\mathrm{\ensuremath{\epsilon}}}_{\mathrm{\ensuremath{\infty}}}$(x) have been determined and compare well with data from optical spectroscopy and EELS in reflection, but not with photoemission results. This discrepancy is a result of the photoemission-data evaluation in which the conduction-band degeneracy was neglected. Na 2p core-level excitation energies argue against an admixture of sodium orbitals to the conduction band near the metal-nonmetal transition at x\ensuremath{\sim}0.2. Na 3s states admixed to O 2p states are observed at about 10--11 eV above the Fermi level in O 1s absorption edges. The x dependence of ${\mathit{m}}^{\mathrm{*}}$ and of the width of the O 1s absorption edge of ${\mathrm{Na}}_{\mathit{x}}$${\mathrm{WO}}_{3}$ supports a model of conduction-band narrowing with increasing Na concentration.