Optical properties of the sodium-tungsten bronzes and tungsten trioxide

Abstract

A polarization-modulation ellipsometric technique was used to make direct measurements of the optical dielectric constants of single-crystal specimens of the nonstoichiometric tungsten-bronze compound ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$ ($0.52<x<\mathrm{}0.94\mathrm{}$) and W${\mathrm{O}}_3$, in the energy range from 1.0 to 5.5 eV. A method for determining the optical constants of anisotropic materials from modulation ellipsometry was developed in the study of tungsten trioxide. The behavior of the sodium bronzes as a function of sodium concentration is in agreement with recent calculations of the band structures for these materials. The system exhibits almost rigid-band behavior. The data were fit to the classical Drude free-electron model for the optical properties of metals. The W${\mathrm{O}}_3$ dielectric constants were used to directly determine the contribution of higher-energy bound-electron transitions to the optical constants of ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$ in the free-electron region. The results of jointdensity-of-states calculations were used in conjunction with the free-electron model to demonstrate that a relatively large discrepancy between conduction-electron relaxation times derived from the free-electron model alone and those determined from the dc conductivity may result, in part, from underlying interband transitions.