Polaron interaction energies in reduced tungsten trioxide

Consideration of the properties of reduced tungsten trioxide suggest that the mobile charge carriers are polarons. As it is uncertain how the presence of polarons will influence the microstructures of the crystallographic shear (CS) planes present in reduced tungsten trioxide we have calculated both the polaron-CS plane and polaron-polaron interaction energy for a variety of circumstances. Three CS plane geometries were considered, {102}, {103}, and {001} 1CS plane arrays, and the nominal compositions of the crystals ranged from WO_2.70 to WO_3.0. The polarons were assumed to have radii from 0.6 to 1.0 nm and the polaron-CS plane electrostatic interaction was assumed to be screened. The results suggest that for the most part the total interaction energy is small and is unlikely to be of major importance in controlling the microstructures found in CS planes. However, at very high polaron densities the interaction energy could be appreciable and may have some influence on the existence range of CS phases.