Single-Crystal Studies of Electrical Conductivity, Seebeck Effect, and Hall Voltage in Sodium Vanadium Bronze and a Crystal-Field Model of Electron Transport

Abstract

New data are presented for single crystals of Na0.33V2O5. Conductivity along the b axis follows a dependence of the form σT = A exp( − E / kT) with E = 0.067 eV below 140°K and E = 0.057 eV above 140°K. The Seebeck coefficient changes from − 225 μV deg−1 at 70°K to − 135 μV deg −1 at 150°K; thereafter, it remains constant to 300°K. The Hall coefficient at 300°K is − 3 × 10−3cc C−1 which corresponds to n-type carriers at a density of 2.2 = 1021 cc−1 and a Hall mobility of 0.2 cm2V−·sec−1. At 189°K, the Hall data indicate identical carrier density but a mobility about half as large as at room temperature. All the above data together with reported magnetic susceptibility results can be fitted by a small-polaron (hopping) model. Donor states are believed to be Γ6 levels of V4+. These are 0.016 eV below Γ7 conduction states between which hopping occurs with an activation energy of 0.050 eV. Detailed calculation shows a good fit with a crystal-field model in which d1-ion levels are split under tetragonal distortion Δ = 0.10 eV with spin-orbit coupling constant λ = 0.02 eV, and delocalization parameter k = 1.0. Arguments are given for believing that the electrons responsible for the conduction and the observed paramagnetism hop from vanadium to vanadium and are not delocalized over the oxygen framework through V(3d) − O(pπ) overlap. There is, however, evidence for considerable covalent bonding of the σ type between the vanadium and oxygen atoms.