Conductivities and Seebeck coefficients of boron carbides: Softening bipolaron hopping
Abstract
The electrical conductivities and Seebeck coefficients of boron carbides ${\mathrm{B}}_{12+x}{\mathrm{C}}_{3\ensuremath{-}x}$ with $0.06\ensuremath{\lesssim}x\ensuremath{\lesssim}1.7$ have been measured from 8 K to as high as 1750 K. At high temperature, the temperature dependence of the conductivities is Arrhenius and the activation energy, \ensuremath{\approx}0.16 eV, is independent of the carbon concentration. The preexponential factors of the conductivity exhibit a nonmonotonic dependence on x, peaking near $x=1.$ These results are consistent with a previously proposed model based on holes forming singlet bipolarons on the boron carbide ${\mathrm{B}}_{11}\mathrm{C}$ icosahedra. At low temperature, the boron carbide conductivities are non-Arrhenius with a temperature dependence that is a strong function of the composition x. This strong sensitivity to composition indicates that percolation effects, arising from boron carbides having carbon atoms in inequivalent locations, influence the conductivity at low temperature. With x holes per unit cell, boron carbides have very large Seebeck coefficients that depend only weakly on x. The magnitudes and temperature dependences of the Seebeck coefficients are consistent with large contributions from carrier-induced softening of local vibrations. Softening effects can be exceptionally large when singlet bipolarons are stabilized among degenerate electronic energy levels by their softening of symmetry-breaking vibrations: ``softening bipolarons.'' The boron carbide transport properties are generally consistent with those expected of softening bipolarons. Finally, two high-temperature effects are observed in the boron carbide conductivities. The conductivities of samples having high carrier densities, $x\ensuremath{\approx}1,$ are suppressed above 700 K. This suppression can arise when the rapid hopping of nearby carriers disrupts the energy coincidence required for a carrier's hop. At even higher temperatures, a sharp increase in the boron carbide conductivities $(\ensuremath{\sigma}\ensuremath{\propto}{T}^{4})$ suggests a radiation-induced excitation of mobile charge carriers.