ac hopping conductivities, dielectric constants, and reflectivities of boron carbides

The dielectric functions of several boron carbides with composition spanning the single-phase region (9–19 at. % C) have been measured over a broad range of frequencies (${10}^2$–${10}^{15}$ Hz), making it possible to evaluate the various polarization contributions to the dielectric response. The high-frequency (electronic) contributions to the real part of the dielectric constants (ɛ′) are sizable (${\mathrm{\varepsilon }}_{\mathrm{\infty }}^{\prime }$≃7), whereas the lattice (ionic) contributions are small (${\mathrm{\varepsilon }}_{\mathrm{l}}^{\prime }$⩽2). This result implies that the electron-lattice interaction in these materials is of short range, like that of covalent semiconductors. The low-frequency dielectric properties and ac conductivities are dominated by the hopping motion of localized charge carriers which are believed to be bipolaronic (paired) holes on ${\mathrm{B}}_{11}$C icosahedra. The frequency, temperature, and carbon-concentration dependences of these properties can be understood in terms of a recent model for adiabatic small-polaronic hopping between spatially close pairs of nearly degenerate sites. Distinctively, both the dielectric constant and conductivitiy exhibit peaks as a function of carbon content. This feature is consistent with a model that describes the evolution of the structure with increasing carbon content and results in peaking of the localized hole density at 1313 at. % carbon. It is argued that the boron carbides are an ideal system for studying adiabatic small-polaron type hopping transport.