The dielectric response of boron carbide due to hopping conduction

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Abstract
We present a quantitative analysis of ac electrical conductivity and dielectric constant measurements that were performed on boron carbide samples. This material is crystalline but disordered on the atomic scale because of the existence of a large stoichiometry range from B9C to B4C. The polaronic character of the hopping process is well recognized in this disordered solid. Moreover, the boron carbides of this study are also ceramic materials with grain sizes ranging from 1 to 100 μm, depending on the sample. After having considered most of the models which account for the dielectric response, we have applied Dyre’s model which assumes a uniform distribution of activation energies between two extreme values and uses an effective-medium-type calculation. It permits an elegant interpolation between dc and ac results and a reasonable estimate of the density of localized states (∼1018/cm3 K). The microstructure has little or no influence on the dielectric response in the explored frequency and temperature ranges (10 kHz to 1 GHz and 4 to 100 K). However, when T≳100 K microstructural effects were visible at higher frequencies in a preliminary experiment performed at 9 GHz.