Configurational order-disorder induced metal-nonmetal transition in B$_{13}$C$_{2}$ studied with first-principles superatom-special quasirandom structure method

Due to a large discrepancy between theory and experiment, the electronic character of crystalline boron carbide B$_{13}$C$_{2}$ has been a controversial topic in the field of icosahedral boron-rich solids. We demonstrate that this discrepancy is removed when configurational disorder is accurately considered in the theoretical calculations. We find that while ordered ground state B$_{13}$C$_{2}$ is metallic, configurationally disordered B$_{13}$C$_{2}$, modeled with a superatom-special quasirandom structure method, goes through a metal to non-metal transition as the degree of disorder is increased with increasing temperature. Specifically, one of the chain-end carbon atoms in the CBC chains substitutes a neighboring equatorial boron atom in a B$_{12}$ icosahedron bonded to it, giving rise to a B$_{11}$C$^{e}$(BBC) unit. The atomic configuration of the substitutionally disordered B$_{13}$C$_{2}$ thus tends to be dominated by a mixture between B$_{12}$(CBC) and B$_{11}$C$^{e}$(BBC). Due to splitting of valence states in B$_{11}$C$^{e}$(BBC), the electron deficiency in B$_{12}$(CBC) is gradually compensated.