Theoretical study of the structure of boron carbide B13C2

We have resolved long-standing discrepancies between the theoretical and experimental crystal structures of boron carbide B13C2. Theoretical studies predict that B13C2 should be stoichiometric and have the highest symmetry of the boron carbides. Experimentally, B13C2 is a semiconductor and many defect states have been reported, particularly in the CBC chain. Reconciling the disordered states of the chain, the chemical composition, and the lowest-energy state is problematic. We have solved this problem by constructing a structural model where approximately three-quarters of the unit cells contain (B11C)(CBC) and one-quarter of them contain (B-12)(B-4). This structural model explains many experimental results, such as the large thermal factors in x-ray diffraction and the broadening of the Raman spectra, without introducing unstable CBB chains. The model also solves the energy-gap problem. We show that there are many arrangements of these two types of unit cells, which are energetically almost degenerate. This demonstrates that boron carbides are well described by a geometrically frustrated system, similar to that proposed for beta-rhombohedral boron.