A Free Energy Model of Boron Carbide

The assessed phase diagram of the boron-carbon system contains a single nonstoichiometric boron-carbide phase of rhombohedral symmetry with a broad, thermodynamically improbable, low temperature composition range. We combine first principles total energy calculations with phenomenological thermodynamic modeling to propose a revised low temperature phase diagram that contains two boron-carbide phases of differing symmetries and compositions. One structure has composition B4C and consists of B11C icosahedra and C-B-C chains, with the placement of carbon on the icosahedron breaking rhombohedral symmetry. This phase is destabilized above 600 K by the configurational entropy of alternate carbon substitutions. The other structure, of ideal composition B13C2, has a broad composition range at high temperature, with rhombohedral symmetry throughout, as observed experimentally.