Phase diagram of boron carbide with variable carbon composition

Boron carbide exhibits intrinsic substitutional disorder over a broad composition range. The structure consists of 12-atom icosahedra placed at the vertices of a rhombohedral lattice, together with a 3-atom chain along the threefold axis. In the high-carbon limit, one or two carbon atoms can replace boron atoms on the icosahedra while the chains are primarily of type C-B-C. We fit an interatomic pair interaction model to density-functional-theory total energies to investigate the substitutional carbon disorder. Monte Carlo simulations with sampling improved by replica exchange and augmented by two-dimensional multiple histogram analysis predict three phases. The low-temperature, high-carbon-composition monoclinic $Cm$ structure disorders through a pair of phase transitions, first via an Ising-like transition to a monoclinic centrosymmetric state with space group $C2/m$, then via a first-order three-state Potts-like transition to the experimentally observed rhombohedral $R\overline{3}m$ symmetry.