Phase Transitions of Boron Carbide: Pair Interaction Model of High   Carbon Limit
  Boron Carbide exhibits a broad composition range, implying a degree of intrinsic substitutional disorder. While the observed phase has rhombohedral symmetry (space group R3(bar)m), the enthalpy minimizing structure has lower, monoclinic, symmetry (space group Cm). The crystallographic primitive cell consists of a 12-atom icosahedron placed at the vertex of a rhombohedral lattice, together with a 3-atom chain along the 3-fold axis. In the limit of high carbon content, approaching 20% carbon, the icosahedra are usually of type B11Cp, where the p indicates the carbon resides on a polar site, while the chains are of type C-B-C. We establish an atomic interaction model for this composition limit, fit to density functional theory total energies, that allows us to investigate the substitutional disorder using Monte Carlo simulations augmented by multiple histogram analysis. We find that the low temperature monoclinic Cm structure disorders through a pair of phase transitions, first via a 3-state Potts-like transition to space group R3m, then via an Ising-like transition to the experimentally observed R3(bar)m symmetry. The R3m and Cm phases are electrically polarized, while the high temperature R3(bar)m phase is nonpolar. 
Sanxi Yao, W. P. Huhn, M. Widom
cond-mat.mtrl-sci