C under high pressure from first principles*

Despite decades of investigations, the atomic structure of boron carbide below 20% atomic carbon concentration is still subject to debates [1,2]. In particular, the experimental Raman spectrum of B_4.3C is not yet understood: while most of the peaks have for long been explained by the low-energy theoretical ground state structure B₄C with 20% atomic carbon concentration [3], two large bands at low frequencies remain unexplained even when common point defects are introduced into the atomic structure [1,2]. Moreover, the behavior of the two bands under high pressure is uncommon [4]. Finding a theoretical explanation of this behavior certainly requires a detailed understanding of the underlying atomic structure. 

Beside the B₄C unit cell that consists of one  (B₁₁C^p ) icosahedron and one C-B-C chain, new building blocks such as C-B-C-B chains and B<B₂>B pantograph-like intericosahedral blocks have been identified with HRTEM [5]. Two crystalline unit-cells with either building blocks have been confirmed theoretically to be part of the B-C phase diagram at respectively 13.0% (B_6.7CC, named OPO₂) and 8.7% (B_10.5C, named OPO₁) atomic C concentrations [6].  In the present work, the unexplained Raman bands will be discussed in light of calculations under high pressure within the density functional perturbation theory for the lattice vibrational frequencies and with Raman intensityies computed with the 2^nd order response [7]. The respective roles of the building blocks and of disorder will be highlighted.