Theoretical phase diagram of boron carbide from ambient to high pressure and temperature

The phase diagram of boron carbide is calculated within the density functional theory as a function of temperature and pressure up to 80 GPa, accounting for icosahedral, graphitelike, and diamondlike atomic structures. Only some icosahedral phases turn out to be thermodynamically stable with atomic carbon concentrations (c) of 8.7% (B_10.5C), 13.0% (B_6.7C), 20% (B₄C), and 28.6% (B_2.5C), respectively. Their respective ranges of stability under pressure and temperature are calculated, and the theoretical T-P-c phase diagram boundaries are discussed. At ambient conditions, the introduction in the phase diagram of the new phase B_10.5C with an ordered crystalline motif of 414 atoms is shown to bring the theoretical solubility range of carbon in boron close to the experimental one. The link with the experimental phase diagram consisting of one single phase having the R 3 m space group is discussed, and the concept of partial occupation of Wyckoff's site is introduced. At high pressure, the phase diagram is defined by a new carbon-rich phase B_2.5C, which is stabilized by both pressure and temperature in our calculations. All of the other diamond and graphite phases reported previously turn out to be thermodynamically unstable in our calculations, although some of them are observed in high pressure experiments.