  Density Functional Theory calculations using the quasi-harmonic approximation
have been used to calculate the solid Hugoniot of two polytypes of boron
carbide up to 100 GPa. Under the assumption that segregation into the elemental
phases occurs around the pressure that the B11Cp(CBC) polytype becomes
thermodynamically unstable with respect to boron and carbon, two
discontinuities in the Hugoniot, one at 50 GPa and one at 90-100 GPa, are
predicted. The former is a result of phase segregation, and the latter a phase
transition within boron. First principles molecular dynamics (FPMD) simulations
were employed to calculate the liquid Hugoniot of B4C up to 1.5 TPa, and the
results are compared to recent experiments carried out at the Omega Laser
Facility up to 700 GPa [Phys. Rev. B 94, 184107 (2016)]. A generally good
agreement between theory and experiment was observed. Analysis of the FPMD
simulations provides evidence for an amorphous, but covalently bound, fluid
below 438 GPa, and an atomistic fluid at higher pressures and temperatures.
