## Carbon Under Extreme Conditions, a First Principles Theoretical StudyIn this thesis, I report on the properties of carbon in the pressure and temperature range of 15 to 2000 GPa and 0 to 20000 K, as obtained from first principles calculations based on Density Functional Theory. We have investigated solid/liquid phase boundaries and analyzed structural and electronic transformations as pressure and temperature are increased. In particular, we have determined diamond and BC8 melting lines and predicted the location of the diamond/BC8/liquid triple point, inferred from the crossing of computed phase boundaries. This new phase diagram of the high pressure phases is used to construct a novel multiphase equation of state for carbon. |

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A3/atom ABINIT anharmonic anharmonic term BC8 phase carbon Clapeyron equation coeﬃcients coexistence cold curve compression computed conﬁgurational coordination crystalline cubic Debye model Debye temperature deﬁned Density Functional Theory described diamond and BC8 diamond melting diamond phase diﬀerent diﬃcult diﬀusion dP dT Ecut electronic excitations electronic gap energy and pressure entropy entropy diﬀerences experimental Figure ﬁnd ﬁt ﬁtting ﬁxed FPMD free energy model function of pressure Gibbs free energies high pressure high temperature Hugoniot interface internal energy ion-thermal liquid EOS model liquid free energy liquid phase low temperature MD simulations melt curves melting lines melting temperature molecular dynamics obtained PDOS phase boundaries phase diagram phase lines phase of carbon phonon phonon density potential predicted pressure and temperature pseudopotential QBOX quasiharmonic Section slope solid phases solid-solid transition solidiﬁcation speciﬁc stable thermodynamic transition pressure triple point two-phase method two-phase simulation zero point energy zero temperature