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[1]The phase diagram was obtained from the calculation of the Gibbs free energies G of the compared phases in the quasiharmonic approximation: G(P,T)=E_0(V)+PV+U_0(V)+F_{vib}(T,V) where E0, U0, and Fvib are the total energy from the DFT calculations, while the zero-point and vibrational energies are calculated from the following relations: U_0(V)=1/2\int g(V,\omega)\hbar \omega d\omega F_{vib}(T,V)=k_BT\int_{\Omega}g(V,\omega)ln[1-exp(-\frac{\hbar \omega}{k_BT})]d\omega Here g(\omega) is the phonon density of states at the given pressure calculated using the density-functional perturbation theory.[2] The phonon density of states (PhDOS) was calculated for each value of equilibrium volume for each studied structure, using density functional perturbation theory. Then the PhDOS integrations above yield the zero-point (U0) and vibrational (Fvib) energies, for every chosen temperature.

[1]
Kvashnin, A. G.; Chernozatonskii, L. A.; Yakobson, B. I.; Sorokin, P. B. Phase Diagram of Quasi-Two-Dimensional Carbon, from Graphene to Diamond. Nano Lett, 2014, 14, 676–681.
[2]
Baroni, S.; de Gironcoli, S.; Dal Corso, A.; Giannozzi, P. Phonons and Related Crystal Properties from Density-Functional Perturbation Theory. Rev. Mod. Phys. 2001, 73, 515–562.