High-accuracy first-principles determination of the structural,   vibrational and thermodynamical properties of diamond, graphite, and   derivatives
  The structural, dynamical, and thermodynamical properties of diamond, graphite and layered derivatives (graphene, rhombohedral graphite) are computed using a combination of density-functional theory (DFT) total-energy calculations and density-functional perturbation theory (DFPT) lattice dynamics at the GGA-PBE level. Overall, very good agreement is found for the structural properties and phonon dispersions, with the exception of the c/a ratio in graphite and the associated elastic constants and phonon dispersions. Both the C_33 elastic constant and the Gamma to A phonon dispersions are brought to close agreement with available data once the experimental c/a is chosen for the calculations. The thermal expansion, the temperature dependence of the elastic moduli and the specific heat have been calculated via the quasi-harmonic approximation. Graphite shows a distinctive in-plane negative thermal-expansion coefficient that reaches the minimum around room temperature, in very good agreement with experiments. Thermal contraction in graphene is found to be three times as large; in both cases, ZA acoustic modes are shown to be responsible for the contraction, in a direct manifestation of the membrane effect predicted by Lifshitz over fifty years ago. 
Nicolas Mounet and Nicola Marzari