All-electron full-potential calculation of the electronic band structure, elastic constants, and equation of state for graphite

Abstract

The all-electron full-potential linear combinations of Gaussian-type orbitals—fitting-function technique has been used to calculate the electronic structure, equation of state (EOS), and elastic constants for crystalline graphite. An analysis of the zero-pressure band structure is used to resolve inconsistencies between previous local-density-approximation (LDA) calculations. The calculated band structure is consistent with experimental data to the extent expected given the known limits of LDA one-electron energies. The in-plane lattice constant found here exhibits the usual LDA-induced contraction, whereas the interlayer separation and the unit-cell volume exhibit an anomalous expansion due to a LDA underestimate of the weak interlayer bonding. The calculated values of ${\mathrm{C}}_{11}$+${\mathrm{C}}_{12}$ and ${\mathrm{C}}_{33}$ are in good agreement with ultrasound measurements, while the value of ${\mathrm{C}}_{13}$ (≈0) is much smaller than the ultrasound value. The bulk modulus and pressure derivatives of the lattice constants derived from the theoretical elastic constants are in very good agreement with diamond anvil cell (DAC) data, suggesting that the theoretical value for ${\mathrm{C}}_{13}$ is more reliable than the ultrasound measurement. An analytical EOS has been determined for pressures up to 50 GPa, well beyond the range of stability for the graphite structure. The EOS and the pressure dependencies of c/a and the optical transition energies (${\mathrm{A}}_1$ and ${\mathrm{A}}_2$) are in reasonable agreement with DAC data up to 14 GPa.