Thermodynamics of Fcc Al Crystal from First Principles - Performance of Local Density and Generalized Gradient Approximations

Phonon dispersion relations in fcc Al crystal were calculated from first principles using density functional perturbation theory, as implemented in ABINIT code. The results are compared with experimental data as well as with the results of previously done ab initio calculations based on the direct method. A slightly better agreement of density functional perturbation theory phonons with experiment can be observed. The ab initio phonon energies were used to evaluate the partition function of the crystal, using the Monkhorst-Pack integration scheme. The quasiharmonic approximation was applied to relate the temperature dependent part of the free energy to volume. The lattice constant dependence of phonon energies was found to be almost linear, so the second order polynomial was considered as sufficient to approximate the dependence. A few examples of thermodynamic characteristics were evaluated: isobaric specific heat, linear thermal expansion coefficient, isothermal bulk modulus, and compared with the experimental data. The calculation was done both in the local density and the generalized gradient approximations for the exchange-correlation energy. The agreement with the experimental data appears to be very satisfactory, although better in the local density approximation than in the generalized gradient approximation.