First-principles thermodynamics from phonon and Debye model: Application to Ni and Ni3Al

Starting from first-principles projector-augmented wave method, finite temperature thermodynamic properties of Ni and Ni3Al, including thermal expansion coefficient, bulk modulus, entropy, enthalpy and heat capacity, have been studied in terms of quasiharmonic approach. The thermal electronic contribution to Helmholtz free energy is estimated from the integration over the electronic density of state. The vibrational contribution to Helmholtz free energy is described by two methods: (i) the first-principles phonon via the supercell method and (ii) the Debye model with the Debye temperatures determined by Debye–Grüneisen approach and Debye–Wang approach. At 0 K, nine 4-parameter and 5-parameter equations of state (EOS’s) are employed to fit the first-principles calculated static energy (without zero-point vibrational energy) vs. volume points, and it is found that the Birch-Murnaghan EOS gives a good account for both Ni and Ni3Al among the 4-parameter EOS’s, while the Murnaghan EOS and the logarithmic EOS are the worse ones. By comparing the experiments with respect to the ones from phonon, Debye–Grüneisen and Debye–Wang models, it is found that the thermodynamic properties of Ni and Ni3Al studied herein (except for the bulk modulus) are depicted well by the phonon calculations, and also by the Debye models through choosing suitable parameters. The presently comparative studies of Ni and Ni3Al by phonon and Debye models, as well as by different EOS’s, provide helpful insights into the study of thermodynamics for solid phases at elevated temperatures.