Performance of the standard exchange-correlation functionals in predicting melting properties fully from first principles: Application to Al and magnetic Ni

We apply the efficient two-optimized references thermodynamic integration using Langevin dynamics method [Phys. Rev. B 96, 224202 (2017)] to calculate highly accurate melting properties of Al and magnetic Ni from first principles. For Ni we carefully investigate the impact of magnetism on the liquid and solid free energies including longitudinal spin fluctuations and the reverse influence of atomic vibrations on magnetic properties. We show that magnetic fluctuations are effectively canceling out for both phases and are thus not altering the predicted melting temperature. For both elements, the generalized gradient approximation (GGA) and the local-density approximation (LDA) are used for the exchange-correlation functional revealing a reliable ab initio confidence interval capturing the respective experimental melting point, enthalpy of fusion, and entropy of fusion.

Figure 1

Speed-up factors of the “ref2” potentials in the thermodynamic integration to DFT with respect to well-developed EAM potentials from the literature (“lit”; red bars) and the “ref1” potentials fitted to the DFT solid phase (blue bars). The speed-up factor is defined as ${(\sigma /{\sigma }_{\mathrm{ref}2})}^2$, where $\sigma$ is the standard deviation of the corresponding potential and ${\sigma }_{\mathrm{ref}2}$ is the standard deviation of the “ref2” potential.

Figure 2

Thermodynamic properties of Al calculated with TOR-TILD using the GGA-PBE and LDA functional.

Figure 3

Thermodynamic properties of Ni calculated with TOR-TILD using the GGA-PBE and LDA functional.

Figure 4

(a) Temperature dependence of the local magnetic moments for fcc and liquid ferromagnetic (FM) Ni from GGA. (b) Comparison between the 0 K electronic DOS of fcc Ni (blue dashed line) vs its averaged high-temperature counterpart (blue solid line) and the DOS of the liquid phase (red solid line) for the minority spin channel within GGA. The high-temperature electronic DOSs of fcc and liquid Ni feature a very similar dependence on the energy. The gray shaded region indicates the electronic entropy distribution at 1728 K, i.e., the relevant part of the DOS that contributes to the electronic free energy.

Figure 5

(a) Ab initio confidence interval from GGA and LDA for the experimental melting points of Al, Cu, and Ni. (b) Correlation between the deviation from experiment for the lattice constants $\mathrm{\Delta }a$ and the melting temperature $\mathrm{\Delta }{T}^{\mathrm{m}}$.

Figure 6

Impact of the LSFs on the electronic DOSs of the fcc and liquid phase at $V=12.22$ ${\AA }^3$ and $T=1750$ K using LDA. The LSFs further broaden the electronic DOSs of both phases as compared to the ferromagnetic (FM) results, and render their shapes even more similar.