Simple calculation of ab initio melting curves: Application to aluminum

We present a simple, fast, and promising method to compute the melting curves of materials with ab initio molecular dynamics. It is based on the two-phase thermodynamic model of Lin et al [J. Chem. Phys. 119, 11792 (2003)] and its improved version given by Desjarlais [Phys. Rev. E 88, 062145 (2013)]. In this model, the velocity autocorrelation function is utilized to calculate the contribution of the nuclei motion to the entropy of the solid and liquid phases. It is then possible to find the thermodynamic conditions of equal Gibbs free energy between these phases, defining the melting curve. The first benchmark on the face-centered cubic melting curve of aluminum from 0 to 300 GPa demonstrates how to obtain an accuracy of 5%–10%, comparable to the most sophisticated methods, for a much lower computational cost.

Figure 1

Phonon DOS of aluminum at 300 K and $2.7{\mathrm{g}/\mathrm{cm}}^3$ obtained from the Fourier transform of the VACF (black solid line) and from the experimental phonon-dispersion curves [27] (gray area).

Figure 2

Fourier transform $F\left(\nu \right)$ of the VACF of aluminum at 4000 K and $0.3125 {\mathrm{cm}}^3{\mathrm{g}}^{-1}$ and the gaslike and solidlike contributions in linear-linear plot (top) and in log-log plot (bottom). The black solid line is the raw $F\left(\nu \right)$ signal, the red dashed (green dot-dashed) line is the 2M (4M) gaslike contribution, and the gray area is the solidlike DOS deduced from the 2M model.

Figure 3

Internal energy for the melting and solidification branches along the 4000 K isotherm of aluminum. $P_m$ indicates the melting pressure, and $P_l$ (respectively $P_h$) is the highest (lowest) pressure for which liquid (solid) phase is metastable. Insets display typical radial distribution functions $g\left(r\right)$ at $P<P_h,P\sim P_m$, and $P>P_l$.

Figure 4

Volume (top) and entropy (bottom) for the melting (black dashed lines) and solidification (red solid lines) branches along the 4000 K isotherm of aluminum. $P_m$ is the melting pressure. For entropy, plus (cross) symbols correspond to 2M (4M) model.

Figure 5

Gibbs free energies of the liquid $\left(G_L\right)$ and solid $\left(G_S\right)$ phases for the 4000 K isotherm of aluminum with the 4M model. Difference of Gibbs free energies are displayed in the inset.

Figure 6

Comparison between the present 2PT-MF method and other methods, all within GGA, for the fcc melting curve of aluminum. Experimental data [16, 17, 18] are plotted in open blue symbols. HUM (green filled circles), hysteresis method (green stars), Z method (green crosses), and TPA (green filled triangles) results have been obtained by Bouchet et al. [3]. Results obtained by Vočadlo and Alfè [6] using thermodynamic integration (red solid line) are the reference values. Plus (cross) symbols stand for the 2M (4M) model. Dashed bold lines are the derivatives of melting temperatures [Eq. (16)]. The gray area represents the estimated uncertainties.

Figure 7

Volume (top) and entropy (bottom) changes at melting. Green lines correspond to the reference results of Vočadlo and Alfè [6]; open black circles are experimental values at ambient conditions [32, 33]. Plus (cross) symbols stand for 2M (4M) method. Gray areas represent the estimated uncertainties.