First-Principles Simulations on the Nature of the Melting Line of Sodium

We report a first-principles molecular dynamics study of the reentering behavior that has been recently observed experimentally in the melting line of bcc sodium [Gregoryanz et al., Phys. Rev. Lett. 94, 185502 (2005)]. Our results show the liquid phase to be more compressible than the solid phase, and to remain so at high pressures, eventually becoming denser than the solid phase and hence causing the change of slope in the melting line from positive to negative. The maximum of the melting line thus occurs without any accompanying first-order liquid-liquid phase transition.

Figure 1

Pressure difference between the liquid ($P_l$) and solid ($P_s$) phases as a function of volume. The continuous line with square symbols was obtained at conditions which approximately follow the experimental melting line, while the dotted line with circles was obtained along the $T=1000\mathrm{K}$ isotherm. The error bars reflect the standard deviation of the average pressure in our simulations. Pressure values of the solid phase are given in the upper abscissa axis. The inset displays the bulk modulus obtained for the bcc and liquid phases for volumes corresponding to pressures equal and larger than that at which the melting-line maximum is observed. At larger volumes (lower pressures) the bulk moduli are practically indistinguishable.

Figure 2

Radial distribution function and pair distribution functions of the 16 nearest neighbors in the liquid phase. Results obtained at volumes of $20.8{\AA }^3/\mathrm{\text{atom}}$ and at $12.75{\AA }^3/\mathrm{\text{atom}}$ are shown. These volumes correspond to pressures of 12.1 and 60 GPa, respectively.

Figure 3

Distribution of cosine values of the bond angles present in the liquid at volumes of $20.8{\AA }^3/\mathrm{\text{atom}}$ (12.1 GPa) and $12.75{\AA }^3/\mathrm{\text{atom}}$ (60 GPa). Also shown are the cosines of bond angles present in a perfect bcc cluster of 15 atoms, and in an fcc cluster of 13 atoms. The inset shows the frequency histograms of the ${\overline{W}}_6$ parameter of Steinhardt et al. [16], for the clusters found in l-Na at the same conditions of volume. The two histograms are nearly indistinguishable from each other. The values of ${\overline{W}}_6$ for the ideal icosahedral, fcc, and bcc clusters are indicated by arrows.