Structural and electronic transition in liquid rubidium

Rubidium, like the other alkali metals, exhibits multiple structural transformations in its solid phase upon application of pressure. Recent experiments and calculations suggest it also goes through a phase transformation in its liquid state, along the 573 K isotherm, slightly above its melting curve. We employ ab initio molecular dynamic simulations to study the structural and electronic characteristics of this liquid-liquid transition. Applying the quasicrystalline model, we find that the short-range order of liquid Rb changes abruptly from bcc-like to $\beta$-Sn-like at a pressure significantly lower than the bcc to $\beta$-Sn transition in the solid phase at lower temperatures. In contrast to previous claims, the transition in the liquid cannot be related to the Peierls transition, as the liquid does not exhibit formation of a pseudogap at the Fermi level, nor to the transfer of charge from the $s$ state to the $d$ state, which is found to progress monotonically with pressure. Instead, a qualitative change in the shape of the electronic $d$ band is shown to occur at the same pressure range as the structural phase transition, which leads to the conclusion that the $\mathit{sd}$ hybridization must be accompanied by a significant change in the electronic band structure, observed in the solid phase, in order to produce a phase transition.

Figure 1

Pressure-density isotherm calculated at 600 K (triangles), compared with previous calculations [15] (solid curve) and experimental results [20] (circles)

Figure 2

Rubidium atomic positions at two snapshots taken from 5 GPa (a) and 20 GPa (b) simulations. Colors denote the coordination number of each atom with cutoff radius 5 $\AA$ (a) and 3.8 $\AA$ (b).

Figure 3

Calculated radial distribution functions of liquid Rb at pressures ranging from 1 to 30 GPa along the 600 K isotherm. The inset shows the coordination number $N_{NN}$ as a function of pressure.

Figure 4

(a) Structure factor and (b) radial distribution function of liquid Rb at 5 and 23 GPa, compared to experimental data of Gorelli et al. [20]. The experimental RDF was calculated from the reported structure factor using the asymptotic extension method [36]

Figure 5

(a) Simulated bond-angle distribution of liquid Rb at various pressures, using the radii of the first minima in $g\left(R\right)$ as the cutoff radii $R_c$. The dependence on the cutoff radius is given in the lower panels for the simulations at (b) 1 GPa and (c) 20 GPa, where $R_{\max }$ denotes the radius of the first peak in $g\left(R\right)$ and $R_{\min }$ denotes the radius of the first minimum. Vertical lines indicate permitted angles for (b) bcc and (c) $\beta$-Sn crystals for the first- and second-nearest neighbors

Figure 6

Radial distribution functions of liquid Rb (black) obtained from (a) the AIMD simulation at 5 GPa, (b) experiment at 6 GPa, (c) the AIMD simulation at 20 GPa, and (d) experiment at 23 GPa. QCM fits to (a) and (b) bcc and (c) and (d) $\beta$-Sn structures are drawn in red.

Figure 7

Calculated projected density of states (PDOS) of liquid Rb at (a) 1 GPa and (b) 20 GPa. DOS of solid Rb in (a) bcc and (b) tI4 crystals are drawn as dotted lines for comparison.

Figure 8

The $4d$-electron band of liquid Rb at different pressures. The inset shows the pressure dependence of the effective number of electrons in the $5s$ band (dashed) and $4d$ band (solid).

Figure 9

The electronic band structure of bcc Rb at three pressures: 0 GPa (blue), 10 GPa (green), and 20 GPa (red). The corresponding $l$-projected DOS of the d- states is drawn on the right.