High-pressure transformations in liquid rubidium

An electronic-driven liquid-liquid phase transition in rubidium is revealed by picosecond acoustic measurements combined with ab initio calculations. Picosecond acoustics were used to measure the melting line up to 10 GPa, finding the maximum in the melting curve at 7 GPa and 555 K. We observe the onset of a continuous liquid-liquid phase transition beginning around the melting maxima through until 16 GPa. Sound velocity shows a softening similar to that reported for liquid caesium, caused by a change in the bulk modulus during a crossover from the low-density to the high-density liquid. Guided by the ab initio calculations, we relate the changes in the thermoelastic properties to the progressive localization of the valence electrons in the pressure range of 6–16 GPa. At high pressure rubidium forms an electride liquid quantified by the appearance of interstitial quasiatoms localized in the valence electron density.

Figure 1

Phase diagram of Rb: Solid (blue squares) and liquid (red squares) phases were detected using PA. The melting line is shown up to 10 GPa (dashed line) according to the functional form given by Kechin [40]. The melting maximum is at 7 GPa, 555 K (empty star). Transitions from bcc to fcc (crosses) and melting (pluses) are from Boehler [41]. Data at high p-T [11, 22, 41] is scarce and not always consistent. Sound velocity measurements in this work were performed along the 573 K isotherm as in Gorelli et al. [11] (red circles).

Figure 2

Adiabatic sound velocities of liquid rubidium at 573 K as a function of pressure, measured by PA (black points), AIMD simulations (blue squares), and a two-state thermodynamic model (magenta) [33]. For comparison, ultrasonic measurements are shown from Shaw et al. [46] to 0.7 GPa and the AIMD and IXS measurements from Bryk et al. [10].

Figure 3

Thermodynamic properties of liquid Rb at 573 K as a function of pressure including literature data from Gorelli [11] (XRD, pink), Bryk [10] (AIMD, black), and Shaw [46] (from ultrasonic measurements, blue). (a) Density; at the maxium of melting curve, the density of the solid (open dotted circle) is equal to that of the liquid. (b) Isothermal bulk modulus $B_T$ with dashed lines to guide the eye. (c) Thermal expansivity; inset: Specific heat capacities. (d) Adiabatic ratio $\gamma =C_p/C_V$.

Figure 4

Electronic and structural properties of liquid Rb as a function of pressure at 573 K. (a) Average charge inside interstitial Bader maxima (blue) and their frequency (red) per Rb ion. (b) Electron localization function ($\max =0.70$) 100 cuts from AIMD snapshots at 1 and 20 GPa showing localized interstitial charge (yellow to red amorphous shapes) appear between ions (red circles). (c) Coordination numbers for Rb ions to ISQs calculated by integrating PDFs up to the first minima and (d) for Rb-Rb ions. (e) Normalized Rb-Rb PDFs at selected pressures showing the first minima evolve into a new maxima, and a Rb-ISQ PDF at 13.8 GPa demonstrates the interstitial occupation of electride sites.