Behavior of rubidium at over eightfold static compression

The high pressure phases of Rb have previously been investigated to 101 GPa, above which Rb is predicted to adopt a double-hexagonal close-packed (dhcp, Pearson hP4) structure similar to that already observed in cesium at 72 GPa. Previous ab initio structure searches have indicated that the hP4 phase should become stable in rubidium at $143\mathrm{GPa}$. We present data from static compression experiments on Rb up to $264\left(8\right)\mathrm{GPa}$, showing the onset of the hP4 phase at $207\left(6\right)\mathrm{GPa}$. The $V/V_0$ of $\sim 0.121$ measured at $264\mathrm{GPa}$ constitutes the highest compression ratio (more than eightfold) at which structural information has been obtained from a metal using x-ray diffraction methods and is second only to x-ray measurements performed on hydrogen at $V/V_0\sim 0.094$ at $190\mathrm{GPa}$. At these extreme compression ratios, the compressive behavior of rubidium shifts from that of a free electron metal to that of a regular $d$-block metal.

Figure 1

The 2D Debye-Scherrer diffraction image from Rb at $232\mathrm{GPa}$ as collected with the $850\times 850{\mathrm{nm}}^2$ x-ray beam at PETRA-III. The masked sections are shown as shaded areas, with the rectangular mask corresponding to the mounting arm for the beam stop and the central circular mask to the beam stop itself.

Figure 2

Rietveld refinement of the oC16 structure to a background-subtracted diffraction profile from Rb at $189\mathrm{GPa}$, showing the observed (solid line) and calculated (crosses) diffraction patterns. The collection time of the diffraction image was $60\mathrm{s}$ and the sample was not oscillated during exposure. The calculated reflection positions (vertical bars) for the oC16 phase (Rietveld) and Re gasket (Le Bail), and the difference profile (lower line), are also shown. Owing to the submicron x-ray beam the Re diffraction signal is very weak.

Figure 3

Background-subtracted diffraction profiles obtained from Rb on pressure increase above (a) $189\mathrm{GPa}$, where the sample is in the oC16 phase (see Fig. 2). On pressure increase to (b) $204\mathrm{GPa}$ the appearance of a new peak [identified with an arrow in (b) and (d)] marks the transition to hP4. On further pressure increase to (c) $222\mathrm{GPa}$ and (d) $232\mathrm{GPa}$ the peaks from hP4 increase in intensity, but peaks from oC16 were still visible at the highest pressure reached, $264\mathrm{GPa}$. The tick marks beneath profile (a) show the calculated peak positions of oC16 at this pressure, while the tick marks beneath pattern (c) similarly indicate those of the oC16 and hP4 (dhcp) phases. The pressures in this sample were determined from the lattice parameters via the EoS determined from the other samples. The peak marked with an asterisk in profile (a) is from the Re gasket. All patterns were collected over $60\mathrm{s}$.

Figure 4

The compression curve of Rb to $264\left(8\right)\mathrm{GPa}$ with data from the different phases identified by the different symbols. The filled symbols are data reproduced from Refs. [30, 43, 44], and the dashed lines are the compression data and the extrapolated EoS of yttrium from Ref. [26]. The inset shows the measured volumes of the oC16 and hP4 phases above $200\mathrm{GPa}$, illustrating the volume change of $2.3\left(5\right)\%$ that occurs at the phase transition. The uncertainties on the volume, and those on the pressure below $100\mathrm{GPa}$, are smaller than the symbols used to plot the data and have been omitted. The uncertainties in pressure above $100\mathrm{GPa}$, as determined from the diamond edge scale, are $\pm 3\%$ [38, 39, 40].

Figure 5

Linearization of the compressibility of Rb in the form of an ${\eta }_{\text{APL}}\text{−}\sigma$ plot, where $\sigma ={\sigma }_{0}x$. The data from the different phases of Rb obtained in this study are plotted using different unfilled symbols, while the filled symbols are data taken from Refs. [30, 43, 44]. Note that pressure increases nonlinearly from right to left. Due to the nonlinear nature of the horizontal axes the high-pressure domain occupies a disproportionately small area of the plot. The inset therefore shows an enlarged view of the pressure range $50\text{–}270\mathrm{GPa}$. The solid line shows the best-fitting AP1 EoS to the data above $30\mathrm{GPa}$ and the dashed line is the ideal AP1 EoS for Rb.

Figure 6

The compressibility of Rb to $264\mathrm{GPa}$ (symbols) and the best-fitting AP1 EoS (solid line) to tI4 and oC16 from 30 to $264\mathrm{GPa}$, the parameters of which are given in Table 4. It is clear that this simple EoS accurately captures the compression behavior of Rb above $30\mathrm{GPa}$, including that of the oC16 phase. The inset shows an enlarged view of the data and AP1 fit up to $40\mathrm{GPa}$, as well as the Vinet fit to the bcc data (dotted line) and compression data of Y for comparison (dashed line [26]). The bcc phase is less compressible than predicted by the AP1 EoS, while the fcc phase is more compressible. As a result, the EoS and the data coincide above $30\mathrm{GPa}$.