High-pressure phase transformations, pressure-induced amorphization, and polyamorphic transition of the clathrate ${\text{Rb}}_{6.15}{\text{Si}}_{46}$

The type-I clathrate ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ with partly empty cage sites has been studied up to 36 GPa using Raman spectroscopy, synchrotron x-ray diffraction in diamond-anvil cells, and ab initio total-energy and lattice-dynamics calculations. A first phase transition is observed at $13\pm 1\text{GPa}$ and a “volume collapse” transition within the clathrate structure is then observed at $24\pm 1\text{GPa}$. Pressure-induced amorphization into a high-density amorphous (HDA) state occurs above $P=33\pm 1\text{GPa}$. The HDA form transforms into a low-density amorphous polymorph during decompression. During the compression study using angle dispersive synchrotron x-ray diffraction techniques we measured bulk modulus parameters for rocksalt-structured TaO, included adventitiously in the clathrate sample [$K_0=293\left(3\right)\text{GPa}$ and $K_0^{\prime }=5.4\left(3\right)$].

Figure 1

(Color online) X-ray diffraction pattern including Rietveld refinement of the sample at room pressure in the diamond-anvil cell. Three phases are present: the type-I clathrate ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ $\left(Pm\overline{3}n\right)$, the $\epsilon$ phase of TaN $\left(P6\overline{2}m\right)$, and TaO with rocksalt structure $\left(Fm\overline{3}m\right)$.

Figure 2

(Color online) Selected x-ray diffraction patterns with increasing pressure. The peaks due to the $\epsilon \text{-TaN}$ phase and TaO are identified with asterisks and open circles, respectively. At pressure higher than 33 GPa the diffraction peaks from the clathrate ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ disappear and are replaced by a broad amorphous signal indicating the occurrence of pressure-induced amorphization. The additional peaks are due to crystalline TaN and TaO. An estimated background line is drawn to show the likely amorphous contribution to the x-ray scattering at high pressure. Inset: intensity ratio between the (320) clathrate peak and the (200) TaO peak used as a standard. A small decrease of this ratio is observed between ambient pressure and 10 GPa followed by a sudden decrease of the ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ peak intensity with a complete disappearance by 33 GPa that indicates amorphization of the clathrate structure.

Figure 3

(a) $V/V_0$ plot for ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ as a function of pressure (points) along with a third-order Birch-Murnaghan equation of state fitted to the data with $K_0=61.4\left(7\right)\text{GPa}$ and $K_0^{\prime }=6.7\left(2\right)$ (solid line). The $K_0$ and $K_0^{\prime }$ values were obtained from a reduced variable $\left(F\text{−}f\right)$ plot. (b) Plot of the normalized pressure $\left(F\right)$ as a function of the Eulerian strain variable $\left(f\right)$ for ${\text{Rb}}_{6.15}{\text{Si}}_{46}$.

Figure 4

Selected x-ray diffraction patterns during decompression. The broad feature under the crystalline peaks of TaN and TaO are due to the amorphous Rb-Si alloy obtained at pressure higher than 33 GPa. Dashed lines and solid lines are guides for the eyes, emphasizing the background and the amorphous halo, respectively.

Figure 5

(a) Change in $d$ spacing for (320), (321), and (222) clathrate reflections with increasing pressure. Two regimes are distinguished with a transition occurring at around 13 GPa. (b) Linearized $F\text{−}f$ plot based on the data obtained for the (222) peak. (c) $F\text{−}f$ plot from the (320) peak data. (d) $F\text{−}f$ from the (321) peak data.

Figure 6

TaO is used as an internal standard to estimate intrinsic broadening of the clathrate peak. Ratio of the width of selected ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ reflections with respect to the width of the TaO (222) peak: (a) ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ (320), (b) ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ (222), and (c) ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ (321).

Figure 7

Raman spectrum of ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ measured at 1 atm and room temperature.

Figure 8

Raman spectra of ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ during quasihydrostatic compression (using argon as pressure-transmitting medium).

Figure 9

Raman frequencies of ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ plotted as a function of pressure (for quasihydrostatic compression). Lines are drawn as visual aids. Open symbols: Raman frequency of the most intense peak under nonhydrostatic compression.

Figure 10

Raman spectra of ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ during decompression after quasihydrostatic compression to 36 GPa.

Figure 11

Raman spectra of ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ during a nonhydrostatic compression (no pressure-transmitting medium) to 16.7 GPa. Asterisk shows the initially most intense peak at around $190{\text{cm}}^{-1}$.

Figure 12

Raman spectra of ${\text{Rb}}_{6.15}{\text{Si}}_{46}$ during decompression after nonhydrostatic compression to 16.7 GPa. Asterisk shows the initially most intense peak of the clathrate structure at around $190{\text{cm}}^{-1}$.

Figure 13

Ab initio calculated systematic changes in the bulk modulus $\left(K_0\right)$ and its pressure derivative $\left(K_0^{\prime }\right)$ as a function of the cell parameter $a_0$ with progressive filling of the nanocages ($x=0$, 2, 6, and 8) in the type-I clathrate structure. In ${\text{Ba}}_x{\text{Si}}_{46}$, the effect on $K_0$ and $K_0^{\prime }$ is negligible. In ${\text{Rb}}_x{\text{Si}}_{46}$, as soon as the smaller ${\text{Si}}_{20}$ cages begin to be filled the structure begins to become mechanically weaker.