Structural Stability and Phase Transitions in ${\mathrm{K}}_8{\mathrm{S}\mathrm{i}}_{46}$ Clathrate under High Pressure

The structural stability of type-I ${\mathrm{K}}_8{\mathrm{S}\mathrm{i}}_{46}$ clathrate has been investigated at high pressure by synchrotron x-ray diffraction. In contrast to that observed in the Na-doped structure-II analogue [A. San-Miguel et al., Phys. Rev. Lett. 83, 5290 (1999)], no phase separation into the $\beta \mathrm{\text{−}}\mathrm{S}\mathrm{n}$ Si structure was identified at 11 GPa. Instead, ${\mathrm{K}}_8{\mathrm{S}\mathrm{i}}_{46}$ is found to undergo a transition to an isostructural positional disordered phase at around 15 GPa. Ab initio phonon band structure calculations reveal a novel phenomenon of phonon instabilities of K atoms in the large cavities is responsible for this transition. Above 32 GPa, the new structure transforms into an amorphous phase.

Figure 1

Angle dispersive x-ray diffraction patterns of ${\mathrm{K}}_8{\mathrm{S}\mathrm{i}}_{46}$ at selected pressures at room temperature. Indicated pressures were measured using the ruby and the Cu gauges, for samples A and B, respectively. The vertical arrow and the asterisks indicate a gasket and Cu x-ray diffraction lines, respectively. Vertical dotted lines indicate x-ray diffraction lines which are external to the sample as they do not shift with pressure. The sequences of x-ray diffraction patterns clearly indicate no change of crystalline structure from 15 to 32 GPa and the loss of crystallinity (amorphization) at high pressure. Partial crystallinity is also observed upon complete decompression of sample B.

Figure 2

Comparison of experimental and calculated volume compression curves for ${\mathrm{K}}_8{\mathrm{S}\mathrm{i}}_{46}$. Symbols correspond to experimental data points (samples A and B) obtained at 300 K, and the solid line corresponds to the calculated equation of state.

Figure 3

Theoretical phonon band structure for ${\mathrm{K}}_8{\mathrm{S}\mathrm{i}}_{46}$ at (a) 5 GPa, (b) 16 GPa, and (c) phonon vibrational density of states (DOS) at 5 GPa (features at 100 and $167{\mathrm{c}\mathrm{m}}^{-1}$ are indicated by arrows; see text); (d) the force acting on a K atom at $(1/4,1/2,0)$ when displaced from the symmetry site in the large cage along the $b$ direction. Positive force along the crystallographic $b$ axis favors the displacement while negative values indicate restoring forces.