Pressure-induced isostructural phase transition of metal-doped silicon clathrates

We propose an atomistic model for the pressure-induced isostructural phase transition of metal-doped silicon clathrates ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ and ${\mathrm{K}}_8{\mathrm{Si}}_{46}$ that has been observed at 14 and $23\mathrm{GPa}$, respectively. The model successfully explains the equation of state, transition pressure, change of Raman spectra, and dependence on the doped cations as well as the effects of substituting $\mathrm{Si}\left(6c\right)$ atoms with noble metals.

Figure 1

(a) Equation of state for the nominal ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$. Symbols indicate the experimental data (Ref. 14). Solid lines indicate the theoretical results for ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$, and the dashed lines for ${\mathrm{Ba}}_8{\mathrm{Si}}_{43}$. (b) Equation of state for the nominal ${\mathrm{K}}_8{\mathrm{Si}}_{46}$. Symbols indicate the experimental data (Ref. 9). Solid lines indicate the theoretical results for ${\mathrm{K}}_8{\mathrm{Si}}_{46}$, and the dashed lines for ${\mathrm{K}}_8{\mathrm{Si}}_{45}$.

Figure 2

(a) Enthalpy of ${\mathrm{Ba}}_8{\mathrm{Si}}_{40}$, ${\mathrm{Ba}}_8{\mathrm{Si}}_{43}$, and ${\mathrm{Ba}}_8{\mathrm{Si}}_{45}$ relative to ${\mathrm{Ba}}_8{\mathrm{Si}}_{46}$ estimated by first principles calculation. (b) Enthalpy of ${\mathrm{K}}_8{\mathrm{Si}}_{43}$, ${\mathrm{K}}_8{\mathrm{Si}}_{44}$, and ${\mathrm{K}}_8{\mathrm{Si}}_{45}$ relative to ${\mathrm{K}}_8{\mathrm{Si}}_{46}$.

Figure 3

Enthalpy of a vacancy relative to the formation enthalpy at $6c$ site $(P=15\mathrm{GPa})$ is presented along the covalent framework.