First-principles study of the electronic, vibrational properties and anharmonic effects of some Si-based type-II binary clathrates

Electronic, vibrational, and anharmonic studies on some binary clathrate A _x Si ₁₃₆ (A = Na, K, Rb, Cs; 0 < x ≤ 24) are theoretically presented. The Fermi energy lies in the range of 1.1 eV to 1.4 eV for Na _x Si ₁₃₆ and increases as stoichiometry (x) is tuned from 8 to 12 to 16. The determined isotropic "Mexican-hat" shape of the guest-host potential describing Na motion in the Si ₂₈ cage indicates the "off-center" position when the temperature is elevated beyond zero. Accordingly, the calculated Na "off-center" displacements correlate well with the X-Ray Diffraction (XRD) data (0.4 Å-0.5 Å) for a similar composition range (0 < x < 24). The lack of first-principles analysis on quartic anharmonicity motivates us to initiate a self-consistent model to examine the temperature-dependent rattling frequency Ω(T) of the guest (Na, Rb). The predicted values of Ω(T) for Na ₂₄ Si ₁₃₆ at 300 K are significantly higher (approximately six times larger) than the value at absolute zero, which contrasts with the case of Rb ₈ Si ₁₃₆ . Moreover, underestimation of the isotropic atomic displacement parameter U _iso is caused by the temperature-dependent quartic anharmonicity of Na, and this discrepancy might be offset by the square of the "off-center" displacement.