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.