First-Principles Study of the Electronic, Vibrational Properties and Anharmonic Effects of Some Si-Based Type-II Binary Clathrates

Abstract

Electronic, vibrational, and anharmonic studies on some binary clathrate AxSi136 (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 NaxSi136 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 Si28 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 Na24Si136 at 300 K are significantly higher (approximately six times larger) than the value at absolute zero, which contrasts with the case of Rb8Si136. Moreover, underestimation of the isotropic atomic displacement parameter Uiso is caused by the temperature-dependent quartic anharmonicity of Na, and this discrepancy might be offset by the square of the “off-center” displacement.