| Summary: | Electronic, vibrational, and anharmonic studies on some binary clathrate A<i><sub>x</sub></i>Si<sub>136</sub> (A = Na, K, Rb, Cs; 0 < <i>x</i> ≤ 24) are theoretically presented. The Fermi energy lies in the range of 1.1 eV to 1.4 eV for Na<i><sub>x</sub></i>Si<sub>136</sub> and increases as stoichiometry (<i>x</i>) 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<sub>28</sub> 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 < <i>x</i> < 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 <i>Ω</i>(<i>T</i>) of the guest (Na, Rb). The predicted values of <i>Ω</i>(<i>T</i>) for Na<sub>24</sub>Si<sub>136</sub> at 300 K are significantly higher (approximately six times larger) than the value at absolute zero, which contrasts with the case of Rb<sub>8</sub>Si<sub>136</sub>. Moreover, underestimation of the isotropic atomic displacement parameter <i>U</i><sub>iso</sub> is caused by the temperature-dependent quartic anharmonicity of Na, and this discrepancy might be offset by the square of the “off-center„ displacement.
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