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.
Highlights
Type-II inorganic clathrates have attracted considerable interest due to their unique crystal structures and promising thermodynamic applications [1,2,3,4,5,6]
We study the electronic density of states, which indicates the occurrence of temperature-dependent Knight shift behavior, and when possible, we compare our calculations with some experimental results for (Na,K)16 Rb8 Si136, which share similar characteristics [13]
One of the main electronic characteristics is that the electronic density of states remains nearly unchanged as the Na composition x changes from 8 to 12 to 16 in Nax Si136
Summary
Type-II inorganic clathrates have attracted considerable interest due to their unique crystal structures and promising thermodynamic applications [1,2,3,4,5,6]. We first report the results of a systematic, first-principles computational and theoretical study of the electronic properties of some of the binary type-II Si-based clathrates Ax Si136. One interesting and useful property of the type-II clathrate materials is that their novel cage-structured framework lattice is capable of housing impurity atoms that can form host-guest complexes. Of particular interest are the vibrational properties of these host-guest complexes, the existence of low-frequency guest-associated “rattling” modes. We report the results of a systematic, first-principles study of such anharmonic vibrational modes due to alkali atoms in a large Si28 cage in the clathrates A8 Si136. We note that some previous reports of guest anharmonicity did not include a quartic anharmonicity interaction when examining the low-frequency rattling mode of the guests [14,15]
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