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.

Thermal and mechanical properties of the clathrate-II Na24Si136

“…Moreover, both inter-and intracage disorders in the off-centering are likely present, making the guest atom 214114-4 dynamics and their effects on the dispersion more complex and difficult to model. Xue and Myles provided an indication from first-principles calculation that the effective potential that Na@Si 28 in Na 24 Si 136 experiences is broad and relatively flat with no clear off-center minimum (in general agreement with our results discussed above) and concluded the anharmonic rattling results in a strongly temperature-dependent rattling frequency, increasing by more than a factor of 3 from 0 K to room temperature [52]. We, therefore, conclude that the anharmonic Na@Si 28 rattling may not be well described by the harmonic approximation applied here.…”

“…Extended x-ray absorption fine-structure analysis [49,50] suggested a dimerization of Na guests in adjacent cages such that the Na@Si 28 guests shift off-center toward each other along the direction perpendicular to the shared hexagonal face of adjacent Si 28 cages. A related model has been applied in structure refinements using powder-diffraction data for Na x Si 136 (x < 24) [26] where the Na@Si 28 guest atoms randomly occupy one of four equivalent positions in the large cage that are shifted off-center toward the hexagonal face of the Si 28 cage with the extent of the shift becoming more pronounced as the Na content decreases [26,51,52]. We note that diffraction data cannot differentiate between ordered dimerization vs random dimerization vs random off-centering (disorder).…”

“…We note that previous x-ray powder-diffraction refinements for Na x Si 136 (0 < x < 24) have suggested that the off-centering becomes more pronounced as x decreases, perhaps due to the presence of empty adjacent Si 28 cages [26,51]. In their first-principles study of Na x Si 136 (x = 4, 8, 12, 16, and 24), Xue and Myles estimated the effective potential experienced by Na@Si 28 and found clear off-center potential minima for Na 4 Si 136 , whereas the potential well was significantly flatter (without clear off-center minima) in the case of Na 24 Si 136 [52]. Those authors also predicted the off-center displacement becomes less pronounced as x increases, in agreement with experiment [26].…”