A study of low-energy guest phonon modes in clathrate-II Na(x)Si136 (x = 3, 23, and 24)

First Principles Study of the Vibrational and Thermal Properties of Sn-Based Type II Clathrates, CsxSn136 (0 ≤ x ≤ 24) and Rb24Ga24Sn112

After performing first-principles calculations of structural and vibrational properties of the semiconducting clathrates Rb24Ga24Sn112 along with binary CsxSn136 (0 ≤ x ≤ 24), we obtained equilibrium geometries and harmonic phonon modes. For the filled clathrate Rb24Ga24Sn112, the phonon dispersion relation predicts an upshift of the low-lying rattling modes (~25 cm−1) for the Rb (“rattler”) compared to Cs vibration in CsxSn136. It is also found that the large isotropic atomic displacement parameter (Uiso) exists when Rb occupies the “over-sized” cage (28 atom cage) rather than the 20 atom counterpart. These guest modes are expected to contribute significantly to minimizing the lattice’s thermal conductivity (κL). Our calculation of the vibrational contribution to the specific heat and our evaluation on κL are quantitatively presented and discussed. Specifically, the heat capacity diagram regarding CV/T3 vs. T exhibits the Einstein-peak-like hump that is mainly attributable to the guest oscillator in a 28 atom cage, with a characteristic temperature 36.82 K for Rb24Ga24Sn112. Our calculated rattling modes are around 25 cm−1 for the Rb trapped in a 28 atom cage, and 65.4 cm−1 for the Rb encapsulated in a 20 atom cage. These results are utilized to predict the lattice’s thermal conductivity (approximately 0.62 W/m/K) in Rb24Ga24Sn112 within the kinetic theory approximation.

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_xSi₁₃₆ (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_xSi₁₃₆ 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 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.

Effect of Guest Atom Composition on the Structural and Vibrational Properties of the Type II Clathrate-Based Materials AxSi136, AxGe136 and AxSn136 (A = Na, K, Rb, Cs; 0 ≤ x ≤ 24)

Type II clathrates are interesting due to their potential thermoelectric applications. Powdered X-ray diffraction (XRD) data and density functional calculations for Na_xSi₁₃₆ found a lattice contraction as x increases for 0 < x < 8 and an expansion as x increases for x > 8. This is explained by XRD data that shows that as x increases, the Si₂₈ cages are filled first for x < 8 and the Si₂₀ cages are then filled for x > 8. Motivated by this work, here we report the results of first-principles calculations of the structural and vibrational properties of the Type II clathrate compounds A_xSi₁₃₆, A_xGe₁₃₆, and A_xSn₁₃₆. We present results for the variation of the lattice constants, bulk moduli, and other structural parameters with x. These are contrasted for the Si, Ge, and Sn compounds and for guests A = Na, K, Rb, and Cs. We also present calculated results of phonon dispersion relations for Na₄Si₁₃₆, Na₄Ge₁₃₆, and Na₄Sn₁₃₆ and we compare these for the three materials. Finally, we present calculated results for the elastic constants in Na_xSi₁₃₆, Na_xGe₁₃₆, and Na_xSn₁₃₆ for x = 4 and 8. These are compared for the three hosts, as well as for the two compositions.

Influence of guest loading on thermal properties of NaxSi136 clathrates

Thermal properties of a series of type II clathrates of the formula NaxSi136 with 0 < x < 24 and Na guests occupying the Si cages have been investigated over the temperature range from 2 to 300 K. Heat capacity and thermal conductivity results show that the structure is remarkably responsive to the loading of Na guests. The response is phononic: the host lattice expands in a non-monotonic way, and first stiffens, then relaxes at low loading into the larger Si28 cages (x < 9), then stiffens again as the Na concentration increases further. The response is also electronic, through changes in electronic properties as additional Na is loaded into the smaller Si20 cages at high loading (x > 9). In total, the influence of the guest loading illustrates the complexities of structure-property relations in a guest-host system.