First-Principles Investigation on Type-II Aluminum-Substituted Ternary and Quaternary Clathrate Semiconductors R8Al8Si128 (R = Cs, Rb), Cs8Na16Al24Si112

Structural and vibrational properties of the aluminium-substituted ternary and quaternary clathrates R8Al8Si128 (R = Cs, Rb), Cs8Na16Al24Si112 are investigated. The equilibrium volume of R8Si136 expands when all Si atoms at the 8a crystallographic sites are replaced by Al. Formation of the Al–Si bond is thus anticipated to correlate with decreased guest vibration modes. Underestimation of the predicted lattice phonon conductivity κL (1.15 W m−1 K−1) compared to a previous experiment (1.9 W m−1 K−1) in Cs8Na16Si136 is thought to arise from our evaluation on the phonon mean free path λ using the “scattering centers” model. Accordingly, we expect that the “three-phonon” processes dominate the determination of the phonon relaxation time, leading to a more reasonable λ in the R8Al8Si128 system. Additionally, the “avoided-crossing” effect causes no appreciable difference in the sound speed for acoustic phonons in this framework. Starting with configuration optimization about aluminium arrangements in Cs8Na16Al24Si112, the calculated lattice parameter agrees well quantitatively with the experiment. The reduced Uiso of Cs from this calculation is anticipated to be primarily related to temperature-dependent quartic anharmonicity. Meanwhile, the predicted κL for Cs8Na16Al24Si112 remains not sensitive to the Al arrangement on 96g Wyckoff sites.