### Abstract

Type II clathrates are interesting due to their potential thermoelectric applications. Powdered X-ray diffraction (XRD) data and density functional calculations for NaxSi136 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 Si_{28} cages are filled first for x < 8 and the Si_{20} 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_{x}Si_{136}, A_{x}Ge_{136}, and A_{x}Sn_{136}. 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 Na_{4}Si_{136}, Na_{4}Ge_{136}, and Na_{4}Sn_{136} and we compare these for the three materials. Finally, we present calculated results for the elastic constants in Na_{x}Si_{136}, Na_{x}Ge_{136}, and Na_{x}Sn_{136} for x = 4 and 8. These are compared for the three hosts, as well as for the two compositions.

Original language | English |
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Article number | 691 |

Journal | Materials |

Volume | 9 |

Issue number | 8 |

DOIs | |

State | Published - Aug 11 2016 |

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### Keywords

- Alkali atoms
- Clathrates
- Elastic constants
- First principles theory
- Group 14
- Guests
- Phonon
- Type II-structure
- VASP

### Cite this

_{x}Si

_{136}, A

_{x}Ge

_{136}and A

_{x}Sn

_{136}(A = Na, K, Rb, Cs; 0 ≤ x ≤ 24).

*Materials*,

*9*(8), [691]. https://doi.org/10.3390/ma9080691