Structure and stability of the clathrates Ba8Ga16Ge30, Sr8Ga16Ge30, Ba8Ga16Si30, and Ba8In16Sn30

Abstract

We use density functional calculations and single-crystal x-ray diffraction measurements to study structure and bonding in the solid state clathrates Ba 8 Ga 16 Ge 30 , Ba 8 Ga 16 Si 30 , Sr 8 Ga 16 Ge 30 , and Ba 8 In 16 Sn 30 . The structures calculated by minimizing the energy provided by the density functional theory agree well with those determined by x-ray scattering. The preferred stoichiometry is found to always have 8 group II, 16 group III, and 30 group IV elements. The resultant structures are shown to be substantially more stable than the constituent elements in their standard states at room temperature and pressure. Calculations show that the group III elements prefer to be located in the six rings of the structure and are distributed to avoid bonding to one another. Motion of the group II atom ͑the guest͒ within the cages is facile, with estimated frequencies for vibration ranging from 40 to 100 cm Ϫ1 . While these results may suggest a weak guest-frame bond, we find that the binding energy is over 4 eV per guest. We demonstrate that the formation of A 8 B 16 C 30 from A 8 and B 16 C 30 takes place through the donation of 16 electrons ͑per unit cell͒ from the bands of A 8 into the empty bands of B 16 C 30 . The guest atoms are thus charge donors. However, the spatial charge distribution of the eight donor orbitals of A 8 is found to be very similar to that of the eight acceptor orbitals of B 16 C 30 . Thus while the guest is an electron donor, it is not ionic in these materials.

NMR experiments and electronic structure calculations in type-I BaAlGe clathrates

“…8 of the configurations are the same as considered in Ref. 31 Computed NMR lineshapes could be distinguished by the shapes of the noncentral portions of the lines, and we found that Al atoms situated in Al-Al pairs contributed the largest EFG's. For configurations with 3 or more Al-Al pairs this led to broad simulated lines providing poor agreement with the data.…”

First principles calculations of the structural and electronic properties of the type-I semiconductor clathrate alloysBa8Ga16SixG

“…Blake et al 20 showed that the placement of the Ga atoms in the clathrate framework affects the stability of the compound. Since each substitutional Ga has one fewer valence electron than Ge or Si, the Ga concentration and its spatial correlation affect the energetics and the structure of the material.…”

“…The details of the symmetries of each of these sites are described in detail in Ref. 20. For each calculation, we searched for a low total energy configuration by placing different numbers of the 16 Ga atoms on each symmetry site, by optimizing the geometry, and then by calculating the GGA total energy.…”

Universal Relation between Guest Free Space and Lattice Thermal Conductivity Reduction by Anharmonic Rattling in Type-I Clathrates

“…The cage atoms are mostly from group 14 elements (Si, Ge, Sn) and/or group 13 (Al, Ga, In), but also transition metals and group 15 elements. On the other hand, the guest atoms are alkali metals (Na, K, Rb, Cs), [1][2][3][4] alkaline-earth or divalent rare-earth metals (Sr, Ba, Eu), [5][6][7][8][9] and halogens (Cl, Br, I) 10,11 which are loosely bound to the cage. Most of the compounds follow the Zintl rule, where the cage atoms are partially substituted by acceptor atoms for charge compensation between guest and cage.…”