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The structural and electronic properties of the clathrate compoundsBa$_{8}$Al$_{x}$Si$_{46-x}$ and Sr$_{8}$Al$_{x}$Si$_{46-x}$ are studied fromfirst principles, considering an Al content $x$ between 6 and 16. Due to thelarge number of possible substitutional configurations we make use of a specialiterative cluster-expansion approach, to predict ground states andquasi-degenerate structures in a highly efficient way. These are found from asimulated annealing technique where millions of configurations are sampled. Forboth compounds, we find a linear increase of the lattice constant with thenumber of Al substituents, confirming experimental observations forBa$_{8}$Al$_{x}$Si$_{46-x}$. Also the calculated bond distances betweenhigh-symmetry sites agree well with experiment for the full compositionalrange. For $x$ being below 16, all configurations are metallic for bothmaterials. At the charge-balanced composition ($x=16$), the substitutionalordering leads to a metal-semiconductor transition, and the ground states ofBa$_{8}$Al$_{16}$Si$_{30}$ and Sr$_{8}$Al$_{16}$Si$_{30}$ exhibit indirectKohn-Sham band gaps of 0.36 and 0.30 eV, respectively, while configurationshigher in energy are metals. The finding of semiconducting behavior is apromising result in view of exploiting these materials in thermoelectricapplications.

chemistry of materials

Predicting ground-state configurations and electronic properties of the  thermoelectric clathrates Ba$_{8}$Al$_{x}$Si$_{46-x}$ and  Sr$_{8}$Al$_{x}$Si$_{46-x}$