clathrates*

Thermoelectric clathrates consists of semiconducting framework of group-IV host encapsulating metal guest. Filling of guest often results in bizzare structural changes such as the formation of vacancies (■), which in turn changes their electronic and vibrational properties. We use density-functional theory to compute the formation energies of type-I Ba₈Zn_xGe_46-x-y■_y clathrates with y vacancies in their framework as a function of Zn substitutions x [1]. Our study confirms the experimental observation that the framework vacancies are destabilized with increase in Zn substitution. Up to three vacancies per formula unit can be stabilized for 0 <x < 6, while they are unstable for x ≥ 6. This behavior is driven by the high energetic gain associated with the population of the valence electronic states of Zn as compared to the energetic gain upon saturation of the electronic vacancy states. We further analyse the thermodynamic stability and temperature induced changes in the carrier concentration of these compositions.

[1] Unraveling the role of vacancies in potentially promising thermoelectric clathrates Ba₈Zn_xGe_46-x-y■_y, Amrita Bhattacharya and Saswata Bhattacharya, Phys. Rev. B, 34, 094345 (2016).