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Abstract

Using density-functional theory we compute the formation energies of vacancies □ in the framework of type I Ba₈Zn_xGe_46−x−y□_y clathrates as a function of Zn substitutions. While resolving the contradiction on the experimental reports on the relation between the concentration of Zn, x, and the number of framework vacancies, y, our study confirms the observations that vacancies are destabilized with the increase in x: Up to three vacancies per formula unit can be stabilized for 0≤x<6, while they are unstable for x≥6. This behavior arises from the lower formation energy of (charged) Zn substitution in the Ge framework as compared to a (charged) vacancy creation. Finally our study reveals the stability of a high-temperature T phase Ba₈Zn₆Ge₄₀ that has high electronic carrier concentration, whereby the carriers also show high-T-induced variation effective for its thermoelectric application.