Formation of Vacancies in Si- and Ge-based Clathrates: Role of Electron Localization and Symmetry Breaking.

The formation of framework vacancies in Si- and Ge-based type-I clathrates is studied using density-functional theory as a function of filling the cages with K and Ba atoms. Our analysis reveals the relevance of structural disorder, geometric relaxation, and electronic saturation as well as vibrational and configurational entropy. In the Si clathrates, we find that vacancies are unstable, but very differently, in Ge clathrates, up to three vacancies per unit cell can be stabilized. This contrasting behavior is largely driven by the different energy gain on populating the electronic vacancy states, which originates from the different degree of localization of the valence orbitals of Si and Ge. This also actuates a qualitatively different atomic relaxation of the framework.