Formation, properties, and function of vacancies in Si/Ge Clathrates: The importance of broken symmetries

Inclusion compounds, such as clathrates, are cage-like crystal structures that can encapsulate guest atoms. Since this allows to tune their electronic and vibrational properties, they are regarded as interesting materials for thermoelectric applications. Progress in this field is, however, hindered by the fact that filling of group-IV clathrates often results in complex and unexpected structural changes, e.g., the spontaneous formation of vacancies in certain hosts: In Ge$_{46}$ clathrates filled with K or Ba, the most favourable phases K$_8$Ge$_{44}$/ Ba$_8$Ge$_{43}$ feature two/three vacancies. Conversely, the framework of the isoelectronic Si$_{46}$ clathrate remains intact~(K$_8$Si$_{46}$/Ba$_8$Si$_{46}$) upon filling with the exact same guests. Our first-principles calculations of the formation energies and of the thermodynamic phase stabilities confirm this experimental scenario and shed light on the underlying mechanisms. Due to the spatially more delocalized 4sp$^3$ orbitals in Ge compared to the more localized 3sp$^3$ orbitals in Si, fundamentally different symmetry breaking distortions become possible to stabilize the vacancies. Eventually, we discuss the implications of these findings for the thermoelectric properties of clathrates.