Investigating the Chemical Ordering in Quaternary Clathrate Ba8AlxGa16-xGe30

Recently there has been an increased interest in quaternary clathrate systems as promising thermoelectric materials. Owing to their increased complexity, the chemical ordering in the host framework of quaternary clathrates has, however, not yet been comprehensively analyzed. Here, we have synthesized a prototypical quaternary type-I clathrate Ba₈Al_xGa_16-xGe₃₀ by Czochralski and flux methods, and employed a combination of X-ray and neutron diffraction along with atomic scale simulations to investigate chemical ordering in this material. We show that the site occupancy factors of trivalent elements at the 6c site differ depending on the synthesis methods, which can be attributed to the level of equilibration that is achievable in either route. The flux-grown samples are consistent with the simulated high-temperature disordered configuration, while the degree of ordering for the Czochralski sample lies between the ground and high-temperature state. Moreover, we demonstrate that the atomic displacement parameters of the Ba atoms in the larger tetrakaidecahedral cages are related to chemical ordering. Specifically, Ba atoms are either displaced towards the periphery or localized at the cage centers. This study, consequently, reveals key relationships between the chemical ordering in the quaternary clathrates Ba₈Al_xGa_16-xGe₃₀ and the structural properties, thereby offering new perspectives on designing these materials and optimizing their thermoelectric properties.