A DFT Computational Study of Type-I Clathrates A₈Sn_46-x (A = Cs or NH₄, x = 0 or 2)

Semiconducting clathrates have attracted considerable interest in the field of thermoelectric materials. We report here a computational study on the crystal structure, the enthalpy of formation, and the physical properties of the following type-I clathrates: (a) experimentally studied Cs₈Sn₄₄ and hypothetical Cs₈Sn₄₆ and (b) hypothetical (NH₄)₈Sn_46-x (x = 0 or 2). The ab initio VASP calculations for the nominal stoichiometries include the geometry optimization of the initial structural models, enthalpies of formation, and the electronic and phonon density of states. Comparison of the chemical bonding of the structural models is performed via the electron localization function. The results show that the presence and distribution of defects in the Sn framework for both Cs₈Sn_46-x and (NH₄)₈Sn_46-x systems significantly alters the formation energy and its electrical properties, ranging from metallic to semiconducting behavior. In particular, one defect per six-membered Sn ring in a 3D spiro-network is the thermodynamically preferred configuration that results in the Cs₈Sn₄₄ and (NH₄)₈Sn₄₄ stoichiometries with narrow-band gap semiconducting behavior. Moreover, the rotation of the ammonium cation in the polyhedral cavities is an interesting feature that may promote the use of ammonium or other small molecular cations as guests in clathrates for thermoelectric applications; this is due to the decrease in the lattice thermal conductivity.