Properties of the type I Ge-based clathrates Ba8Al13Ge33 and Ba8Al16Ge30

The type I clathrate lattice is simple cubic with 46 atoms per unit cell. The cages in this lattice can host ``guests'' and the framework can have substituted atoms. Here, we focus on the ``alloy'' system Ba₈Al_xGe_30-x (x is an integer; 0<x<15). The Ba are guests and Al substitutes for some Ge framework atoms. Using the local density approximation (LDA), we have calculated some properties of the type I clathrates Ba₈Al₁₃Ge₃₃ and Ba₈Al₁₆Ge₃₀. Our calculations of the equilibrium structures predict that Ba₈Al₁₆Ge₃₀ and Ba₈Al₁₃Ge₃₃ have approximately the same lattice constant and that Ba₈Al₁₃Ge₃₃ is expected to be slightly more stable than Ba₈Al₁₆Ge₃₀. Our band structures and electronic density of states results predict that Ba₈Al₁₃Ge₃₃ is metallic and that Ba₈Al₁₆Ge₃₀ is a semiconductor with an indirect fundamental band gap of 0.3 eV. The vibrational spectrum predicts low frequency rattling modes caused by the Ba guests that are loosely bound in the Al-Ge framework cages. Such modes may scatter the heat-carrying acoustic vibrational framework modes, potentially reducing the thermal conductivity.