Why clathrates are good thermoelectrics: A theoretical study of Sr8Ga16Ge30

Recent measurements have shown that the inorganic clathrate Sr8Ga16Ge30 has good thermoelectric properties. This discovery has caused intense experimental activity to synthesize and test other compounds in this class. It has been conjectured that clathrates may be good thermoelectrics if they satisfy several conditions. The Sr atoms, trapped inside the clathrate cages, scatter phonons efficiently, leading to low thermal conductivity. Electric conductivity takes place mostly through the clathrate frame and the conduction electrons are not scattered by Sr vibrations. The compounds, being made of atoms that are semiconductors in the solid state, may have a high Seebeck coefficient. There has been no direct evidence, experimental or theoretical, for this scenario. By performing density functional calculations we show that these ideas are correct. The Sr atoms are weakly bound to the cage and do undergo large-amplitude motion. An analysis of conductivity shows that the largest contribution comes from a band in which the electrons are located on the clathrate frame. Bands originating from the Sr atoms contribute little to conductivity. There is very little charge transfer between the Sr atoms and the frame, and as a result, Sr vibrations are weakly coupled to the conduction electrons. The calculated Seebeck coefficient is in reasonable agreement with the measured one. We find that it is strongly affected by the positions of the Ga atoms in the frame and by doping.