We report extended x-ray absorption fine-structure (EXAFS) studies of $n$- and $p$-type ${\text{Ba}}_8{\text{Ga}}_{16}{\text{Ge}}_{30}$ samples (type-I clathrate) at the Ga, Ge, and Ba $K$ edges, to probe the local structure, particularly around the Ba atoms located inside 20- and 24-atom cages (Ba1 and Ba2 sites, respectively) composed of Ga/Ge atoms. In agreement with diffraction analysis, we find Ba2 is off center, with a component in the $bc$ plane $\left(0.15\text{Å}\right)$ comparable to that found in diffraction. However, under the assumption of a stiff cage, we also require a significant $a$ component. This suggests a coupling or attraction between the Ba2 atoms and the hexagonal rings at the top or bottom of the cage that encloses the Ba2 site. Further, changing the $a$ component can change the number of shortest Ba2-Ga/Ge neighbors and hence the coupling of Ba2 to the surrounding cage. Within the cage structures which enclose both Ba sites, the Ga-Ga/Ge distances are slightly longer, while the Ge-Ga/Ge distances are slightly shorter than the average distance reported from diffraction. The longer Ga-Ga/Ge distances indicate that the Ba1 and Ba2 cages may be dimpled or distorted. At the second Ga/Ge distance, the local distortions in the Ba clathrate are smaller than those observed in the Eu clathrate, which likely plays a role in understanding the higher thermal conductivity of Ba clathrates compared to that of Eu clathrates. However, there is no clear difference in the EXAFS between the $n$- and $p$-type materials for either the Ba, Ga, or Ge $K$-edge data, which would explain the difference in thermal conductivity between $n$- and $p$-type materials. Finally, an average Einstein temperature for the shortest Ba2-Ga/Ge bonds is comparable to that for Ba1-Ga/Ge. This indicates a large effective spring constant for the closest Ga/Ge atoms to Ba2. We also develop a simple vibrational model to show explicitly the three types of vibration for Ba2 within the type-2 cage.

• Received 24 January 2008

DOI:https://doi.org/10.1103/PhysRevB.78.014111