(a) The clathrate type I structure with polygons showing the two different cages. (b) Close-up of the cages with Wyckoff notation of the host structure atoms. The structure has been overlaid on the structure to illustrate the relative displacement of the atom. The arrows indicate the direction of the displacement.
The ADPs as a function of temperature for , , and (left to right). Triangles pointing up are , circles are , squares are , and inverted triangles are averaged host structure . The lines represent the Einstein and Debye fits.
Powder INS spectra for with (diamonds), (triangles), (circles), and (squares). The spectra have been successively offset by 200 counts for clarity.
The effect of the cage volume on rattler energy and lattice thermal conductivity. The volume goes from smallest to largest for , , , , and . Open circles are rattler energies extracted from the powder INS spectra, whereas Einstein temperatures extracted from x-ray data are shown as x’s. The lines are guides to the eyes. The solid squares are the results from the INS pressure experiment. Triangles are to lattice thermal conductivities at 250 K.
INS spectra of . Squares indicate data collected at ambient pressure with an aluminum sample holder, circles are for data collected at ambient pressure with the sample loaded into the pressure cell, and triangles are for the sample under an applied pressure of 9 kbars. The spectra have been offset for clarity.
INS spectra collected as a function of temperature for and . The temperatures of 300, 200, and 100 K are shown with squares, circles, and triangles, respectively. The spectra have been offset for clarity.
The energy of the first (solid) and second (open) peaks observed by INS as function of temperature. and - and are shown as circles, squares, and diamonds, respectively, and the corresponding fits are shown as dotted, solid, and dashed lines.
Electrical resistivity as a function of temperature for (diamonds), (triangles), and (circles).
Seebeck coefficient as a function of temperature for (diamonds), (triangles), and (circles).
Lattice thermal conductivity as a function of temperature for (diamonds), (triangles), and (circles). The charge carrier contribution has been subtracted from the observed thermal conductivity using Wiedemann–Franz law. For comparison the thermal conductivity for - and is included (Ref. 31).
The dimensionless thermoelectric figure of merit, , for (diamonds), (triangles), and (circles).
Selected results from Rietveld refinements of the x-ray powder diffraction data. The structural parameters are as follows: Ba1, and Ba2, , and for the host structure , , and . For further details see supplementary material. The fractional volume and the volume of the large tetrakaidecahedral cage have been calculated according to procedures explained in the supporting material. The rattler energy from the powder INS data is given at room temperature. The scattering length , atomic mass, and atomic radius is listed for in . The corresponding values for Ge are as follows: , , and atomic .
Selected results from refinements of the 300 K single crystal x-ray diffraction data. The guest atoms are refined with the following structural parameters: Ba1, and Ba2, , and host structure atoms with , , and . Details from the refinement of data at other temperatures are given in supplementary materials.
Einstein and Debye temperatures and the disorder parameter obtained from multitemperature single crystal x-ray diffraction data. Literature values are listed for comparison.
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