Encapsulating cage structures, pentagonal dodecahedron and open dodecahedron and distorted cube of the type-III clathrate compound. The white and black spheres stand for trigonally (Tr) and tertragonally (Tt) bonded framework atoms, respectively.
SEM backscattered electron images of alloys with (a) , (b) , (c) , and (d) .
Phase equilibria among phases [type-III clathrate, type-I clathrate, and phases] present near the Ge corner of the Ba–Al–Ge ternary phase diagram.
X-ray powder diffraction patterns in the range from 3° to 12° for alloys with , 9, and 12. The arrows indicate additional reflections from the type-I clathrate phase.
(a) Electrical resistivity, (b) Seebeck coefficient, and (c) thermoelectric power factor for alloys with plotted as a function of temperature. Data points for the alloy are also plotted for comparison.
(a) Temperature dependence of thermal conductivity for alloys up to . Data points for the alloy are also plotted for comparison. (b) Values of electronic and lattice thermal conductivities for alloys at room temperature plotted as a function of Al content . Data points similarly calculated for alloys are also plotted.
Dimensionless figure of merit for alloys with plotted as a function of temperature. Data points for the alloy are also plotted for comparison.
(a) Lattice constant of the type-III clathrate compound, , and (b) split distance of the Ba(2) atom in the sites plotted as a function of temperature. The dash line indicates the disorder parameter derived from the temperature dependence of value for the Ba(2) atom.
Values of ADP for guest and framework atoms in the type-III clathrate compound, , plotted as a function of temperature.
Values of the average interatomic distance between the Ba(2) and cage atoms in the open dodecahedron (Ba(2)–Tt/Tr), between trigonally bonded cage atoms forming the distorted square window of the open dodecahedron (Tr–Tr), between Ba(2) and trigonally bonded Ge atoms (Ba(2)–Tr) and between Ba(3) and trigonally bonded Ge atoms (Ba(3)–Tr) in the cage framework plotted as a function of Al content , respectively.
Results of crystal structure refinement for the type-III clathrate phase in the specimen with . Reliability factors of fit, (%) and , are 2.26% and 1.31 for single-site model [Ba(2) site] 2.27% and 1.32 for spite-site model [Ba(2) site].
Lattice constants and average bond lengths between the framework atoms for the type-III clathrate phase in the specimen with , 9, and 12.
Einstein temperatures and disorder parameters evaluated from the temperature dependence of ADPs of Ba atoms in
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