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Crystal structure and thermoelectric properties of K x Ba8− x Zn y Ge46− y clathrates
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10.1063/1.4711100
/content/aip/journal/jap/111/9/10.1063/1.4711100
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/9/10.1063/1.4711100

Figures

Image of FIG. 1.
FIG. 1.

Crystal structure of the type-I clathrate Ba8(X,Ge)46. Large balls represent Ba atoms and smaller balls represent X and Ge atoms; black, gray, and white balls are at the 6c, 16i, and 24k sites, respectively. This figure was drawn using the vesta program (Ref. 10).

Image of FIG. 2.
FIG. 2.

(a) Powder neutron diffraction pattern of the K4Ba4Zn6Ge40 sample and (b) powder x-ray diffraction pattern of the K8Zn4Ge42 sample, refined by Rietveld analysis.

Image of FIG. 3.
FIG. 3.

Band structures and densities-of-state for (a) Ba8Zn8Ge38 and (b) K8Zn4Ge42 clathrates calculated in the virtual crystal approximation. The solid curve in the right-hand side of the figure indicates the total DOS, and the black, dark gray, and light gray areas indicate partial DOSs of the K/Ba atoms at the 2a site, of the K/Ba atoms at the 6d site, and of all the Zn/Ge atoms, respectively.

Image of FIG. 4.
FIG. 4.

Room-temperature Hall mobility as a function of carrier concentration for the K x Ba8− x Zn y Ge46− y samples and some related clathrates: Ba8(Zn,Ge)46 (Ref. 14), Ba8(Ga,Ge)46 (Ref. 11), Ba8(Ni,Ga,Ge)46 (Ref. 8), and Ba8(Cu,Ga,Ge)46 (Ref. 13). The lines fit (: constant).

Image of FIG. 5.
FIG. 5.

Room-temperature weighted mobility as a function of carrier concentration for K x Ba8− x Zn y Ge46− y and some Ba-containing Ge clathrates (Refs. 8, 11, 13, and 14). The line is a guide for the eyes.

Image of FIG. 6.
FIG. 6.

Temperature dependences of (a) Hall mobility and (b) the ) value for the K x Ba8− x Zn8− x /2 Ge38+ x /2 and Ba8Ga16Ge30 samples. The thin lines in proportion to and represent the temperature dependences of mobilities dominated by alloy disorder scattering and acoustic phonon scattering, respectively. The thick solid and dotted curves fit the relation (, : constant).

Image of FIG. 7.
FIG. 7.

Band structures and densities-of-state for hypothetical (a) Na8Zn4Ge42 and (b) Cs8Zn4Ge42 clathrates calculated in the virtual crystal approximation. The solid curve in the right-hand side of the figure indicates the total DOS, and the black, dark gray, and light gray areas indicate partial DOSs of the Na/Cs atoms at the 2 site, of the Na/Cs atoms at the 6 site, and of all the Zn/Ge atoms, respectively.

Image of FIG. 8.
FIG. 8.

Temperature dependences of (a) thermal conductivity , (b) lattice thermal conductivity , (c) Seebeck coefficient , (d) electrical conductivity , (e) power factor , and (f) dimensionless figure-of-merit for the K x Ba8− x Zn8− x /2 Ge38+ x /2 and Ba8Ga16Ge30 samples. The curves in (a) and (f) are guides for the eyes; the solid curves in (b) fit the relation (, : constant), and the dotted curve in (b) represents the theoretical minimum value of Ge (Ref. 38).

Tables

Generic image for table
Table I.

Structural parameters for the K x Ba8− x Zn8− x /2Ge38+ x /2 clathrate (No. 223, ) samples, refined by the Rietveld method using powder neutron and x-ray diffraction under the following conditions: (1) no vacancy exists; (2) K and Ba atoms occupy 2 (0, 0, 0) and 24 (1/4, , 1/2 + ) sites, and Zn and Ge atoms occupy 6 (1/4, 0, 1/2), 16 (, , ), and 24 (0, , ) sites; (3) both the K/Ba and Zn/Ge ratios are the same as those determined by electron probe microanalysis; (4) equivalent atomic displacement parameters are equal at each site.

Generic image for table
Table II.

Room-temperature properties of the K x Ba8− x Zn y Ge46− y clathrate samples: (g/cm3), density; (1020 cm−3), carrier concentration; (cm2 V−1 s−1), Hall mobility; (), effective mass;  =  (cm2 V−1 s−1), weighted mobility; (mW cm−1 K−1), lattice thermal conductivity;  =  (103 cm3 K V−1 J−1), materials factor.

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/content/aip/journal/jap/111/9/10.1063/1.4711100
2012-05-07
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Crystal structure and thermoelectric properties of KxBa8−xZnyGe46−y clathrates
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/9/10.1063/1.4711100
10.1063/1.4711100
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