Preparation and thermoelectric properties of sintered type-II clathrates (K,Ba)24(Al,Sn)136

Accepted Manuscript Preparation and thermoelectric properties of sintered type-II clathrates (K,Ba)24(Al,Sn)136 Suguru Utsunomiya, Kengo Kishimoto, Shota Koda, Koji Akai, Ryo Fujita, Hironori Asada, Tsuyoshi Koyanagi PII:

S0925-8388(16)32985-1

DOI:

10.1016/j.jallcom.2016.09.231

Reference:

JALCOM 39065

To appear in:

Journal of Alloys and Compounds

Received Date: 24 April 2016 Revised Date:

17 September 2016

Accepted Date: 21 September 2016

Please cite this article as: S. Utsunomiya, K. Kishimoto, S. Koda, K. Akai, R. Fujita, H. Asada, T. Koyanagi, Preparation and thermoelectric properties of sintered type-II clathrates (K,Ba)24(Al,Sn)136, Journal of Alloys and Compounds (2016), doi: 10.1016/j.jallcom.2016.09.231. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Preparation and thermoelectric properties of sintered type-II clathrates (K,Ba)24(Al,Sn)136

Suguru Utsunomiyaa , Kengo Kishimotoa,∗, Shota Kodaa , Koji Akaib , Ryo Fujitaa , Hironori Asadaa , Tsuyoshi Koyanagia Graduate School of Sciences and Technology for Innovation, Yamaguchi University, 2-16-1 Tokiwadai, Ube, Yamaguchi 755-8611, Japan b Faculty of Global and Science Studies, Yamaguchi University, 1677-1 Yoshida, Yamaguchi 753-8511, Japan

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a

Abstract

The maximum dimensionless figures of merit were 0.57 at 590 K and 0.82 at 640 K for the K9 Ba15 Al38 Sn98 and K9 Ba15 Al31 Ga8 Sn97 sintered samples, respectively, which were lower than that 1.17 of K6 Ba18 Ga40 Sn96 . The

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substituting atom for Sn in the framework of this clathrate affected its electronic and electrical properties significantly. Compared to Ga substitution,

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Al substitution damaged dispersive bands at the conduction-band edge, resulting in a larger inertial mass. This substitution also caused larger defect

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densities in the sintered samples. As a result, the Al-substituted sintered samples had room-temperature carrier mobilities of only 30–40 cm2 V−1 s−1 ,

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which were lower than that ∼ 170 cm2 V−1 s−1 of the Ga-substituted ones. On the other hand, the substituting atom did not influence the thermal properties very much. The Al-substituted sintered samples had as low lattice thermal conductivities as 5 mW cm−1 K−1 due to a strong rattling effect like ∗

Corresponding author Email address: [email protected] (Kengo Kishimoto)

Preprint submitted to Journal of Alloys and Compounds

September 21, 2016

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the Ga-substituted ones.

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Keywords:

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thermoelectric materials, type-II clathrate, Sn clathrate, aluminum

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1. Introduction

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The dimensionless figure of merit ZT of a thermoelectric material is given

by S 2 σT /κ (S, Seebeck coefficient; σ, electrical conductivity; T , absolute temperature; κ, thermal conductivity). Also, ZT can be expressed approx-

imately by ZT ∝ m∗ 3/2 µT /κL (m∗ , density-of-states (DOS) effective mass;

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µ, mobility). [1] The weighted mobility m∗ 3/2 µ is governed mainly by the band structure of the material. For a multivalleyed material, m∗ is given by

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NV 2/3 mN (NV , the number of valleys; mN , single-valley DOS effective mass). NV and mN are determined by the band-edge structure. mN and the inertial mass mI affect µ. For example, the mobility governed by acoustic phonon scattering or ionized impurity scattering is proportional to mN −3/2 mI −1 or mI −1/2 , respectively. [1] Thus, a good band-structure material would provide a high ZT value.

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Clathrate compounds with the guest-host crystal structure are one of

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high-efficiency thermoelectric materials because of their low κL values resulting from the rattling effect. [2, 3, 4, 5] Recently, we reported a high ZT value

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of 1.2 for the Sn-based K8 Ba16 Ga40 Sn96 with the type-II clathrate structure. [6, 7] Sn-based clathrates would be used for low- and mid-temperature applications. A few Sn-based type-II clathrates were prepared, although their

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thermoelectric properties have been little investigated. [8, 9, 10, 11] The band structures of clathrate compounds are affected by the host and

guest atoms. For example, the substituting atoms in the host of Sn-based type-I clathrates K8 M8 Sn38 (M = Al, Ga, In) modified the conduction-band edges of the electronic structures and thermoelectric properties substantially. [12] We thus prepared type-II K-Ba-Al-Sn clathrates by using Al instead 3

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of Ga in order to investigate their thermoelectric properties, including the

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electronic structure and transport properties. It is noted that the K-Ba-AlSn clathrates are superior to the K-Ba-Ga-Sn ones in light weight and the raw material cost.

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2. Experimental

The experimental procedure of this study was almost the same as those

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previously reported. [6, 7] Additional explanation is as follows: We obtained the sintered samples of K8 Ba16 Al40+x Sn96−x by using direct melting of the elements, the spark plasma sintering (SPS), and annealing. We also prepared K8 Ba16 Al40+x−y Gay Sn96−x samples in order to control their carrier concentrations. The starting materials were K(99.5%), Ba(99.9%), Al(99.999%), Ga(99.9999%), and Sn(99.999%). The sintering temperature and interval

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were 773–798 K and 1 h, respectively; the annealing temperature and time

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were 733 K and 168 h, respectively.

We used powder x-ray diffraction (XRD) and the Rietveld analysis pro-

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gram RIETAN-FP [13] for Rietveld analyses, which provided the weight percentages of impurity phases in the samples. Differential scanning calorimetry (DSC) measurements were performed using a RIGAKU DSC8270 calorime-

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ter, with Al2 O3 as a standard material. The carrier concentrations n of the

samples were given by 1/(eRH ), where e is the electric charge and RH is the Hall coefficient. The DOS effective masses m∗ were obtained using the equa-

tions S = (k/e){2F1 (η ∗ )/F0 (η ∗ ) − η ∗ } and n = 4π(2m∗ kT /h2 )3/2 F1/2 (η ∗ ), R∞ xt dx where k is the Boltzmann constant, Ft (η ∗ ) = 0 1+exp(x−η ∗ ) is a Fermi integral of order t, η ∗ is the reduced Fermi energy, and h is Planck’s con4

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stant. [1] The thermal conductivities κ were obtained using the relationship

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κ = αCρ; the thermal diffusivities α were measured using the laser-flash method (Shinku-riko TC-7000 instrument) and the specific heats C were calculated using the Dulong–Petit law. The lattice thermal conductivities κL

were estimated as κL = κ − LσT , where the Lorenz number L is given by

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(k/e)2 {3F2 (η ∗ )/F0 (η ∗ ) − 4F1 2 (η ∗ )/F0 2 (η ∗ )}. The electronic structures were

calculated using a full-potential augmented plane-wave method with a gen-

3. Results and Discussion

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eralized gradient approximation. [14, 15, 16]

3.1. Sample preparation, crystal structure, and carrier concentration Before sintering, the raw materials contained an impurity phase of βSn. During sintering, 5–7wt.% of the raw materials placed in the graphite

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dies melted and flowed out. The flowed-out materials were considered to

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come from mainly the impurity phase, although the sintered samples did not consist entirely of a single phase. The nominal and actual compositions of

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the samples differed from each other. This is similar to our previous work for (K,Ba)24 (Ga,Sn)136 . [6, 7] We used several nominal compositions. As a result, we obtained a K8 Ba16 Al38 Sn98

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sample having the smallest amount of the impurity phases β-Sn of 3.7wt% and BaAl4 of 0.5wt% from the nominal composition of K8 Ba16 Al41 Sn95 . This sample exhibited the primary phase of the type-II clathrate structure (No. 227-2, F d¯3m). Figure 1 shows the XRD pattern of the sample. Table 1 lists the structural parameters of the sample refined by Rietveld analysis. The lattice constant of the (K,Ba)24 (Al,Sn)136 sample was larger 5

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K7.8(0.4)Ba16.2Al41.6(0.6)Sn94.4

4

2 1

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F d −3 m (No.227) a = 1.71498(5) nm Rwp = 10.36 Rp = 7.50, S = 1.11 β−Sn: 3.7 wt.%

3

0

20

40

60 80 2θ (deg.)

100

120

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3

XRD intensity (10 count)

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Figure 1: XRD pattern of sintered type-II clathrate K-Ba-Al-Sn sample refined by Rietveld analysis.

than that of (K,Ba)24 (Ga,Sn)136 . This is consistent with that the atomic radius of Al is larger than that of Ga. The occupancies of Al were large in order of the 96g, 8a, and 32e sites. This is the same as that of Ga in

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(K,Ba)24 (Ga,Sn)136 . [6]

In a previous study, we changed the nominal Ga/Sn ratio of (K,Ba)24 (Ga,Sn)136

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to control the carrier concentration. [7] In this study, we changed the nominal Al/Sn ratio similarly, but the amount of impurity phases increased substan-

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tially. Instead, we added some amounts of Ga to K8 Ba16 Al40 Sn96 . As a result, we could obtain (K,Ba)24 (Al,Sn)136 samples with smaller carrier con-

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centrations as well as small amounts of impurity phases. Table 2 lists the samples studied along with their RT properties. Figure 2 shows the temperature dependences of the carrier concentrations for the samples. The carrier concentrations did not depend on the temperature very much. Figure 3 shows the DSC curves of the type-II clathrate (K,Ba)24 (Al,Ga,Sn)136

samples. The melting point of (K,Ba)24 (Al,Ga,Sn)136 was slightly higher than

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Table 1: Structural parameters of sintered type-II clathrate K-Ba-Al-Sn sample (No. 227-

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2, F d¯ 3m, a = 17.1498(5) ˚ A), refined by the Rietveld method using powder x-ray diffraction under the following conditions: 1) no vacancy existed; 2) the Ba/Al ratio was the same

as the value 2.56 determined by electron probe microanalysis; 3) equivalent atomic displacement parameters Ueq were equal at each site. The sample was determined to have

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the chemical composition of K7.8(0.4) Ba16.2 Al41.6(0.6) Sn94.4 , and included 3.7 and 0.5 wt% of impurity phases, β-Sn and BaAl4 , respectively. Goodness of fit: S = 1.11; Rwp = 10.36 and Rp = 7.50.

Occupancy

K/Ba

32e

0.15(1)/0.10

K/Ba

16c

0.18/0.82

Al/Sn

8a

0.25(1)/0.75

Al/Sn

32e

0.147(7)/0.853

Al/Sn

96g

0.363(4)/0.637

y

z

Ueq (˚ A2 )

0.400(6)

x

x

0.46(10)

0

0

0

0.022(1)

1/8

1/8

1/8

0.009(2)

0.2190(1)

x

x

0.008(1)

0.06802(8)

x

0.3734(1)

0.0109(6)

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4

(K,Ba)24(Al,Ga,Sn)136

3

2

AG4 AG8

N21 (K,Ba)24(Ga,Sn)136

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2

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19

−3

cm )

5

1/(e RH ) (10

x

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Site

D

Atom

4

6 8 1000/T (1/K)

10

Figure 2: Temperature dependences of carrier concentrations 1/(eRH ) for type-II clathrate

(K,Ba)24 (Al,Ga,Sn)136 samples. The result of a (K,Ba)24 (Ga,Sn)136 sample is also plotted for comparison (Ref. [7]).

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Table 2: List of type-II clathrate (K,Ba)24 (Al,Ga,Sn)136 samples with some roomcarrier concentration; m∗ (me ), DOS effective mass. Sample ID

Composition

a

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temperature properties: a (nm), lattice constant; ρ (g cm−3 ), density; n (1019 cm−3 ), Impuritiesb

ρ

n

m∗

actuala

A45

K8 Ba16 Al41 Sn95

K9 Ba15 Al38 Sn98

1.71498(5)

3.7,0.5,-

4.923

4.5

0.90

AG4

K8 Ba16 Al40 Sn96 +4Ga

K10 Ba14 Al35 Ga4 Sn97

1.71215(5)

1.5,-,-

4.953

2.4

0.93

AG8

K8 Ba16 Al40 Sn96 +8Ga

K9 Ba15 Al31 Ga8 Sn97

1.71077(5)

1.0,-,-

5.028

2.3

0.90

N21c K8 Ba16 Ga40 Sn96 K6 Ba18 Ga40 Sn96 1.7039(1) 2.3,-,0.3 5.544 a) Chemical compositions determined by electron probe microanalysis; the total number

2.1

0.65

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nominal

of K and Ba atoms was set at 24 per unit cell, and the total number of Al, Ga and Sn atoms was normalized to be 136.

b) Weight percentage of impurity phases. The first, second, and third values are for β-Sn, BaAl4 , and type-I clathrate, respectively.

c) a (K,Ba)24 (Ga,Sn)136 sample (Ref. [7]) is also listed for comparison.

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that of (K,Ba)24 (Ga,Sn)136 . In addition to it, the melting point of Al is much

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higher than that of Ga. These may be associated with that the amount of impurity phases increased with a change in nominal Al/Sn ratio, as mentioned above. The elements with off-stoichiometric compositions in the K-Ba-Al-

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Sn system seem to be more difficult to melt together uniformly than in the K-Ba-Ga-Sn system. Possibly, higher melting temperatures during sample

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preparation help us to obtain K-Ba-Al-Sn samples with smaller amounts of impurities.

3.2. Band structure and effective mass Figure 4 shows the band structure and DOS around the band gap for

the type-II clathrate K8 Ba16 Al40 Sn96 . This is largely the same as that of K8 Ba16 Ga40 Sn96 . [6] The bands near the band gap are formed mainly from 8

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1.2 +1.2 +0.8 0.8 +0.4 0.4

A45

(K,Ba)24(Al,Ga,Sn)136

AG4

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Heat flow (W/g)

1.6

AG8

0.0

N21 (K,Ba)24(Ga,Sn)136

−0.4 heating 10 K/min

Figure

400

3:

500 600 700 800 Temperature (K)

Differential

900

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−1.2 300

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endothermic −0.8

scanning

calorimetry

curves

of

(K,Ba)24 (Al,Ga,Sn)136 samples on heating at 10 K/min.

type-II

clathrate

The result of a

(K,Ba)24 (Ga,Sn)136 sample is also plotted for comparison (Ref. [7]).

the orbitals of the host atoms, whereas the conduction band is formed from

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the orbitals of the guest Ba atoms partially. In addition, there are dispersive

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bands at the conduction-band edge. The bands were very important for high carrier mobilities. [6]

However, the dispersive bands of K8 Ba16 Al40 Sn96 are flatter than those

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of K8 Ba16 Ga40 Sn96 . A similar difference in the band structure was observed between the type-I clathrates K8 Al8 Sn38 and K8 Ga8 Sn38 in a previous study.

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[12] The inertial mass mI , the single-valley DOS effective mass mN , and the DOS mass m∗ were calculated to be 0.25, 0.25, and 0.63me , respectively, from the curvatures of the four bottom bands, whereas the corresponding values for K8 Ba16 Ga40 Sn96 were 0.19, 0.21, and 0.52me , respectively. [6] [17] In addition, since the DOS of the dispersive bands is too small to receive the carrier electrons, the electrons partly existed in the flat bands at ∼ 0.3 eV

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type−II K8Ba16Al40Sn96 (P1)

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1 Sn Al Ba K

0

Γ

X

M

Γ 60 120 180 DOS (states/(eV cell))

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−1 R

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Energy (eV)

2

Figure 4: Band structure and density-of-states (DOS) near the band gap for type-II clathrate K8 Ba16 Al40 Sn96 . The solid curve in the right-hand side of the figure indicates the total DOS, and the black, dark gray, light gray, and white areas indicate partial DOS of the K, Ba, Al, and Sn atoms, respectively.

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upper from the bottom edge for K8 Ba16 Al40 Sn96 unlike for K8 Ba16 Ga40 Sn96 .

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The “effective” mI , mN , and m∗ values were larger than the above values accordingly. The magnitude relation in m∗ between both clathrates is consistent with the experimental results listed in Table 2.

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In case that a dominant scattering is acoustic phonon scattering, K8 Ba16 Al40 Sn96 is inferior to K8 Ba16 Ga40 Sn96 in the band structure because of its larger in-

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ertial mass mI and smaller weighted mobility m∗ 3/2 µ. [1] 3.3. Mobility

Figure 5 (a) shows the temperature dependences of the Hall mobilities

µH . For comparison, we also plotted the data of the samples N21, N11, and N08 of (K,Ba)24 (Ga,Sn)136 with n = 2.1, 1.1, and 0.76 × 1019 cm−3 , respectively. [7] The (K,Ba)24 (Al,Ga,Sn)136 samples exhibited a similar trend for 10

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4000

AG8

40

(a) 102

µ HT

20

1/2

A45 (K,Ba)24(Al,Ga,Sn)136 AG4 4

1000 800 600

6 8 1000/T (1/K)

10

(b)

400 200

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N08

100 80 60

2000

(K,Ba)24(Ga,Sn)136

100 0

2

4 6 1000/T (1/K)

perature 1000/T for sintered type-II clathrates (K,Ba)24 (Al,Ga,Sn)136 . The data of the (K,Ba)24 (Ga,Sn)136 samples are also plotted for comparison (Ref. [7]). Solid lines are fits

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the mobilities to the (K,Ba)24 (Ga,Sn)136 samples. The (K,Ba)24 (Ga,Sn)136 samples suffered from potential barrier scattering at low temperatures and

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from acoustic phonon scattering at high temperatures.

[6, 7] Probably,

the (K,Ba)24 (Al,Ga,Sn)136 samples suffered from the same scatterings. Al-

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though the trends in the behaviors of the mobilities were similar, the values of the (K,Ba)24 (Al,Ga,Sn)136 samples were much smaller than those of the

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(K,Ba)24 (Ga,Sn)136 samples. Let us examine the potential barrier scattering at low temperatures. Fig-

ure 5 (b) shows the µH T 1/2 values as a function of inverse temperature. The mobility governed by potential barrier scattering at grain boundaries is given by[18]

11

N11

A45 AG4 AG8 (K,Ba)24(Al,Ga,Sn)136

Figure 5: (a) Hall mobilities µH and (b) µH T 1/2 values as a function of inverse tem-

to the experimental data.

N21

N08

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(K,Ba)24(Ga,Sn)136

2 −1 −1 1/2

N11

(cm V s K )

N21

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2 −1 −1

Hall mobility µ H (cm V s )

200

8

10

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1 Eb )1/2 exp(− ), 2πmN kT kT

Eb =

e2 Qt 2 , 8ε0 εr n

(1)

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µb = le(

(2)

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where l is the grain size, or the barrier interval, Eb is the barrier height,

Qt is the trapping state density, ε0 is the vacuum permittivity, and εr is the dielectric constant. The Qt values of the samples A45, AG4, and AG8

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were estimated to be 7.3, 7.4, and 7.2 × 1012 cm−2 , respectively, using εr = 24 for α-Sn. [19] In a previous study, annealing after sintering for the (K,Ba)24 (Ga,Sn)136 samples decreased the Qt values from ∼ 8 × 1012 cm−2 to ∼ 3 × 1012 cm−2 . [7] However, the annealing for the (K,Ba)24 (Al,Ga,Sn)136 samples did not decrease the Qt values. These large Qt values led to de-

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graded carrier mobilities. Such large Qt values were caused by larger amount of impurity phases in the samples, as mentioned above.

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The mobility governed by acoustic phonon scattering µac is proportional to mI −1 mN 3/2 . [1] As seen in Sec. 3.2, the (K,Ba)24 (Al,Sn)136 had larger mI

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and mN values. These larger values were another reason for smaller carrier mobilities of the (K,Ba)24 (Al,Ga,Sn)136 samples.

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3.4. Thermoelectric properties Figure 6 shows the temperature dependences of thermoelectric properties

of the samples. The Seebeck coefficients and electrical conductivities were almost typical of a degenerate semiconductor (Figs 6 (a) and (b)), whereas the electrical conductivities at low temperatures suffered from potential barrier scattering as seen before. Since the absolute Seebeck coefficients reached 12

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their optimum value of ∼ 200 µV/K, the carrier compensation was accom-

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plished enough.

The (K,Ba)24 (Al,Ga,Sn)136 samples had total thermal conductivities of

5–7 mW cm−1 K−1 (Fig 6 (c)). Their lattice thermal conductivities κL were as low as the theoretical minimum value κmin of Sn (Fig 6 (d)). [20] Ta-

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ble 1 indicates that the (K,Ba)24 (Al,Ga,Sn)136 samples had a large split-

ting of the rattler’s 32e site and its large atomic displacement parameter

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Ueq . The splitting and Ueq value were almost the same as those of the (K,Ba)24 (Ga,Sn)136 samples. [6, 7, 9] Probably, a strong rattling occurred in the (K,Ba)24 (Al,Ga,Sn)136 samples, resulting in decreasing thermal conductivity. [9, 21] In addition, alloy-disorder phonon scattering might decrease the κL values of the (K,Ba)24 (Al,Ga,Sn)136 samples.

Figure 6 (e)) shows the temperature dependences of ZT . The maximum

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ZT values were 0.57 at 590 K and 0.82 at 640 K for the (K,Ba)24 (Al,Sn)136

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and (K,Ba)24 (Al,Ga,Sn)136 samples, respectively. These were lower than that of the (K,Ba)24 (Ga,Sn)136 sample. This weakness was due to their lower electrical properties, resulting mainly from a larger inertial mass and larger

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defect densities.

In a previous study, we succeeded in improving ZT for the sintered p-type

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Ba8 Ga16 Sn30 with the type-VIII clathrate structure. [22] It suffered from potential barrier scattering like the type-II clathrate samples in this study. The Ge substitution for Sn increased the mobility, leading to an increase in ZT . Similarly, the Ge substitution for Sn in the type-II clathrates may decrease the defect densities to increase the carrier mobilities.

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−150 −100 −50 200

300 400 500 Temperature (K)

10

−1 −1

4 2

300

100

200

300 400 500 Temperature (K)

400 500 600 Temperature (K)

700

κmin (Sn)

2

0

(d)

300

400 500 600 Temperature (K)

ZT

0.4 0.2

(e)

700

4

0.6

0.0

600

6

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0.8

50

EP

1.2 1.0

(b)

κL (mW cm K )

6

(c)

700

8

8

0

600

100 80

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−1 −1

Thermal conductivity (mW cm K )

100

200

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0

(a)

(K,Ba)24(Al,Ga,Sn)136 A45 AG4 AG8

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−200

500

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Electrical conductivity σ (S/cm)

800

(K,Ba)24(Ga,Sn)136 −250 N21

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Seebeck coefficient S (µV/K)

−300

300

400 500 600 Temperature (K)

700

Figure 6: Temperature dependences of (a) Seebeck coefficients S, (b) electrical conduc-

14 lattice thermal conductivities κL , and (e) tivities σ, (c) thermal conductivities κ, (d) dimensionless figures of merit ZT for sintered type-II clathrates (K,Ba)24 (Al,Ga,Sn)136 . Dotted curves represent the data for type-II clathrate (K,Ba)24 (Ga,Sn)136 (Ref. [7]); solid curve κmin (Sn) in (d) represents the theoretical minimum value of Sn (Ref. [20]).

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4. Conclusions

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We prepared almost single-phase sintered samples of the type-II clathrate (K,Ba)24 (Al,Sn)136 and its Ga-substituted compound. Their carrier concentrations were compensated enough so that their maximum absolute Seebeck

coefficients reached ∼ 200 µV/K, which corresponds to an optimum value for

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a high ZT . The (K,Ba)24 (Al,Ga,Sn)136 samples had smaller RT carrier mobilities of 30–40 cm2 V−1 s−1 than that 170 cm2 V−1 s−1 of the (K,Ba)24 (Ga,Sn)136

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samples. Band structure calculation demonstrated that K8 Ba16 Al40 Sn96 has flat bands with large inertial masses at the conduction-band edge compared to K8 Ba16 Ga40 Sn96 . In addition, the (K,Ba)24 (Al,Ga,Sn)136 samples possessed larger defect densities than the (K,Ba)24 (Ga,Sn)136 samples. These two factors are associated with small carrier mobilities. On the other hand, the (K,Ba)24 (Al,Ga,Sn)136 samples had as low lattice thermal conductivities

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of 4–5 mW cm−1 K−1 as the theoretical minimum value of Sn. The crystal

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structure analysis indicated that the rattling effect was strong for the samples. The maximum ZT values were 0.57 at 590 K and 0.82 at 640 K for the

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K9 Ba15 Al38 Sn98 and K9 Ba15 Al31 Ga8 Sn97 sintered samples, respectively, Acknowledgements

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The authors would like to acknowledge use of the PC cluster resources

of the Media and Information Technology Center, Yamaguchi University, for calculations of the electronic structure. This work was partly supported by JSPS KAKENHI Grant Nos. 26289377 and 15K06487. [1] H. J. Goldsmid, Introduction to Thermoelectricity (Springer, Heidelberg, 2009), Chap. 3, pp. 23–41. 15

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[2] G. A. Slack, in Materials Research Society Symposium Proceedings

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vol. 478, edited by T. M. Tritt, M. G. Kanatzidis, H. B. Lyon, Jr., G. D. Mahan (Mater. Res. Soc., Pittsburgh, 1997), pp. 47–54.

[3] G. S. Nolas, J. L. Cohn, G. A. Slack, S. B. Schujman, Appl. Phys. Lett.

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73 (1998) 178.

[4] V. L. Kuznetsov, L. A. Kuznetsova, A. E. Kaliazin, D. M. Rowe, J.

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Appl. Phys. 87 (2000) 7871.

[5] The Physics and Chemistry of Inorganic Clathrates, edited by G. S. Nolas (Springer, Dordrecht, 2014).

[6] S. Koda, K. Kishimoto, K. Akai, H. Asada, T. Koyanagi, J. Appl. Phys. 116 (2014) 023710.

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[7] K. Kishimoto, S. Koda, K. Akai, T. Koyanagi, J. Appl. Phys. 118 (2015)

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125103.

[8] R. Kr¨oner, K. Peters, H. G. V. Schnering, R. Nesper, Z. Kristallogr. -

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New Cryst. Struct. 213 (1998) 664. [9] S. Mano, T. Onimaru, S. Yamanaka, T. Takabatake, Phys. Rev. B 84

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(2011) 214101.

[10] M. C. Sch¨afer, S. Bobev, J. Am. Chem. Soc. 135 (2013) 1696. [11] M. C. Sch¨afer, S. Bobev, Acta Cryst. C 69 (2013) 319. [12] M. Hayashi, K. Kishimoto, K. Akai, H. Asada, K. Kishio, T. Koyanagi, J. Phys. D: Appl. Phys. 45 (2012) 455308. 16

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[13] F. Izumi, K. Momma, Solid State Phenom. 130 (2007) 15.

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[14] P. Blaha, K. Schwarz, G. Madsen, D. Kvasnicka, J. Luitz, Program package WIEN2k, Technical University of Vienna (2001).

[15] J. .P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865.

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[16] The structural parameters of K8 Ba16 Al40 Sn96 were set to the data obtained by Rietveld analysis. The crystal symmetry was P 1, and the

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numbers of the Al atoms sitting at 8a, 32e, and 96g sites in the host framework were set to be 2, 4, and 34, respectively. The muffin-tin radii, RMT , for K, Ba, Al, and Sn atoms were 2.8, 2.6, 2.4, and 2.4 a.u., respectively, and the plane-wave cutoff, Kmax , was 7.0/RMT . In the selfconsistent calculation, 1000 k-points were taken in the whole cell.

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[17] In a previous study (Ref. 5), we mistook to calculate the mI value for

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K8 Ba16 Ga40 Sn96 to be 0.15me .

[18] J. Y. W. Seto, J. Appl. Phys. 46 (1975) 5247.

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[19] R. F. Lindquist, A. W. Ewald, Phys. Rev. 135 (1964) A191.

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[20] D. G. Cahill, S. K. Watson, R. O. Pohl, Phys. Rev. B 46 (1992) 6131. [21] Y. Takasu, T. Hasegawa, N. Ogita, M. Udagawa, M. A. Avila, K. Suekuni, I. Ishii, T. Suzuki, and T. Takabatake, Phys. Rev. B 74 (2006) 174303.

[22] K. Kishimoto, H. Yamamoto, K. Akai, and T. Koyanagi, J. Phys. D: Appl. Phys. 45 (2012) 445306.

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ACCEPTED MANUSCRIPT Substituting atoms for the framework affects the electronic and electrical properties significantly. The sintered samples had room-temperature carrier mobilities of only 3040 cm2/(Vs).

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They had as low lattice thermal conductivities as 4-5 mW/(cm K).