Lone Pair Electrons Minimize the Lattice Thermal Conductivity


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Electronic Supplementary Material (ESI) for Energy & Environmental Science This journal is © The Royal Society of Chemistry 2013
Lone Pair Electrons Minimize the Lattice Thermal Conductivity Supplementary information
Michele D. Nielsen1, Vidvuds Ozolins2,* and Joseph P. Heremans1,3,* 1. Department of Mechanical and Aerospace Engineering, Ohio State University, Columbus, Ohio, USA 2. Department of Materials Science and Engineering, University of California, Los Angeles, USA 3. Department of Physics, Ohio State University, Columbus, Ohio, USA 1. X-ray diffraction (XRD) data
XRD data on all samples are reported in Fig. S1; all index to rocksalt structures, except for trigonal AgBiSe2. No reference data were found for NaBiTe2.
Figure S1: X-ray diffraction data on the compounds prepared for this study. Except for AgBiSe2, which was prepared in both its trigonal and rocksalt form by varying the heat treatment, all samples index in the NaCl structure. The dots are reference peaks from the International Centre for Diffraction Data PDF database.
The lattice parameters of the Ag1-xNaxSbTe2 alloys, shown in Fig. S2, follow a linear dependence on x, consistent with Vegard’s law.
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Electronic Supplementary Material (ESI) for Energy & Environmental Science This journal is © The Royal Society of Chemistry 2013

6.4

Lattice Constant (Å)

6.3

6.2

6.1 0

20

40

60

80 100

% Na (Ag1-xNaxSbTe2)

Figure S2: The lattice parameter (in the rocksalt unit cell) of Ag1-xNaxSbTe2 alloys as a

function of composition.

We show typical temperature-dependent X-ray diffraction data in Fig. S3.

500 ºC 400 ºC 300 ºC 200 ºC 100 ºC 35 ºC

Angle (2)

Tem peratu re (ºC )

Figure S3 Typical temperature-dependent X-ray spectra of measured cubic compounds. 2

Electronic Supplementary Material (ESI) for Energy & Environmental Science This journal is © The Royal Society of Chemistry 2013

From these, the temperature-dependent lattice parameter can be calculated. The results are plotted Fig. S4: the lattice parameter increases linearly with T, so a single isotropic linear thermal expansion  can be derived and is reported in Table 1 (main text). The data reported for the nominal composition AgSbTe2 were in fact obtained on Ag0.73Sb1.12Te2.

Molar Volume (cm3 mol-1)

Molar Volume as a Function of Temperature

y = 0.003158x + 39.015274

41

R2 = 0.990

39 37 35 33 31 29 27
0

y = 0.0032x + 37.863 R2 = 0.998
y = 0.003155x + 33.559048 R2 = 0.998
y = 0.002229x + 31.781301 R2 = 0.994
y = 0.002961x + 29.529662 R2 = 0.995
y = 0.002180x + 29.072883 R2 = 0.961

AgSbTe
NaSbSe2
AgSbSe2
NaSbTe2
AgBiSe2 cubic NaBiTe2

40 80 120 160 200 240 280 320 360 400 440 480 520 560 Temperature (C)

Figure S4 Temperature-dependence of the lattice parameter calculated from data like
Fig. S3. The linear thermal expansion coefficients  are calculated from the slope of these curves.

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Electronic Supplementary Material (ESI) for Energy & Environmental Science This journal is © The Royal Society of Chemistry 2013
2. Electrical properties The electrical resistivity of most compounds studied experimentally is shown in Fig.
S5. NaSbSe2 is too electrically insulating to be measured. Except for NaSbTe2, all compounds behave like semiconductors; NaBiTe2 behaves like a doped one. Consistently with previous results on AgSbTe2,1 Ag0.73Sb1.12Te2 behaves like a very narrow-gap semiconductor. All this implies that the density of native defects, to the extent that they act as donors or acceptors, is limited to sub-percentage levels.
Figure S5: Electrical conductivity of NaSbTe2, Ag0.73Sb1.12Te2, NaBiTe2, AgSbSe2, AgBiSe2 (trigonal), and AgBiSe2 (cubic). NaSbSe2 was electrically insulating.
1 V. Jovovic and J. P. Heremans, Energy Band Gap and Valence Band Structure of AgSbTe2, Phys. Rev. B 77 245204 (2008)
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3. Calculated phonon spectra: summary The calculated phonon dispersions are reported in sections 5 and 6. From them, mode-
averaged Grüneisen parameters , sound velocities and the zone edge energies, expressed as Debye temperatures i can be derived and tabulated in Table S1. Select data were reproduced in Table 1 of the main text. Lattice parameters a and bulk moduli B were calculated from the variation of the total energy vs. volume E (V) by fitting the calculated points to 3rd-order polynomials in V. Table S1. The interatomic spacing (a/2), calculated bulk modulus B, mode-and-frequency averaged Grüneisen parameter, sound velocities, and zone-boundary Debye energy kBi for phonons along the axes indicated.

Theory
NaSbSe2 NaSbTe2 NaBiTe2
AgSbSe2 AgSbTe2 AgBiSe2 AgBiTe2

a/2

B

(nm) (GPa)

0.2906 44 0.3103 35 0.3138 34

0.2819 78 0.2972 67 0.2893 74 0.3018 66

 Sound velocities(m/s)

Zone‐boundary energy i (K)

Gamma‐to‐X [x 0 ‐x]

X [¾ 0 ‐¾]

TA1 TA2

LA

TA1

TA2

LA

1.7 2132 2770

4329

76

89

114

1.6 1664 2430

3630

63

85

94

1.5 1295 2055

3131

40

56

56

Gamma‐to‐K [0 x x]

K [0 ¾ ¾ ]

TA1 TA2

LA

TA1

TA2

LA

3.5 1362 2105

3433

47

52

62

2.3 1325 2469

3526

53

56

65

2.5

2.5 1278 2116

3223

47

47

55

Note that the Debye temperature values D fitted to the specific heat (Table 1) are nearly twice the Debye temperatures i calculated from the zone-boundary acoustic phonon energies kBi in Table S1. Two factors contribute to this. Firstly, there is a contribution of the optical modes to the high-temperature value of C. Secondly, Fig. 2 of the main text shows that many acoustic modes do not have monotonic energy-momentum relations, so that the maximum phonon energy is higher than the energy kBi at the zone boundary.
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The calculated mode-averaged Grüneisen parameters for all 72 compounds (8 Group I cations  3 Group V cations  3 Group VI anions) are given in Table S2 below. Table S2: Calculated mode-averaged Grüneisen parameters γ for all 72 compounds grouped by the group I cation. Higher γ values (stronger anharmonicity) correspond to warmer colors. Red squares indicate that the compounds have unstable phonon modes at the calculated equilibrium lattice parameter. AgSbSe2 is predicted to have a weakly unstable L-point TA mode, and is found experimentally to have the lowest thermal conductivity of all materials considered in our study.
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AuBX 2 As

Sb

3.

Bi S
As

3.7

Se

Te

KBX 2

2.9

1.6

Sb

1.7

1.4

Bi 1.6

1.5

1.4

S

Se

Te

RbBX 2

As

1.5

Sb

1.8

1.4

Bi 1.6

1.5

1.4

S

Se

Te

NaBX 2

As

2.1

1.6

Sb 2.9

1.8

1.6

Bi 1.6

1.5

1.5

S

Se

Te

CsBX 2

As

1.5

Sb

1.9

1.4

Bi 1.7

1.5

1.4

S

Se

Te

TlBX 2

As

2.3

1.8

Sb 2.3

1.9

1.7

Bi 1.8

1.7

1.7

S

Se

Te

7

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4. Literature with structural information of known ABX2 compounds. In agreement with our calculations, the crystal structures of several of the ABX2 compounds have been determined experimentally and found to be either not rocksalt based or resemble highly distorted variants of rocksalt. The references are: CuSbS2: Razmara, M.F.; Henderson, C.M.B.; Pattrick, R.A.D. Mineralogical Magazine 61, 79-88 (1997) CuBiS2: Portheine, J.C.; Nowacki, W. Zeitschrift fuer Kristallographie, Kristallgeometrie, Kristallphysik, Kristallchemie 141, 387-402 (1975); CuSbSe2: Imamov, R.M.; Pinsker, Z.G.; Ivchenko, A.I. Kristallografiya 9, 853-856 (1964); AgSbS2: Effenberger, H.; Paar, W.H.; Topa, D.; Criddle, A.J.; Fleck, M. American Mineralogist 87, 753-764 (2002); NaAsS2: Palazzi, M.; Jaulmes, S. Acta Cryst. B 33, 908-910 (1977); KSbS2: Graf, H.A.; Schaefer, H. Zeitschrift fuer Anorganische und Allgemeine Chemie 414, 211-219 (1975); CsSbS2: Kanishcheva, A.S.; Mikhailov, Yu.N.; Kuznetsov, V.G.; Batog, B.N. Doklady Akademii Nauk SSSR 251, 603-605 (1980); RbAsSe2: Sheldrick, W.S.; Haeusler, H.J. Zeitschrift fuer Anorganische und Allgemeine Chemie 561, 139-148 (1988); RbSbS2: Kanishcheva, A.S.; Kuznetsov, V.G.; Lazarev, V.B.; Tarasova, T.G. Zhurnal Strukturnoi Khimii 18, 1069-1072 (1977) Rocksalt CuBiSe2, AgAsSe2, AgSbSe2: Zhuze, V.P.; Sergeeva, V.M.; Shtrum, E.L. Soviet physics - Technical physics 3, (10) 1925-1938 (1958); Tomaszewski, K. Phase Transition 38, 127-220 (1992); Geller, S.; Wernick, J.H. Acta Crystallographica 12, 46-54 (1959).
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Electronic Supplementary Material (ESI) for Energy & Environmental Science This journal is © The Royal Society of Chemistry 2013
5. Calculated phonon spectra of the rocksalt compounds The Brillouin zone of the rocksalt compounds, with the atomic arrangement of Fig. 1a,
is shown in Fig. S6. The calculated phonon dispersions of rocksalt compounds follow with the compound name indicated above each panel. Compounds with spectra that contain imaginary calculated frequencies are not shown, with the exception of AgSbSe2, which has been synthesized in the cubic structure in this study and in previous ones (Ref. 13 of the main text).
Figure S6. Brillouin zone of cubic D4 (AF-IIb), and phonon dispersions of the stable noble metal D4 rocksalt-based ABX2 compounds with A=noble metal (see below)
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250

CuSbTe2

200

150

Frequency (1/cm)

100

50

0

-50 G

X WK

G

L

Phonon wave vector

UW

L

K|U X

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Lone Pair Electrons Minimize the Lattice Thermal Conductivity