Supporting information：

Investigation into the Extremely Low Thermal Conductivity in Ba heavily doped BiCuSeO

Dan Fenga,b, Fengshan Zhenga,c, Di Wua, Minghui Wua, Wei Lia, Li Huanga, Li-Dong Zhaod, Jiaqing Hea,*

aShenzhen Key Laboratory of Thermoelectric Materials，Department of physics, South University of Science and Technology of China, Shenzhen 518055, China.

bState Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an 710049, China.

cErnst Ruska Centre for Microscopy and Spectroscopy with Electrons (ER-C), ForschungszentrumJülich GmbH, Jülich 52425, Germany

dSchool of Materials Science and Engineering, Beihang University, Beijing 100191, China.

Email: he.jq@sustc.edu.cn

Keywords: Thermoelectrics, spherical aberration-corrected transmission electron microscopy, lattice thermal conductivity, oxychalcogenide

1) Density Functional Theory (DFT) calculations

The first-principles DFT calculations are performed using the projector-augmented wave (PAW) method, as implemented in Vienna Ab initio Simulation Package.[1-5] The exchange-correlation interaction is treated in the generalized gradient approximation (GGA) of Perdew, Burke, Ernzerholf (PBE). The van der Waals density functional (vdW-DF) method is employed using the optB86b-vdW functional to account for the non-local correlation energies. The Kohn-Sham orbitals are expanded in plane waves with an energy cutoff of 450eV. The energy convergence criterion is chosen to be 10-6eV and the Hellman-Feynman forces on all atoms are below 0.01eV/Å. It is well known that the GGA cannot adequately describe the exchange-correlation effects of strongly localized Cu 3d electrons, DFT + U method is chosen to correct this problem. The effective Coulomb repulsion parameter U here is set as 4eV based on previous reports on Cu-based ternary semiconductors.[6-8] Spin-orbit coupling (SOC) effects are also included because the heavy elements present in this material. The optimized lattice parameters are found to be a = b = 3.934 Å and c = 8.969 Å, which are in good agreement with the experimental values. A 3×3×2 supercell with 144 atoms is used to model the perfect layered quaternary oxychalogenide BiCuSeO. A Monkhorst-Pack Γ-centered 5×5×3 k-point grid is used for Brillouin zone sampling.

The formation energy Ef of a defect D in the charge state of q is given by

Ef(D,q)= Etot(D, q) − Etot(0) – ∑niµi+ q(EVBM + EF + ΔV) (S1)

Where Etot(D, q) and Etot(0) are the total energies of the supercell with and without the defect. EF is the Fermi level with respect to the valence band maximum (VBM) of the host system, EVBM, in the defect-free supercell.[9] For non-degenerate semiconductors valid values of EF range from the VBM to the conduction band minimum (CBM), i.e., from 0 to the value of the band gap. The defect is created by adding (positive) or removing (negative) ni atoms with chemical potential µi, which depends on the experimental condition under which the material is grown, from the defect-free supercell. In this calculation, µBi and µCu are obtained from the most stable pure phases, the elemental bulk systems. While µBa is obtained from the BaO in order to avoid the formation of the second phases. In a periodic supercell, an absolute reference potential is ill-defined, and the calculated eigenvalue spectra from different calculations are not directly comparable. So an alignment term ΔV is added to align the electrostatic potentials between the defect and the pure cells, a common reference (the deep 1s core levels of the atoms far away from the defects) is used in our approach.[10]

2) Thermoelectric (TE) properties

Figure S6 shows the temperature dependence of the thermoelectric properties for Bi1-xBaxCuSeO (x=0, 0.05, 0.125). The electrical conductivity σ and Seebeck coefficient S are shown in Figure S6(a) and S5(b), respectively. As shown, the electrical conductivity of Bi0.95Ba0.05CuSeO and Bi0.875Ba0.125CuSeO increase with temperature rising while the Seebeck coefficients have an opposite trend, indicating a degenerate doped semiconductor behavior. Furthermore, BiCuSeO exhibits extremely low σ over the entire temperature but relatively high Seebeck coefficient due to the initial low carrier concentration. With rising Ba doping, the electrical conductivity show a significantly increase, specifically, from 1.12Scm-1 to 454 Scm-1 at room temperature, and Seebeck coefficients contrary, from 349.5μVK-1 to 81μVK-1 at 300K, which is consistent with the carrier concentration increase because negative charge are introduced by Ba doping. Indeed, the positive Seebeck coefficient indicates a p-type semiconductor behavior. Figure S6(c) shows the power factor calculated by S2σ, combine the enhanced electrical conductivity and the decreased Seebeck coefficient, the maximum power factor about 6.33μWcm-1K-2 at 923K obtained by Bi0.875Ba0.125CuSeO.

Moreover, combining the electrical and thermal transport properties, Figure S6(d) shows the calculated ZT, it is the electrical conductivity optimization together with lattice thermal conductivity reduction that leads to the maximum ZT of 1.1 for heavily doped Bi0.875Ba0.125CuSeO.

3) Callaway’s model

Theoretical lattice thermal calculation based on Callaway’s model,[11] which mainly depends on the integration of the relaxation time from Umklapp processes, Normal processes, precipitates and point defects scatterings. The lattice thermal conductivity can be expressed as:

(S2)

Where the kB is the Boltzmann constant, is reduced Plank’s constant, is the average sound (phonon-group) velocity, θD is the Debye temperature, and is defined as , is the total relaxation time and calculated by the above scattering mechanisms as:

(S3)

Their individual contribution to the total relaxation time is listed as follows:

Umklapp process[12] (S4)

Normal process[13] (S5)

Alloy scattering[14, 15] (S6)

Precipitates scattering[16, 17] (S7)

Extra point defects (S8)

Where the scattering cross-section in short- and long- wavelength regimes are and, respectively; D and ΔD are the mass density of host and density difference between host and nano-particles; VP is the number density of nano-scale particle phases.

Note: γ is the Grüneisen parameter, M is the molar mass, v is the average phonon group velocity, θD is the Debye temperature, β is a fitting parameter for Normal process (5.4) (this parameter was tuned to fit the Boltzmann transport equation results, as shown in Figure S7), δ is the radius of impurity atom in host matrix, x is the ratio of point defects, ΔM is the mass difference between impurity and host atoms, ε is a phenomenological factor as a function of Grüneisen parameter. It is notable that extra point defects are introduced by ball milling process. Combining with TEM observations to obtain necessary structural parameters, for example radius and number density of precipitates, we can easily calculate the lattice thermal conductivities of every chemical composition in different processing conditions. Parameters used in lattice thermal conductivities calculation have been listed in Table S1and S2.

Figure S1.(a) BF-STEM micrograph with crystal structure inside and (b) HAADF-STEM micrograph for BiCuSeO view along [110] axis; (c) Enlarged HAADF-STEM image; (d)-(h) elemental mapping of Bi/Ba/Cu/Se/O corresponding to (c).

Figure S2. (a) Enlarged HAADF-STEM image of a precipitate; (b)-(f) elemental mapping of Bi/Ba/Cu/Se/O corresponding to (a).

Figure S3. (a) SEM observation of Bi0.875Ba0.125CuSeO; (b) size distribution of precipitates; (c) statistical results of EDS point analysis for the matrix and (d) for the precipitates.

Figure S4. (a) SEM observation of Bi0.875Ba0.125CuSeO and (b) corresponding line scanning of the precipitate.

Figure S5. The composition of the precipitates in Bi0.875Ba0.125CuSeO.

Figure S6.Thermoelectric properties as a function of temperature for Bi1-xBaxCuSeO (x=0, 0.05, 0.125). (a) Electrical conductivity. (b) Seebeck coefficient. (c) Power factor. (d) Figure of merit, ZT.

Figure S7. Calculated lattice thermal conductivity of pristine BiCuSeO along a/b (black) and c (red) directions and their average value (blue) via Boltzmann transport equation; best fitting by Callaway model was made to determine the parameter β for the Normal processes.

Table S1Parameter used in the simulation for Ba-Bi substitutional point defect.

Parameters

Atomic Mass of Pb/amu

MBi

208.98

Ba

MBa

137.33

Radius of Pb/pm

rBi

154.8

Ba

rBa

217.4

TableS2Parameter for lattice thermal conductivities calculation

Parameters

Symbol

Unit

BiCuSeO

space group

　

　

P4/nmm

Lattice constant

a, b, c

Angstrom

a=3.921 b=3.921 c=8.913

density of mass

ρ

g/cm3

8.9

Debye Temperature

θD

K

243

sound velocity

υ

m/s

2107

Gruneisen parameter

γ

　

2.5

a phenomenological factor

ε

45

extra point defects

A

s3

9 x 10-39

Reference

[1] G. Kresse, J. Furthmüller, Physical Review B, 54 (1996) 11169.

[2] G. Kresse, J. Furthmüller, Computational Materials Science, 6 (1996) 15-50.

[3] J.P. Perdew, Y. Wang, Physical Review B, 45 (1992) 13244.

[4] P.E. Blöchl, Physical Review B, 50 (1994) 17953.

[5] G. Kresse, D. Joubert, Physical Review B, 59 (1999) 1758.

[6] J.P. Perdew, K. Burke, M. Ernzerhof, Physical review letters, 77 (1996) 3865.

[7] V.I. Anisimov, J. Zaanen, O.K. Andersen, Physical Review B, 44 (1991) 943.

[8] Y. Zhang, X. Yuan, X. Sun, B.-C. Shih, P. Zhang, W. Zhang, Physical Review B, 84 (2011) 075127.

[9] C.G. Van de Walle, J. Neugebauer, Journal of Applied Physics, 95 (2004) 3851-3879.

[10] S. Chen, A. Walsh, X.G. Gong, S.H. Wei, Adv Mater, 25 (2013) 1522-1539.

[11] D. Wu, L.-D. Zhao, X. Tong, W. Li, L. Wu, Q. Tan, Y. Pei, L. Huang, J.-F. Li, Y. Zhu, M.G. Kanatzidis, J. He, Energy Environ. Sci., 8 (2015) 2056-2068.

[12] D. Morelli, J. Heremans, G. Slack, Physical Review B, 66 (2002).

[13] J. He, S.N. Girard, M.G. Kanatzidis, V.P. Dravid, Advanced Functional Materials, 20 (2010) 764-772.

[14] J. Yang, G. Meisner, L. Chen, Applied Physics Letters, 85 (2004) 1140-1142.

[15] B. Abeles, Physical Review, 131 (1963) 1906.

[16] W. Kim, A. Majumdar, Journal of Applied Physics, 99 (2006) 084306.

[17] N. Mingo, D. Hauser, N.P. Kobayashi, M. Plissonnier, A. Shakouri, Nano Lett, 9 (2009) 711-715.

1

3

4

/

22

0

2(1)

D

x

T

BB

latc

x

kkT

xe

dx

e

q

kt

pu

æö

=

ç÷

-

èø

ò

h

h

u

x

w

h

B

kT

/

11111

cUNPPD

ttttt

-----

=+++

2

12

2

exp()

3

D

U

D

T

MT

q

g

tv

uq

-

»-

h

11

NU

tbt

--

»

43

122

3

(1)[(/)(/)]

4

D

xxMM

vd

tedd

pu

-

=-D+D

1111

()

PlsP

vV

tss

----

=+

14

ex

A

tw

-

=

2

2

S

R

sp

=

224

4

(/)(/)

9

l

RDDR

spvu

=D