Supporting Information for

Intrinsically Low Thermal Conductivity from Quasi-One-Dimensional Crystal Structure and Enhanced Electrical Conductivity Network via Pb doping in SbCrSe3

Dingfeng Yang,1,3,6 Wei Yao,2 Yanci Yan,2 Wujie Qiu,5 Lijie Guo,2 Xu Lu,2 Ctirad Uher,4 Xiaodong Han,6 Guoyu Wang,*1,7 Tao Yang,*3 Xiaoyuan Zhou,*2 1Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences, Chongqing 400714, P. R. China.2College of Physics, Chongqing University, Chongqing 401331, P. R. China.3College of Chemistry and Chemical Engineering, Chongqing University, Chongqing 400044, P. R. China.4Department of Physics, University of Michigan, Ann Arbor MI 48109, USA.5State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China.

6Institute of Microstructure and Properties of Advanced Materials, Beijing University of Technology, Beijing, 100124, China.

7Universit of Chinese Academy of Sciences, Beijing, 100004, China.

1. Experimental and calculated Section

1.1 Specific heat measurement

Figure S1: Temperature dependent specific heat of pristine SbCrSe3

The temperature dependence of specific heat for the calculation of total thermal conductivity is shown in Figure S1. The experiment values present a slight increase trend as the increase of temperature, and the value at room temperature is comparable to the theoretical value as estimated by dulong-Petit law.

1.2 UV-vis optical absorption spectrum

Figure S2: UV-vis optical absorption spectrum for pristine SbCrSe3 sample.

FigureS2 represents the UV-vis optical absorption spectrum of as-obtained SbCrSe3 sample. As can be seen, the estimated optical absorption Eg is about 0.7eV, which is larger than that of DFT calculation (0.45eV).

1.3 The upper valence band charge density of SbCrSe3 and Pb0.0625Sb0.9375CrSe3

Figure S3 (a): The upper valence band charge densities of SbCrSe3 (Iso-surface levels are 0.001)

(b): The upper valence band charge densities of Pb0.0625Sb0.9375CrSe3(Iso-surface levels are 0.001)

1.4 The theoretical and experimental lattice thermal conductivity

Figure S4: (a) Temperature-dependent lattice thermal conductivity of SbCrSe3. The black dotted line and the red dotted line refer to the experimental and calculated results respectively.

1.5 The SEM image of SbCrSe3 after SPS

Figure S5: SEM image of SbCrSe3

The SEM pictures of the fresh fractured SPS sample of SbCrSe3 is represented in Figure S5. From the above picture, we observed that the crystallized grains are closely packed, which indicated that a high density of the obtained sample. The grain sizes are dispersed in the range of hundreds of nanometers to a few micrometers.

1.6 Anisotropic thermoelectric measurements and anisotropic thermal stability of sample Pb0.05Sb0.95CrSe3

Figure S6: Anisotropic thermoelectric measurements of sample Pb0.05Sb0.95CrSe3. (a) Seebeck coefficient (b) electrical conductivity (c) power factor (d) ZT value.

Figure S7: Anisotropic thermal stability of sample Pb0.05Sb0.95CrSe3.(a) pressure direction (b)⊥ //pressure direction

Considering the intrinsic quasi-one dimensional crystal structure of the SbCrSe3, the anisotropies of

thermoelectric properties of the obtained polycrystalline should be tested to confirm the validity of the

zT performance using in-plane(perpendicular to the SPS pressure direction) and cross-plane(parallel to

the SPS pressure direction) properties. Figure S6 presents the anisotropic thermoelectric measurements

of sample Pb0.05Sb0.95CrSe3. The result presents a weak dependence of the pressure direction, which

might be caused by the random grain orientations in our polycrystalline samples. The anisotropic

thermal stability of our sample Pb0.05Sb0.95CrSe3 is shown in Figure S7. It is clearly seen that the

samples from two difference directions are stable in the measurement temperature range 300K to 900K.

1.7 Debye-Callaway Model to Interpret the Defect Phonon Scattering Mechanism Induced by

Disorder Atom Pb/Sb at Room Temperature.

The point defect scattering parameter A can be expressed as A= Ω4 π ν3 Γ . Here,Ω is the volume of

the primitive unit cell andΓ is the disorder scattering parameter that characterizes the strength of

phonon scattering on point defects. Point defect scattering is contributed from the mass difference

(mass fluctuations) and differences in the atomic size and interatomic coupling force (strain field

fluctuations) between the host and the impurity atoms. Providing that the grain boundary scattering can

be ignored in polycrystalline materials with grain sizes larger than the phonon mean free path on

account of the temperature exceeding the Debye temperatureθd , we analyze the effect of Pb

substituting on site of Sb on the lattice thermal conductivity at room temperature. Based on the above

assumptions, only Umklapp scattering and point defect scattering are considered here. The ratio of κ L

of a crystal with disorder to that of a crystal without disorder κL0 can be expressed as [1]:

κLκL0

=tan−1(u)u

①

u2=π2θdΩhν2 κ L0Γ exp ②

Here u,ν, Ω , h andΓ are the disorder scaling parameter, the average sound velocity, the average

volume per atom, the Planck`s constant and the experimental disorder scattering parameter,

respectively. Γexp can be derived from the measured κL using the above Eqs. ①②. The disorder

scattering parameter, Γexp=Γcal=Γm+Γ s, where the disorder scattering parameters Γm and Γ s are

due to the mass and strain fluctuations, respectively. For SbCrSe3, Γm and Γ s are given by

Γm=15 (MM ) x (1−x )(M 1−M 2

M )2

Γ s=15 (MM ) x (1− x ) ε ( r 1−r2

r )2

M=M 1 x+M 2(1−x )

M=15M+ 1

5M 3+

35M 4

r=r1 x+r2(1−x) ③

Where M 1,M 2,M 3 andM 4 are the atomic weights of Pb, Sb, Cr and Se, respectively. r1 and r2 are the

Shannon ionic radii of Pb (0.98 Å) and Sb (0.74 Å), respectively. ε is equal to 44 , which can be

calculated via the following formula:

ε=29 (6.4 γ (1+ν p)

1−νp )2

γ=32 ( 1+ν p

2−3ν p )

νp=1−2 (ν t /ν l )

2

2−2 (ν t /ν l )2 ④

Here,γ is the Grüneisen parameter and νp is the Poisson ratio.

Table S1. Calculated disorder scaling parameter (u) and scattering parameters of Pb xSb1-xCrSe3 (x=0,

0.01, 0.03, 0.05)

Nominal composition u Γcal Γmass Γstrain Kexp (Wm-1K-1) Kcal(Wm-1K-1)

x=0 - - - - 1.08 -

x=0.01 0.574 0.018 0.002 0.016 0.92 0.953

x=0.03 0.987 0.054 0.006 0.048 0.84 0.828

x=0.05 1.265 0.089 0.010 0.078 0.78 0.749

As listed in the table S1, the disorder scaling parameter u and the disorder scattering parameter Γcal

both increase with the increasing Pb content, resulting in a decreased lattice thermal conductivity L.

Using the measured value of L of the parent compound SbCrSe3, where κL 0=κ exp=1.08Wm-1K-1,

the lattice thermal conductivity with point defect scattering can be calculated from the above equation.

Reference

[1] X. Chen, S. N. Girard, F. Meng, E. L. Curzio, S. Jin, J. B. Goodenough, J. S. Zhou and L. Shi. Adv.

Energy. Mater. 2014, 4, 1400452-1400462.