Enhanced Thermoelectric Performance of Quaternary Cu2

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Functional Inorganic Materials and Devices

Enhanced Thermoelectric Performance of Quaternary Cu2-2xAg2xSe1-xSx Liquid-like Chalcogenides Mengjia Guan, Kunpeng Zhao, Pengfei Qiu, Dudi Ren, Xun Shi, and Lidong Chen ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b01643 • Publication Date (Web): 15 Mar 2019 Downloaded from http://pubs.acs.org on March 17, 2019

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ACS Applied Materials & Interfaces

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Enhanced Thermoelectric Performance of Quaternary

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Cu2-2xAg2xSe1-xSx Liquid-like Chalcogenides

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Mengjia Guan,†,‡ Kunpeng Zhao,*,§ Pengfei Qiu,† Dudi Ren,† Xun Shi,*,†,§ and Lidong

4

Chen,†

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†State

Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China.

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‡Center

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of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China. §School

of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.

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ABSTRACT

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Liquid-like binary Cu2-δX (X = S, Se, and Te) chalcogenides and their ternary solid solutions

14

have gained notable attention in thermoelectrics due to their interesting and abnormal thermal

15

and electrical transport properties. However, the previous studies mainly focus on the single

16

element alloying at either anion or cation site, whereas the investigation on cation/anion co-

17

alloying is very rare so far. Here, a series of quaternary Cu2-2xAg2xSe1-xSx (x = 0.01, 0.03, 0.05,

18

0.1, 0.15) liquid-like copper chalcogenide materials have been fabricated and the effects of Ag/S

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co-alloying on the thermoelectric properties of Cu2Se have been systematically studied. It is

20

found that all compounds are mixed phases at room temperature but single cubic phase at high

21

temperatures. The introduction of Ag and S in Cu2Se brings about large mass fluctuation rather

22

than strain field fluctuation that effectively suppress the lattice thermal conductivity.

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Furthermore, with increasing the Ag and S contents, the high electrical conductivity of pristine

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Cu2Se is well tuned to the optimal range deriving from the single parabolic band model analysis.

25

Consequently, a peak zT of 1.6 at 900 K is achieved in Cu1.8Ag0.2Se0.9S0.1, which is about 33%

26

higher than that of binary Cu2Se.

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ACS Paragon Plus Environment

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KEYWORDS: thermoelectric; liquid-like; co-alloying; chalcogenides; mass fluctuation

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INTRODUCTION

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Thermoelectric (TE) technology enables the direct energy conversion between heat and

5

electricity, showing a great potential in the applications of power generation and refrigeration

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with the advantage of vast solubility, long lifetime as well as no emissions.1-4 However,

7

currently, the application of TE technology is limited in a small scale, which is mainly attributed

8

to the low energy conversion efficiency.5, 6 The key parameter assessing the energy conversion

9

efficiency is the material’s dimensionless TE figure of merit, defined as zT = 2T/κ, where  is

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the Seebeck coefficient,  is the electrical conductivity, T is the absolute temperature, and κ is

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the total thermal conductivity. In order to make the TE technology functional in large-scale use,

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materials with high zT values are required. In the past decade, many strategies have been

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proposed to enhance the zT such as minimizing the thermal conductivity and optimizing the

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electrical properties.7-9

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Recently, liquid-like materials have attracted great attentions in thermoelectrics due to their

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extremely low lattice thermal conductivity and moderate electrical transports.10-13 The liquid-like

17

materials usually contain two sublattices inside the crystal structure.14 One is rigid anion

18

sublattice that provides crystalline pathways for carrier transport, and the other one is liquid-like

19

cation sublattice that can strongly scatter the heat-carrying phonons as well as eliminate part of

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the transverse vibrational modes, yielding ultralow lattice thermal conductivities.10, 15 Cu2X (X =

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S, Se, and Te) is one family of typical liquid-like materials. Despite of their simple chemical

22

compositions, Cu2X (X = S, Se, and Te) compounds have quite complex crystal structures and

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phase transition features.11, 16 For instance, the crystal structure of the room-temperature Cu2Se

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phase is reported to be either monoclinic or trigonal,17,

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Cu2S phase is reported to be monoclinic.11 Furthermore, at room-temperature, Cu2Te is reported

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to be a mixture of two phases with orthorhombic structure and hexagonal structure.19 Upon

27

heating, these low-symmetry structures finally convert into the high-symmetry cubic anti-fluorite

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structure with the detailed Cu atom positions dependent on the type of chalcogen element. High

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zT with values of 0.6-1.9 for Cu2S,11, 20, 21 1.5-2.6 for Cu2Se,10, 22-24 0.6-1.1 for Cu2Te,19, 25 have

30

been successively reported. More interestingly, despite their different crystal structures at room

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while that of the room-temperature


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temperature, any two binary Cu2X (X = S, Se, and Te) compounds can form ternary solid

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solutions.26-28 These ternary solid solutions not only possess enhanced TE performance but also

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very interesting and special microstructure and crystal structure. For example, He et al. found

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that Cu2S and Cu2Te can form complete solid solutions with hexagonal structure that is different

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with those of Cu2S and Cu2Te at room temperature. Likewise, a special mosaic microstructure is

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observed in the Cu2S0.5Te0.5 solid solution accompanying with some interesting and abnormal

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electrical and thermal transport properties, which greatly enrich the investigation on the liquid-

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like materials.28

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Being the same with Cu2X (X = S, Se, and Te) compounds, Ag2X (X = S, Se, and Te)

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compounds also represent a family of liquid-like materials.29-31 However, although Cu and Ag

11

elements possess similar chemical and physical properties, the crystal structures, phase transition

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feature, and physical properties of Ag-based chalcogenides are quite different from those of Cu-

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based chalcogenides. For example, the crystal structure of the room-temperature Ag2Se phase is

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reported to be orthorhombic. It experiences a first-order phase transition at around 443 K and

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transforms into face-centered cubic phase16. More importantly, Ag2X compounds are n-type

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semiconductors, which is in contrary to the p-type conduction of Cu2X.31, 32 Thus, forming the

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solid solutions between Cu2X and Ag2X might also create some interesting and abnormal

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phenomenon. For instance, Tristan et al. found that the substitution of Cu by Ag could

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effectively reduce the carrier concentration and thus enhance the TE performance of Cu2Se.33

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All in all, both alloying at anion site or cation site play a significant role on the structural

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evolution and TE transport properties of Cu2X and Ag2X. However, the previous studies mainly

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focus on the single element alloying at either anion or cation site.34-37 The effect of cation/anion

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co-alloying on the structural evolution and TE performance have not been studied so far. Thus, a

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detailed investigation on the crystal structure, phase transition, and TE transport properties of

25

(Cu, Ag)2(S, Se, Te) is still desirable.

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Herein we successfully synthesized a series of Cu2-2xAg2xSe1-xSx quaternary compounds by a

27

melting-annealing approach followed by spark plasma sintering. The effects of Ag and S

28

alloying on the phase composition, crystal structure, phase transition feature, and TE properties

29

of Cu2Se have been systematically studied. Besides, an effective single parabolic band model is


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used to provide theoretical insight into the enhanced TE performance. The present study provides

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a comprehensive understanding on the TE properties of Cu2-2xAg2xSe1-xSx liquid-like materials.

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EXPERIMENTAL

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Synthesis. Polycrystalline Cu2-2xAg2xSe1-xSx (x = 0, 0.01, 0.03, 0.05, 0.1, and 0.15) samples

6

were synthesized via melting-annealing-sintering processes. Stoichiometric high-purity raw

7

elements Cu (shots, 99.999%, Alfa Aesar), Ag (shots, 99.999%, Alfa Aesar), Se (pieces,

8

99.999%, Alfa Aesar), and S (pieces, 99.999%, Alfa Aesar) were weighted out and put into

9

boron nitride crucibles, and then sealed in silica tubes under a vacuum level of -100 kPa. The

10

sealed tubes were slowly raised to 1423 K and dwelled for 12 h, and then slowly cooled down to

11

923 K. After annealing for 7 days at 923 K, these tubes were naturally cooled to room

12

temperature. Finally, the ingots were pulverized into powders in agate mortars and sintered by

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spark plasma sintering (SPS, Sumitomo SPS-2040) at 673-773 K under a pressure of 65 MPa for

14

5 min. The sintering temperatures for x = 0, 0.01, 0.03, 0.05, 0.1, and 0.15 samples are 773 K,

15

753 K, 733 K, 713 K, 693 K, 673 K, respectively. Electrically insulating and thermally

16

conducting boron nitride layers were sprayed onto the surface of carbon foils to prevent Cu/Ag

17

migration or precipitation during sintering.

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Characterization. The room temperature crystal structures were examined by X-ray

19

diffraction (XRD, Rigaku D/max 2550V) with Cu K radiation. The high temperature crystal

20

structures were identified by a Bruker D8 ADVANCE (BRUKER AXS GMBH, Germany) from

21

300 K to 700 K. For high-temperature XRD measurement, the heating rate is 5 K/min and

22

holding time at each temperature is 10 min. The sample morphologies and elemental distribution

23

were measured by backscattered electron image (BSE, ZEISS Supra 55) as well as energy

24

dispersive spectroscopy (EDS, Oxford Horiba 250). The shear and longitudinal sound velocities

25

at room temperature were obtained by use of ultrasonic measurement system UMS-100. The

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electrical conductivity  and Seebeck coefficient  were characterized by Ulvac ZEM-3, while

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the thermal diffusivity () was measured by Netzsch LFA 457 using the laser flash method in Ar

28

atmosphere. The heat capacity (Cp) was determined using a Netzsch DSC 404FE at a heating rate

29

of 5 K min-1. The sample densities () were obtained by the Archimedes method and the relative


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densities for all samples were larger than 98%. Then the total thermal conductivity  was

2

calculated by relation  = Cp. Uncertainties for the electrical conductivity, Seebeck

3

coefficient, and thermal diffusivity are around 3%, 5%, and 7%, respectively.

4 5

3. RESULTS AND DISCUSSION

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Figure 1 shows the backscattered electron (BSE) image and energy dispersive spectroscopy

7

(EDS) mapping for Cu2-2xAg2xSe1-xSx (x = 0.01, 0.1, and 0.15) samples. Clearly, the Se and S

8

elements are homogeneously distributed throughout the detected region for all samples. This

9

phenomenon is coinciding with those in ternary Cu2Se1-xSx solid solutions. However, Ag-

10

enriched region can be clearly observed even in Cu1.98Ag0.02Se0.99S0.01, indicating the solubility

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of Ag in Cu2Se is quite low at room temperature. The alloyed Ag atoms prefer to form the

12

secondary phase rather than entering the crystal lattice. This observation is also in accordance

13

with previous studies of Tristan et al.33

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Figure 1. Backscattered electron (BSE) image and energy dispersive spectroscopy (EDS)

16

mapping for Cu2-2xAg2xSe1-xSx (x = 0.01, 0.1, and 0.15) samples.

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Figure 2. (a) Room-temperature X-ray diffraction (XRD) patterns for powder Cu2-2xAg2xSe1-xSx

3

(x = 0, 0.01, 0.03, 0.05, 0.1, and 0.15) samples. (b) Temperature dependence of the heat capacity

4

(Cp) for Cu2-2xAg2xSe1-xSx (x = 0, 0.01 and 0.1) at constant pressure. The inset in Figure 2b

5

illustrates the high-temperature crystal structure of Cu2-2xAg2xSe1-xSx. The anions Se/S form the

6

face-centered cubic framework, while the cations Cu/Ag are randomly distributed in 8c and 32f

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Wyckoff sites. High-temperature X-ray diffraction patterns for (c) Cu1.98Ag0.02Se0.99S0.01 and (d)

8

Cu1.8Ag0.2Se0.9S0.1 measured from 300 K to 700 K.

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Figure 2a displays the room temperature X-ray diffraction (XRD) patterns for powder Cu2-

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2xAg2xSe1-xSx

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= 0.01, are introduced to Cu2Se, nearly all diffraction patterns can be still indexed to trigonal

13

Cu2Se phase. The second phases observed in EDS mapping are not detected because their low

14

content is beyond the detection limit of XRD measurements. As x increase to 0.03, the

(x = 0, 0.01, 0.03, 0.05, 0.1, and 0.15) samples. When a tiny content of Ag and S, x


6

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diffraction peaks belonging to orthorhombic CuAgSe phase (PDF#25-1180) begin to appear, and

2

intensity of these new diffraction peaks become stronger with increasing Ag and S contents. This

3

indicates that the Ag-enriched phases observed by EDS are CuAgSe. Although all quaternary

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Cu2-2xAg2xSe1-xSx samples are mixed phased at room temperature, they convert into pure single

5

phase at high temperatures. As shown in Figure 2c and 2d, with the increase of temperature, the

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diffraction peaks belonging to Cu2Se and CuAgSe gradually disappear and some new diffraction

7

peaks emerge, suggesting the accompaniment of phase transitions at 400-500 K. The newly

8

appeared diffraction peaks can be well indexed to the cubic phase (PDF#46-1129) with the space

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group of Fm3m (see the inset in Figure 2b). This suggests that the CuAgSe phase obseved at

10

room temperature have dissolved into the Cu2Se matrix and finally form a solid solution after

11

experiencing certain phase transitions.

12

Alloying Ag and S in Cu2Se not only alters the crystal structures but also changes the phase

13

transition features. Figure 2b plots the temperature dependent heat capacity (Cp) curves for Cu2-

14

2xAg2xSe1-xSx

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observed at around 400 K, corresponding to the transition from room-temperature trigonal phase

16

to high-temperature cubic phase. While for Cu1.98Ag0.02Se0.99S0.01 and Cu1.8Ag0.2Se0.9S0.1, two

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adjacent peaks are detected in their Cp curves. One of the peaks should be attributed to phase

18

transition in Cu2Se phase, and the other might be ascribed to the existence of CuAgSe phase with

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phase transition from orthorhombic structure to cubic structure. This is in well accordance with

20

our high-temperature XRD measurements. Moreover, the temperatures of these peaks are shifted

21

to lower temperatures, suggesting that the S and Ag contents directly influences the phase

22

transition character. Such reduced phase transition temperature is the common phenomenon for

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most liquid-like solid solutions such as Te-alloyed Cu7PSe6 and S-alloyed Cu2Se.38, 39 It should

24

be noted that the phase transitions of TE materials are detrimental for actual applications because

25

the sudden change of thermal expansion coefficient could bring about high internal stress

26

between the materials and the electrodes in the device, resulting in poor contact and deteriorated

27

performance.

(x = 0, 0.01 and 0.1). For the pristine Cu2Se, only one endothermic peak is


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Figure 3. Temperature dependences of (a) electrical conductivity , (b) Seebeck coefficient ,

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(c) power factor PF, (d) total thermal conductivity , (e) lattice thermal conductivity L, and (f)

4

TE figure of merit zT for Cu2-2xAg2xSe1-xSx (x = 0, 0.01, 0.03, 0.05, 0.1, and 0.15).

5 6

The TE transport properties for Cu2-2xAg2xSe1-xSx (x = 0, 0.01, 0.03, 0.05, 0.1, and 0.15)

7

samples were measured from 300 to 900 K, and the results are shown in Figure 3. To increase


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the readability, all data are broken into two parts. The part at low temperature range represents

2

the data for the mixed phases while the part at high temperature range represents the data for the

3

single cubic phase. With increasing Ag and S contents, the electrical conductivity is roughly

4

decreased in the entire temperature range. Specifically, the  at 500 K for Cu1.7Ag0.3Se0.85S0.15 is

5

decreased by a factor of 19 in comparison with that for pristine Cu2Se. Such variation is much

6

larger than that of Cu2Se1-xSx with similar x, illustrating that Ag also plays an important role in

7

adjusting electrical transport properties.40 Besides, the electrical conductivity of all compounds

8

decreases monotonically with increasing temperature before 800 K, behaving as highly

9

degenerate semiconductors. The slight upturn above 800 K might be ascribed to the bipolar

10

conduction. At room temperature,  is roughly decreased when increasing the Ag/S contents.

11

The reason for this should be that Cu2Se is a p-type semiconductor while CuAgSe is an n-type

12

semiconductor, thus the total Seebeck coefficient is partly counterbalanced.41 Nevertheless,

13

above 500 K, all the samples convert to the single cubic phase and their  values monotonically

14

increase with increasing the Ag/S alloying contents. The increased  together with the decreased

15

 imply that the hole concentration is lowered in their high temperature phases. Besides, we

16

have also measured the electrical transport properties for Cu1.9Ag0.1Se0.95S0.05 sample along two

17

different directions. As shown in Figure S1, the sample exhibits similar electrical transport

18

properties over the entire temperature range along directions perpendicular and parallel to the

19

pressing direction, indicating isotropic TE properties. The recycling tests of electrical transport

20

properties demonstrateare Cu2-2xAg2xSe1-xSx are stable at high temperature (see Figure S2). Based

21

on the measured  and  the power factor (PF = ) of Cu2-2xAg2xSe1-xSx are calculated and

22

shown in Figure 3c. With increasing x, PFs are gradually reduced owing to the strongly

23

suppressed electrical conductivity.

24

The total thermal conductivity  as a function of temperature is displayed in Figure 3d. At

25

room temperature, no clear composition dependence is observed due to the influence of mixed

26

phases. Above 450 K, the  values are significantly lowered when increasing the Ag and S

27

alloying contents, which is on account of the simultaneously suppressed carrier thermal

28

conductivity (C) and lattice thermal conductivity (L). Specifically, the  at 500 K for

29

Cu1.7Ag0.3Se0.85S0.15 is only 0.34 W m-1 K-1, which is only one-quarter of that for pristine Cu2Se.

30

The lattice thermal conductivity L is calculated through subtracting the carrier thermal


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conductivity (C) from total thermal conductivity () via the Wiedemann-Franz law C = LT,

2

where L is the Lorenz number determined by the single parabolic band (SPB) model with

3

acoustic scattering (Figure S3). All samples exhibit extremely low L with values below 0.5 W

4

m-1 K-1 in the whole measured temperature range, which are among the lowest values reported in

5

most state-of-the-art TE materials. The L is roughly decreased with increasing the Ag and S

6

alloying contents. Besides, the L temperature dependences for these quaternary Cu2-2xAg2xSe1-

7

xSx

8

normal crystalline compounds.9

samples are relatively weak, which is different with the strong temperature dependency of

9

The TE figure of merit zT (= T/) as a function of temperature is calculated and plotted

10

in Figure 3f. Although the PFs of Cu2-2xAg2xSe1-xSx are reduced, an overall enhancement of zT is

11

achieved with the help of much reduced thermal conductivity. The highest zT value of 1.6 is

12

obtained at 900 K for Cu1.8Ag0.2Se0.9S0.1, which represents about 33% enhancement over that of

13

pristine Cu2Se.

14 15

Figure 4. (a) Lattice thermal conductivity L as a function of alloying content x for Cu2-

16

2xAg2xSe1-xSx

17

L of Cu2Se1-xSx are calculated using the  and  from ref. 40. The dashed lines are calculated

18

based on the Callaway model. (b) Mass fluctuation scattering parameter M and strain field

19

fluctuation scattering parameter S as a function of alloying content x. M, S and S, S represent

20

the mass fluctuation and strain field fluctuation induced by S alloying at Se sites, while M, Ag

21

and S, Ag represent the mass fluctuation and strain field fluctuation induced by Ag alloying at Cu

22

sites.

(x = 0, 0.01, 0.03, 0.05, 0.1, and 0.15) and Cu2Se1-xSx solid solutions at 500 K. The


10

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1 2

At high temperatures, all quaternary Cu2-2xAg2xSe1-xSx samples are solid solutions with

3

single cubic phase. Thus the random distribution of Ag and S atoms on the Cu and Se site will

4

definitely introduce additional mass and strain fluctuations to scatter phonons, leading to

5

reduction of lattice thermal conductivity. In order to clarify this issue, the Callaway model is

6

used to analyze the composition dependence of L for Cu2-2xAg2xSe1-xSx compounds. Provided

7

the grain structures of all samples are similar, the scattering mechanisms governing heat

8

transport are Umklapp processes and point defect scattering. Then, the lattice thermal

9

conductivity L of a solid solution can be expressed as

10

tan 1  u  L  u  pure

11

u2 

(1)

 2 D   pure  h s 2

(2)

12

where u is the disorder scaling parameter, s is the mean sound velocity, h is the Planck constant,

13

D is the Debye temperature, pure is the lattice thermal conductivity of pure Cu2Se matrix,  is

14

the unit cell volume and  is the scattering parameter. The scattering parameter includes two

15

parts: M and S, which are related to mass fluctuation and strain field fluctuation, respectively.

16

They can be expressed as: 2

17

 M i  1 2  M i1  M i2  c   fi fi   i Mi i 1 M     M  n     ci   i 1 

18

 M i  1 2  ri1  ri 2  c   fi fi  i   i ri  i 1 M    S   n    ci   i 1 

n

n

2

2

(3)

2

(4)


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Page 12 of 23

1

where n = 2. ci are the relative degeneracies of the respective sites, and the parameter i is a

2

function of the Grüneisen parameter  that characterizes the anharmonicity of the lattice. In

3

general,  is regarded as an adjustable parameter and usually obtained by fitting the experimental

4

results. If there are k different types of atoms that occupy each sublattice, the kth atom of the ith

5

sublattice has mass M ik , radius ri k , and fractional occupation f i k . The average mass and radius of

6

atoms on the ith sublattice are

M i  fi1M i1  fi 2 M i2 , r i  fi1ri1  fi 2 ri 2

7 8

(5)

and the average atomic mass of the compound is n

9

M

c M i 1

i

i

 n    ci   i 1 

.

(6)

10

Based on the above formulas, we firstly calculated the L-x relation for Cu2Se1-xSx solid solutions

11

and obtained the scattering parameters M, S and S, S resulting from Se/S disorder. 40, 42-44 Then,

12

we calculated the L-x relation for Cu2-2xAg2xSe1-xSx solid solutions and obtained the scattering

13

parameters M, Ag and S, Ag for Cu/Ag disorder by subtracting M, S and S, S from the total M

14

and S. As shown in Figure 4a, the symbols stand for the experimental data at 500 K and the

15

dashed lines are the calculated results based on the Callaway model. The scattering parameters

16

M and S, as a function of alloying content x, are shown in Figure 4b. Obviously, the values of

17

both S, S and S, Ag are small due to relatively small ionic radius difference between S and Se,

18

and between Cu and Ag. Thus, the strain field fluctuation scattering in Cu2-2xAg2xSe1-xSx solid

19

solutions is nearly negligible. In contrast, the values of M, S and M, Ag are much larger, which

20

implies that the mass fluctuation introduced by S alloying at Se sites or Ag alloying at Cu sites

21

are the major contributions to phonon scattering and should be responsible for the large reduction

22

of L in Cu2-2xAg2xSe1-xSx.

23


12

Page 13 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1 2

Figure 5. (a) Seebeck coefficient  (b) power factor PF, (c) total thermal conductivity , (d)

3

figure of merit zT as a function of electrical conductivity  at 500 K for Cu2-2xAg2xSe1-xSx (x = 0,

4

0.01, 0.03, 0.05, 0.1, and 0.15) samples. The red sphere symbols are experimental data in this

5

work. The other symbols are the data of Cu2Se-based compounds taken from refs. 10, 22, 33, 40,

6

and 45-49. The dashed lines are the prediction based on the SPB model.

7 8

To shed light on the origin of enhanced TE performance of Cu2-2xAg2xSe1-xSx, we modeled

9

their TE properties using the single parabolic band (SPB) model. The experimental data of

10

Cu2Se-based compounds from previous studies are also included for comparison.10, 22, 33, 40, 45-49

11

The temperature is selected to be 500 K because all samples possess single cubic phase at this

12

temperature, then the influence of different crystal structures can be excluded. Based on the

13

Boltzmann statistics, the Seebeck coefficient , carrier concentration p and electrical

14

conductivity of semiconductors can be respectively expressed as


13


1



kB  s  5 / 2   e

Page 14 of 23

(7)

2

p  N c exp   =2  8 3 m*k BT / h 2 

exp  

(8)

3

  pe  2e  8 3k BT / h 2  exp    m*3/2

(9)

3/2

3/2

4

where e is the electron charge, s is the scattering parameter (-1/2 for acoustic phonon scattering),

5

and  (= EF/kBT) is the reduced Fermi energy. Through Equations (7-9), the relationship between

6

 and  can be obtained when m*3/2 (called weighted mobility parameter) is assigned to a value.

7

50, 51

8

s-1me3/2. All the experimental data agree well with calculated line, implying that all Cu2Se-based

9

samples possess comparable weighted mobility parameter μm*3/2 at 500 K. However, we are not

10

sure whether  is changed or not because the regulation of electrical conductivity through

11

alloying or doping may change the effective mass m*. The PF- relation is calculated from  and

12

 depicted in Figure 5b. All the data fall around on the theoretical line. The  for Cu2-2xAg2xSe1-

13

xSx

14

Thus, its PF is relatively low compared with pristine Cu2Se.

The red dashed line in Figure 5a is calculated by taking m*3/2 with a value of 24.6 cm2 V-1

solid solutions are lower than the optimal electrical conductivity opt,

PF

for maximal PF.

15

The L of Cu2Se-based compounds can vary from 0.2 to 0.6 W m-1 K-1 by various

16

approaches such as doping, alloying or nanostructuring. Thus, here two L values of 0.2 and 0.6

17

W m-1 K-1 are separately taken to calculate the total thermal conductivity . As shown in Figure

18

5c, the  for all Cu2Se-based compounds lie in between these two predicted lines. With

19

increasing ,  is significantly improved especially when  is larger than 105 S m-1.

20

Based on the calculated PF and  shown above, the relationship between zT and  is

21

calculated, as shown in Figure 5d. Almost all experimental data locate in the range (red shadow

22

area) set by calculations. The upper and lower boundaries of the shadow area are calculated with

23

L of 0.2 and 0.6 W m-1 K-1, respectively. Apparently, the maximal zT value is greatly improved

24

when decreasing the lattice thermal conductivity. This indicates that decreasing L is one of the

25

most effective ways to improve the TE properties of Cu2Se-based cmopounds. In addition, the

26

optimal electrical conductivity opt, zT for the maximal zT is around (1-4)×104 S m-1, which is


14

Page 15 of 23 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1

slightly lower than that for PF because of the contribution from carrier thermal conductivity. In

2

this study, after alloyed with S and Ag, the  of Cu2Se is much lowered to locate in the range of

3

optimal electrical conductivity opt,

4

performance of quaternary Cu2-2xAg2xSe1-xSx is much enhanced, among the highest zT values

5

reported for Cu2Se-based materials.

zT.

In combination with the notably reduced L, the TE

6 7

CONCLUSION

8

A series of quaternary Cu2-2xAg2xSe1-xSx (x = 0.01, 0.03, 0.05, 0.1, 0.15) chalcogenides have

9

been synthesized in this study. The phase composition, crystal structure, phase transition feature,

10

and TE properties of these samples have been systematically studied. After alloyed with Ag and

11

S, all compounds exist in mixed phases at room temperature but convert into single cubic phase

12

at elevated temperature. The lattice thermal conductivity is significantly suppressed because of

13

the strong phonon scattering from additional mass fluctuations induced by Ag and S co-alloying.

14

Furthermore, the electrical conductivity is much lowered after introduction of Ag and S, leading

15

to slight reduction of both electrical thermal conductivity and power factor. The SPB model

16

analysis demonstrates that the electrial transport has been well tuned to the optimal range. As a

17

result, a peak zT of 1.6 was achieved at 900 K for Cu1.8Ag0.2Se0.9S0.1, which represents an

18

enhancement of 33% over that of pristine Cu2Se.

19 20

ASSOCIATED CONTENT

21

Supporting Information

22

The Supporting Information is available free of charge on the ACS Publications website at DOI:

23

10.1021/acsami.

24

TE properties along different directions; recycling tests; Lorenz number (PDF)

25 26


15


1

AUTHOR INFORMATION

2

Corresponding Authors:

3

*E-mail: [email protected] (K.Z.).

4

*E-mail: [email protected] (X.S.).

Page 16 of 23

5 6

NOTES

7

There are no conflicts to declare.

8 9

ACKNOWLEDGEMENTS

10

This work was supported by the National Key Research and Development Program of China

11

(2018YFB0703600), the National Natural Science Foundation of China (NSFC) under the No.

12

51625205 and 11574333, the Key Research Program of Chinese Academy of Sciences (Grant

13

No. KFZD-SW-421), and the Shanghai Government (16520721400).

14 15

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Abstract Graphic

2


23

Enhanced Thermoelectric Performance of Quaternary Cu2

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