A High Temperature Structural and Thermoelectric study of Argyrodite

Subscriber access provided by University of Winnipeg Library

Functional Inorganic Materials and Devices

A High Temperature Structural and Thermoelectric study of Argyrodite Ag8GeSe6 Xingchen Shen, Chun-Chuen Yang, Yamei Liu, Guiwen Wang, Huan Tan, Yung-Hsiang Tung, Guoyu Wang, Xu Lu, Jian He, and Xiaoyuan Zhou ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b19819 • Publication Date (Web): 21 Dec 2018 Downloaded from http://pubs.acs.org on December 23, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 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

ACS Applied Materials & Interfaces

A High Temperature Structural and Thermoelectric study of Argyrodite Ag8GeSe6 Xingchen Shena,b,c, Chun-Chuen Yangd, Yamei Liu b, Guiwen Wang e, Huan Tana, Yung-Hsiang Tungd, Guoyu Wangc, Xu Lua, Jian He* b, Xiaoyuan Zhou*a,e a Chongqing

Key Laboratory of Soft Condensed Matter Physics and Smart Materials, College of Physics,

Chongqing University, Chongqing 401331, P. R. China b Department c Chongqing

of Physics and Astronomy, Clemson University, Clemson, South Carolina 29634, USA

Institute of Green and Intelligent Technology, Chinese Academy of Science, Chongqing 400714,

P. R. China, Chongqing 400714, P. R. China and University of Chinese Academy of Sciences, Beijing, 100044, P. R. China d Department e Analytical

of Chemistry, Chun Yuan Christian University, Chung-Li District, Taoyuan City 32023, Taiwan

and Testing Center of Chongqing University, Chongqing 401331, P. R. China

*Corresponding

[email protected], [email protected]

Abstract Argyrodites with a general chemical formula of A8BX6 (A = Cu, Ag; B = Si, Ge, Sn; and X = S, Se, and Te) are known for the intimate interplay among mobile ions, electrons, and phonons, which yields rich material physics and materials chemistry phenomena. In particular, the coexistence of fast ionic conduction and promising thermoelectric performance in Ag8GeTe6, Ag8SnSe6, Ag8SiTe6, Ag8SiSe6, Cu8GeSe6 at high temperatures ushered us to their chemical neighbor Ag8GeSe6, whose high temperature crystal structure and thermoelectric properties are not yet reported. In this work, we have employed a growth-from-the-melt technique followed by hot pressing to prepare polycrystalline Ag8GeSe6 samples, on which the crystal structure, micro-morphology, compositional analysis, UV-vis absorption, specific heat, speed of sound, and thermoelectric properties were characterized as a function of the Se-deficiency ratio and temperature. We found (i) the crystal structure of Ag8GeSe6 evolved from orthorhombic at room temperature to face center cubic above 410 K, with a region of

ACS Paragon Plus Environment

ACS Applied Materials & Interfaces 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

Page 2 of 23

phase separations in between; (ii) like other Argyrodite 816 phases, Ag8GeSe6 exhibited ultralow thermal conductivities over a wide temperature range as the phonon mean free path was down to the order of inter-atomic spacing; and (iii) Varying Se deficiency effectively optimized the carrier concentration and power factor, a figure of merit zT value ~ 0.55 was achieved at 923 K in Ag8GeSe5.88. These results not only fill a knowledge gap of Ag8GeSe6 but also contribute to a comprehensive understanding of 816 phase Argyrodites at large.

Keywords: Ag8GeSe6, Argyrodites, crystal structure, lattice dynamics, elastic properties, thermoelectric properties

1. Introduction In the wake of aggravating environment crisis and increasing demand for sustainable energy, thermoelectric (TE) materials research has attracted intensive interest at both fundamental and application level. Thermoelectric materials directly convert waste heat into electricity with neither moving parts nor greenhouse liquids, showing great promise in green energy harvesting and heat management. The performance of TE material, which governs the conversion efficiency of TE device, is measured by the figure of merit 𝑧𝑇 = 𝜎𝑆2𝑇/(𝜅𝑒 + 𝜅𝐿), where σ, S, 𝜅𝑒, 𝜅𝐿, and T are the electrical conductivity, the Seebeck coefficient, the electronic and lattice thermal conductivity, and the absolute temperature, respectively1-4. Developing state-of-the-art TE materials is hinged on searching for novel materials that possess peculiar crystal, electronic and phononic structure5-8 so as to decouple the otherwise inter-dependent {𝜎, 𝑆, 𝜅𝑒, 𝜅𝐿} via electronic and phononic band engineering9-12. Notably, increasing attention is paid to those materials with intrinsically low lattice conductivity, e.g., SnSe5, 1314,

MgAgSb8 , BiCuSeO15, Cu3SbSe316, Ag2Te17, and Cu2Se4,18. These materials possess one or more


Page 3 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


of the following characters: strong anharmonicity, rattling modes, part-crystalline-part liquid hybrid sublattices, and order-disorder transitions. Of special interest are the mixed electronic ionic conductors (MEICs), in which the complex interplay among mobile ions and between mobile ions and the rest of crystal lattice leads to intrinsically low lattice thermal conductivity19-29. Other than the well-known Cu2Se4 and Ag2Te17, the Argyrodites with a general chemical formula A8BX6 (A = Cu, Ag; B = Si, Ge, Sn; and X = S, Se, and Te) are interesting in their own right30. In the realm of thermoelectric materials research, these 816 Argyrodites hold a special status in that (i) they tend to undergo multiple phase transitions, indicative of closely competing thermodynamic states, with increasing temperature towards a face centered cubic structure at elevated temperatures; (ii) there are rich materials physics and materials chemistry phenomena derived from their hybrid crystal structure in which the partially occupied mobile A-sublattice interpenetrates a rigid network of BX4 tetrahedra and isolated X ions; and (iii) the lattice thermal conductivities of 816 Argyrodites measured to date exhibited weak temperature dependence and low magnitude, reminiscent of the thermal conductivity behavior of amorphous materials despite the well proved crystallinity and the wide variation of A, B and X elements25. These features (i) (ii) and (iii) are in line with the “phonon glass” aspect of the “electron crystal-phonon glass” (ECPG) paradigm. With regard to the “electron crystal” aspect, tuning the stoichiometry of MEICs turned out to be an effective approach26. Inspired by these early results, we in this work report synthesis, structural, micro-morphology, mechanical, and thermoelectric study of Ag8GeSe6, a scarcely studied member of 816 Argyrodites family. Specifically, we intend to investigate the crystal structural evolution above room temperature. To our best knowledge, the crystal structure of Ag8GeSe6 at high temperatures, where the fast ionic conduction and promising TE performance tend to coexist in other Argyrodite 816 phases, is not yet



Page 4 of 23

reported (at least, no X-ray powder diffraction pdf card is available). Even with a definite high temperature crystal structure, theoretical calculations of electronic and phononic band structure and corresponding transport properties would be a grand change due to the mobile Ag ions on a partially occupied Ag-sublattice. Hence, experimental study is the only feasible way to study the TE properties of Ag8GeSe6. We herein utilized the X-site occupancy, aka Se deficiency, as the primary control parameter to tune the TE properties of Ag8GeSe6. The data were analyzed in conjunction with the results of temperature variable X-ray powder diffraction, electron microscopy, elemental analysis, UV-vis spectroscopy, specific heat, speed of sound, and Hall coefficient measurements. Notably, all Ag8GeSe6(1-x) samples exhibited very low lattice thermal conductivity value (0.3~0.4 W/m K) over a wide temperature range, comparable in magnitude with other 816 Argyrodites19-26. With measured speed of sound and heat capacity data, we estimated the phonon mean free path and found it was on the order of inter-atomic spacing at elevated temperatures. Upon proper Se deficient, a zT value of about 0.55 was attained at 923 K for Ag8GeSe5.88, compared with a zT value of 0.35 for pristine Ag8GeSe6, testifying the promise of self-doping approach in the TE study of 816 phase Argyrodites.

2. Experimental section 2.1 Sample preparation Proper amounts of high-purity elemental Ag (5N), Ge (5N), Se (5N) were weighted according to the nominal compositions Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02). The starting materials were mixed and sealed in evacuated silica tubes, heated at 1223 K for 12 hours, quenched in cold water and then annealed at 900 K for 72 hours. The as obtained ingots were ground into powders, and hot


Page 5 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


pressed under a uniaxial pressure of 45 MPa for 30 minutes into pellets that have a packing density about 98% of the theoretical density. 2.2 Sample characterization The phase and structural evolution of hot-pressed samples were checked by temperature-dependent powder X-ray diffraction (XRD) with a Cu 𝐾𝛼 radiation line (𝜆 = 1.5406 Å) on a Bruker® D8 diffractometer. The micro-morphology and compositional analysis of hot-pressed samples were studied using a field emission scanning electron microscopy (SEM, JSM-7800F, JEOL®) equipped with an energy dispersive spectrometer (EDS). The electrical transport properties including Seebeck coefficient and electrical conductivity were measured by a Linseis® LSR-3 system, while the thermal diffusivity (𝐷) from room temperature to 923 K was obtained on a Netzsch® LFA 457 laser flash system. The thermal conductivity was calculated from the formula 𝜅 = 𝜌𝐶𝑝𝐷, where 𝐷 is the density of pellet measured by an Archimedes method and 𝐶𝑝 is the heat capacity obtained on a Differential Scanning Calorimeter (Netzsch® 404 F3). Low temperature (2.1-299.1 K) specific heat and lattice thermal conductivity of HP-ed products were measured by a Quantum Design® Physical Property Measurement System (PPMS). The Hall coefficients ( RH ) were measured on a home-made apparatus. The longitudinal and transverse sound velocities of Ag8GeSe6 was collected by an ultrasonic instrument (Ultrasonic® Pulser/Receiver Model 5058PR).

3. Results and discussion 3.1 Crystal structure evolution above room temperature Figure 1(a) and 2 present the XRD patterns taken at 8 temperature points between 298 K and 873 K and the corresponding structural refinements, respectively. The results of Rietveld refinements show



Page 6 of 23

that Ag8GeSe6 adopts an orthorhombic structure with a space group Pmn21 and lattice parameters a = 7.8432(10) Å, b =7.7365(9) Å, c =10.9155(13) Å at room temperature, consistent with an early report by Alverdiev et al.31. As illustrated in Figure 1(b), there are five fully occupied non-equivalent Ag sites, namely Ag1-Ag5, the Ag sublattice interpenetrates the anionic framework [GeSe4]-4 tetrahedra. Specifically, the Ag1 and Ag5 sites are located on a 2a Wyckoff site while the rest Ag sites are located on a 4b Wyckoff site (Table S1 in the Supporting Information). Given the different site symmetry (Table S1 and S2), we expect, to the first order, the thermal vibrations of Ag ions will be accordingly different, which we shall invoke to analyze the low temperature specific heat data in the following. The Rietveld refinements of XRD data above 473 K confirm that the high temperature phase of Ag8GeSe6 is cubic with a space group F4-3m. The crystal structure the detailed atomic positions are shown in Figure 1(d) and Table S3, respectively. On the other hand, our high temperature heat capacity measurements detected three phase transitions at 320 K, 350 K and 410 K (Figure S1). The analysis of transitional phase regime between 320 K and 410 K is given in the Supporting Information. The refined temperature variable lattice constant and the occupancy of Ag site in high temperature phase of Ag8GeSe6 are presented in Figure 3(a) and 3(b), respectively. As shown in Figure 3(a), the lattice constants systematically increase with increasing temperature in the cubic phase of Ag8GeSe6 above 373 K, corroborating anharmonicity of Ag8GeSe6. Meanwhile, the occupancy of Ag site systematically decreases with increasing temperature through the orthorhombic-to-cubic phase change, suggesting the Ag ions undergo a crossover from order to disorder. For the Se-deficient samples Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02), their room temperature XRD patterns are well indexed by an orthorhombic structure (PDF card: 71-1690), and the lattice parameters decrease with increasing (nominal ratio of) Se vacancy (Figure S2). We can use


Page 7 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


the XRD peak width to estimate the coherence length of sample, and the derived values also help crosscheck the measured carrier concentrations. In the case of low Se vacancy content, the coherence length is basically the average distance between Se vacancies. Herein we employ the Scherrer's equation32 to semi-quantitatively estimate the coherence length: 𝐾𝜆

(1),

𝐿ℎ𝑘𝑙 = 𝛽𝐶𝑂𝑆𝜃

where 𝐿ℎ𝑘𝑙 is the coherence length along the direction of [hkl], K is the shape factor taken as 0.5 here, 𝜆 is 1.54056 Å of the XRD instrument wavelength, 𝛽 is the linewidth at half maximum of the XRD peak derived by JADE®, and 𝜃 is the Bragg angle32. As the observed XRD peak linewidth is at least an order of magnitude larger than the instrumental broadening in this study, it is a good approximation to attribute the XRD peak broadening to Se vacancies. The Figure 3(c) displays the coherence length λ030 derived from the (030) peak, the strongest XRD peak observed, as a function of se-deficient content. As shown, the derived coherence length decreases with increasing Se-deficient. If further assuming each Se vacancy contributes two electrons, one can estimate the carrier concentration using Equation (2), and the results are presented in Figure 3(c). The results are fairly close to the carrier concentrations derived from Hall coefficient measurements (Table 1). 𝑛ℎ𝑘𝑙 ≈ (𝐿

2

ℎ𝑘𝑙)

(2),

3

Table 1 Experimentally measured carrier concentration and the electrical properties of Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02) samples at room temperature. Compositions x = 0.0 x = 0.003 x = 0.008 x = 0.01 x = 0.02

𝒏𝑯 (1016 cm-3) 1.15 2.45 2.35 2.52 10.6

𝝁 (cm2/V s) 4769 2739 2499 2714 1851

𝝈 (S/m) 880 1075 942 1096 6275


S (µV/K) -207 -172 -201 -196 -110

PF (𝜇W/cm K2 ) 0.38 0.32 0.38 0.42 0.75


Page 8 of 23

3.2 UV-vis and Scanning Electron Microscopy Study The UV-vis spectroscopy measurements yielded a roughly constant band gap ~ 0.81 eV for Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02) samples (Figure 3(d)), close to the literature data.33 Figure S4 shows the SEM-EDS mapping results of a fresh fractured surface of the x = 0.02 sample. As shown, the compositional distribution is uniform across the sample. 3.3 Thermal conductivity and heat capacity In all Ag8GeSe6(1-x) samples and over the temperature range from 293 to 923 K, the total thermal conductivity 𝜅 is dominated by the lattice component 𝜅𝐿 in view of the low electrical conductivity 𝜎 (Figure S5 and Figure 4(a)). The 𝜅𝐿 = 𝜅 ― 𝜅𝑒, where the carrier component is estimated by the Wiedemann-Franz relation 𝜅𝑒 = 𝐿𝜎𝑇 using a Lorenz number 1.5 × 10-8 W Ω/K2 for non-degenerate semiconductors34,35. As expected for Argyrodite 816 compounds, all Ag8GeSe6(1-x) samples exhibit low 𝜅𝐿values of 0.3-0.4 W/m K in the entire temperature range, among the lowest values in TE materials reported so far4-8, 16, 19, 22, 24,25, 28,29, 35-38. Specifically, the 𝜅𝐿 of Ag8GeSe6(1-x) samples lie close to the amorphous limit or minimal lattice thermal conductivity based on the Cahill’s model25,39: 1

𝜅𝑚𝑖𝑛 =

2

( ) 𝐾𝐵(𝑛𝑎) ∑ 𝑣𝑖( 𝜋 6

3

3

𝑖

𝑇 2 𝛩𝑖 𝑥3𝑒𝑥 𝛩𝑖) ∫0 (𝑒𝑥 ― 1)2𝑑𝑥

(3),

where na is the number of atoms per unit volume, vi is the sound velocity for the polarization i, and 𝛩𝑖 1

( )(

is the cut-off frequency for the polarization i, and 𝛩𝑖 = 𝑣𝑖

ℎ

𝐾𝐵

3𝑛𝑎

4𝜋 )

3

.

The room temperature elastic properties of Ag8GeSe6, including the transverse wave speed (ν𝑡), longitudinal wave speed (ν𝑙), average wave velocity (ν𝑎), Poisson ratio (ν𝑝), Young's modulus (E), shear modulus (G), and Debye temperature (𝛩𝐷), are listed in Table 2 along with the calculated Grüneisen parameter. The Grüneisen parameter 𝛾 is a measure of lattice anharmonicity, which shortens phonon lifetime and suppresses 𝜅𝐿 via phonon-phonon interactions40. In view of the polycrystalline isotropic Ag8GeSe6(1-x) samples, here we calculated the Grüneisen parameter from the


Page 9 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


Poisson’s ratio and averaged bulk modulus41. More details of calculations can be found in the Supporting Information. The derived 𝛾 value ~ 1.3 of Ag8GeSe is not high as most materials exhibit 𝛾 values between 1 and 2. Nonetheless, the thermal expansion revealed in Figure 3(a) is a direct evidence of anharmonicity. More evidence of anharmonicity will be provided when we discuss the data of heat capacity and lattice thermal conductivity in the following.

Table 2 Room temperature elastic properties and Grüneisen parameter of Ag8GeSe6. Composition

𝜈𝑡 (m/s)

𝜈𝑙 (m/s)

𝜈𝑎 (m/s)

p

E (GPa)

G (GPa)

𝛾

𝛩𝐷 (K)

Ag8GeSe6

1806

3049

2054

0.20

58.2

13.2

1.30

219

To gain more insights into the lattice dynamics underlying the low lattice thermal conductivity, we measured heat capacity 𝐶𝑝 of Ag8GeSe6 from 2.1 K to 299.1 K (Figure S6). The low temperature 𝐶𝑝 data doesn’t show any anomaly, indicating no phase transition below room temperature through 2.1 K. As shown in Figure 4(b), the 𝐶𝑝 data can be well described by one Debye mode and two Einstein oscillators according to the following equation: 𝛩𝐸1

𝐶𝑝 𝑇

= 𝜑 + 𝛽𝑇2 +𝐴(𝛩𝐸1)2𝑇3 (𝑒

𝑒

𝑇

( )2𝑇3 2 +𝐵 𝛩𝐸2

𝛩𝐸1 𝑇

𝛩𝐸2

― 1)

(𝑒

𝑒 𝛩𝐸2 𝑇

𝑇 2

(4),

― 1)

In Equation (4), 𝜑 is the Sommerfeld coefficient, representing the electronic contribution to heat capacity, 𝛩𝐸1 and 𝛩𝐸2 are the characteristic temperatures of two Einstein modes, A and B are constants. The values of fitting parameters for the best fitting can be found in Table S4. The 𝛽𝑇2 term in Equation (4) is the Debye term based on long wavelength acoustic modes. The best fitting yielded 1

4

a 𝛩𝐷 = 211 K through the relation 𝛩𝐷 = (12𝜋 𝑛𝑎𝑅/5𝛽)3, this value agrees well with the value 𝛩𝐷



Page 10 of 23

= 219 K derived from acoustics measurements at room temperature (cf. Table 2). The fitting values A+B = 7.8 is closed to 8, aka the number of Ag atoms per molecular formula, testifying the trustworthiness of fitting. Notably, two Einstein modes with characteristic temperatures 𝛩𝐸1 = 70 K and 𝛩𝐸2 = 35 K are identified, consistent with the two different symmetry sites of Ag ions (Table S2). It is interesting to see whether these low-energy Einstein modes would disrupt the heat-carrying lowwavelength acoustic phonon modes2, 42-44, thereby reducing 𝜅𝐿. The high temperature 𝐶𝑝 values are near or slightly lower than the Dulong-Petit limit at T > 𝛩𝐷 (cf. Figure S1), suggesting pre-melting of Ag sublattice. The reasons are listed as follows. The thermal expansion of lattice constant presented in Figure 3(a) indicates anharmonicity. In light of the relation 𝐶p = Cv +9𝛼2𝐵𝑉𝑇19, where 𝐶𝑝, 𝐶𝑣, 𝛼, 𝐵 and V are the isobaric specific heat, isochoric specific heat, bulk thermal expansion coefficient, bulk elastic modulus, and average volume per atom, respectively, the presence of anharmonicity would make 𝐶𝑝 > 𝐶𝑣 at elevated temperatures. The Dulong-Petit limit is the limit of 𝐶𝑣 at sufficiently high temperatures (T > 𝛩𝐷). On the other hand, the pre-melting of Ag sublattice, in which Ag ions behave like a liquid and gradually lose transverse vibrational degrees of freedom, reduces the heat capacity per atom from 3 kB toward 2 kB4,19. Apparently, the anharmonicity induced 𝐶𝑝 increment and the sublattice pre-melting induced 𝐶𝑝 decrease nearly cancel out in Ag8GeSe6. The lattice thermal conductivity of Ag8GeSe6 between 5 K and 923 K is displayed in Figure 4(c). For completeness, we present the raw data as is. Note that the kink near ~ 12 K is most likely a glitch of measurement because specific heat measurements didn’t show any anomaly near 12 K. While the overall temperature dependence of lattice thermal conductivity of Ag8GeSe6 is typical of a crystalline material, we observed a lattice thermal conductivity peak at ~ 7 K. In general, a lattice thermal


Page 11 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


conductivity peak marks the onset of the Umklapp process, typically at a temperature ~10-20% of the Debye temperature. As such, the peak temperature at ~ 7 K is surprisingly low in light of the 𝛩𝐷 value ~ 211 K or 219 K. On one hand, we have confirmed the lattice thermal conductivity peak at ~ 7 K by repeated measurements on the PPMS. On the other hand, why 𝜅𝐿 peaks at such an unusually low temperature? At low temperatures (T two orders of magnitude between 7 K and 70 K. This temperature regime is close to the characteristic Einstein temperatures (aka 35 K and 70 K), corroborating strong anharmonic interactions between low-lying Einstein modes and heat-carrying long wavelength acoustic phonon modes. 3.4 Electrical transport properties and Figure of merit The temperature dependent electrical transport properties of all Ag8GeSe6(1-x) samples are displayed in Figure 5. As shown in Figure 5(a), the electrical conductivity of all Se-deficient samples is higher than that of the pristine Ag8GeSe6 over the entire temperature range studied due to increased



Page 12 of 23

carrier concentrations. Specifically, the room temperature electrical conductivity of Ag8GeSe5.88 drastically rises by about six times compared with that of the pristine compound owing to the increment of carrier concentration from the order of 1016 cm-3 to 1017 cm-3. As shown in Table 1, all Ag8GeSe6(1-x) samples exhibit high values of carrier mobility at room temperature. We note that the carrier mobility of Argyrodite 816 phase tends to be sensitive to its carrier concentration. For example, Heep et al.24 reported a room temperature mobility value ~ 1500 cm2/V s in Ag8SiSe6 with the carrier concentration on the order of 1018 cm-3. In Ag8SnSe619-20, a room temperature mobility value of ~ 900 cm2/V s was reported at a carrier concentration on the order of 1018 cm-3. By contrast, doped Cu8GeSe6 with a carrier concentration on the order of 1020 cm-3 exhibited a low room temperature mobility value of ~ 6 cm2/V s 45. Hence, the observed high mobility values in Ag8GeSe6(1-x) samples are not a surprise given their low carrier concentrations on the order of 10161017 cm-3. The temperature-dependent Seebeck coefficient for all Ag8GeSe6(1-x) samples is depicted in Figure 5(b) and the negative values indicates a domain n-type conduction. The systematic decrease of the absolute value of Seebeck coefficient with increasing Se deficient is consistent with the increased carrier concentration deduced from Hall coefficient measurements (Table 1). Owing to the largely enhanced electrical conductivity and the moderately degraded Seebeck coefficient, the highest power factor of 2.5 μW/cm K2 is attained at 923 K in Ag8GeSe5.88 sample, a 25% enhancement compared to the pristine sample (Figure 5(c)). Combining the optimized power factor and low lattice thermal conductivity of Se-deficient samples, the highest zT value 0.55 has been achieved in Ag8GeSe5.88, an improvement about 57% than that of Ag8GeSe6 (Figure 5(d)), indicating that Se-deficiency is effective in improving the TE properties of Ag8GeSe6 compounds.


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


4. Conclusion In this study, we focused on the crystal structure evolution, lattice dynamics, and thermoelectric properties of Se-deficient Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02) over a wide temperature range. We found a structural evolution from orthorhombic at room temperature to cubic above 410 K, with a translational phase regime in between. In low temperature specific heat, we have revealed two low-lying Einstein modes and attribute them to vibrations of Ag ions. The coupling between these Einstein modes and heat-carrying phonons, strong anharmonicity, and small group velocity accounted for intrinsically low lattice thermal conductivity. We found Se-deficiency was effective in optimizing the carrier concentration toward high thermoelectric performance in Ag8GeSe6 and hopefully in other 816 phase Argyrodites.

Conflicts of interest The authors declare no competing financial interests.

Acknowledgements This work was financially supported in part by the National Natural Science Foundation of China (Grant Nos. 51772035, 11674040, 51472036), the Fundamental Research Funds for the Central Universities (No. 106112017CDJQJ308821 and 2018CDYJSY0055) and the CSC scholarship (No. 201806050180). This work was also financially supported by Key Research Program of Frontier Sciences, CAS, Grant No. QYZDB-SSW-SLH016, the Project for Fundamental and Frontier Research in Chongqing (CSTC2015JCYJBX0026 and CSTC2017JCYJAX0388).



Page 14 of 23

References 1.

He, J.; Tritt, T. M., Advances in Thermoelectric Materials Research: Looking Back and Moving Forward. Science 2017,

357 (6358): eaak9997. 2.

Zhu, T.; Liu, Y.; Fu, C.; Heremans, J. P.; Snyder, J. G.; Zhao, X., Compromise and Synergy in High-Efficiency

Thermoelectric Materials. Adv. Mater. 2017, 29 (14), 1605884. 3.

Tan, G.; Zhao, L. D.; Kanatzidis, M. G., Rationally Designing High-Performance Bulk Thermoelectric Materials. Chem.

Rev. 2016, 116 (19), 12123-12149. 4.

Nunna, R.; Qiu, P. F.; Yin, M. J.; Chen, H. Y.; Hanus, R.; Song, Q. F.; Zhang, T. S.; Chou, M. Y.; Agne, M. T.; He, J. Q.;

Snyder, G. J.; Shi, X.; Chen, L. D., Ultrahigh Thermoelectric Performance in Cu2Se-based Hybrid Materials with Highly Dispersed Molecular CNTs. Energ. Environ. Sci. 2017, 10 (9), 1928-1935. 5.

Zhao, L. D.; Lo, S. H.; Zhang, Y. S.; Sun, H.; Tan, G. J.; Uher, C.; Wolverton, C.; Dravid, V. P.; Kanatzidis, M. G., Ultralow

Thermal Conductivity and High Thermoelectric Figure of Merit in SnSe Crystals. Nature 2014, 508 (7496), 373-+. 6.

Jana, M. K.; Pal, K.; Waghmare, U. V.; Biswas, K., The Origin of Ultralow Thermal Conductivity in InTe: Lone-Pair-

Induced Anharmonic Rattling. Angew Chem Int Ed Engl 2016, 55 (27), 7792-6. 7.

Samanta, M.; Pal, K.; Pal, P.; Waghmare, U. V.; Biswas, K., Localized Vibrations of Bi Bilayer Leading to Ultralow

Lattice Thermal Conductivity and High Thermoelectric Performance in Weak Topological Insulator n-Type BiSe. J. Am. Chem. Soc. 2018, 140 (17), 5866-5872. 8.

Ying, P.; Li, X.; Wang, Y.; Yang, J.; Fu, C.; Zhang, W.; Zhao, X.; Zhu, T., Hierarchical Chemical Bonds Contributing to

the Intrinsically Low Thermal Conductivity in α-MgAgSb Thermoelectric Materials. Advanced Functional Materials 2017, 27 (1), 1604145. 9.

Pei, Y.; Shi, X.; LaLonde, A.; Wang, H.; Chen, L.; Snyder, G. J., Convergence of Electronic Bands for High Performance

Bulk Thermoelectrics. Nature 2011, 473 (7345), 66. 10. Pei, Y.; Wang, H.; Snyder, G. J., Band Engineering of Thermoelectric Materials. Adv Mater 2012, 24 (46), 6125-35. 11. Toberer, E. S.; Zevalkink, A.; Snyder, G. J., Phonon Engineering through Crystal Chemistry. Journal of Materials Chemistry 2011, 21 (40), 15843. 12. Chen, Z. W.; Zhang, X. Y.; Pei, Y. Z., Manipulation of Phonon Transport in Thermoelectrics. Advanced Materials 2018, 30 (17), 1705617. 13. Chang, C.; Wu, M. H.; He, D. S.; Pei, Y. L.; Wu, C. F.; Wu, X. F.; Yu, H. L.; Zhu, F. Y.; Wang, K. D.; Chen, Y.; Huang, L.; Li, J. F.; He, J. Q.; Zhao, L. D., 3D Charge and 2D Phonon Transports Leading to High Out-of-Plane ZT in n-Type SnSe crystals. Science 2018, 360 (6390), 778-782. 14. Peng, K. L.; Lu, X.; Zhan, H.; Hui, S.; Tang, X. D.; Wang, G. W.; Dai, J. Y.; Uher, C.; Wang, G. Y.; Zhou, X. Y., Broad Temperature Plateau for High ZTs in Heavily Doped p-Type SnSe Single Crystals. Energ. Environ. Sci. 2016, 9 (2), 454-460. 15. Ren, G.-K.; Wang, S.-Y.; Zhu, Y.-C.; Ventura, K. J.; Tan, X.; Xu, W.; Lin, Y.-H.; Yang, J.; Nan, C.-W., Enhancing Thermoelectric Performance in Hierarchically Structured BiCuSeO by Increasing Bond Covalency and Weakening Carrier– Phonon Coupling. Energ. Environ. Sci. 2017, 10 (7), 1590-1599. 16. Tyagi, K.; Gahtori, B.; Bathula, S.; Srivastava, A. K.; Shukla, A. K.; Auluck, S.; Dhar, A., Thermoelectric Properties of Cu3SbSe3 with Intrinsically Ultralow Lattice Thermal Conductivity. J. Mater. Chem. A. 2014, 2 (38), 15829-15835. 17. Fujikane, M.; Kurosaki, K.; Muta, H.; Yamanaka, S., Thermoelectric Properties of Alpha- and Beta-Ag2Te. Journal of Alloys and Compounds 2005, 393 (1-2), 299-301. 18. Jana, M. K.; Biswas, K., Crystalline Solids with Intrinsically Low Lattice Thermal Conductivity for Thermoelectric


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


Energy Conversion. ACS Energy Letters 2018, 3 (6), 1315-1324. 19. Li, L.; Liu, Y.; Dai, J.; Hong, A.; Zeng, M.; Yan, Z.; Xu, J.; Zhang, D.; Shan, D.; Liu, S.; Ren, Z.; Liu, J.-M., High Thermoelectric Performance of Superionic Argyrodite Compound Ag8SnSe6. Journal of Materials Chemistry C 2016, 4 (24), 5806-5813. 20. Li, W.; Lin, S.; Ge, B.; Yang, J.; Zhang, W.; Pei, Y., Low Sound Velocity Contributing to the High Thermoelectric Performance of Ag8SnSe6. Adv. Sci. 2016, 3 (11), 1600196. 21. Charoenphakdee, A.; Kurosaki, K.; Muta, H.; Uno, M.; Yamanaka, S., Reinvestigation of the Thermoelectric Properties of Ag8GeTe6. physica status solidi (RRL) – Rapid Research Letters 2008, 2 (2), 65-67. 22. Charoenphakdee, A.; Kurosaki, K.; Muta, H.; Uno, M.; Yamanaka, S., Ag8SiTe6: A New Thermoelectric Material with Low Thermal Conductivity. Japanese Journal of Applied Physics 2009, 48 (1), 011603. 23. Fujikane, M.; Kurosaki, K.; Muta, H.; Yamanaka, S., Thermoelectric Properties of Ag8GeTe6. Journal of Alloys and Compounds 2005, 396 (1-2), 280-282. 24. Heep, B. K.; Weldert, K. S.; Krysiak, Y.; Day, T. W.; Zeier, W. G.; Kolb, U.; Snyder, G. J.; Tremel, W., High Electron Mobility and Disorder Induced by Silver Ion Migration Lead to Good Thermoelectric Performance in the Argyrodite Ag8SiSe6. Chemistry of Materials 2017, 29 (11), 4833-4839. 25. Jiang, B.; Qiu, P.; Eikeland, E.; Chen, H.; Song, Q.; Ren, D.; Zhang, T.; Yang, J.; Iversen, B. B.; Shi, X.; Chen, L., Cu8GeSe6based Thermoelectric Materials with An Argyrodite Structure. Journal of Materials Chemistry C 2017, 5 (4), 943-952. 26. Zhu, T. J.; Zhang, S. N.; Yang, S. H.; Zhao, X. B., Improved Thermoelectric Figure of Merit of Self-Doped Ag8-xGeTe6 Compounds with Glass-Like Thermal Conductivity. physica status solidi (RRL) - Rapid Research Letters 2010, 4 (11), 317319. 27. Lin, S.; Li, W.; Li, S.; Zhang, X.; Chen, Z.; Xu, Y.; Chen, Y.; Pei, Y., High Thermoelectric Performance of Ag9GaSe6 Enabled by Low Cutoff Frequency of Acoustic Phonons. Joule 2017, 1 (4), 816-830. 28. Jiang, B.; Qiu, P.; Chen, H.; Zhang, Q.; Zhao, K.; Ren, D.; Shi, X.; Chen, L., An Argyrodite-Type Ag9GaSe6 Liquid-Like Material with Ultralow Thermal Conductivity and High Thermoelectric Performance. Chem. Commun. 2017, 53 (85), 11658-11661. 29. Li, W.; Lin, S.; Weiss, M.; Chen, Z.; Li, J.; Xu, Y.; Zeier, W. G.; Pei, Y., Crystal Structure Induced Ultralow Lattice Thermal Conductivity in Thermoelectric Ag9AlSe6. Adv. Energy Mater. 2018, 8 (18), 1800030. 30. Kuhs, W. F.; Nitsche, R.; Scheunemann, K., Argyrodites - New Family of Tetrahedrally Close-Packed Structures. Mater. Res. Bull. 1979, 14 (2), 241-248. 31. Alverdiev, I. J.; Bagheri, S. M.; Aliyeva, Z. M.; Yusibov, Y. A.; Babanly, M. B., Phase Equilibria in the Ag2Se–GeSe2– SnSe2 System and Thermodynamic Properties of Ag8Ge1–xSnxSe6 Solid Solutions. Inorganic Materials 2017, 53 (8), 786796. 32. He, H. F.; Zhao, B.; Qi, N.; Wang, B.; Chen, Z. Q.; Su, X. L.; Tang, X. F., Role of Vacancy Defects on the Lattice Thermal Conductivity in In2O3 Thermoelectric Nanocrystals: A Positron Annihilation Study. J. Mater. Sci. 2018, 53 (18), 1296112973. 33. Bendorius, R.; Irzikevicius, A.; Kindurys, A.; Tsvetkova, E. V., Absorption-Spectra of Ag8mivse6 and Ag8gex6(Vi) Compounds. Physica Status Solidi a-Applied Research 1975, 28 (2), K125-K127. 34. Weldert, K. S.; Zeier, W. G.; Day, T. W.; Panthofer, M.; Snyder, G. J.; Tremel, W., Thermoelectric Transport in Cu7PSe6 with High Copper Ionic Mobility. J. Am. Chem. Soc. 2014, 136 (34), 12035-12040. 35. Yang, D. F.; Yao, W.; Chen, Q. F.; Peng, K. L.; Jiang, P. F.; Lu, X.; Uher, C.; Yang, T.; Wang, G. Y.; Zhou, X. Y., Cr2Ge2Te6: High Thermoelectric Performance from Layered Structure with High Symmetry. Chemistry of Materials 2016, 28 (6), 16111615. 36. Peng, K. L.; Zhang, B.; Wu, H.; Cao, X. L.; Li, A.; Yang, D. F.; Lu, X.; Wang, G. Y.; Han, X. D.; Uher, C.; Zhou, X. Y., UltraHigh Average Figure of Merit in Synergistic Band Engineered SnxNa1-xSe0.9S0.1 Single Crystals. Mater. Today 2018, 21 (5),



Page 16 of 23

501-507. 37. Zhang, A. J.; Shen, X. C.; Zhang, Z.; Lu, X.; Yao, W.; Dai, J. Y.; Xie, D. D.; Guo, L. J.; Wang, G. Y.; Zhou, X. Y., Large-Scale Colloidal Synthesis of Cu5FeS4 Compounds and Their Application in Thermoelectrics. Journal of Materials Chemistry C 2017, 5 (2), 301-308. 38. Zhang, X.; Zhang, B.; Peng, K. L.; Shen, X. C.; Wu, G. T.; Yan, Y. C.; Luo, S. J.; Lu, X.; Wang, G. Y.; Gu, H. S.; Zhou, X. Y., Spontaneously Promoted Carrier Mobility and Strengthened Phonon Scattering in p-Type YbZn2Sb2 via A Nanocompositing Approach. Nano Energy 2018, 43, 159-167. 39. He, J.; Hitchcock, D.; Bredeson, I.; Hickman, N.; Tritt, T. M.; Zhang, S. N., Probing Lattice Dynamics of Cd2Re2O7 Pyrochlore: Thermal Transport and Thermodynamics Study. Phys. Rev. B 2010, 81 (13), 134302. 40. Chang, C.; Zhao, L. D., Anharmoncity and Low Thermal Conductivity in Thermoelectrics. Mater. Today Phys. 2018, 4, 50-57. 41. Sanditov, D. S.; Belomestnykh, V. N., Relation Between the Parameters of the Elasticity Theory and Averaged Bulk Modulus of Solids. Tech. Phys. 2011, 56 (11), 1619-1623.

42. Toberer, E. S.; Zevalkink, A.; Snyder, G. J., Phonon Engineering through Crystal Chemistry. Journal of Materials Chemistry 2011, 21 (40), 15843-15852. 43. Tan, G. J.; Hao, S. G.; Zhao, J.; Wolverton, C.; Kanatzidis, M. G., High Thermoelectric Performance in Electron-Doped AgBi3S5 with Ultralow Thermal Conductivity. J. Am. Chem. Soc. 2017, 139 (18), 6467-6473. 44 Shen, X. C.; Xia, Y.; Wang, G. W.; Zhou, F.; Ozolins, V.; Lu, X.; Wang, G. Y.; Zhou, X. Y., High Thermoelectric Performance in Complex Phosphides Enabled by Stereochemically Active Lone Pair Electrons. J. Mater. Chem. A 2018, 6, 24877-24884. 45. Jiang, B. B.; Qiu, P. F.; Eikeland, E.; Chen, H. Y.; Song, Q. F.; Ren, D.; Zhang, T. S.; Yang, J.; Iversen, B. B.; Shi, X.; Chen, L. D., Cu8GeSe6-based Thermoelectric Materials with An Argyrodite Structure. Journal of Materials Chemistry C 2017, 5 (4), 943-952.


Page 17 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


Figure Captions Figure 1(a) Temperature variable XRD patterns of Ag8GeSe6 above room temperature. (b) The orthorhombic crystal structure of Ag8GeSe6. (c) room temperature XRD patterns of Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02). (d) The cubic crystal structure of Ag8GeSe6 at 473 K. Partial site occupancy is indicated by partial coloring of the atoms. Figure 2 Observed (crosses) and calculated (solid lines) XRD patterns of Ag8GeSe6 that were collected at the temperatures of (a) 298 K, (b) 323 K, (c)373 K, (d) 473 K, (e) 573 K, (f) 673 K, (g) 773 K, and (h) 873 K. The difference between observed and calculated pattern are plotted at the bottom of figures. Solid short dashes reveal the calculated positions of Bragg reflections of the proposed crystal structure. Figure 3(a) The temperature variable lattice constant of Ag8GeSe6. The a- and b-axis below 350 K are all times the square root of 2. (b) Occupancy of the crystallographic positions of Ag. There are two non-equivalent positions in cubic phase and five in orthorhombic phase. (c) The room temperature coherence length of Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02) samples along the direction of [030] and the estimated carrier concentration of Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02) samples at room temperature. (d) The optical band gap of Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02) samples at room temperature. Figure 4(a) The calculated lattice thermal conductivity of Ag8GeSe6(1-x) samples (x = 0.0, 0.003, 0.008, 0.01 and 0.02) from 293 to 923 K. The data points in the vicinity of three phase transitions (denoted by dashed lines) should be taken with caution in view of the transition-induced fluctuations. (b) Cp/T versus T2 for Ag8GeSe6 (black circles). The red solid line represents the fitted curve by using a Debye model plus two Einstein modes. The other colored lines represent the electronic term 𝜑, Debye term 𝛽, and two Einstein temperatures, 𝛩𝐸2 and 𝛩𝐸2, respectively. (c) The lattice thermal conductivity of Ag8GeSe6 from 5 K to 923 K. (d) The estimated mean free path of Ag8GeSe6 as a function of temperature. Figure 5 The temperature-dependent (a) electrical conductivity, (b) Seebeck coefficient, (c) power factor (d) figure of merit zT of Ag8GeSe6(1-x) (x = 0.0, 0.003, 0.008, 0.01 and 0.02) samples. The data points in the vicinity of three phase transitions should be taken with caution.



Figure 1


Page 18 of 23

Page 19 of 23

Figure 2

Orthorhomic Pmn21

(a)

o

a = 7.8432(10) A o b = 7.7365(9) A o c = 10.9155(13) A Rp = 5.84 %

0.9

Rwp = 7.72 % 2

 = 1.669

0.6 0.3 0.0

Orthorhomic Pmn21

(b)

o

a = 7.8483(11) A o b = 7.7435(9) A o c = 10.9234(13) A Rp = 5.99 %

0.9

Rwp = 7.80 % 2

 = 1.701

0.6 0.3

50

60

70

Scattering angle 2 ( deg. )

T = 373 K

80

90

Phase 1 : Ag8GeSe6 (76 %) Phase 2 : Ag (14 %) Phase 3 : AgGe0.56Se0.74 (10 %)

(c)

Rp = 5.96 % Rwp = 7.88 %

0.9

2

 = 1.689

0.6 0.3 Ag8GeSe6 AgGe0.56Se0.74

10

20

1.8 1.5

40

50

60

70


80

90

Cubic F -4 3 m

(e)

o

a = 11.0167(16) A Rp = 5.72 % Rwp = 7.47 % 2

0.9

 = 1.548

0.6 0.3

40

50

60

70


80

90

Ag8GeSe6

T = 773 K

Cubic F -4 3 m

(g)

o

a = 11.0520(17) A Rp = 5.79 %

80

90

80

90

80

90

80

90

o

a = 11.0027(17) A Rp = 5.70 % Rwp = 7.50 % 2

 = 1.566

0.6 0.3

20

1.5 1.2

30

40

50

60

70

Scattering angle 2 ( deg. ) Ag8GeSe6

T = 673 K

Cubic F -4 3 m

(f)

o

a = 11.0256(14) A Rp = 5.64 % Rwp = 7.36 % 2

0.9

 = 1.510

0.6 0.3

10

20

1.5 1.2

30

40

2

 = 1.636

0.6 0.3 0.0

50

60

70

Scattering angle 2 ( deg. ) Ag8GeSe6

T = 873 K

Cubic F -4 3 m

(h)

o

a = 11.0834(12) A Rp = 5.67 % Rwp = 7.39 %

3

Rwp = 7.63 %

0.9

10

70

Cubic F -4 3 m

(d)

1.8

Intensity ( 10 counts )

30

3

1.2

60

0.0 20

1.8 1.5

50

Ag8GeSe6

0.9

10

0.0 10

1.2

40

T = 473 K

1.8

Ag8GeSe6

T = 573 K

3

1.2

1.5

30


0.0

Ag

30

20

3

0.0

10 1.8

3

1.2

40


3

1.5

30


20

1.8


1.2

Ag8GeSe6

T = 323 K

0.0

10


1.5

3

1.2


1.5

1.8

Ag8GeSe6

T = 298 K

3


1.8


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


2

0.9

 = 1.539

0.6 0.3 0.0

20

30

40

50

60

70


80

90

10

20

30

40

50

60

70




Figure 3


Page 20 of 23

Page 21 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


Figure 4



Figure 5


Page 22 of 23

Page 23 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


We reported crystal structure evolution, lattice dynamics, and thermoelectric properties of Argyrodites Ag8GeSe(6-x) (x = 0.0, 0.3%, 0.8%, 1%, 2%).


A High Temperature Structural and Thermoelectric study of Argyrodite

Recommend Documents