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Argyrodite-type Ag9GaSe6 liquid-like material with ultralow thermal conductivity and high thermoelectric performance Received 00th January 20xx, Accepted 00th January 20xx
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Binbin Jiang, Pengfei Qiu, Hongyi Chen, Qihao Zhang, Kunpeng Zhao, Dudi Ren, Xun Shi, ac and Lidong Chen
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DOI: 10.1039/x0xx00000x www.rsc.org/
We report a ternary Argyrodite-type Ag9GaSe6 compound as a promising thermoelectric material in moderate temperature range. Due to the high carrier mobility and ultralow lattice thermal conductivity, a maximal ZT of 1.1 was obtained in stoichiometric Ag9GaSe6 at 800 K. Via introducing slight Sedeficiency to optimize the carrier concentration, the maximal ZT is further enhanced to 1.3. Thermoelectric (TE) technology can directly convert thermal energy into electricity and vice versa.1-3 The energy conversion efficiency of a TE material is determined by the dimensionless TE figure of merit, ZT = S2σT/κ, where σ is the electrical conductivity, S is the Seebeck coefficient, κ is the total thermal conductivity, and T is the absolute temperature. The κ is composed by the lattice thermal conductivity (κL) and the electronic thermal conductivity (κe = LσT, where L is the Lorenz number). A high-performance TE material requires a high S, a large σ, and a low κ.1-3 However, it is very hard to simultaneously achieve these optimized parameters in one material because σ, S, and κ are strongly interrelated with each other. For example, a high σ usually corresponds to a low S and a high κe. One well-accepted strategy to discover new high-performance TE materials is to explore those materials with intrinsically low κL because κL correlates weakly with the other parameters (S, σ and κe) among these TE transport parameters.4 Along this direction, many new highperformance TE materials have been successfully reported in recent years, especially for the compounds with Argyroditetype structures.5-10 The Argyrodite-type compounds have a general formula Am+(12n+ 2m+ = Li+，Cu+，or Ag+, Bn+ = Ga3+，Si4+，Ge4+， n)/mB X 6 (A 4+ 5+ Sn ， P , or As5+, and X = S, Se, or Te).11 At room
temperature, they could crystallize in complex monoclinic, orthorhombic, hexagonal, or cubic structures, depending on the component elements wherein. Nevertheless, at high temperatures, they usually crystalize in high-symmetry cubic or hexagonal structures, where A-cations are mobile and disorderly distributed inside the rigid sublattice formed by the 11 B-cations and X-anions. Thus, these high-temperature superionic phases agree well with the “Phonon-liquid Electroncrystal” concept, which is proposed to explain the abnormal TE 12 properties in superionic TE materials. There are dozens of types of Argyrodite-type compounds. A few of them, with m = m+ n+ 27 or 8 and n = 4 or 5 in A (12-n)/mB X 6, such as Ag8GeTe6,5 6 7 8,9 10 Ag8SiTe6, Cu7PSe6, Ag8SnSe6, and Cu8GeSe6, have been reported with intrinsically ultralow κL values around 0.15-0.35 -1 -1 W m K and high TE performance. In this communication, we report a new promising Argyrodite-type compound, Ag9GaSe6, with m = 9 and n = 3, which also exhibits an intrinsically low κL (around 0.2 W m-1 K-1) and a high ZT of 1.3 at 800 K. The crystal structure of Ag9GaSe6 has been firstly reported by Deloume in 1978.13 Ag9GaSe6 has one temperature-dependent phase transition at around 281 K.14 As shown in Fig. 1a, the low-temperature Ag9GaSe6 β-phase has a cubic structure (space group P213) with a = 1.1126 nm and Z = 4.13 In this large unit cell, the [GaSe4]5- tetrahedral (see Fig. 1b) with C3 symmetry and Se2- anions construct the anion framework. The electropositive Ag atoms are orderly located at three 12b sites inside the anion framework, with each of them bonding with three nearby Se atoms in an almost trigonal-planar arrangement (see Fig. 1b). Above 281 K, the low-temperature Ag9GaSe6 β-phase converts to the high-temperature Ag9GaSe6 α-phase (see Fig. 1c),14 which has a higher symmetry structure (space group F-43m) but the same cell parameters (a = 1.1126 nm and Z = 4) with the β-phase. Similarly, the anion framework of Ag9GaSe6 α-phase is still composed by the [GaSe4]5tetrahedral and Se2- anions. However, the Ag atoms disorderedly arranged in the anion framework at three different sites: 48h (0.232, 0.232, 0.029), 48h (-0.169, -0.169, 0.031), and 96i (-0.160, 0.073, 0.129), with the occupancies of 0.25, 0.25, and 0.125, respectively.14 The Ag atoms at 48h sites
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Fig. 1 (a) Low-temperature crystal structure of Ag9GaSe6 β-phase. (b) Two prominent structural features: [GaSe4]5- tetrahedral and trigonal-planar Ag atoms. (c) Hightemperature crystal structure of Ag9GaSe6 α-phase. The atomic site occupancy is indicated by partial coloring of the atoms. (d) (1-R)2/2R as a function of photon energy hν. The extrapolation of the spectra (black line) is used to estimate optical band gap value for Ag9GaSe6 powder using the Kubelka-Munk method.15
bonded with three nearby Se atoms, but the Ag atoms at 96i sites are located in the tetrahedrons formed by four nearby Se atoms. Being similar with the cations in other Argyrodite-type compounds, the Ag ions can consecutive jump from one equilibrium position to another within very short time displaying liquid-like behavior. Thus, Ag9GaSe6 is also a liquidlike material. The large unit cell, complicate atomic occupation, liquid-like Ag ions definitely lead to the intrinsically low κL in Ag9GaSe6. More importantly, as shown in Fig. 1d, Ag9GaSe6 is a narrow gap semiconductor with the band gap (Eg) about 0.53 eV, which is benefit for achieving high electrical transports. Thus, Ag9GaSe6 is expected to have good ZTs. The detailed synthesis process of Ag9GaSe6 is shown in supporting information. The phase purity and crystal structure were examined by the powder X-ray diffraction (PXRD) with Cu Kα radiation at 300 K. As shown in Fig. 2a, the XRD pattern of the synthesized Ag9GaSe6 sample can be well indexed to the high-temperature α-phase with F-43m structure (PDF #712448).14 No impurity phases are detected. Fig. 2b and Fig. 2c show the high resolution transmission electron microscope (HRTEM) image and inverse fast Fourier transformation image for Ag9GaSe6. Clearly, the sample has high degrees of crystallinity. No obvious lattice distortions, dislocations, or amorphous phases are observed. The selected area electron diffraction (SAED) pattern shown in Fig. 2d further confirms that the prepared Ag9GaSe6 crystalizes in face-centered cubic structure, which is consistent with the result of XRD characterization. Based on the fast Fourier transformation (FFT) image shown in the inset picture of Fig. 2b, the spacing of
[-13-1] plane (d[-13-1]) in Ag9GaSe6 α-phase is calculated with a
Fig. 2 (a) XRD patterns for Ag9GaSe6-x (x=0, 0.01, 0.02, 0.03) samples at 300 K. (b) High resolution transmission electron microscopy (HRTEM) image for Ag9GaSe6. The fast Fourier transformation is carried out on the boxed region. (c) Inverse fast Fourier transformation image and (d) selected area electron diffraction (SAED) pattern for Ag9GaSe6.
value of 3.41 , which is close to the value obtained from the X-ray analysis (3.3546 , ⁄√ ). Similarly, the spacing of [220] and [-31-1] planes are indexed as 3.96 and 3.36 , respectively. These results are also close to the values (3.9336 and 3.3546 ) obtained from the X-ray analysis. Fig. 3 shows the measured TE properties for the prepared Ag9GaSe6 sample. The details can be found in supporting information. At 300-800 K, Ag9GaSe6 belongs to the α-phase. It possess negative Seebeck coefficient (S) throughout the entire measured temperature range, indicating that electrons are the dominate carriers. In fact, most of the Ag-based superionic TE compounds reported so far are n-type materials, which might be caused by the presence of interstitial Ag ions inside the 8,9,16,17 crystal structure. The electrical conductivity σ of 4 -1 Ag9GaSe6 is quite low with a value of about 0.5 × 10 S m at 300 K. This low σ is mainly contributed by the low carrier 18 -3 concentration, about 0.43× 10 cm at 300 K. Above 450 K, the σ increases with increasing temperature, proving that Ag9GaSe6 is a typical semiconductor. This is consistent with the diffuse reflectance spectrum shown in Fig. 1d, which suggests that the band gap of Ag9GaSe6 is 0.53 eV. The thermal conductivity κ of Ag9GaSe6 is very low, with a value of 0.26 W m-1 K-1 at 300 K and 0.45 W m-1 K-1 at 800 K. Thus, although the power factor (PF = S2σ) of Ag9GaSe6 is not high (see Fig. S1), the intrinsically low κ leads to a maximal ZT of 1.1 at 800 K. This ZT value is comparable with those of the state-of-the-art TE materials when they were firstly reported.
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still maintain the trigonal-planar arrangement (see Fig. 1b)
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Fig. 3 Temperature dependences of (a) Seebeck coefficient (S), (b) electrical conductivity (σ), (c) total thermal conductivity (κ), and (d) ZT values for Ag9GaSe6-x (x=0, 0.01, 0.02, 0.03).
The low carrier concentration and the narrow band gap in Ag9GaSe6 suggest that the electrical transport properties should have a large space to be improved. We thus try to introduce composition off-stoichiometry to optimize the material’s carrier concentrations. Here, a tiny amount of Sedeficiency is introduced into Ag9GaSe6, which is expected to provide more electrons to increase the carrier concentration. Fig. 2a shows the XRD patterns for these Se-deficiency Ag9GaSe6-x (x=0, 0.01, 0.02, 0.03) samples at 300 K, which also match well with the PDF card (#71-2448). As we expected, the carrier concentration increases with increasing the Sedeficiency content. When x = 0.03, the measured carrier concentration is 5.1× 1018 cm-3 at 300 K, about one order of magnitude higher than that of the stoichiometric Ag9GaSe6. Correspondingly, the σ is greatly increased to about 5.8× 104 S m-1 at 300 K for Ag9GaSe5.97 and its temperature-dependency converts into the heavily-doped semiconductor behavior. In contrast, the S of the Se-deficiency samples is decreased with the increase of the Se-deficiency content. These lead to the significantly enhanced PFs for the Se-deficiency samples, especially at low and medium temperatures, as shown in Fig. S1. Because of the intrinsically ultralow κ of Ag9GaSe6, introducing Se-deficiency only slightly increases κ by increasing the electronic thermal conductivity. Consequently, enhanced ZTs with a maximal value of 1.3 at 800 K are obtained for these Se-deficiency samples. Ag9GaSe6 has the superionic phase in a wide temperature range, even around room temperature. In contrast, almost all 18 12 the reported superionic TE materials, such as Cu2S, Cu2Se, 19 16 8,9 20 Cu2Se1-xSx, Ag2Se, Ag8SnSe6, and TmCuTe2, belong to normal solids around room temperature. Thus, Ag9GaSe6 αphase provides a good possibility to understand the “Phononliquid Electron-crystal” concept at room temperature. Generally, amorphous materials (such as glass or liquid) possess much lower carrier mobilities than the crystals. We calculated the Hall carrier mobility (µH) of Ag9GaSe6 α-phase based on the measured Hall coefficient and electrical conductivity. Surprisingly, as shown in Fig. 4a, the µH of
Fig. 4 Hall carrier concentration (n) dependences of (a) carrier mobility and (b) Seebeck coefficient for Ag9GaSe6-x at 300 K. The carrier mobilities of some typical TE materials 9 21 22 24 25 are also included for comparison, Ag8SnSe6, Bi2Te3, ZrNiSn, CoSb3, PbTe. The symbols are the measured data and the solid curves are calculated based on the single parabolic band (SPB) model with m* = 0.11m e dominated by acoustic phonon scattering. Temperature dependences of (c) lattice thermal conductivity (κL) and specific heat capacity for Ag9GaSe6. (d) Transverse sound velocities of some typical TE materials.12,18,26-31 2
-1
-1
Ag9GaSe6 α-phase is as high as 860 cm V s , which is much higher than most of the state-of-the-art TE materials, such as 2 -1 -1 2 -1 -1 173 cm V s for Bi2Te2.7Se0.321 and 28 cm V s for 22 Hf0.65Zr0.35NiSn. In the Se-deficiency samples, the µH values 2 -1 -1 are reduced, but the numbers are still above 670 cm V s . These high µH values strongly suggest that Ag9GaSe6 α-phase may possess “Electron-crystal” feature in spite of the presence of a large amount of “liquid-like” Ag ions inside the crystal structure of Ag9GaSe6. As shown in Fig. 4b, a theoretical Pisarenko plot (S vs. n) calculated by the single parabolic band 23 (SPB) model with an electronic effective mass m* of 0.11me can well interpret the experimental data. The small m*, which is much lower than those for most state-of-the-art TE 21 materials, such as 1.12 me for Bi2Te2.7Se0.3 and 2.9 me for 22 Hf0.65Zr0.35NiSn, can well explain the high µH values observed in Ag9GaSe6 α-phase. In addition, it also indicates of the very light band at the bottom of conduction band of Ag9GaSe6 αphase, which allows the high velocities for the electrons wherein. As a result of such high µH and low m*, the stoichiometric Ag9GaSe6 α-phase shows high ZTs above unit 17 even under very low carrier concentration (such as 4.3× 10 -3 cm ), which is about two or three orders of magnitude lower 19 20 -3 than the optimal carrier concentration (around 10 -10 cm ) 21-25 for the state-of-the-art TE materials. Fig. 4c shows the lattice thermal conductivity (κL) of Ag9GaSe6. During 300-800 K, the κL of Ag9GaSe6 is about 0.2-0.3 W m-1 K1 , which is not only much lower than most state-of-the-art TE materials,21-25 but also lower than the typical superionic TE materials such as Cu2S (0.35 W m-1 K-1)18 and Cu2Se (0.6 W m-1 K-1)12. In the entire temperature range, the κL almost shows a temperature-independent trend, which is also a common phenomenon observed in many superionic TE materials.9,12,18 Fig. 4c presents the heat capacity data of Ag9GaSe6. Generally, 3NkB is the limit Cv value in a solid while 2NkB is the limit Cv
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value in a liquid. At temperature above 450 K, CV for Ag9GaSe6 is between 2NkB and 3NkB, consistent with the liquid-like 12 18 feature observed in Cu2Se andCu2S . Clearly, the mobile “liquid-like” Ag atoms among different equilibrium positions in the crystal structure are responsible for such ultralow κ L and abnormal CV. Generally, sound velocity is another important parameter to understand the thermal transport in a solid. The measured longitudinal (νl), transverse (νt), and average (νa) sound -1 -1 velocities for Ag9GaSe6 α-phase are 2865 ms , 1130 ms , 1281 -1 m s , respectively. As shown in Fig. 4d, the νt of Ag9GaSe6 α26-31 phase is much lower than most TE materials, even for -1 12 -1 18 Cu2Se (2320 m s ) and Cu2S (1773 m s ) . This proves that the shear modes in Ag9GaSe6 α-phase are extraordinarily soft, which is consistent with the reduced CV values mentioned above. Based on these sound velocities, we also calculate the Grüneisen parameter (γ) for Ag9GaSe6 α-phase, which is usually used as a key parameter to evaluate the magnitude of lattice vibrational anharmonicity. The calculation details are shown in Supporting materials. As we expected, very high γ value, about 2.72, is obtained in Ag9GaSe6 α-phase, which is much higher than most of the state-of-the-art TE materials (γ = 26,32 1.0~2.5). This suggests the strong anharmonic lattice vibrations in Ag9GaSe6 α-phase. In addition, due to the large unit cell in Ag9GaSe6 α-phase, the optical modes wherein can push down the acoustic modes, which will also lead to the 33 expected low lattice thermal conductivity. In conclusion, a novel Argyrodite-type TE material Ag9GaSe6 with ultralow thermal conductivity has been successfully fabricated. A maximal ZT of 1.3 is obtained in this new TE material. Beyond Ag9GaSe6, we believe that other Argyroditetype compounds with the general chemical formula A9BX6 might also be promising thermoelectric materials. Thus, this study sheds light on the further investigation of the TE Argyrodite-type compounds. This work was supported by National Basic Research Program of China (973-program) under Project No. 2013CB632501, National Natural Science Foundation of China (NSFC) under the No. 51625205, Key Research Program of Chinese Academy of Sciences (Grant No. KGZD-EW-T06), and Shanghai Government (16XD1403900). P.Q. thanks for the support by the Youth Innovation Promotion Association of CAS under Grant No. 2016232.
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Conflicts of interest
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There are no conflicts to declare.
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Notes and references 1 2 3 4
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Argyrodite-type Ag9GaSe6 liquid-like material with ultralow thermal conductivity and high thermoelectric performance Received 00th January 20xx, Accepted 00th January 20xx
ab
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Binbin Jiang, Pengfei Qiu, Hongyi Chen, Qihao Zhang, Kunpeng Zhao, Dudi Ren, Xun Shi, ac and Lidong Chen
a*
DOI: 10.1039/x0xx00000x www.rsc.org/
We report a ternary Argyrodite-type Ag9GaSe6 compound as a promising thermoelectric material in moderate temperature range. Due to the high carrier mobility and ultralow lattice thermal conductivity, a maximal ZT of 1.1 was obtained in stoichiometric Ag9GaSe6 at 800 K. Via introducing slight Sedeficiency to optimize the carrier concentration, the maximal ZT is further enhanced to 1.3. Thermoelectric (TE) technology can directly convert thermal energy into electricity and vice versa.1-3 The energy conversion efficiency of a TE material is determined by the dimensionless TE figure of merit, ZT = S2σT/κ, where σ is the electrical conductivity, S is the Seebeck coefficient, κ is the total thermal conductivity, and T is the absolute temperature. The κ is composed by the lattice thermal conductivity (κL) and the electronic thermal conductivity (κe = LσT, where L is the Lorenz number). A high-performance TE material requires a high S, a large σ, and a low κ.1-3 However, it is very hard to simultaneously achieve these optimized parameters in one material because σ, S, and κ are strongly interrelated with each other. For example, a high σ usually corresponds to a low S and a high κe. One well-accepted strategy to discover new high-performance TE materials is to explore those materials with intrinsically low κL because κL correlates weakly with the other parameters (S, σ and κe) among these TE transport parameters.4 Along this direction, many new highperformance TE materials have been successfully reported in recent years, especially for the compounds with Argyroditetype structures.5-10 The Argyrodite-type compounds have a general formula Am+(12n+ 2m+ = Li+，Cu+，or Ag+, Bn+ = Ga3+，Si4+，Ge4+， n)/mB X 6 (A 4+ 5+ Sn ， P , or As5+, and X = S, Se, or Te).11 At room
temperature, they could crystallize in complex monoclinic, orthorhombic, hexagonal, or cubic structures, depending on the component elements wherein. Nevertheless, at high temperatures, they usually crystalize in high-symmetry cubic or hexagonal structures, where A-cations are mobile and disorderly distributed inside the rigid sublattice formed by the 11 B-cations and X-anions. Thus, these high-temperature superionic phases agree well with the “Phonon-liquid Electroncrystal” concept, which is proposed to explain the abnormal TE 12 properties in superionic TE materials. There are dozens of types of Argyrodite-type compounds. A few of them, with m = m+ n+ 27 or 8 and n = 4 or 5 in A (12-n)/mB X 6, such as Ag8GeTe6,5 6 7 8,9 10 Ag8SiTe6, Cu7PSe6, Ag8SnSe6, and Cu8GeSe6, have been reported with intrinsically ultralow κL values around 0.15-0.35 -1 -1 W m K and high TE performance. In this communication, we report a new promising Argyrodite-type compound, Ag9GaSe6, with m = 9 and n = 3, which also exhibits an intrinsically low κL (around 0.2 W m-1 K-1) and a high ZT of 1.3 at 800 K. The crystal structure of Ag9GaSe6 has been firstly reported by Deloume in 1978.13 Ag9GaSe6 has one temperature-dependent phase transition at around 281 K.14 As shown in Fig. 1a, the low-temperature Ag9GaSe6 β-phase has a cubic structure (space group P213) with a = 1.1126 nm and Z = 4.13 In this large unit cell, the [GaSe4]5- tetrahedral (see Fig. 1b) with C3 symmetry and Se2- anions construct the anion framework. The electropositive Ag atoms are orderly located at three 12b sites inside the anion framework, with each of them bonding with three nearby Se atoms in an almost trigonal-planar arrangement (see Fig. 1b). Above 281 K, the low-temperature Ag9GaSe6 β-phase converts to the high-temperature Ag9GaSe6 α-phase (see Fig. 1c),14 which has a higher symmetry structure (space group F-43m) but the same cell parameters (a = 1.1126 nm and Z = 4) with the β-phase. Similarly, the anion framework of Ag9GaSe6 α-phase is still composed by the [GaSe4]5tetrahedral and Se2- anions. However, the Ag atoms disorderedly arranged in the anion framework at three different sites: 48h (0.232, 0.232, 0.029), 48h (-0.169, -0.169, 0.031), and 96i (-0.160, 0.073, 0.129), with the occupancies of 0.25, 0.25, and 0.125, respectively.14 The Ag atoms at 48h sites
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Fig. 1 (a) Low-temperature crystal structure of Ag9GaSe6 β-phase. (b) Two prominent structural features: [GaSe4]5- tetrahedral and trigonal-planar Ag atoms. (c) Hightemperature crystal structure of Ag9GaSe6 α-phase. The atomic site occupancy is indicated by partial coloring of the atoms. (d) (1-R)2/2R as a function of photon energy hν. The extrapolation of the spectra (black line) is used to estimate optical band gap value for Ag9GaSe6 powder using the Kubelka-Munk method.15
bonded with three nearby Se atoms, but the Ag atoms at 96i sites are located in the tetrahedrons formed by four nearby Se atoms. Being similar with the cations in other Argyrodite-type compounds, the Ag ions can consecutive jump from one equilibrium position to another within very short time displaying liquid-like behavior. Thus, Ag9GaSe6 is also a liquidlike material. The large unit cell, complicate atomic occupation, liquid-like Ag ions definitely lead to the intrinsically low κL in Ag9GaSe6. More importantly, as shown in Fig. 1d, Ag9GaSe6 is a narrow gap semiconductor with the band gap (Eg) about 0.53 eV, which is benefit for achieving high electrical transports. Thus, Ag9GaSe6 is expected to have good ZTs. The detailed synthesis process of Ag9GaSe6 is shown in supporting information. The phase purity and crystal structure were examined by the powder X-ray diffraction (PXRD) with Cu Kα radiation at 300 K. As shown in Fig. 2a, the XRD pattern of the synthesized Ag9GaSe6 sample can be well indexed to the high-temperature α-phase with F-43m structure (PDF #712448).14 No impurity phases are detected. Fig. 2b and Fig. 2c show the high resolution transmission electron microscope (HRTEM) image and inverse fast Fourier transformation image for Ag9GaSe6. Clearly, the sample has high degrees of crystallinity. No obvious lattice distortions, dislocations, or amorphous phases are observed. The selected area electron diffraction (SAED) pattern shown in Fig. 2d further confirms that the prepared Ag9GaSe6 crystalizes in face-centered cubic structure, which is consistent with the result of XRD characterization. Based on the fast Fourier transformation (FFT) image shown in the inset picture of Fig. 2b, the spacing of
[-13-1] plane (d[-13-1]) in Ag9GaSe6 α-phase is calculated with a
Fig. 2 (a) XRD patterns for Ag9GaSe6-x (x=0, 0.01, 0.02, 0.03) samples at 300 K. (b) High resolution transmission electron microscopy (HRTEM) image for Ag9GaSe6. The fast Fourier transformation is carried out on the boxed region. (c) Inverse fast Fourier transformation image and (d) selected area electron diffraction (SAED) pattern for Ag9GaSe6.
value of 3.41 , which is close to the value obtained from the X-ray analysis (3.3546 , ⁄√ ). Similarly, the spacing of [220] and [-31-1] planes are indexed as 3.96 and 3.36 , respectively. These results are also close to the values (3.9336 and 3.3546 ) obtained from the X-ray analysis. Fig. 3 shows the measured TE properties for the prepared Ag9GaSe6 sample. The details can be found in supporting information. At 300-800 K, Ag9GaSe6 belongs to the α-phase. It possess negative Seebeck coefficient (S) throughout the entire measured temperature range, indicating that electrons are the dominate carriers. In fact, most of the Ag-based superionic TE compounds reported so far are n-type materials, which might be caused by the presence of interstitial Ag ions inside the 8,9,16,17 crystal structure. The electrical conductivity σ of 4 -1 Ag9GaSe6 is quite low with a value of about 0.5 × 10 S m at 300 K. This low σ is mainly contributed by the low carrier 18 -3 concentration, about 0.43× 10 cm at 300 K. Above 450 K, the σ increases with increasing temperature, proving that Ag9GaSe6 is a typical semiconductor. This is consistent with the diffuse reflectance spectrum shown in Fig. 1d, which suggests that the band gap of Ag9GaSe6 is 0.53 eV. The thermal conductivity κ of Ag9GaSe6 is very low, with a value of 0.26 W m-1 K-1 at 300 K and 0.45 W m-1 K-1 at 800 K. Thus, although the power factor (PF = S2σ) of Ag9GaSe6 is not high (see Fig. S1), the intrinsically low κ leads to a maximal ZT of 1.1 at 800 K. This ZT value is comparable with those of the state-of-the-art TE materials when they were firstly reported.
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still maintain the trigonal-planar arrangement (see Fig. 1b)
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Fig. 3 Temperature dependences of (a) Seebeck coefficient (S), (b) electrical conductivity (σ), (c) total thermal conductivity (κ), and (d) ZT values for Ag9GaSe6-x (x=0, 0.01, 0.02, 0.03).
The low carrier concentration and the narrow band gap in Ag9GaSe6 suggest that the electrical transport properties should have a large space to be improved. We thus try to introduce composition off-stoichiometry to optimize the material’s carrier concentrations. Here, a tiny amount of Sedeficiency is introduced into Ag9GaSe6, which is expected to provide more electrons to increase the carrier concentration. Fig. 2a shows the XRD patterns for these Se-deficiency Ag9GaSe6-x (x=0, 0.01, 0.02, 0.03) samples at 300 K, which also match well with the PDF card (#71-2448). As we expected, the carrier concentration increases with increasing the Sedeficiency content. When x = 0.03, the measured carrier concentration is 5.1× 1018 cm-3 at 300 K, about one order of magnitude higher than that of the stoichiometric Ag9GaSe6. Correspondingly, the σ is greatly increased to about 5.8× 104 S m-1 at 300 K for Ag9GaSe5.97 and its temperature-dependency converts into the heavily-doped semiconductor behavior. In contrast, the S of the Se-deficiency samples is decreased with the increase of the Se-deficiency content. These lead to the significantly enhanced PFs for the Se-deficiency samples, especially at low and medium temperatures, as shown in Fig. S1. Because of the intrinsically ultralow κ of Ag9GaSe6, introducing Se-deficiency only slightly increases κ by increasing the electronic thermal conductivity. Consequently, enhanced ZTs with a maximal value of 1.3 at 800 K are obtained for these Se-deficiency samples. Ag9GaSe6 has the superionic phase in a wide temperature range, even around room temperature. In contrast, almost all 18 12 the reported superionic TE materials, such as Cu2S, Cu2Se, 19 16 8,9 20 Cu2Se1-xSx, Ag2Se, Ag8SnSe6, and TmCuTe2, belong to normal solids around room temperature. Thus, Ag9GaSe6 αphase provides a good possibility to understand the “Phononliquid Electron-crystal” concept at room temperature. Generally, amorphous materials (such as glass or liquid) possess much lower carrier mobilities than the crystals. We calculated the Hall carrier mobility (µH) of Ag9GaSe6 α-phase based on the measured Hall coefficient and electrical conductivity. Surprisingly, as shown in Fig. 4a, the µH of
Fig. 4 Hall carrier concentration (n) dependences of (a) carrier mobility and (b) Seebeck coefficient for Ag9GaSe6-x at 300 K. The carrier mobilities of some typical TE materials 9 21 22 24 25 are also included for comparison, Ag8SnSe6, Bi2Te3, ZrNiSn, CoSb3, PbTe. The symbols are the measured data and the solid curves are calculated based on the single parabolic band (SPB) model with m* = 0.11m e dominated by acoustic phonon scattering. Temperature dependences of (c) lattice thermal conductivity (κL) and specific heat capacity for Ag9GaSe6. (d) Transverse sound velocities of some typical TE materials.12,18,26-31 2
-1
-1
Ag9GaSe6 α-phase is as high as 860 cm V s , which is much higher than most of the state-of-the-art TE materials, such as 2 -1 -1 2 -1 -1 173 cm V s for Bi2Te2.7Se0.321 and 28 cm V s for 22 Hf0.65Zr0.35NiSn. In the Se-deficiency samples, the µH values 2 -1 -1 are reduced, but the numbers are still above 670 cm V s . These high µH values strongly suggest that Ag9GaSe6 α-phase may possess “Electron-crystal” feature in spite of the presence of a large amount of “liquid-like” Ag ions inside the crystal structure of Ag9GaSe6. As shown in Fig. 4b, a theoretical Pisarenko plot (S vs. n) calculated by the single parabolic band 23 (SPB) model with an electronic effective mass m* of 0.11me can well interpret the experimental data. The small m*, which is much lower than those for most state-of-the-art TE 21 materials, such as 1.12 me for Bi2Te2.7Se0.3 and 2.9 me for 22 Hf0.65Zr0.35NiSn, can well explain the high µH values observed in Ag9GaSe6 α-phase. In addition, it also indicates of the very light band at the bottom of conduction band of Ag9GaSe6 αphase, which allows the high velocities for the electrons wherein. As a result of such high µH and low m*, the stoichiometric Ag9GaSe6 α-phase shows high ZTs above unit 17 even under very low carrier concentration (such as 4.3× 10 -3 cm ), which is about two or three orders of magnitude lower 19 20 -3 than the optimal carrier concentration (around 10 -10 cm ) 21-25 for the state-of-the-art TE materials. Fig. 4c shows the lattice thermal conductivity (κL) of Ag9GaSe6. During 300-800 K, the κL of Ag9GaSe6 is about 0.2-0.3 W m-1 K1 , which is not only much lower than most state-of-the-art TE materials,21-25 but also lower than the typical superionic TE materials such as Cu2S (0.35 W m-1 K-1)18 and Cu2Se (0.6 W m-1 K-1)12. In the entire temperature range, the κL almost shows a temperature-independent trend, which is also a common phenomenon observed in many superionic TE materials.9,12,18 Fig. 4c presents the heat capacity data of Ag9GaSe6. Generally, 3NkB is the limit Cv value in a solid while 2NkB is the limit Cv
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value in a liquid. At temperature above 450 K, CV for Ag9GaSe6 is between 2NkB and 3NkB, consistent with the liquid-like 12 18 feature observed in Cu2Se andCu2S . Clearly, the mobile “liquid-like” Ag atoms among different equilibrium positions in the crystal structure are responsible for such ultralow κ L and abnormal CV. Generally, sound velocity is another important parameter to understand the thermal transport in a solid. The measured longitudinal (νl), transverse (νt), and average (νa) sound -1 -1 velocities for Ag9GaSe6 α-phase are 2865 ms , 1130 ms , 1281 -1 m s , respectively. As shown in Fig. 4d, the νt of Ag9GaSe6 α26-31 phase is much lower than most TE materials, even for -1 12 -1 18 Cu2Se (2320 m s ) and Cu2S (1773 m s ) . This proves that the shear modes in Ag9GaSe6 α-phase are extraordinarily soft, which is consistent with the reduced CV values mentioned above. Based on these sound velocities, we also calculate the Grüneisen parameter (γ) for Ag9GaSe6 α-phase, which is usually used as a key parameter to evaluate the magnitude of lattice vibrational anharmonicity. The calculation details are shown in Supporting materials. As we expected, very high γ value, about 2.72, is obtained in Ag9GaSe6 α-phase, which is much higher than most of the state-of-the-art TE materials (γ = 26,32 1.0~2.5). This suggests the strong anharmonic lattice vibrations in Ag9GaSe6 α-phase. In addition, due to the large unit cell in Ag9GaSe6 α-phase, the optical modes wherein can push down the acoustic modes, which will also lead to the 33 expected low lattice thermal conductivity. In conclusion, a novel Argyrodite-type TE material Ag9GaSe6 with ultralow thermal conductivity has been successfully fabricated. A maximal ZT of 1.3 is obtained in this new TE material. Beyond Ag9GaSe6, we believe that other Argyroditetype compounds with the general chemical formula A9BX6 might also be promising thermoelectric materials. Thus, this study sheds light on the further investigation of the TE Argyrodite-type compounds. This work was supported by National Basic Research Program of China (973-program) under Project No. 2013CB632501, National Natural Science Foundation of China (NSFC) under the No. 51625205, Key Research Program of Chinese Academy of Sciences (Grant No. KGZD-EW-T06), and Shanghai Government (16XD1403900). P.Q. thanks for the support by the Youth Innovation Promotion Association of CAS under Grant No. 2016232.
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Conflicts of interest
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There are no conflicts to declare.
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Notes and references 1 2 3 4
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