Intrinsically High Thermoelectric Performance in AgInSe₂ n‐Type Diamond‐Like Compounds

Abstract

Diamond‐like compounds are a promising class of thermoelectric materials, very suitable for real applications. However, almost all high‐performance diamond‐like thermoelectric materials are p‐type semiconductors. The lack of high‐performance n‐type diamond‐like thermoelectric materials greatly restricts the fabrication of diamond‐like material‐based modules and their real applications. In this work, it is revealed that n‐type AgInSe₂ diamond‐like compound has intrinsically high thermoelectric performance with a figure of merit (zT ) of 1.1 at 900 K, comparable to the best p‐type diamond‐like thermoelectric materials reported before. Such high zT is mainly due to the ultralow lattice thermal conductivity, which is fundamentally limited by the low‐frequency Ag‐Se “cluster vibrations,” as confirmed by ab initio lattice dynamic calculations. Doping Cd at Ag sites significantly improves the thermoelectric performance in the low and medium temperature ranges. By using such high‐performance n‐type AgInSe₂‐based compounds, the diamond‐like thermoelectric module has been fabricated for the first time. An output power of 0.06 W under a temperature difference of 520 K between the two ends of the module is obtained. This work opens a new window for the applications using the diamond‐like thermoelectric materials.

1 Introduction

Nowadays, advanced technologies based on high‐performance energy materials have triggered a worldwide attention in response to the world's increasing energy crisis and deteriorating environment. One of the promising technologies is the thermoelectric (TE) energy conversion with its ability of directly converting thermal energy into electricity.1, 2 Efficient TE conversion requires high performing n‐ as well as p‐type elements (legs) that are assembled electrically in series and thermally in parallel in a module. To ensure long‐term service reliability and stability,3 the n‐ and p‐type TE legs should have closely matching physical and chemical properties, such as the chemical composition, melting points, and thermal expansion coefficients. The energy conversion efficiency of a TE material is specified by the dimensionless TE figure of merit zT = S ²σT /(κ_L+κ_e). The expression can be viewed as consisting of two distinct contributions: the dominator reflecting the electronic efficiency of a material as expressed via the power factor S ²σ, where S is the Seebeck coefficient and σ is the electrical conductivity, and the denominator representing the heat conduction ability and consisting of the lattice thermal conductivity κ_L and the electronic thermal conductivity κ_e. In order to achieve high TE performance, it is essential to enhance the electronic properties (S ²σ) and minimize the total thermal conductivity (κ = κ_L +κ_e). However, the transport parameters are closely correlated and interdependent. For example, S generally decreases with the increasing carrier concentration, that is, with the increasing electrical conductivity. Moreover, since the electronic thermal conductivity is related to the electrical conductivity via the Wiedemann–Franz law, κ_e = LσT , it increases with the increasing electrical conductivity. Therefore, it is challenging to simultaneously achieve excellent electronic properties and low thermal conductivity in a given material.

While several families of classical TE materials have been developed and improved, among them SiGe,4 Bi₂Te₃,5 PbTe,6 and skutterudites,7 they either contain expensive elements or are environmentally harmful. Consequently, there is a worldwide effort to identify and develop new high‐performing TE materials. Recently, many new prospective TE materials have been discovered, and Cu‐based compounds8 have generated much interest. Among them, diamond‐like compounds possessing a relatively low thermal conductivity and decent electronic transport properties are especially interesting.9-30 There are about 1000 types of diamond‐like compounds and several of them exhibit very good TE performances. Examples include Cu₂ZnSn_0.90In_0.10Se₄ with a zT of 0.95 at 850 K,9 Cu₂Sn_0.90In_0.10Se₃ with a zT of 1.14 at 850 K,10 Ag_0.95GaTe₂ with a zT of 0.77 at 850 K,11 Cu₃Sb_0.97Ge_0.03Se_2.8S_1.2 with a zT of 0.89 at 650 K,12 CuGaTe₂ with a zT of 1.4 at 950 K,13-17 Cu_2.075Zn_0.925GeSe₄ with a zT of 0.45 at 670 K,18 CuInTe₂ with a zT of 1.18 at 850 K,19, 20 Cu₂TM (TM = Mn, Fe, Co)SnSe₄ with a zT of 0.7 at 850 K,21 and many others.22-25 These exciting results make the diamond‐like compounds a new and prospective class of TE materials. However, all the above diamond‐like compounds are p‐type materials. To date, only two examples of n‐type diamond‐like compounds have been reported on and both of them show a rather poor performance: AgInSe₂ with a zT of 0.34 at 724 K26, 27 and Cu_0.92Zn_0.08FeS₂ with a zT of 0.26 at 630 K28-30 (as shown in Figure 1a). Therefore, the lack of high‐performance n‐type diamond‐like TE materials has, so far, impeded the construction of efficient TE modules based on these compounds.

Figure 1

a) Thermoelectric figure of merit zT for some typical diamond‐like materials. The yellow columns are for p‐type while the purple and red columns are for n‐type diamond‐like compounds. The data are taken from refs. 9-30. b) Images of fabricated two‐pair TE module by using high‐performance Ag_0.9Cd_0.1InSe₂ diamond‐like compound as the n‐type leg and Cu_0.99In_0.6Ga_0.4Te₂16 diamond‐like compound as the p‐type leg.

In this work, we report on n‐type AgInSe₂ that has an intrinsically low lattice thermal conductivity and its maximal zT reaches a value of 1.1 at 900 K. Such high zT is mainly due to the ultralow lattice thermal conductivity caused by the Ag‐Se “cluster vibrations” at low phonon frequencies. Furthermore, the average zT value of AgInSe₂ is optimized via substituting Cd at Ag sites to improve the TE performance in the low and medium temperature ranges. In addition, a two‐couple TE module based on these diamond‐like compounds has been fabricated for the first time (as shown in Figure 1b), and has achieved the maximum output power of 0.06 W under a temperature difference of 520 K.

2 Results and Discussion

AgInSe₂ is a semiconductor with the band gap of ≈1.19 eV,31 which has been extensively investigated for solar energy applications, optoelectronic applications, as well as photoelectrochemical applications.32, 33 It possesses a typical tetragonal chalcopyrite structure with the space group I‐42d , which is derived from the sphalerite structure with Ag/In orderly replacing Zn.31 The powder X‐ray diffraction (XRD) patterns of AgInSe₂ are shown in Figure S1 (Supporting Information). The XRD data match well with the PDF card (#No. 35‐1099) for AgInSe₂ compounds. The scanning electron microscopy (SEM) results for AgInSe₂ are shown in Figure S2 (Supporting Information) and demonstrate that a small amount of Ag₂Se second phase (<3%) exists in the prepared sample. The TE properties of AgInSe₂ are shown in Figure 2. The electrical conductivity σ of AgInSe₂ is very low with the values on the order of 10⁻¹ S m⁻¹ around room temperature and 10³ S m⁻¹ at 900 K. Correspondingly, the Seebeck coefficient S is quite large with a value of −820 µV K⁻¹ around room temperature and −295 µV K⁻¹ at 900 K. These data indicate that AgInSe₂ is a typical semiconductor with a very low carrier concentration. This is consistent with our Hall effect measurements, which shows that the carrier concentration of AgInSe₂ is about 1.3 × 10¹³ cm⁻³ at 300 K. Consequently, the power factor (PF = S ²σ) of AgInSe₂ is also very low with a maximum value module 2.92 µW cm⁻¹ K⁻² at 900 K (see Figure S5, Supporting Information). The thermal conductivity for the pristine AgInSe₂ prepared in our work is as low as 0.99 W m⁻¹ K⁻¹ at room temperature and decreases to 0.39 W m⁻¹ K⁻¹ at 900 K, which is close to the theoretical minimum lattice thermal conductivity κ_min calculated by the Cahill's model (Equation (S1), Supporting Information).34 All these lead to a zT of 0.7 at 900 K in AgInSe₂ although its electrical conductivity is low (as shown in Figure 2d).

Figure 2

Temperature dependences of a) electrical conductivity σ, b) Seebeck coefficient S , c) thermal conductivity κ, and d) zT for polycrystalline Ag_1+x InSe₂ (x = 0, 0.01, 0.02) and Ag_1−x Cd_x InSe₂ (x = 0.08, 0.1) compounds. The inset shown in (d) is the average zTs for AgInSe₂, Ag_1.02InSe₂, and Ag_0.9Cd_0.1InSe₂ in the temperature range 300–900 K.

The low carrier concentration in AgInSe₂ suggests that the low zT shown above as well as that reported in the literature26, 27 should have a large room for improvement. In order to change the material's carrier concentration, we thus tried to introduce off‐stoichiometry in the composition. Specifically, we added an excess amount of Ag to AgInSe₂ to generate interstitial Ag atoms, expecting to increase the density of electrons. The powder XRD patterns for Ag_1+x InSe₂ (x = 0, 0.01, 0.02) are shown in Figure S1 (Supporting Information), and they match well with the PDF card (No. 35‐1099) for the AgInSe₂ compound. The SEM results for Ag_1.02InSe₂ are shown in Figure S3 (Supporting Information) and they too indicate the presence of a small amount of a second phase (Ag₂Se) in the compound. The TE properties of Ag_1+x InSe₂ are shown in Figure 2. As we expected, the electrical conductivity σ of Ag_1+x InSe₂ compounds with excess of Ag has increased to ≈10 S m⁻¹ at room temperature, about 1–2 orders of magnitude in comparison to the stoichiometric AgInSe₂ compound. At 900 K, σ has also significantly increased. The enhancement in σ is mainly derived from the drastically increased carrier concentrations by the excess amount of Ag. The measured carrier concentration at 300 K is 2.5 × 10¹⁵ cm⁻³ for Ag_1.01InSe₂ and 1.6 × 10¹⁶ cm⁻³ for Ag_1.02InSe₂, about 2–3 orders of magnitude enhancement as compared with the stoichiometric AgInSe₂ compound. The room‐temperature Hall mobility μ_H of Ag_1+x InSe₂ is in the range of 26–68 cm² V⁻¹ s⁻¹. In contrast, the Seebeck coefficient S for the Ag‐excess Ag_1+x InSe₂ compounds has decreased with the increasing content of Ag throughout the whole temperature range investigated. Around room temperature, the S for Ag_1.02InSe₂ has greatly decreased to −355 µV K⁻¹. In spite of this decrease, as shown in Figure S5 (Supporting Information), the power factor has significantly increased in the entire temperature range. Compared to the stoichiometric AgInSe₂ around room temperature, the PF for Ag‐excess AgInSe₂ has increased by about 50 times. Moreover, the maximum PF value of 5 µW cm⁻¹ K⁻² have been reached in Ag_1.02InSe₂ at 900 K, an enhancement of about 72% over the value of the stoichiometric AgInSe₂ compound.

The thermal conductivity κ, on the other hand, is almost unchanged upon introducing an excess amount of Ag in AgInSe₂, as shown in Figure 2c. The thermal conductivity has a low value of 1.1 W m⁻¹ K⁻¹ at 300 K and decreases to 0.4 W m⁻¹ K⁻¹ at 900 K. Combining the significantly improved electronic transport properties with the essentially unchanged and low thermal conductivity, a high zT of 1.1 is achieved for Ag_1.02InSe₂ at 900 K, an increase of about 62% compared to the stoichiometric AgInSe₂ compound. The value of zT stands as the best n‐type diamond‐like TE material reported so far, and is comparable to the best p‐type diamond‐like TE materials shown in Figure 1a. Having both n‐ and p‐type high‐performance diamond‐like materials available bodes well for fabrication of high‐efficiency TE modules.

Perhaps the most striking feature of AgInSe₂ is its ultralow lattice thermal conductivity κ_L. The temperature dependence of κ_L for AgInSe₂ and other typical diamond‐like compounds is shown in Figure 3. The κ_L of the stoichiometric AgInSe₂ compound is about 0.99 W m⁻¹ K⁻¹ at 300 K, which is much lower than all other Cu‐based diamond‐like compounds, including Cu₂ZnSnSe₄ (3.3 W m⁻¹ K⁻¹ at 300 K),9 CuGaTe₂ (7.4 W m⁻¹ K⁻¹ at 300 K),16 CuInTe₂ (5.4 W m⁻¹ K⁻¹ at 300 K),19 CuFeS₂ (5.7 W m⁻¹ K⁻¹ at 300 K),29 and CuInSe₂ (4.6 W m⁻¹ K⁻¹ at 300 K).35 In particular, as shown in Figure 3, even though the Ag(Ga,In)Te₂‐based diamond‐like compounds contain a heavy Te element, their lattice thermal conductivity at 300 K is almost twice the value of AgInSe₂ that has a lighter Se element.11, 36

Figure 3

Temperature dependence of the lattice thermal conductivity κ_L for AgInSe₂‐based compounds and other diamond‐like compounds taken from ref. 9, 11, 16, 19, 29, 35, and 36.

In order to rationalize this abnormal situation, we performed ab initio lattice dynamics calculations for AgInSe₂ (see Figure 4a). For comparison, the results for CuInSe₂ and AgInTe₂ are also included in Figure 4a. The line thickness in Figure 4a denotes the contributions from Ag or Cu atoms. For crystalline compounds, the low sound velocity, large lattice anharmonicity, and low frequency optic phonons definitely lead to a low lattice thermal conductivity.37 Given a phonon spectrum, the sound velocity can be easily obtained by calculating the zone center derivative of acoustic phonon dispersions. The sound velocities for AgInSe₂, CuInSe₂, and AgInTe₂, including longitudinal (v _l), transverse (v _t), and average (v _avg.) sound velocities (calculated by Equation (S2), Supporting Information), as well as the Grüneisen parameters (γ) of these three compounds, are listed in Table 1. The experimental sound velocities for AgInSe₂, CuInSe₂,38 and AgInTe₂ are also included for comparison. As we expected, CuInSe₂ possesses the largest sound velocities among the three compounds due to its lightest average atomic mass. The values, however, are lower than those for the CoSb₃‐based skutterudites (v _l = 4590 m s⁻¹, v _t = 2643 m s⁻¹).39 Between the two Ag‐based diamond‐like compounds, our calculation suggests that AgInSe₂ has a slightly faster v _t and v _l than AgInTe₂, which is confirmed by our experimental data shown in Table 1. However, such a small difference between sound velocities in AgInSe₂ and AgInTe₂ obviously cannot account for the much lower κ_L in AgInSe₂ as compared with that in AgInTe₂. In addition, the Grüneisen parameters obtained either from ab initio lattice dynamics calculations or from measured sound velocities for AgInSe₂ and AgInTe₂ are close to each other, and therefore cannot explain the large difference in κ_L between the two compounds.

Figure 4

a) Calculated phonon spectra of AgInSe₂, CuInSe₂, and AgInTe₂. The line thickness denotes contributions from Ag or Cu atoms. b) Energy difference ΔE as a function of the phonon amplitude for the first optic mode caused by Ag‐Se (or Cu‐Se, or Ag‐Te) clusters. The curves are fitted by a second‐order polynomial ΔE = kx 2, and the force constants k for these three investigated compounds are labeled.

Table 1. Sound velocities and Grüneisen parameters (γ) for AgInSe₂, CuInSe₂, and AgInTe₂ diamond‐like compounds obtained from ab initio lattice dynamics calculations and experimental measurements. Equations (S3) and (S4) (Supporting Information) are used to calculate γ from the measured sound velocities

	AgInSe2		CuInSe2		AgInTe2
	Cal.	Expt.	Cal.	Expt.38	Cal.	Expt.
v t [m s^−1]	1867	1515	2131	2100	1726	1516
v l [m s^−1]	3430	3296	4060	3770	3239	3159
v avg. [m s^−1]	2082	1707	2383	2338	1928	1704
γ	1.78	2.27	1.83	1.63	1.71	2.13

The most distinct feature of AgInSe₂ regarding its lattice dynamics is the low‐frequency optic phonons, which cover the frequency range from 3.0 to 7.4 meV (see Figure 4a). These low‐frequency optic phonons can introduce additional phonon scattering channels and scattering rates, or phenomenologically, the resonant scattering that impedes the normal transport of acoustic phonons with similar frequencies, leading to an extremely low heat conduction.37 Similar phenomena have also been observed in many other compounds with low lattice thermal conductivity, such as filled skutterudites, Cu₂Se, and α‐MgAgSb.7, 40, 41 As shown in Figure 4a, the low‐lying optic phonons are also observed in the phonon dispersions of AgInTe₂. However, the lowest‐lying optic phonons appear already at 3 meV in AgInSe₂ but at a higher frequency of 4 meV in AgInTe₂. Furthermore, the range of low‐lying optical phonons in AgInSe₂ is wider covering 3.0–7.4 meV than that in AgInTe₂ where it covers the range of 4.0–6.3 meV. These features suggest that the low‐lying optic phonons in AgInSe₂ not only scatter the acoustic phonons of lower frequencies but also scatter the acoustic phonons over a wider range of frequencies. Therefore, the wider scattering channels with lower frequencies are the main reason for the lower κ_L observed in AgInSe₂ than in AgInTe₂.

In order to further understand the origin of the low‐frequency optic phonons in AgInSe₂, the phonon animation analysis was performed (see such animation in the Supporting Information). Interestingly, we observed collaborative motions of Ag‐Se clusters (red and yellow balls), while In atoms (green balls) stand still. This strongly suggests that the interaction between Ag and Se is quite strong, while the interaction between the Ag‐Se cluster and In is quite weak in AgInSe₂. Generally, the interactions between the neighboring atoms can be semi‐quantitatively evaluated by the force constant (k ) derived from the calculated potential energy variation (ΔE ) as a function of the phonon amplitude (x ).42 A smaller k usually indicates a weaker interaction and thus a larger space for the motion. Figure 4b shows the calculated potential energy variation (ΔE ) as a function of the phonon amplitude (x ) for the first optic mode in AgInSe₂, which is mainly contributed by the Ag‐Se clusters. The ΔE versus x curve can be well fitted by the second‐order polynomial with ΔE = kx 2 and k = 0.191. Likewise, Figure 4b also shows the ΔE versus x curves and the corresponding k values for AgInTe₂ and CuInSe₂. Clearly, AgInSe₂ has the lowest k value among these three compounds, proving that the Ag‐Se clusters have the weakest interactions with the neighboring In atoms. Such well‐bonded Ag and Se atoms and weakly connected In atoms in AgInSe₂ lead to special Ag‐Se cluster motions with large mass and thus low‐frequency optic phonons. Similar phenomenon has also been found in S‐ and Se‐filled CoSb₃ skutterudites, where the strong S(Se)Sb bonds cause “cluster vibrations” with low frequencies.43 Furthermore, since the low‐frequency optic phonons relate to the vibrations of Ag‐Se clusters, it is expected that thus‐caused low κ_L can also be found in other diamond‐like compounds containing Ag and Se. For example, the room‐temperature κ_L of single‐crystalline AgGaSe₂ is 1.2 W m⁻¹ K⁻¹,44 much lower than that of AgGaTe₂ shown in Figure 3a, indicating the generality of the findings in this work.

In addition, low thermal conductivity also relies on strong phonon scattering by grain boundaries, impurities, and various kinds of defects. Figure 5a shows a low‐magnification transmission electron microscopy (TEM) image for stoichiometric AgInSe₂, in which electron diffraction indicates the tetragonal structure. Figure 5b,c are high‐resolution transmission electron microscopy (HRTEM) images for the red ellipse area marked as I and II in Figure 5a, respectively. Several dislocations or imperfections are notable in area I, which are clearly confirmed through the inversed fast Fourier transform (IFFT) image inserted in Figure 5b. Besides, as shown in Figure 5d, the IFFT image for the square area in Figure 5c depicts obvious stacking faults. All the aforementioned dislocations, imperfections, and stacking faults enhance phonon scattering,6 which also contributes to the intrinsically ultralow κ_L observed in Figure 5a.

Figure 5

a) Low‐magnification TEM image for stoichiometric AgInSe₂. The inset is the electron diffraction pattern. b) HRTEM image for area I shown in (a). The inset is the inverse fast Fourier transform (IFFT) image for the square area. c) HRTEM image for area II shown in (a). d) IFFT image for the square area shown in (c).

The high TE performance in AgInSe₂ makes it a good candidate to fabricate n‐type legs of TE devices. However, the electron concentration is still too low for an efficient energy conversion in the low and medium temperature ranges. Since it is difficult to enhance the carrier concentration further by introducing more Ag ions (such extra Ag ions would form impurities with no ability to enhance the electron concentration), we have attempted to enhance the concentration of electrons and increase the electrical conductivity at low and medium temperatures by substituting Cd at the Ag sites.

Powder XRD patterns for the Ag_1−x Cd_x InSe₂ (x = 0.08, 0.1) compounds are shown in Figure S1 (Supporting Information). XRD patterns match well with the PDF card (No. 35‐1099) for the AgInSe₂ compound. There is also a trace of a secondary Ag₂Se phase detected in SEM‐EDS of the Ag_0.9Cd_0.1InSe₂ compound (see Figure S4, Supporting Information). The temperature dependence of the electrical conductivity σ, the Seebeck coefficient S , the thermal conductivity κ, and the figure of merit zT for Ag_1−x Cd_x InSe₂ (x = 0.08, 0.1) compounds is shown in Figure 2. The electrical conductivity σ around 300 K has increased by 3–4 orders of magnitude through doping Cd at the Ag sites. Even at high temperatures, the σ values for Cd‐doped compounds are still larger by an order of magnitude than for the stoichiometric AgInSe₂ compound. Correspondingly, the Seebeck coefficient S at 300 K is decreased to a value of −387 and −253 µV K⁻¹ in Ag_0.92Cd_0.08InSe₂ and Ag_0.9Cd_0.1InSe₂, respectively. Finally, the PFs for the Cd‐doped AgInSe₂ compounds are further increased as compared with the Ag‐excess AgInSe₂ compounds (see Figure S5, Supporting Information). All these features are clearly a result of the much increased electron concentration. In Ag_0.9Cd_0.1InSe₂, the n is increased to 2.2 × 10¹⁸ cm⁻³ at room temperature, about five orders of magnitude higher than the value of ≈10¹³ cm⁻³ for AgInSe₂ and two orders of magnitude higher than the value of ≈10¹⁶ cm⁻³ for Ag‐excess AgInSe₂. In addition, the thermal conductivity of Cd‐doped AgInSe₂ is also reduced at low and medium temperatures due to the extra point defect phonon scattering by Cd dopants. Especially, the thermal conductivity for Ag_0.9Cd_0.1InSe₂ has been reduced to 0.69 W m⁻¹ K⁻¹ at 300 K, a decrease of 46% compared to the stoichiometric AgInSe₂ compound. As a result, the zT is more optimized through the whole temperature range. The average zT between 300 and 900 K has increased to 0.46, an ≈188 and 92% enhancement as compared to the stoichiometric AgInSe₂ compound and the Ag‐excess AgInSe₂ compound, respectively (see the inset in Figure 2d). Figure S6 (Supporting Information) shows the reproducibility test of the electronic transport properties of the Ag_0.9Cd_0.1InSe₂ sample. The data are almost reproducible during three independent runs. Figure S7 (Supporting Information) shows the stability test for the Ag_0.9Cd_0.1InSe₂ sample under the current density of 12 A cm⁻², which is usually used for the test of superionic TE materials.45, 46 The relative resistance (R /R ₀, where R ₀ is the sample's initial resistance) for AgInSe₂ is almost unchanged after about 50 000 s (14 h) test, proving that the Ag_0.9Cd_0.1InSe₂ sample has a good stability under large current.

The discovered high TE performance in n‐type AgInSe₂‐based diamond‐like materials makes them suitable, in conjunction with high‐performance p‐type structures, for fabrication of diamond‐like TE modules. Here, we have chosen Ag_0.9Cd_0.1InSe₂ as the n‐type leg and Cu_0.99In_0.6Ga_0.4Te₂16 as the p‐type leg. A two‐couple diamond‐like TE module was successfully fabricated for the first time. As shown in Figure 6a, the cylinder‐shaped samples with a diameter of 12.7 mm and a height of 4 mm were obtained by hot‐pressing (HP) sintering. The ingots were cut into 4 mm × 4 mm × 8 mm rectangles by electrospark wire‐electrode cutting. The two square lateral faces of the samples were electroplated with nickel in a NiCl₂ solution with an ampere density of 10 mA cm⁻² for 90 s. Subsequently, the electroplated samples were welded to Mo₅₀Cu₅₀ alloy blocks with the Cu‐P brazing filler metal (T _melt ≈ 580 °C) at the hot side and the copper clad ceramic substrates with Sn₄₂Bi₅₈ (T _melt ≈ 138 °C) at the cold side. Figure 6b shows schematically the structure of our fabricated diamond‐like TE module. The two π‐pairs were assembled to attain a two‐couple diamond‐like TE module (see Figure 1b). The gap between the two couples was filled with a thermally insulation material to reduce the heat loss. PEM‐2 testing system (ULVAC‐RIKO, Inc.) was used to measure the performance of this module. As shown in Figure 6c, a maximum output power of 0.06 W was obtained with a temperature difference (ΔT ) of 520 K between the two ends of the TE module. This is the first diamond‐like TE module, clearly showing that it is feasible to fabricate efficient TE devices and perhaps even systems based on the diamond‐like materials. Thus, this work opens the door for applications of diamond‐like TE materials.

Figure 6

a) Schematic of the fabrication process for diamond‐like modules, including cutting the hot‐pressed cylinder samples into rectangular samples, and the following electroplating process. b) Schematic of the structure of the fabricated diamond‐like module. c) Output voltage (black) and power (blue) as a function of the current for the TE module based on the diamond‐like materials. The temperature difference between the cold side and the hot side of the module is 420, 470, and 520 K, respectively.

3 Conclusion

In summary, we have successfully fabricated a series of AgInSe₂‐based diamond‐like compounds. They are n‐type TE materials. The stoichiometric AgInSe₂ has very low electron concentration and lattice thermal conductivity as compared with the other diamond‐like materials. Via introducing extra Ag into the material and doping Cd at the Ag sites, the electron concentration has been significantly increased, leading to a much enhanced TE performance with a maximal value of 1.1 at 900 K, comparable to the best p‐type diamond‐like compounds reported before. All the present data strongly suggest that the AgInSe₂‐based material is currently the best n‐type diamond‐like thermoelectric material. Furthermore, we have succeeded to fabricate a diamond‐like TE module for the first time by using our AgInSe₂‐based n‐type material. The maximal output power of 0.06 W under a temperature difference ΔT of 520 K was obtained, indicating that diamond‐like materials can be a potential candidate for TE applications.

4 Experimental Section

Ag_1+x InSe₂ (x = 0, 0.01, 0.02) and Ag_1−x Cd_x InSe₂ (x = 0.08, 0.1) compounds were fabricated by directly reacting Ag (shots, 99.999%, Alfa Aesar), In (shots, 99.999%, Alfa Aesar), Se (shots, 99.999%, Alfa Aesar), and Cd (shots, 99.999%, Alfa Aesar) in sealed silica tubes. The raw materials were weighed out in a stoichiometric ratio and then sealed in silica tubes under vacuum in a glove box. The ingots were obtained by melting the mixture at 1273 K for 12 h, quenched into the icy water and then annealed at 923 K for 5 d. Fine powders were obtained by grinding the ingots in an agate mortar by hand. The powders were then loaded into a graphite die and sintered by hot pressing sintering (MRF Inc., USA) for 30 min at 823 K in vacuum. High‐density pellets (>98% of the theoretical density) were obtained.

The X‐ray diffraction (XRD) analysis (D8 ADVANCE, Bruker Co. Ltd.) was employed to characterize the structure and the purity of the samples. The chemical composition and the microstructure analysis were examined by scanning electron microscopy (SEM, ZEISS Supra 55). The cell parameters were estimated by the Fullprof software (Version February‐2015). The HRTEM images were obtained by JEOL 2100F by using powder samples to investigate the microstructures. The electrical conductivity and the Seebeck coefficient were measured by ZEM‐3 (ULVAC Co. Ltd.) apparatus under helium atmosphere from 300 to 900 K while the thermal diffusivities were measured by the laser flash method (NETZSCH LFA 427) in argon atmosphere. The Neumann–Kopp law was applied to estimate the heat capacity for all samples and the Archimedes method was used to measure the density. The thermal conductivity κ was calculated by κ = λC _pρ. The experimental sound velocities v _t and v _l were obtained by using a ultrasonic measurement system UMS‐100 based on the resonance interference method. The measurements were carried out on the pellet samples with the diameter of 10 mm and the height of 6 mm. The Hall coefficients (R _H) were measured by the Quantum Design Physical properties measurement system (PPMS) from 10 to 300 K with the magnetic field sweeping up to 3 T in both positive and negative directions. The electron concentration (n ) and the Hall carrier mobility (μ_H) were calculated by n = 1/R _He and μ_H =R _Hσ, respectively, where e is the elementary charge. The thermal expansion coefficient was measured by Netzsch DIL 402 C.

Lattice Dynamics Calculations : First‐principles calculations were performed with Vienna ab initio simulation package (VASP). The generalized gradient approximation (GGA) of the form Perdew–Burke–Ernzerhof and projected augmented wave (PAW) method47, 48 were adopted. The lattice dynamics calculations for the diamond‐like compounds were carried out by the frozen phonon method, as implemented in the Phonopy package.49 3 × 3 × 3 unit cell (containing a total of 216 atoms in the supercell) was constructed to ensure the convergence of Hellmann–Feynman forces. Accurate convergence criteria, that is, 5 × 10⁻⁵ eV Å⁻¹ for structural relaxation of the unit cell and 10⁻⁷ eV for static calculation of displaced supercell were used.

Thermoelectric Modules : Two n‐p couple module was assembled with n‐type Ag_0.9Cd_0.1InSe₂ and p‐type Cu_0.8Ag_0.2In_0.5Ga_0.5Te₂ compounds. Both n‐type and p‐type hot pressing sintered cylinder samples with a size of Φ12.7 mm × 4 mm were processed into 4 mm × 4 mm × 8 mm rectangles with electrospark wire‐electrode cutting. PEM‐2 testing system (ULVAC‐RIKO, Inc.) was employed to evaluate the power output and internal resistance of the module. The electrodes were stable throughout the measured temperature range from 300 to 873 K.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC) under Grant Nos. 11234012 and 51625205, the Key Research Program of Chinese Academy of Sciences (Grant No. KGZD‐EW‐T06), and the Shanghai Government (Grant No. 15JC1400301). P.F. thanks the support from the Youth Innovation Promotion Association, CAS (Grant No. 2016232). The authors thank Prof. Ctirad Uher in the University of Michigan for helpful discussions and language polishing.

Conflict of Interest

The authors declare no conflict of interest.