Discovery of High-Performance Thermoelectric Chalcogenides

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Discovery of High Performance Thermoelectric Chalcogenides through Reliable High Throughput Material Screening Lili Xi, Shanshan Pan, Xin Li, Yonglin Xu, Jianyue Ni, Xin Sun, Jiong Yang, Jun Luo, Jinyang Xi, Wenhao Zhu, Xinran Li, Di Jiang, Richard Dronskowski, Xun Shi, G. Jeffrey Snyder, and Wenqing Zhang J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 08 Aug 2018 Downloaded from http://pubs.acs.org on August 8, 2018

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Journal of the American Chemical Society

Discovery of High Perform Performance Thermoelectric Chalcogenides through Reliable High Throughput Material Screening Lili Xi†, Shanshan Pan‡, Xin Li†, Yonglin Xu§, Jianyue Ni§, Xin Sun†, Jiong Yang*†, Jun Luo*†‡, Jinyang Xi†, Wenhao Zhu§, Xinran Li†‖, Di Jiang†‖, Richard Dronskowski⏇, Xun Shi⋇, G. Jeffrey Snyder#, and Wenqing Zhang*┴ †Materials

Genome Institute, Shanghai University, 99 Shangda Road, Shanghai 200444, China. of Materials Science and Engineering, Shanghai University, 99 Shangda Road, Shanghai 200444, China. §School of Computer Engineering and Science, Shanghai University, 99 Shangda Road, Shanghai 200444, China. ‡School

‖

Qianweichang College, Shanghai University, 99 Shangda Road, Shanghai 200444, China.

⏇Chair

of Solid-State and Quantum Chemistry, RWTH Aachen University, D-52056 Aachen, Germany. Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Dingxi Road, Shanghai 200050, China. #Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States. ┴ Department of Physics, Southern University of Science and Technology, No. 1088 Xueyuan Road, Shenzhen, Guangdong, Shenzhen 518055, China. ⋇State

ABSTRACT: High-throughput (HTP) material design is an emerging field and has been proved to be powerful in the prediction of novel functional materials. In this work, an HTP effort has been carried out for thermoelectric chalcogenides with diamond-like structures on the newly established Materials Informatics Platform (MIP). Specifically, the relaxation time is evaluated by a reliable yet efficient method, which greatly improves the accuracy of HTP electrical transport calculations. The Results show that all the compounds may have power factors over 10 µW/cm-K2 if fully optimized. A new series of diamond-like chalcogenides with atomic ratio 1:2:4 possess relatively higher electrical transport properties among all the compounds investigated. One particular compound CdIn2Te4 and its variations have been verified experimentally with a peak ZT over 1.0. Further analysis reveals the existence of general conductive networks and the similar Pisarenko relations under the same anion sublattice; and the transport distribution function is found to be a good indicator for the power factors for the compounds investigated. This work demonstrates a successful case study in the HTP material screening.

Introduction Thermoelectric (TE) materials have received great attentions due to their applications in refrigeration and waste heat recovery.1-4 From the material perspective, the key parameter for measuring the TE properties is the dimensionless figure of merit ZT=TS2σ/(κe+κL), where S is the Seebeck coefficient, σ the electrical conductivity, κe the electronic thermal conductivity, κL the lattice thermal conductivity, respectively, and T is the absolute temperature. Particularly, S2σ is called the power factor, serving as a comprehensive measure of the electrical properties. High ZT needs high S, high σ, and low thermal conductivity. Due to the intercorrelation of the transport parameters,5 the improvement of ZT is proved to be a challenging task and puzzles the community for decades. Historically, the TE materials have experienced two big leaps. The first one was driven by the classical semiconductor theory in the early 1960s,6 leading to the discover-

ies of semiconducting alloys with ZT reached 1.0, such as Bi2Te3, PbTe, and SiGe etc.1,7,8 The second impetus of TE materials is based on new concepts and technologies, e.g., “phonon glass electron crystal”, nanostructure, electron band and scattering engineering, complex unit cells, large anharmonicity, and more recently, phonon liquid behavior.9-13 A pack of new TE materials with excellent TE properties have been revealed by the guidance of these concepts. The data-driven pattern in high throughput (HTP) study may initiate the third leap in TEs and the discovery of new candidates. The reason is two-folded. The material databases used in HTP study often contain ~105 or more entries, several orders of magnitude higher than the number of TE materials reported so far. The “big data knowledge”, i.e., the property-structure relation etc. concluded from the HTP study, can also speed up the discovery of new compounds. Over the years, several intriguing HTP studies have been carried out for TE materials. In 2008, Yang et al. studied over 100 half-Heusler entries taken from inorganic crystal structural database (ICSD),14 and highlighted sev-

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eral new half-Heusler candidates with high power factors.15 Some of them, e.g., NbFeSb, have been experimentally verified in recent years.16-17 Based on AFLOW framework,18 Wang et al.19 also proposed new compounds out of 2,500 entries and statistically concluded the strong correlation between the power factors and intrinsic material parameters. Zhu et al.20 predicted the high TE properties of TmAgTe2 and other XYZ2 compounds by screening more than 9,000 materials from the Materials Project, mainly from the power factor calculations. Following this work, Aydemir et al. experimentally studied the isoelectronic alternative YCuTe2 and doubled the ZT.21 Besides these work, Toberer et al.22 and Gibbs et al.23 proposed the descriptors which correlate with the thermal and electrical transport performance. All the aforementioned efforts provide inspirational HTP working patterns for TE materials, as well as new TE candidates. However, in the HTP attempts, the constant relaxation time approximation (CRTA) or equivalents for the electrical transport is assumed.15, 19, 20 The accuracy of the electrical transport calculation under the CRTA has always been questioned. On the other hand, accurate electrical relaxation time can be calculated by full evaluation of electron-phonon coupling (EPC) method;25-27 it is, however, very timeconsuming, and is not applicable for HTP calculations. It is thus very necessary to explore a new strategy of computing the electronic relaxation time. The desirable method should be efficient enough for HTP purpose, and yet accurate comparing with more advanced EPC method. In general, τ is determined by both electron-phonon coupling matrix and the scattering channel. If we assume the electron-phonon coupling matrix is not sensitive to the band variations, then the relaxation time can be rephrased as the following,25 ିଵ ߬௡,‫ܓ‬ = ‫ܥ‬௡,‫ ܓ‬෍ ߜ(ߝ௡,‫ ܓ‬− ߝ௡′ ,‫ܓ‬′ ) . ௡′ ,‫ ܓ‬′

(1)

Where Cn,k is the parameter relating to the electronphonon coupling matrix; n and k are band numbers and momentum vector, respectively. By using Eq. 1, we can deal with the band-related electronic scattering channel explicitly in the relaxation time, and leave the complex part, relating to the electron-phonon coupling, to an undetermined term Cn,k. Considering the interested compounds in this work have triply degenerated valence band maximum (VBM) at Γ point (as shown later), we adopt the long wavelength limit of Cn,k, i.e., Edef2/G.26,27 Here Edef is the deformation potential of the band edge, and G is the Young’s modulus (See the methodology for details).28 We further compare this method with the accurate EPC method, and the result is shown in the subfigure of Figure 1. It demonstrates that the relaxation times calculated by the two methods are comparable within the energy range of 0.2 eV below VBM, which is the dominant energy range of TEs. Thus, in order to balance the dilemma of efficiency and accuracy in the HTP study, the deformation potential, as well as the explicit band structures, are considered in the relaxation time model,

ିଵ ߬௡,‫ܓ‬ =

2π݇஻ ܶ‫ܧ‬ ܸℏ‫ܩ‬

Page 2 of 11 ଶ ௗ௘௙

෍ ߜ(ߝ௡,‫ܓ‬

௡′ ,‫ ܓ‬′

− ߝ௡′,‫ܓ‬′ ) .

(2)

Based on this method, all the electrical transport properties are obtained from ab initio calculations in this work. We then perform HTP calculations of the electrical transport properties for chalcogenides with diamond-like structures for highly reliable HTP materials discovery, based on the newly developed HTP repository Materials Informatics Platform (MIP).29 As will be shown later, due to the existence of the conductive network determined by the anion sublattices, the Edef and G in this work are adopted from the calculated values of three representative compounds CuInS2, CuInSe2, and CuInTe2. (Table S1).

Results and discussion The chalcogenides with the diamond-like structure are one type of promising TE materials. The structures of diamond-like compounds originate from tetrahedrallybonded diamond. The cations and anions in these compounds respectively occupy a face-center-cubic (FCC) sublattice. The numbers of cations and anions in the unit cell follow the simple valence-octet rule. Due to the flexibility of the cation sublattice, the diamond-like compounds have a large number of possible chemical compositions, including binary, ternary, and even quaternary components. Some typical structural types of the compounds investigated are shown in Figure S1. Thermoelectric diamond-like compounds generally have good electrical transport properties; meanwhile, the solid solution nature of the multinary components can reduce the κLs of the compounds significantly. Up to date, only several types of diamond-like chalcogenides have been experimentally studied, such as Cu2Sn(Ge)S(Se)3, Cu2Cd(Zn)Ge(Sn)Se4, AgGaTe2, CuGa(In)Te2, and Cu2HgSnTe4, etc.30-47 The maximum power factor reported so far is around 15 µW/cmK.46 Here we systematically investigate the TE properties of diamond-like chalcogenides by the reliable HTP calculations and then proved in experiments. Figure 1 demonstrates the workflow of the present HTP study, from the material screening all the way to the experiments. We applied three searching criteria on the MIP, 1) IB, IIB, IIIA, IVA as cations and S, Se, Te as anions; 2) FCC anion sublattice; 3) cation coordination number=4. These criteria resulted in 214 entries out of 82,412 in MIP. Automated calculations have been carried out for the filtered entries. Since TE materials are mostly semiconductors, so we adopted the band gap criterion (> 0.1 eV) on the 214, and the entry number was further reduced to 161 for electrical transport calculations. All the data about chemical compositions, the band gaps, the maximum p-type power factors, and the corresponding optimal hole concentrations can be found in Table S2. The calculated power factors, together with other factors, lead us new TE candidates in diamond-like chalcogenides. One of the candidates is further studied experimentally, with the ZT value greater than unity.


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Figure 1. The work flow of the present work. The bandgap screening, power factor screening and relaxation time results are given in the subfigures.

As mentioned above, a successful workflow of the TE material screening, including HTP calculations and experiments, has been demonstrated. Figure 2a shows the maximum power factors at 700 K as a function of the hole concentration, categorized by the anion sublattices. The maximum values are obtained by applying the Ioffe’s criterion (shown later).48 Most of the compounds have the maximum power factors within 13~25 µW/cm·K2. The power factor results indicate that the compounds investigated can reach reasonably good electrical transport properties if the carrier concentrations are fully optimized. The power factor range is close to the available experimental results.30-47 On the other hand, the power factors under constant relaxation time approximation with τ=10-14 s are within 25-43 µW/cm·K2 (Figure S2), apparently larger than experimental findings.

A new series of compounds with IIB1:IIIA2:VIA4 atomic ratio (vacancy-containing chalcogenides, VCCs, empty symbols in Figure 2a),49-51 are shown to possess relatively higher power factors (around 20 µW/cm·K2) than compounds under same anion sublattices. As shown in Figure 2a, the 1:2:4 compounds generally have higher power factors. Since these compounds have rarely been studied in the thermoelectric community, we adopted the empty symbols in Figure 2a and 2b for these compounds, as the highlights for new candidates. The structures of the VCCs are similar with the regular diamond-like compounds with part of the cations replaced by vacancies (Figure S1). The VCCs, due to the high content of vacancy in the structure, offer large freedom of optimizations for the TE performance since the vacancy sites can accommodate beneficial dopants. These compounds have scarcely been reported as TE materials, and thus could be one kinds of novel TE candidates.49-51



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Figure 2. (a) Maximum power factors for S, Se, Te based diamond-like compounds at 700K; (b) The band gaps and average atomic weights for the studied chalcogenides. The empty symbols in (a) and (b) represent the data points for vacancy-containing chalcogenides with 1:2:4 ratio. (c) Temperature dependent electrical conductivity for Cd2Cu3In3Te8, Cd1.8Cu3.2In3Te8, and Cd1.6Cu3.4In3Te8 in experiments; the electrical conductivity of CdIn2Te4 is also shown; (d) Experimental ZT values for Cd2Cu3In3Te8, Cd1.8Cu3.2In3Te8, and Cd1.6Cu3.4In3Te8.

The overall TE properties are related to other factors such as bipolar effects, dopabilities, lattice thermal conductivities, etc. Due to the difficulties of calculating these parameters especially in a HTP way, we instead adopt the band gaps and the average atomic weights for further screening new TE candidates. The optimal band gaps for TE applications are around 10 kBTop, where Top is the operating temperature.48 In this work, the band gap criterion is 0.7±0.4 eV, considering the well-known band gap uncertainties in DFT calculations. The average atomic weight is related to the lattice thermal conductivity. Here we use the average atomic weight > 80 for quick screening of compounds with low sound velocities and lattice thermal conductivities. These two criteria result in the highlighted box in Figure 2b. We labeled the VCCs within this range. In order to verify the TE potentials for the proposed VCCs, we experimentally study the TE properties for CdIn2Te4 and related compounds. The experimental result for the stoichiometric CdIn2Te4 has poor electrical conductivity, 10-6 S/m at room temperature, as shown in Figure 2c. We

calculate the defect formation energies ∆H for cation vacancies of CdIn2Te4. The definition of defect fomation energy is, ∆‫ܧ = ܪ‬஽ − ‫ܧ‬଴ + ݊‫ܧ‬௜ (݅ = cations) , (3) where ∆H is the defect formation energy, ED the total energy of defect containing supercell, E0 the total energy of perfect supercell, n the number of defect (here n=1), and Ei the energy of elementary substance for the cations, respectively. The results are shown in Table S3. As shown in the table, the formation energy of cation vacancy in CdIn2Te4 is pretty high (2.315 eV and 2.996 eV for the defect formation energy of Cd-vacancy and In-vacancy, respectively), directly resulting into the low carrier concentration caused by the vacancies. To overcome the low hole carrier concentration of CdIn2Te4, we designed the Cu intercalated version of the compound, i.e., Cd2Cu3In3Te8. ‫ݑܥ‬ூ௡ ′′ is introduced to balance the electron count. By introducing Cu, i.e., Cd2Cu3In3Te8, the Cu vacancy (∆H=0.402 eV, Table S3) are much easier to form comparing with other cation vacancies, which can significantly increase the hole concentra-


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Figure 3. (a) (c) Band structures, density of states, and plane-wave-projected Crystal Orbital Hamilton Population (COHP) between anions and cations of two typical diamond-like chalcogenides ZnTe and CuInTe2, with the zero energy points representing the EF. (b) (d) The statistical plots of the integrals of the density of states (N’) and pCOHP (IpCOHP) for all the 161 compounds with band gap > 0.1 eV, separated by anion sublattices. The number of N’ (or IpCOHP) within every small intervals are counted and plotted in (b) and (d). The red lines in (b) and (d) indicate the median values of N’ and IpCOHP for different anions.

tions. The newly designed Cd2Cu3In3Te8 has never been reported in any material database. The experimental X-ray powder diffraction (XRD) of Cd2Cu3In3Te8 and the lattice parameters have been shown in Figure S3, which is consistent with the calculated XRD based on the diamond-like structure (Figure S1). Detailed experimental TE properties of Cd2Cu3In3Te8 and compounds with the same atomic ratio will be reported separately. As shown in Figure 2c, the electrical conductivities of the compound and its selfdoping variations are around 104 S/m, 10 orders of magnitude larger than stoichiometric CdIn2Te4. Further enhancement of the carrier concentrations and electrical conductivities can be achieved by the ‫ݑܥ‬஼ௗ ′ defect (Figure 2c and S4a). Due to the further enhanced power factors and overall low thermal conductivities for Cd2-xCu3+xIn3Te8 compounds (Figure S4), the ZT values for these compounds can be optimized. The highest ZT value for the composition Cd1.6Cu3.4In3Te8 has reached 1.04 at 875 K, as shown in Figure 2d. This is the first compound, discovered by the combination of the HTP material screening and TE domain knowledge, with ZT over unity. Further experimental activities on the newly predicted VCCs and related compounds are encouraged. In order to have a general understanding for diamond-like compounds, we analyze the electronic structures and chemical bonding character for all the investigated compounds. Figure 3a and 3c show the band structures and density of states (DOS) for two typical Te-based diamondlike chalcogenides with binary and ternary components. Since we are looking for p-type candidates, bands with energy range around the Fermi level (EF, locating at the

valence band maximum, VBM) are demonstrated. Despite the difference of the cations in the two compounds, ZnTe and CuInTe2 present very similar VBM, which is triply degenerated bands at Γ point. Based on the projected DOS (Figure S5), the VBM of ZnTe is dominated by p states from Te, while the VBM of CuInTe2 is dominated by d states from Cu and Te p states. For all the 161 diamond-like chalcogenides with band gaps > 0.1 eV, 91 % of the entries have Γ-centered VBM. And 84 % of the Γ-centered entries have nearly triply degenerated bands, indicated by |∆CF|=|Γ5v-Γ4v| < 0.2 eV.52 In order to compare the DOS around the EF for a large number of compounds in a robust way, the integral of DOS with 0.5 eV w.r.t. respective EF is calculated,

ࡺ′ = න

ாಷ

۲‫ࡱࢊ ܁۽‬

ாಷ ି૙.૞

.

(4)

It represents the number of electrons N’ within this small energy range. The choice of 0.5 eV below the Fermi level (upper edge of the valence band) is based on the fact that all the electronic states relating to the electrical transport properties are included in the energy window. If the DOS is large in the energy window, N’ will be large as well, and the DOS is large if and only if the bands are flat (localized, atomic-like states). A smaller DOS and a smaller N’ shows that the bands are steep (because of covalent interaction). To better visualize the N’ for all the 161 compounds, we count the number of N’ within every small intervals of N’ values, separated by the anion sublattice, as shown in Figure 3b. The red lines in the plots represent the mean values of all the data sets for all the compounds with the same



anion sublattice. The mean N’ clearly show that the amount of localized electron density is highest for sulfides, a little lower for the selenides and even lower for the tellurides. Indeed, covalency goes inversely proportional with atomic localization, so the descending trend of N’ from S- to Tebased compounds is ruled by the difference in electronegativies between cations and S/Se/Te. The electronegativity of the three anion elements are 2.5 for S, 2.4 for Se, and 2.1

Page 6 of 11

It is intriguing that the bands around the EF of ZnTe and CuInTe2 are similar with each other, especially considering the different content of d states, so a rigid-band model applies here. The Crystal Orbital Hamilton Population (COHP) analysis is thus adopted to reveal the bonding characteristics of the investigated compounds,54-57 as shown in Figure 3a and 3c, here we show the interaction between cations and anions pairs. COHP provides a

Figure 4. (a) Calculated carrier concentration dependent electrical conductivities for CuInX2 (X=S, Se, Te) at room temperature, as well as experimental data for multiple Se- and Te-based diamond-like chalcogenides.30-46,66 (b) Pisarenko curves of S-, Se-, Te-based diamond-like chalcogenides. (c) Maximum power factors as a function of transport distribution functions. (d) Transport distribution functions as a function of IpCOHP. The empty symbols in (c) and (d) represent the data points for vacancy-containing chalcogenides with 1:2:4 ratio.

for Te, respectively.53 According to the Pauling’s definition, the covalency percentage of simple binary compounds (the diamond-like compounds can be seen as the derivatives of binary IIB-VIA compounds) can be approximately evaluated by the electronegativity difference between cations and anions. Lower electronegativity difference, as the Te-based compounds in our study, imply higher bonding covalency. Compounds with higher bonding covalency usually have more delocalized interatomic interactions and dispersive bands. That explains the variations of band widths and DOS in our study, even restricted to the upper part of the valence bands. It is noted that there are variances of N’ in each anion type compounds, caused by different ∆CF and local distortion on cationic sites for multinary chalcogenides.

straightforward view onto bonding characters. For planewave based methods such as the one given here by VASP results, projected COHP (pCOHP) based on contracted Slater-type orbitals was recently introduced in the LOBSTER package to provide similar results analog to those of Linearized Muffin-Tin Orbital (LMTO)-based COHP,55-57 with positive values of -pCOHP denoting the bonding states, negative values anti-bonding states. For ZnTe (Figure 3a), the compound has non-bonding states within EF~EF-1.0 eV, followed by weak anti-bonding states in the lower energy window. CuInTe2 (Figure 3c) has antibonding states within EF~EF-2.0 eV, followed by the bonding states. Similar with the aforementioned study on DOS, we are interested in the energy window around EF. Thus, in this range, ZnTe shows non-bonding states between


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metal and nonmetal; CuInTe2 shows d-p anti-bonding metal-nonmetal states, same with previous conclusions for other Cu chalcogenide compounds.58-60 In order to better demonstrate the COHP results for the 161 diamond-like chalcogenides, the IpCOHP is defined as the following (with the same energy window of N’), ۷‫ܘ‬۱‫۽‬۶‫ = ۾‬න

ࡱࡲ

‫ܘ‬۱‫۽‬۶‫ ࡱࢊ ۾‬.

ࡱࡲ ି૙.૞

(5)

IpCOHP (measured in eV) indicates to which extent the band-structure energy (= sum of the Kohn-Sham eigenvalues) is lowered by the orbital interactions in the given energy range. As can be seen in the Figures 3b and 3d, the DOS and pCOHP integrals in the range from EF-0.5 to EF run parallel. Similar to the DOS integral dubbed N’, we count the number of IpCOHP within every small intervals of the IpCOHP values, classified by the anion sublattice, as shown in Figure 3d. The mean values of IpCOHP for most of the data points are positive, indicating that most of the compounds investigated having d-p anti-bonding states, similar with CuInTe2 in Figure 3c. That is to say that these compounds are too electron-rich, and so these upmost electrons destabilize the metal-nonmetal interactions. We also found some multinary compounds have non-bonding states like ZnTe, i.e., IpCOHP close to zero. All these compounds have no IB elements (Cu or Ag), e.g., the VCCs.49-51 We have recently shown how the chemical composition of related tellurides and similar materials determines the electron count and the nature of the bonding, non-bonding, and anti-bonding states at the Fermi level.61 In thermoeletrics, it is beneficial for compounds to have conductive network, i.e., certain atoms or atomic groups in compounds dominating the electrical transport properties. By altering the atoms out of the conductive network, the carrier concentrations can thus be safely tuned, as shown by the examples of filled-skutterudites,62,63 Cu2SnSe3,64,65 and Cu2Se,58 etc. In the supporting information, based on the quantum mechanics derivation on group velocity, we qualitatively obtained the two criteria for the existence of conductive network: 1) non-overlapping atomic orbitals, and 2) the spatially most extensive atomic ortibals donimating the group velocity (i.e., the conductive network). In the current study, the non-bonding or d-p anti-bonding of the diamond-like chalcogenides meet the no overlapping criterion. In the non-bonding case of ZnTe, the wave function at VBM (Figure S6a) only has the contribution from Te p orbitals, while in the anti-bonding case of CuInTe2, the p orbitals from anions Te are spatially much more extensive than d orbitals from Cu, as shown in Figure S6b. Almost all the compounds investigated follow the two above cases. Therefore, we can conclude that the p orbitals from S, Se, or Te dominate the group velocities and the p-type electrical transport, serving as the general conductive network. Trace amount of vacancies and/or doping on the cationic sites can serve as carrier reservoirs while keeping the band structures unchanged. Figure S7 demonstrates the band structures of stoichiometric CuInTe2, and two cases of cation defects. CuInTe2 with defects clearly show similar valance band structures as that of CuInTe2. The existence of conductive network dominated by anion sublattice is critical to the optimization of diamond-like chalcogenides,

as already proved in the high-entropy alloying Cu(Ag)InTe2.47 The universal conductive network can also be reflected by the electrical transport properties. Figure 4a shows the theoretical room temperature carrier concentration dependent electrical conductivities of CuInX2 (X=S, Se, Te). Experimental results for Se- and Te-based chalcogenides are also shown in Figure 4a. The available experimental data for CuInTe2 agree very well with our predictions, implying the correctness of our methodology for the electronic relaxation times. More importantly, the experimental data, despite the cations and the large carrier concentration span 1019~1021 cm-3, almost sit on the theoretical σ~p curves with the same anion sublattices. This result verify the data calculated from CuInS2, CuInSe2, and CuInTe2, (Table S1) respectively. Figure 4b shows the Pisarenko relations for the p-type S-, Se-, and Te-based chalcogenides at 700 K, and mark as gray, orange, and blue, respectively. The choice of the temperature is based on the fact that the TE diamond-like chalcogenides reported so far hit their maximum ZTs at high temperatures. As can be seen in Figure 4b, all the S-, Se-, and Te-based diamond-like chalcogenides have general Pisarenko curves with small variations, again, due to the conductive networks; the cations do not significantly affect the Seebeck coefficients. Furthermore, the Seebeck coefficients decrease gradually from S to Te, because of the decreasing valnce band effective masses. Based on the Pisarenko relations and single parabolic band (SPB) model, the average effective masses for S-, Se-, and Te-based diamond-like chalcogenides are 2.78 me, 2.48 me, and 1.53me, respectively (Figure 4b). This is consistent with the trend of DOS, as shown in Figure 3b. Figure 4c shows the maximum power factors (700 K) as a function of transport distribution function (TD) 5,61 DOS*vk2*τ at the optimal doping levels. A strong correlation between maximum power factors and TD has been revealed for each anion sublattices. The corresponding Pearson correlation coefficients are 0.85 for sulfides, 0.83 for selenides, and 0.90 for tellurides. The high correlation coefficients imply that TD is a good indicator for the electrical transport properties since it contains the information of both electronic structures and electrical scatterings. In each type of chalcogenides, the TDs for the VCC compounds are relatively high according to Figure 4c. This might relate to the bonding characteristics of VCCs. Figure 4d shows the relation between TD and the IpCOHP. All the compounds with non-bonding interactions (IpCOHP values scattering around zero), e.g., VCCs and binary chalcogenides, have relatively high TDs. Comparing with the compounds with anti-bonding states (IpCOHP values in the positive range), these non-bonding states compounds have slightly more delocalized wave functions and thus more beneficial conductive networks.

Conclusions The electronic structures and electrical transport properties for p-type diamond-like chalcogenides have been calculated on a newly established HTP repository MIP. The deformation potential method and the constant electron-



phonon coupling approximation are used in the relaxation time calculation, which is more accurate than the commonly adopted CRTA. It is found that the VBMs for the studied compounds have d-p anti-bonding or non-bonding states; there exists the general conductive networks composed of the anion sublattice. The existence of the conductive networks results in general trends of the electrical transport properties, categorized by the anion types. Based on our calculations, most of the studied compounds have maximum power factors with 13~25 µW/cm·K2 (700K) if the carrier concentrations can be fully optimized. By considering the TE domain knowledge, together with the HTP calculations, one kinds of the novel compounds with defectchalcopyrite structure, such as CdIn2Te4 and ZnIn2Te4, have been proposed. One of the variations, Cd2Cu3In3Te8, has been experimentally synthesized, and the highest ZT values at high temperatures are above 1.0. Our work shows that the vacancy-containing chalcogenides can be promising TE candidates and worth further investigating.

Methodologies Materials Informatics Platform (MIP) and chalcogenbased infrastructures. There are 82,412 entries, based on Inorganic Crystal Structure Database (ICSD) and other sources, on the newly established Materials Informatics Platform (MIP).29 Based on the MIP, the automated work flow for structural relaxations, electronic structures, and electrical transport properties have been achieved. Ab initio calculations were carried out in projector augmented wave (PAW) method, as implemented in the Vienna ab initio Simulation Package (VASP).67,68 We used the Perdew– Burke–Ernzerhof (PBE) type generalized gradient approximation (GGA) as the exchange–correlation functional.69 The strongly constrained and appropriately normed (SCAN) meta-GGA as implemented in VASP5.4.4 was used in the calculations.70 A plane-wave energy cutoff of 520 eV and an energy convergence criterion of 10-4 eV for selfconsistency were adopted. All the atomic positions were relaxed to equilibrium until the calculated HellmannFeynman force on each atom was less than 10-2 eV/Å. The Monkhorst-Pack uniform k-point sampling with k=60/L (L is the corresponding lattice parameter) for DOS and 180/L for electrical transport properties.71 The chemical-bonding information was extracted from the VASP data by utilizing the LOBSTER package, a tool to reconstruct electronic structures through projection of PAW-based wavefunctions onto atomic-like basis sets.54-57 Transport methods. Electronic transport properties are calculated by using the Transoptic, which evaluates the electronic group velocity through the momentum matrix method.62,72,73 The relaxation time is calculated by deformation potential method and the constant electronphonon coupling approximation. The method for the relaxation time calculations has been implemented in Transoptic. The reference level for the calculations of deformation potentials is Cu 1s state. Young’s moduli G is calculated based on the elastic constant matrix.28 Sample Preparation. In our Cd2Cu3In3Te8 system, the polycrystalline Cd2-xCu3+xIn3Te8(x=0, 0.2, 0.4) samples were prepared from elemental starting materials

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(99.999% Cd, 99.9% Cu, 99.99% In, 99.999% Te) by meltannealing and spark plasma sintering (SPS). Stoichiometric quantities were loaded in graphite crucible and then sealed into an evacuated quartz tube (~ 0.1 Pa). The tube was heated to 1123 K and held at this temperature for 15 h and then annealed at 873K for 2 days. After that, the sample was naturally cooled to room temperature. Characterization. Phase identification and structure analysis were carried out by X-ray powder diffraction (XRD) using a Rigaku D/max 2500 (40 kV, 450 mA) with Cu ‫ܭ‬ఈଵ ( λ=1.54056 Å) radiation. The Seebeck coefficient S and resistivity ρ were measured via the four probe method utilizing a commercially available instrument (ULVAC, ZEM-3). Total thermal conductivity was calculated by ‫ܭ‬௧௢௧௔௟ = ߣߩ‫ܥ‬௣ , where λ, ρ, Cp were the thermal diffusivity, density and specific heat of the sample, respectively. Thermal diffusivity (λ) was measured by the laser flash method using a Netzsch LFA 457. Density of the sample was measured by the Archimedes drainage method. Cp was estimated from CP=3nR/M, where R is the gas constant, n is the number of atoms per formula unit, and M is the molar mass.

ASSOCIATED CONTENT Supporting Information. Some typical crystal structures of the compounds investigated, including binary, ternary and quaternary (Figure S1); Power factor obtained by the constant electron-phonon coupling and constant relaxation time approximations (Figure S2). X-ray powder diffraction and crystal structure for Cd2-xCu3+xIn3Te8 (Figure S3). Experimental power factors and total thermal conductivities for Cd2-xCu3+xIn3Te8 (Figure S4). Electronic density of states and wave functions for ZnTe and CuInTe2 (Figure S5, S6); Unfolding band structures of CuInTe2 related compounds (Figure S7), The deformation potential (Edef) and Elastic constant (G) for CuInX2 (X=S, Se, Te) (Tabel S1), The chemical compositions, band gaps, optimal carrier concentrations, and maximum power factors of the calculated compounds at 700 K (Table S2). The defect formation energies for cation-vacancy in CdIn2Te4 and Cd2Cu3In3Te8 (Table S3). This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author [email protected] [email protected] [email protected]

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This work was supported by the National Key Research and Development Program of China (No. 2017YFB0701600, 2018YFB0703600), the Natural Science Foundation of China (Grant Nos. 51572167, 51632005, 11574333, 11674211, and 51772186), and the 111 project D16002. W. Q. Zhang acknowledges support program of Shanghai Subject Chief Scientist (16XD1401100). J. Yang acknowledges support from the Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (No.


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TP2015041). J. Luo acknowledges the research grant (No. 16DZ2260601) from Science and Technology Commission of Shanghai Municipality. GJS acknowledges support of NSF DMREF 1729487.

REFERENCES (1) Goldsmid. H. J. Thermoelectric Refrigeration, Electrical Engineering, Springer: Boston, MA, 2013. (2) Sales, B. C. Science 2002, 295, 1248-1249. (3) Poudel, B.; Hao, Q.; Ma, Y.; Lan, Y. C.; Minnich, A.; Yu, B.; Yan, X.; Wang, D. Z.; Muto, A.; Vashaee, D.; Chen, X. Y.; Liu, J. M.; Dresselhaus, M. S.; Chen, G.; Ren, Z. F. Science 2008, 320, 634-638. (4) Rowe, D.W., CRC Handbook of Thermoelectrics, CRC press: Boca Raton, FL, 2006. (5) Yang J.; Xi L.; Qiu W.; Wu L.; Shi X.; Chen L.; Zhang W.; Uher C.; Singh D. J. NPJ Comput. Mater 2016, 2, 15015. (6) Sklyarchuk, V. M.; Plevachuk, Y. O. Semiconductors 2002, 6, 1123. (7) Heremans, J. P.; Jovovic, V.; Toberer, E .S.; Saramat, A.; Kurosaki, K.; Charoenphakdee, A., Snyder, G. J. Science 2008, 21, 554-557. (8) Ni, W.; Chen, W. M.; Buyanova, I. A.; Henry A; Hansso,n G. V.; Monemar, B., J. Crystal. Growth. 1995, 57, 242-247. (9) Rowe, D.W. CRC Handbook of Thermoelectrics, CRC Press: Boca Raton, FL, 1995. (10) Minnich, A. J.; Dresselhaus, M. S.; Ren, Z. F.; Chen, G. Energy Environ. Sci 2009, 2, 466-479. (11) Pei, Y. Z.; Wang, H.; Snyder, G. J. Adv. Mater 2012, 24, 6125-6135. (12) Qiu, W.J.; Xi, L.L.; Wei, P.; Ke, X.Z.; Yang, J.H.; Zhang, W.Q. PNAS 2014, 111, 15031-15035. (13) Liu, H.L.; Shi, X.; Xu, F.F.; Zhang, L.L.; Zhang, W.Q.; Chen, L.D.; Li, Q.; Uher, C.; Day, T.; Snyder, G.J. Nat. Mater 2012, 11, 422-425. (14) Inorganic Crystal Structure Database, (ICSD), http://www.fiz-informationsdienste. de/en/DB/icsd. (15) Yang, J.; Li, H.; Wu, T.; Zhang, W. Q.; Chen, L.D.; Yang, J.H. Adv. Funct. Mater 2008, 18, 2880-2888. (16) Fu, C.G.; Zhu, T.J.; Liu, Y.T.; Xie, H.H.; Zhao, X.B. Energy Environ. Sci 2015, 8, 216. (17) Fu, C.G.; Bai, S.Q.; Liu, Y.T.; Tang, Y.S.; Xie, H.H.; Chen, L.D.; Zhao, X.B.; Zhu, T.J. Nature. Commun 2015, 6, 8144. (18) Curtarolo, S.; Setyawan, W.; Hart, G. L.W.; Jahnatek, M.; Chepulskii, R. V.; Taylor, R. H.; Wang, S. D.; Xue, J. K.; Yang, K. S.; Levy, O.; Michael, J. M.; Stokes, H. T.; Demchenko, D. O.; Morgan, D. Comp Mater Sci 2012, 58, 218-226. (19) Wang, S. D.; Wang, Z.; Setyawan, W. Y.; Mingo, N.; Curtarolo, S. Phys. Rev X 2011, 1, 021012. (20) Zhu, H.; Hautier, G.; Aydemir, U.; Gibbs, Z. M.; Li, G. D.; Bajaj, S.; Pohls, J. H.; Broberg, D.; Chen, W.; Jain, A.; White, M. A.; Asta, M.; Snyder, G. J.; Perssonf, K.; Ceder, G. J. Mater. Chem. C 2015, 3, 10554. (21) Aydemir, U; Pohls, J. H; Zhu, H.; Hautier, G.; Bajaj, S.; Gibbs, Z. M.; Chen, W.; Li, G. D.; Ohno, S.; Broberg, D.; Kang, S. D.; Asta, M.; Ceder, G.; White, M. A.; Persson, K.; Jain, A.; Snyder, J. J Mater Chem A 2016, 4, 2461-2472.

(22) Yan, J.; Gorai, P.; Ortiz, B.; Miller, S.; Barnett, S. A.; Mason, T.; Stevanovi, V.; Toberer, E. S. Energy Environ. Sci 2015, 8, 983. (23) Gibbs, Z. M.; Ricci, F.; Li, G.; Zhu, H.; Persson, K.; Ceder, G.; Hautier, G.; Jain, A.; Snyder, G. J. npj Comput. Mater. 2017, 3, 8. (24) Noffsinger, J.; Giustino, F.; Malone, B. D.; Park, C.H.; Louie, S. G.; Cohen, M. L. Comput. Phys. Commun. 2010, 181, 2140. (25) Xi, J.; Wang, D.; Yi, Y.; Shuai, Z. J. Chem. Phys., 2014, 141, 034704. (26) Xi, J.; Wang, D.; Shuai, Z., Wiley Interdisciplinary Reviews: Comput. Molecular Sci. 2015, 5, 215227. (27) Chen, J. M.; Wang, D.; Shuai, Z. G. J. Chem. Theory. Comput. 2012, 8, 3338-3347. (28) Sun, L.; Liu, B.; Wang, J.; Li, Z. J. Am. Ceram. Soc. 2016, 99, 2442-2450. (29) Materials Informatics Platform (MIP), http://mip.shu.edu.cn. (30) Tan, Q.; Sun, W.; Li, Z.; Li, J.-F. J. Alloys. Compounds 2016, 672, 558-563. (31) Liu, F. S.; Wang, B.; Ao, W. Q.; Li, Y.; Li, J. Q. Intermetallics 2014, 55, 15-21. (32) Shi, X. Y.; Xi, L. L.; Fan, J.; Zhang, W. Q.; Chen, L. D. Chem. Mater. 2010, 22, 6029-6031. (33) Cho, J. Y.; Shi, X.; Salvador, J. R.; Meisner, G. P.; Yang, J.; Wang, H.; Wereszczak, A. A.; Zhou, X.; Uher, C. Phys. Rev. B 2011, 84, 085207. (34) Chetty, R.; Dadda, J.; Boor, J. d.; Müller, E.; Mallik, R. C. Intermetallics 2015, 57, 156-162. (35) Xue, L.; Xu, B.; Zhao, D.; Yi, L. Intermetallics 2014, 55, 204-209. (36) Kosuga, A.; Plirdpring, T.; Higashine, R.; Matsuzawa, M. Appl Phys Lett.. 2012, 100, 042108. (37) Yusufu, A.; Kurosaki, K.; Kosuga, A.; Sugahara, T.; Ohishi, Y.; Muta, H.; Yamanaka, S. Appl Phys Lett.. 2011, 99, 061902. (38) Raju, C.; Falmbigl, M.; Rogl, P.; Yan, X.; Bauer, E.; Horky, J.; Zehetbauer, M.; Chandra, M. AIP Advances. 2013, 3, 032106. (39) Navrátil, J.; Kucek, V.; Plechacek, T.; Cernoskva, E.; Laufek, F.; Drasar, C.; Knotek, P. J Electron Mater. 2014, 43, 3719-3725. (40) Shen, J.W.; Chen, Z.W.; Lin, S.Q.; Zheng, L.; Li, W.; Pei, Y.Z. J. Mater. Chem. C, 2016, 4, 209-214. (41) Liu, R.; Xi, L.; Liu, H.; Shi, X.; Zhang, W.; Chen, L. Chem. Commun, 2012, 48, 3818-3820. (42) Liu, R.; Qin, Y.; Cheng, N.; Zhang, J.; Shi, X.; Grin, Y.; Chen, L. Chen, Inorg. Chem. Front, 2016, 3, 11671177. (43) Liu, F. S.; Zheng, J. X.; Huang, M. J.; He, L. P.; Ao, W. Q.; Pan, F.; Li, J. Q. Sci. Rep, 2014, 4, 5774. (44) Qin, Y.; Qiu, P.; Liu, R.; Li, Y.; Hao, F.; Zhang, T.; Chen, L., J Mater. Chem. A, 2016, 4, 1277-1289. (45) Prasad, S.; Rao, A.; Gahtori, B.; Bathula, S.; Dhar, A.; Chang, C. C.; Kuo, Y. K. Physica B: Condensed Matter, 2017, 520, 7-12. (46) Luo, Y.; Yang, J.; Jiang, Q.; Li, W.; Zhang, D.; Zhou, Z.; He, X. Adv. Energy. Mater. 2016, 6, 1600007. (47) Liu, R.; Chen, H.; Zhao, K.; Qin, Y.; Jiang, B.; Zhang, T.; Chen, L. Adv Mater. 2017, 29, 1702712. (48) Ioffe, A. F., Thermoelements and Thermoelectric Cooling, London, UK: Physics Today, 1956.



Page 10 of 11

(49) Kumar, P.; Soni, A.; Bhamu, K. C.; Sahariya, J. Mater.

(61) Deringer, V. L.; Zhang, W.; Rausch, P.; Mazzarello,

Res. Bull, 2017, 86, 131-138. (50) Pandey, C.; Sharma, R.; Sharma, Y. AIP Conference Proceedings 2017, 1832, 110009. (51) Suriwong, T.; Kurosaki, K.; Thongtem, S.; Harnwunggmoung, A.; Plirdpring, T.; Sugahara, T.; Yamanaka, S., J. Alloys Compounds 2011, 509, 7484-7487. (52) Zhang, J.; Liu, R.; Cheng, N.; Zhang, Y.; Yang, J.; Uher, C.; Zhang, W. Adv Mater. 2014, 26, 38483853. (53) Pauling, L., The Nature of the Chemical Bond; Cornell University Press: Ithaca, 1960. (54) Dronskowski, R.; Blöchl, P. E. J. Phys. Chem. 1993, 97, 8617–8624. (55) Deringer, V. L.; Tchougréeff, A. L.; Dronskowski, R. J. Phys. Chem. A 2011, 115, 5461–5466. (56) Maintz, S.; Deringer, V. L.; Tchougréeff, A. L.; Dronskowski, R. J. Comput. Chem. 2013, 34, 25572567. (57) Maintz, S.; Deringer, V. L.; Tchougréeff, A. L.; Dronskowski, R. J. Comput. Chem. 2016, 37, 1030– 1035. (58) Sun, Y.; Xi, L.; Yang, J.; Wu, L.; Shi, X.; Chen, L.; Zhang, W. J. Mater. Chem. A 2017, 5, 5098-5105. (59) Jaffe, J. E., Zunger, Z. Phys. Rev B. 1983, 28, 58225847. (60) Jaffe, J. E., Zunger, Z. Phys. Rev B 1984, 29, 18821906.

R.; Dronskowski, R.; Wuttig, M. J. Mater. Chem. C 2015, 3, 9519–9523. (62) Yang, J.; Xi, L.; Zhang, W.; Chen, L. D. Yang, J. H. J. Electronic Mater. 2009, 38, 1397-1401. (63) Shi, X.; Yang, J.; Salvador, J. R.; Chi, M. F.; Cho, J. Y.; Wang, H.; Bai, S. Q.; Yang, J. H.; Zhang, W. Q.; Chen, L. D. J. Am. Chem. Soc. 2011, 133, 7837-7846. (64) Shi, X. Y.; Xi, L. L.; Fan, J.; Zhang, W. Q.; Chen, L. D. Chem. Mater. 2010, 22, 6029-6031. (65) Xi, L. L.; Zhang, Y. B.; Shi, X. Y.; Yang, J.; Shi, X.; Chen, L. D.; Zhang, W. Q. Phys. Rev. B 2012, 86, 155201. (66) He, Y.; Day, T.; Zhang, T.; Liu, H.; Shi, X.; Chen, L.; Snyder, G. J. Adv Mater. 2014, 26, 3974-3978. (67) G. Kresse, Furthmuller, J. Phys. Rev. B 1996, 54, 11169. (68) Blöchl, P. E. Phys. Rev. B 1994, 50, 17953. (69) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett 1999, 77, 3865. (70) Sun, J.; Ruzsinszky, A.; Perdew, J. P. Phys. Rev. Lett 2017, 115, 036402. (71) Monkhorst H. J.; Pack J. D. Phys. Rev. B 1976, 13, 5188. (72) Transoptic, http://www.mgi.shu.edu.cn/Portals/675/transop tic.zip. (73) Madsen, G. K. H.; Singh, D. J. Comput. Phys. Commun. 2006, 175, 67-71.


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Table of Contents Experimental verification

Searching criteria

MIP

Automated Calculations

82,412

214

Electrical Transport Properties 161

Bandgap screening Eg>0.1 eV

HT Materials Screening

New TE Compounds ZT>1

High Power Factors


11

Discovery of High-Performance Thermoelectric Chalcogenides

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