High-Throughput Screening for Advanced Thermoelectric Materials

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High-Throughput Screening for Advanced Thermoelectric Materials: Diamond-Like ABX2 Compounds Ruoxi Li,† Xin Li,† Lili Xi,*,† Jiong Yang,*,† David J. Singh,‡ and Wenqing Zhang*,#,⊥ †

Materials Genome Institute, Shanghai University, 99 Shangda Road, Shanghai 200444, China Department of Physics and Astronomy, University of Missouri, Columbia, Missouri 65211, United States # Department of Physics and Shenzhen Institute for Quantum Science & Technology, Southern University of Science and Technology, No. 1088 Xueyuan Road, Shenzhen, Guangdong 518055, China ⊥ Center for Quantum Computing, Peng Cheng Laboratory, Shenzhen 518000, China Downloaded via UNIV OF LOUISIANA AT LAFAYETTE on April 26, 2019 at 20:32:02 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

‡

S Supporting Information *

ABSTRACT: High-throughput (HTP) calculations are a highly promising direction for the discovery of novel functional materials. Here we use an HTP framework to investigate the electronic structures and p-type thermoelectric properties of the ABX2 compounds with diamond-like structures. We show application of HTP both to identify compounds and also to identify underlying trends. A total of 65 entries out of 84 908 in the Materials Informatics Platform are selected for this study. The electronic structures and chemical-bonding analyses reveal that there exists a general conductive network consisting of the anion X sublattice, which dominates the electrical transport properties of the compounds. Electrical and thermal transport properties of the 41 pnictide and chalcogenide compounds with sufficient band gaps are studied. Pnictide compounds have relatively smaller Seebeck coefficients than the chalcogenide compounds. This is due to the smaller effective masses around the valence band maxima. The electrical conductivities and power factors, however, are better in pnictide compounds. This is because pnictide compounds have high electronic group velocities and electronic relaxation times. Combined with the predictions of lattice thermal conductivities based on the Slack model, 12 novel p-type and n-type ABX2 materials with high ZT values are predicted. KEYWORDS: high-throughput, conductive network, thermoelectric, diamond-like structures, chalcopyrite clathrates, half-Heuslers, and diamond-like compounds,9−22 among others, emerged as high-performance thermoelectrics. Some of these recently discovered compounds show exceptionally high TE efficiency, leading to the promise of applications in energy technologies23 as well as suggesting that there are other novel high-performance TE materials waiting to be discovered. In recent years, some progress has been made in the study of TE materials by high-throughput (HTP) screening. Using AFLOWLIB,24 Carrete et al. obtained the relationship between power factor and effective mass, through the calculations of more than 2500 compounds.25 On the basis of the Materials Project (MP),26 Zhu et al. screened more than 9000 materials and predicted TmAgTe2 and other XYZ2 compounds with high TE properties,27 but the related experimental ZT values were low. Subsequently, Aydemir et al. studied YCuTe2 through isoelectronic element substitution, and its performance was improved.28 Chen et al. recently studied the classification of TE

1. INTRODUCTION Thermoelectric (TE) materials, as a new type of energy conversion material, are receiving widespread attention because of the direct conversion between electricity and heat.1−3 The conversion efficiency of TE devices closely relates to the dimensionless TE figure of merit, ZT = S2σT/κ. Here S, σ, κ, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and the absolute temperature, respectively. S2σ is the power factor (PF). The total thermal conductivity κ has both lattice and electronic components, κL and κe, respectively. The parameters that determine the ZT value are interrelated. For example, the increase of S causes the decrease of σ. These countercorrelations among σ, S, and κ greatly complicate the optimizing of ZT values.4−6 The electrical transport properties in TE materials are determined by the electronic states within a small energy range, of a few kBT, around the band edge (i.e., valence band maximum (VBM)) or conduction band minimum (CBM). The properties depend strongly on doping level, which must be optimized. In addition to the traditional TE materials such as Bi2Te3, SiGe, and PbTe,1,7,8 compounds with complex structures and multiple components, such as skutterudites, © XXXX American Chemical Society

Special Issue: Materials Discovery and Design Received: January 19, 2019 Accepted: April 15, 2019

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DOI: 10.1021/acsami.9b01196 ACS Appl. Mater. Interfaces XXXX, XXX, XXX−XXX

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ACS Applied Materials & Interfaces materials through HTP computation and machine learning.29 Recently, Xi et al.20 predicted novel high-performance TE materials using an HTP workflow based on the Materials Informatics Platform (MIP)30 applied to a class of compounds. This was followed by experimental verification in chalcogenides with diamond-like structure. A number of the recently discovered TE materials contain “conductive networks”, which are composed frameworks involving a portion of the atoms that dominate the electrical transport properties. Other atoms, because their electronic states are not close to the band edges, only serve as carrier reservoirs. This is related to the Zintl concept but is more general. The existence of conductive networks in a compound facilitates dopability, while retaining mobility, and therefore enables the optimization of carrier concentrations using chemical strategies. Diamond-like materials are a new series of promising TE materials. They are characterized by high Seebeck coefficients and low thermal conductivities.12−21 Examples include AgGaTe2, with a reported ZT of 0.77 at 850 K,17 CuGaTe2, with a κl value as low as 0.89 W/m·K and a ZT of 1.4,18 and CuInTe2, with a ZT of 1.18.19 First-principles studies show that the VBM is characterized by an anion-dominated conductive network at the VBM in chalcogenide diamond-like compounds.20−22 S-, Se-, and Te-based chalcogenide diamond-like compounds have been widely reported. Compounds based on other anions, such as P-, As-, and Sb-based compounds, have been less studied as TE materials,31−33 although many of these have been studied as photovoltaic materials, with findings of reasonable semiconducting properties, such as charge carrier transport.34−36 Here we use the HTP calculations, recently done for chalcogenides,20 to study the TE properties of ternary ABX2 (A = IA, IIA, IIIA, VA, IB, and IIB; B = IA, IIIA, IVA, VA, and IIB, VB, VIII; X = IIIA, VA, VIA, and VIIA) compounds with diamond-like structures.

respectively, Edef is the deformation potential of the band edge, and G is the Young’s modulus. This method was applied in our recent HTP work of Xi et al.,20 where a good balance between efficiency and accuracy was obtained. As discussed in detail below, we found conductive networks at the VBM formed from the anion sublattices. The deformation potential Edef in this work was adopted from the calculated values of six compounds, CuInS2, CuInSe2, CuInTe2, MgSiP2, MgSiAs2, and MgSiSb2, for p-type properties and of the 41 investigated compounds for n-type properties (Tables S1 and S2).20 The Young’s moduli G, which enters the HTP calculation of the relaxation time (eq 1) for the investigated compounds (Table S4) was calculated by the Voigt-ReussHill (VRH) theory.51 Lattice thermal conductivities were calculated through the Slack model52 κL = A ·

M̅ θD3δ γ 2n2/3T

(2)

where M̅ , θD, δ, γ, and n are the average mass per atom in the crystal, the Debye temperature, the volume per atom, the Grüneisen parameter, and the number of atoms in the primitive unit cell, respectively. A is a constant determined by γ. The values are shown in Table S4. All the necessary parameters for κL values can be obtained from elastic constant calculations.53,54 The Slack model has been found to be suitable for diamond-like compounds.52,55 The electronic thermal conductivity is calculated by Boltzmann transport theory, as is the electrical conductivity and Seebeck coefficient.56

3. RESULTS AND DISCUSSION The ternary compounds ABX2 (A = IA, IIA, IIIA, VA, IB, and IIB; B = IA, IIIA, IVA, VA, IIB, VB, and VIII; X = IIIA, VA, VIA, and VIIA) with diamond-like structures can be derived from the zinc blende structure. Figure 1a shows the crystal structures of

2. COMPUTATIONAL METHODS The underlying density functional theory (DFT) calculations related to structure and elastic constants were carried out using the projector augmented wave (PAW) method, as implemented in the Vienna Ab initio Simulation Package (VASP).37,38 The Perdew−Burke−Ernzerhof (PBE) generalized gradient approximation (GGA) was used as the exchange-correlation functional.39A plane-wave energy cutoff of 400 eV and an energy convergence criterion of 10−4 eV for self-consistency were adopted. All the atomic positions were fully relaxed until the calculated Hellmann−Feynman force on each atom was less than 10−4 eV/Å. The electronic structures and transport properties were calculated by using the modified Becke-Johnson (MBJ) meta-GGA potential, and the Hubbard-U correction with Dudarev’s approach was used. This approach has been shown to be effective in other diamondlike TE materials.40−44 Chemical-bonding information was obtained using the band-resolved projected crystal orbital Hamilton populations (COHPs) as implemented in the Local Orbital Basis Suite Towards Electronic-Structure Reconstruction (LOBSTER) package.43−47 Electrical transport properties were calculated based on the Boltzmann transport theory.42 The relaxation time was treated by the deformation potential method and the constant electron−phonon coupling approximation, as implemented in Transoptic.20,48−50

τn−, k1 =

2 2πkBTEdef V ℏG

∑ δ(εn, k − εn′ , k′) n ′ , k′

(1) Figure 1. (a) Crystal structures of zinc blende and ternary compounds ABX2 with diamond-like structures. (b) The high-performance thermoelectric material screening workflow.

2 2πkBTEdef

where Cn,k = is the parameter relating to the electron−phonon V ℏG coupling matrix; n and k are the band indices and wavevector, B


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Figure 2. (a) Band structures and density of states of ZnSnSb2 and CuInTe2. (b) Maximum p-type electronic fitness function (EFF) with respect to the carrier concentration for the maximum value. (c) The band-resolved projected crystal orbital Hamilton populations (COHPs) for Zn−Sb, Sb−Sb, and Sb onsite of ZnSnSb2 as well as Cu−Te, Te−Te,and Te onsite of CuInTe2.

we split the cation site. Differences in the atomic radii and charge states of the constituent elements lead to finite but generally small lattice distortions in the ABX2 structure. These can be described by a lattice distortion parameter η = c/2a, where a and c are the tetragonal lattice parameters.

zinc blende and ABX2. The zinc blende structure belongs to space group 216 (F4̅3m) and can be split to two distinct facecentered cubic (FCC) sublattices. Similarly, the ABX2 diamondlike compounds are based on a further splitting of one site in the zinc blende structure leading to space group of 122 (I4̅2d). Here C


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EFFs are for ZnGeP2 and ZnGeAs2, which are also predicted to be very high-power-factor compounds. In order to further rationalize the chemical interaction between the constituent elements, we calculated the bandresolved projected COHPs47 for the ABX2 compounds with band gaps between 0.1 and 2.5 eV. Figure 2c shows the bandresolved projected COHPs for Zn−Sb, Sb−Sb, and Sb onsite (atomic-like) of ZnSnSb2 as well as Cu−Te, Te−Te,and Te onsite of CuInTe2. The results for the interatomic interactions in the ABX2 compounds investigated are shown in Figure S3. Positive and negative values correspond to the antibonding state and bonding states, respectively, and zero represents nonbonding. The VBM for ZnSnSb2 is mainly composed of the Sb onsite states, whereas the other interatomic interactions are nonbonding states. In the representative Cu containing compound, such as CuInTe2, the Cu−Te antibonding states are non-negligible. Following analysis of the band-resolved projected COHPs for the 41 ABX2 compounds, we conclude that for pnictides, the VBM is mainly composed of X onsite states or nonbonding states. For Cu-based chalcogenides, the major interactions are composed of Cu−X antibonding states and X onsite states. Following the analysis and procedure of ref 20, we find that the VBMs of the 41 ABX2 compounds investigated here all show a conductive network dominated by the anion sublattice. A conductive network indicates that in one compound, certain atoms or atomic groups dominate the electrical transport properties, whereas other atoms are out of the conductive network and serve as carrier reservoirs. The carrier concentration can thus be optimized by doping on the out-of-network atoms, which minimize the alteration on the electronic structure of the base compound. As shown in ref 20, nonbonding state compounds have slightly more delocalized wave functions and thus more beneficial conductive networks than those of antibonding states. Therefore, we can conclude that pnictides may have better p-type electrical transport properties than chalcogenides. The anion sublattice conductive network is reflected in the electrical transport properties. Figure 3a,b shows the Pisarenko relations for the p-type P-, As-, and Sb-based as well as S-, Se-, and Te-based ABX2 compounds at 700 K. The Pisarenko relations can be roughly categorized according to the different anions, indicating again the importance of the anion sublattice conductive networks. The calculated Seebeck effective masses from the Pisarenko analysis are shown in Figure 3a,b and are 2.93, 2.10, and 1.52 me for P-, As-, and Sb-based compounds and 4.59, 3.97, and 2.82 me for S-, Se-, and Te-based compounds. The relative trend of effective masses from 3p to 5p anions21 holds in the pnictide compounds. Figure 3c,d shows the theoretical electrical conductivities as a function of carrier concentrations at 700 K. As a test, the experimental electrical conductivity of Cu2SnS3 is labeled in Figure 3d.60 It can be seen that the experimental value is close to the theoretical value, which supports the accuracy of the methodology. The electrical conductivities are classified by anion sublattices; the electrical conductivities with the same anion sublattice have some deviations. This is understandable, because the electrical conductivities are more sensitive to the subtle variations of the band shapes. It is this property that is measured by the EFF and that allows the effective mass for conductivity to differ from the Pisarenko effective mass and decouple the usual contrary relationship of S and σ on mass. At the same carrier concentration range, P-, As-, and Sb-based compounds have higher electrical conductivities than those of

Figure 1b shows the HTP workflow in this study. We applied three search criteria on the MIP: (1) No. 122 space group; (2) eight atoms per unit cell; (3) atomic ratio of 1:1:2. These criteria selected 65 entries out of 84 908 in the MIP. The first step following this selection is band gap screening. Becuase TE materials are mostly small band gap semiconductors, compounds with the calculated band gap in the range of 0.1−2.5 eV are selected. A total of 41 compounds out of 65 meet this criterion. The band-resolved projected COHP is used to obtain the chemical-bonding characteristics. The p-type and n-type TE properties at 700 K are then obtained. The electronic fitness function (EFF), which is a measure of the extent to which a band structure can resolve the counter-correlation of S and σ (e.g., through complex nonparabolic bands) is calculated.50 Finally, high-performance TE compounds are predicted. Figure 2a shows the band structures and density of states (DOS) of two compounds, ZnSnSb2 and CuInTe2. Both of the VBMs are triply degenerate. These bands are composed of Sb p states in ZnSnSb2 and Cu d and Te p states in CuInTe2. The electronic structures of all the ABX2 compounds are shown in Figure S1. More than 90% of compounds have triple degenerate bands at the VBM. For Cu-based compounds, the VBMs are mainly composed of Cu d and X p states, whereas for the other compounds, the VBM has X p character. Although the band characters at the VBM of the two compounds in Figure 2a are different, their band shapes are similar. This implies that pnictide ABX2 compounds may have a similar conductive network as their chalcogenide counterparts. Furthermore, the VBM of ZnSnSb2 is more dispersive than that of CuInTe2, implying a lower band edge DOS. The pnictides in general show a smaller DOS near the VBM than the chalcogenides do, as seen in Figure S1. This is important for the electrical transport properties, as shown below. On the basis of Ioffe’s theory, the optimal band gaps for TE applications are around 10 kBTop, where Top is the operating temperature.57 At 700 K, the optimal band gap is around 0.7 eV. Considering the uncertainty of the band gap calculation in density functional theory, here we use the band gap range of 0.1∼2.5 eV for the further TE properties. We calculated the phonon spectra of these 41 compounds as shown in Figure S2. All the phonon spectra of these compounds have no imaginary frequencies, so these compounds are considered stable. Figure 2b shows the relationship between the maximum ptype electronic fitness function (EFF)58,59 at 700 K with respect to the carrier concentrations, categorized by the anion sublattice. The EFF identifies the complexity of electronic structures and was recently proposed by Singh and co-workers.58,59 Generally speaking, the higher the value, the better the electrical transport properties of the compound. The EFFs for the chalcogenides are within the range of 3∼7*10−20 W5/3 m s−1/3 K−2 (the EFF values can be seen in Table S3). Interestingly, these values are comparable to those of the sulfide compounds in ref 58, though the latter are not limited to the diamond-like structures. The pnictides, on the other hand, have distinctly larger EFFs than those of chalcogenides by up to 100%. This indicates that from a pure band structure point of view, the pnictides are generally superior to the chalcogenides. The three compounds with the highest EFFs are BeSiP2, BeSiAs2, and BeSiSb2. Interestingly, these are also the compounds with the highest predicted power factors, showing the importance of band structure to the TE properties. Unfortunately, these compounds may be unsuitable due to the presence of Be, which is both light (unfavorable for low κL, especially combined with Si) and toxic. The next highest D


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Figure 4. (a) Calculated and experimental temperature dependent lattice thermal conductivities for CuInTe2 and AgInSe2. (b) Relationship between calculated lattice thermal conductivities (700 K) and mean atomic weights with different anion sublattice. (c,d) Predicted maximum ZT values for 41 p-type compounds at 700 K; the compounds with ZT over 0.6 for p-type and n-type are labeled.

Figure 4b shows the relationship between the κLs at 700 K and the mean atomic weights of 41 ABX2 compounds. Generally speaking, heavy constituents lead to low κLs. It is notable that κLs for the pnictide compounds are usually higher than those for the chalcogenide compounds. This is due to the generally higher elastic moduli for the pnictides (Table S4). Figure 4c,d shows the predicted maximum ZT values by using the calculated power factors and thermal conductivities. Here, total thermal conductivities, both lattice thermal conductivities and electron thermal conductivities, are considered for ZT value prediction. Figure 4c shows the predicted maximum ZT values as a relationship of corresponding carrier concentrations at 700 K for 41 p-type ABX2 compounds. Despite the high PFs, pnictides are comparable with the chalcogenide counterparts in ZTmax because of the cancellation from enhanced κes and κLs. In Figure 4c, 12 compounds with ZT > 0.6 are labeled. CuInTe2 and AgGaTe2 have been experimentally confirmed to be highperformance p-type TE materials, and their experiment ZT values at 700 K are 0.59 and 0.5, respectively, which are consistent with our theoretical results (0.66 and 0.67).17,19 Nomura et al. recently reported that ZnSnSb2 is a promising TE material.32 The other compounds, predicted TE materials CdSnSb2, AgInS2, AgGaSe2, ZnCdTe2, and LiInTe2, have been little studied in this context experimentally, but based on the results above, they are promising TE materials. By the same method, the predicted maximum ZT values of n-type ABX2 compounds at 700 K are shown in Figure 4d, and 12 compounds with ZT > 0.6 are labeled. Among them, ZnSnSb2, AgInS2, AgGaSe2, AgInSe2, and LiInTe2 have high ZT values for both ntype and p-type, which may result in good TE application prospects.

Figure 3. (a,b) Pisarenko plots for P-, As-, and Sb-based as well as S-, Se-, and Te-based compounds. (c,d) Calculated electrical conductivities for P-, As-, and Sb-based as well as S-, Se-, ans Te-based compounds at 700 K. Experimental value of Cu2SnS3 at 700 K is marked in pink.60 (e) The correlations between ΔCF and η. (f) The correlations between power factors and ΔCF.

S-, Se-, and Te-based compounds. The lighter VBMs of pnictides cause larger group velocities (lower transport effective mass) and less electron−phonon scattering phase space, both of which are beneficial to the electrical conductivities and PFs. As shown in Figure 3f, pnictides usually have higher PFs up to 100 μW/cm·K2, much larger than those of chalcogenides (up to 30 μW/cm·K2). The electronic structures and electrical transport properties indicate that there exists a universal conductive network dominated by the anion sublattice in these ABX2 compounds. For the compounds with the same anion sublattice, there are also minor differences in their electronic structures (e.g., the crystal field splitting energy ΔCF (= E(Γ5v) − E(Γ4v), MgSiP2 in Figure S1) at the VBM.16 As shown in Figure S1, the three bands at the VBM are split in some ABX2 compounds (i.e., ΔCF ≠ 0). Figure 3e shows a good linear relationship between ΔCF and the distortion parameter η. When η is close to unity, ΔCF approaches zero, which agrees well with the “the unity-η rule”.16 Figure 3f shows the relationship between calculated PF (with the same carrier concentrations corresponding to the maximum ZT values) at 700 K and ΔCF for the 41 ABX2 compounds. In the chalcogenides, PF is almost unchanged with ΔCF, whereas in the pnictides, there is a rough positive correlation between PF and ΔCF. As mentioned, the lattice thermal conductivities are obtained using the Slack model.58 Figure 4a shows the calculated as well as experimental lattice thermal conductivities at 300−900 K for CuInTe2 and AgInSe2.61,62 The experimental values agree well with theoretical values especially at high temperatures, which indicates that the Slack model is suitable for thermal conductivity prediction in these diamond-like compounds.

4. CONCLUSION An HTP workflow for high-TE-performance screening has been performed for ABX2 compounds with diamond-like structures based on the MIP, and results have been analyzed to extract trends and physical understanding. We find that there is a universal conductive network dominated by the anion sublattice E


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edges the support program of the Shanghai Subject Chief Scientist (16XD1401100), the support from Guangdong I n n o v a t i o n R e s e a r c h T ea m P r o j e c t (G r a n t N o . 2017ZT07C062), and the Shenzhen Pengcheng-Scholarship program. Work at the University of Missouri is supported by the Department of Energy, Basic Energy Sciences, grant number DE-SC0019114.

in both pnictides and chalcogenides. The VBMs of these compounds are triply degenerate (neglecting spin-orbit) or slightly split bands and are mainly composed of antibonding or nonbonding states. The lattice distortion has a minor influence on the band structures for the same anion sublattice. The pnictides have relatively larger PFs than the chalcogenides because of the lighter bands near the VBM. This also leads to lower optimal carrier concentrations. The lattice thermal conductivities are in general negatively correlated with the mean atomic weights of the compounds. In addition, the pnictides have somewhat higher κLs than the chalcogenides, partly compensating for the higher power factors. Finally, 12 promising high-performance TE materials of both n-type and ptype are predicted. Some of these 12 (CuInTe2, AgGaTe2, and ZnSnSb2) have been found experimentally to be good TE materials, supporting the approach used. Some of the predicted compounds, ZnSnSb2, AgInS2, AgGaSe2, AgInSe2, and LiInTe2, have high ZT values for both n-type and p-type, which may have good TE application prospects. The HTP workflow in this study shows the effectiveness in screening novel functional materials.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.9b01196.

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REFERENCES

The deformation potential (Edef) values for p-type and ntype ABX2 compounds (X = S, Se, Te, P, As, Sb) are shown in Tables S1 and S2. The distortion parameters η, crystal field splitting energies ΔCF, band gaps Eg, maximum p-type electronic fitness functions, and the corresponding carrier concentrations p for 41 compounds are listed in Table S3, respectively. Lattice thermal conductivities κL, constants A, mean atomic weights, Young’s moduli G, predicted maximum ZT values and the corresponding carrier concentrations, Seebeck coefficients, and power factors PFs of the 41 investigated compounds at 700 K for both n-type and p-type are shown in Table S4. Figure S1 shows band structures and density of states (DOS) at 700 K for 65 ABX2 compounds. Figure S2 shows the phonon spectra of the 41 compounds. Figure S3 shows band-resolved projected crystal orbital Hamilton populations (COHPs) (A−A, A−X, B−X, X onsite) for 41 compounds (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (L.X.) *E-mail: [email protected]. (J.Y.) *E-mail: [email protected]. (W.Z.) ORCID

Jiong Yang: 0000-0002-5862-5981 David J. Singh: 0000-0001-7750-1485 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the National Key Research and Development Program of China (Nos. 2017YFB0701600 and 2018YFB0703600), the Natural Science Foundation of China (Grant Nos. 51572167, 51632005, 11574333, 11674211, and 51761135127), and the 111 Project D16002. W.Q.Z. acknowlF


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