Data-Driven Design of Ecofriendly Thermoelectric High-Entropy

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Data-Driven Design of Ecofriendly Thermoelectric High-Entropy Sulfides Rui-Zhi Zhang,*,†,‡ Francesco Gucci,† Hongyu Zhu,† Kan Chen,† and Michael J. Reece*,† †

School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, United Kingdom School of Physics, Northwest University, Xi’an 710127, China

‡

Inorg. Chem. Downloaded from pubs.acs.org by UNIV OF NEW ENGLAND on 09/27/18. For personal use only.

S Supporting Information *

ABSTRACT: High-entropy compounds with compositional complexity can be designed as new thermoelectric materials. Here a data-driven model was developed, which chose suitable elements to reduce the enthalpy of formation and hence to increase the chance of single phase formation. Using this model, two high-entropy sulfides were designed, metallic Cu 5 SnMgGeZnS 9 and semiconducting Cu3SnMgInZnS7. They were then successfully fabricated as single-phase dense ceramics with homogeneously distributed cations, and their phase stability and atomic local structures were investigated using density functional theory calculations. Finally, a zT value of 0.58 at 773 K was obtained for Cu5Sn1.2MgGeZnS9, where additional Sn was used to tune the carrier concentration. This work provides a simple approach to find new high-entropy functional materials in the largely unexplored multielement chemical space.

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oxides,12,20−22 forming a promising novel class of materials with potential applications in thermoelectric,19 dielectrics,23 and lithium battery.24 As high-entropy compounds contain multiple elements, their design involves searching in a high-dimension multielement chemical space for thermodynamically stable phases. This will leads to the combinatorial explosion problem, and hence several searching methods and predictive models were developed in the literature, mostly for alloys.9 These methods involve calculating the enthalpies of formation of all the competing binary phases by using density function theory (DFT),25,26 using some algorithms to narrow down the searching space,27,28 or finding proper chemical descriptors such as atomic radius based on the databases of known highentropy alloys.14,29,30 Following the above approach, we here propose a data driven approach to identify high-entropy inorganic compounds, in which the information from Inorganic Crystal Structure Database (ICSD) was analyzed.31 Cu−S based diamond-like compounds were chosen as an example to demonstrate the data driven approach, and the main objective of this paper was to fabricate high-entropy Cu− S based sulfides with five types of cations. Cu−S based compounds were chosen because they have ample compositional variation and most of them are low-cost, ecofriendly minerals.32−34 They usually have maximum zT values of 0.5− 1.5 at 600−700 K, typically with a moderate power factor (∼10−3 W/m2 K2) and a very low lattice thermal conductivity (∼1 W/m K).7 The previous work showed that their good thermoelectric properties relate to their 3D Cu−S tetrahedral

INTRODUCTION For design and discovery of new thermoelectric materials, disorder and complexity within the unit cell have been widely used in the past decade.1−3 Under this design concept, together with the phonon-glass electron-crystal approach, several complex thermoelectric materials were designed.4,5 To name a few, half heusler compounds such as Ti0.5(Zr0.5Hf0.5)0.5NiSn0.998Sb0.002 (zT = 1.5 at 700 K)6 with compositional complexity and Cu−S based minerals including tetrahedrite Cu10.5Ni1.0Zn0.5Sb4S13 (zT = 1.0 at 700 K)7 with topological complexity. Introducing more elements into the unit cell can improve disorder and complexity, which is not only beneficial for thermoelectric properties enhancement8 but also enlarges the chemical space where more potential thermoelectric materials can be found. Despite such advantages, the problem for these multielement compounds can be their stability, as Pauling’s fifth rule (the rule of parsimony) states that “The number of essentially different kinds of constituents in a crystal tends to be small.”. The concepts of “high-entropy”9−11 and configurational entropy-stabilized compounds12 are helpful to solve the stability problem. Generally, the phase with the lowest Gibbs free energy will be the stable phase. As G = H − TS, where G, H, T, and S are Gibbs free energy, enthalpy, temperature, and entropy, respectively, increasing configurational entropy or minimizing the enthalpy of mixing are both favorable for phase stabilization. For multicomponent compounds, the former can be done by using equal or nearly equal quantities of five or more elements,11 and the latter can be done by carefully choosing the constituent elements.13,14 The “high-entropy” concept was first proposed for metal alloys,10,11 then applied to carbides,15,16 diborides,17 nitrides,18 chalcogenides,19 and © XXXX American Chemical Society

Received: August 24, 2018

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DOI: 10.1021/acs.inorgchem.8b02379 Inorg. Chem. XXXX, XXX, XXX−XXX

Inorganic Chemistry

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network,35,36 in which weak Cu−S bonding results in low lattice thermal conductivity37 and corner sharing Cu−S tetrahedrons provide moderate power factor.36

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Article

RESULTS AND DISCUSSION Data Driven Design. As a starting point, 49 Cu−S containing diamond-like compounds are listed in Table S1, among them 47 compounds from ICSD and the other two from the recent literature.43,44 During data cleansing, it was found that the crystal structure of Cu2S4Sn1W1 (ICSD number 602043) is abnormal and inconsistent with a recent report45 and conflicts with the usual coordinate state of W according to Pauling’s rule.35,46 In addition, B1Cu1S2 (ICSD number 156413) was only reported using high-temperature highpressure synthesis. These two compounds were removed from the list. Of the remaining 47 compounds, 18 are wurtzite derivative structures, and the other 29 are zinc blende derivative structures. For a given composition, the enthalpies of formation of wurtzite and zinc blende derivative phases are usually very close,47 and several compounds in Table S1 have been reported in both forms. The cations−sulfur bond lengths of the 47 compounds were calculated using the ICSD crystallographic information files (CIFs), which were then used as a chemical descriptor for high-entropy sulfide design. This descriptor was chosen because the bond lengths of cations are a good indicator of local strain, and small strain is favorable for single-phase stabilization according to Hume−Rothery rule. Figure 1 shows the bond length for 19 types of cations. These cations are also shown in the inset periodic table to

METHODS

Crystal Structure Data Mining. The diamond-like compounds were identified by screening all of the entries in the ICSD containing both Cu and S. This was done in three steps: (1) During the data cleansing procedure, entries which were duplicated or doping/offstoichiometry from a mother phase were removed. This gave 965 phases. (2) A total of 92 phases were then identified, which have Cu− S tetrahedrons, and the number of sulfur atoms is equal to the sum of cations. (3) Then, 92 phases were visualized by VESTA,38 to make sure that all of the cations occupy tetrahedral sites and the cation− sulfur tetrahedral form a 3D network only by corner sharing. After the three steps, 47 diamond-like compounds were finally chosen. More details can be found in our previous work.35 Bond Valence Model. The bond lengths were calculated using BV = exp((R0 − Ri)/0.37), where Ri is the bond length to be calculated, R0 is a tabulated bond length taken from bond-valenceparameters-2016.39 BV is the bond valence for cations which was set to their formal charge: +1 for Cu, +3 for group III elements, +4 for group IV, +5 for group V, and +2 for all others. DFT Calculation. The DFT calculations for geometry optimization were performed using the Quantum-ESPRESSO package.40 We used the Garrity−Bennett−Rabe−Vanderbilt (GBRV) high-throughput pseudopotential library.41 Perdew−Burke−Ernzerhof (PBE) functional was used along with ultrasoft pseudopotentials for all the atoms. The special quasirandom structures (SQS) model was generated using Alloy Theoretic Automated Toolkit (ATAT).42 The supercell sizes are 64 atoms for Cu3SnMgInZn2S8 and 80 atoms for Cu5SnMgGeZn2S10. The composition is slightly different from experiments (with one additional Zn per formula) due to the limitation of supercell size. The partial density of states was calculated using PBE+U, with U = 4 eV for Cu, Zn, and S. Sample Synthesis. Cu (99.5%), S (sublimed, 99.5%), Sn (99.5%), Mg (99.8%), Ge (99.99%), In (99.9%), and Zn (97+%) commercial powders were used. The powders were weighed and were then placed into a stainless-steel vessel with steel balls in a glovebox (Beta, Saffron, UK). The weight ratio of the steel balls to powders was 30:1. The mixtures were ball-milled at 360 rpm in a high-purity argon gas using a planetary ball milling machine (QM-3SP2, Nanjing University, China). The ball mill time was 60 h for both high-entropy sulfides, and 20 h for Cu3SnS4, Cu2MgGeS4 and ZnS. For highentropy sulfides, the powders were put into a graphite die (inner diameter ∼15 mm) and then sintered at 750 °C under 50 MPa with a heating rate of 50 K min−1 and holding time of 5 min in a spark plasma sintering furnace (FCT HPD 25, FCT System GmbH, Germany) in vacuum. It is worth noting that thicker samples (>3 mm) were usually preferred as thin samples often cracked. For the Cu3SnS4−Cu2MgGeS4−ZnS composite, the ball milled powders of the three compounds (Cu3SnS4, Cu2MgGeS4, and ZnS) were weighted as molar ratio 1:1:1, then were put in a mortar for hand mixing for 30 min in a glovebox. The mixed powders were then put into a graphite die and sintered at 600 °C using the same SPS parameters as above. Sample Characterization. The constituent phases of the sintered ceramics were characterized using powder X-ray diffraction (XRD, X’Pert PRO−PANalytical, Cu Kα) in the 2θ range 5−70°. The temperature-dependent electrical resistivity and Seebeck coefficient were measured using a commercial instrument (LSR-3/110, Linseis) in a He atmosphere. The temperature-dependent thermal diffusivity λ was measured using a laser flash method (LFA-457, Netzsch). The specific heat Cp was calculated using the Dulong−Petit law to avoid the large uncertainty in the routine differential scanning calorimetry method. The density d was obtained using the mass and volume of the sintered pellets. The thermal conductivity κ was determined using the equation κ = λCpd.

Figure 1. Bond length calculated using ICSD CIFs and BVM. The inset shows elements’ position in the periodic table.

show the chemical pattern. To make a comparison, the bond lengths were also calculated using the bond valence model (BVM).48,49 In Figure 1, the bond lengths from ICSD CIFs and BVM show generally the same trend, while for the ICSD CIFs there is large variation for several cations, especially Cu, Si, Ge, and Sn. These cations can be considered as “soft” and were used in the high-entropy sulfides design to reduce the local strain energy. For other cations, ecofriendly and nonmagentic cations were considered, the reason for the former is sustainability, and for the latter, it is that spin introduces additional complexity into high-entropy compounds. On the basis of the above, two compositions were selected, (Cu, Sn, Mg, Ge, Zn)S and (Cu, Sn, Mg, In, Zn)S. The cations−anion ratio is 1:1 as with all of the diamond-like compounds. The next step was to determine the proportions of the cations. Equal proportions give the largest configurational entropy.12 However, entropy alone is not sufficient to stabilize B

DOI: 10.1021/acs.inorgchem.8b02379 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry single-phase and enthalpy must also be considered.13 To further reduce enthalpy, a simple criterion was introduced: The designed high-entropy sulfide can be considered as a solid solution of several diamond-like binary/ternary/quaternary compounds. As all of the compounds have diamond-like structures with the same topology with infinite corner sharing tetrahedrons, this can be thought of as a specific case of one of the Hume−Rothery rules “the crystal structures of solute and solvent must be similar”. The criterion of diamond-like compound solid solutions was applied by matching the formula combinations in Table S1. For example, two possible matching combinations for (Cu, Sn, Mg, Ge, Zn)S can be Cu3SnS4 + Cu2MgGeS4 + ZnS or Cu2ZnSnS4+Cu2MgGeS4. As we wanted the high-entropy compounds to be conductive, the first combination containing metallic Cu3SnS4 was chosen. For (Cu, Sn, Mg, In, Zn)S, possible combinations can be Cu2MgSnS4 + CuInS2 + ZnS or Cu3SnS4 + CuInS2 + ZnS + MgS. Although the second contains the metallic Cu3SnS4, it also contains MgS which has a rock-salt structure rather than diamond-like. Therefore, the first combination was chosen. The formulas of the two designed compounds were Cu 5 SnMgGeZnS 9 and Cu3SnMgInZnS7. Cu5SnMgGeZnS9 should be metallic and can be thought of as a solid solution of Cu3SnS4, Cu2MgGeS4 and ZnS. It is worth noting that Cu3SnS4 is the only metallic compound in Table S1, and several reported Cu−S based quaternary compounds with thermoelectric performance can be thought of as solid solution containing Cu3SnS4,50−52 as shown in Table S2. In these reported compounds, the molar fraction of Cu3SnS4 is relatively small (10−20%); hence, the configurational entropy is not significant. While in the current work, configurational entropy was considered for single-phase stabilization by incorporating five cations, four of which are equal molar. In other words, we moved to the central region of the solid solution phase diagram, following the concept proposed in the earliest high-entropy alloy papers.10 The second compound Cu3SnMgInZnS7 should be a semiconductor and can be thought of as a solid solution of Cu2MgSnS4, CuInS2, and ZnS. Phase Identification. Figure 2a shows the XRD patterns of the synthesized Cu5SnMgGeZnS9 and Cu3SnMgInZnS7 ceramics. The relative density of the sintered ceramics were both >95%. Both compounds have tetragonal structure rather than cubic. This means that the cations are not fully random but have some order. Considering that the high-entropy compounds are solid solutions of ZnS, Cu3SnS4 (CuInS2), and Cu2MgGeS4 (Cu2MgSnS4) and two out of three are tetragonal, it is not surprising that the solid solutions are tetragonal. The lattice parameters obtained from Rietveld refinement are shown in Table 1. Rietveld analyses were done with the GSAS-EXPGUI package,53 using Cu2S4Sn1Zn1 (space group I4̅2m, ICSD number 171983) as a reference (black bars in Figure 2a). The Rwp factors were 9.2 and 6.7% for Cu5SnMgGeZnS9 and Cu3SnMgInZnS7, respectively, suggesting a good fit between the experimental and calculated intensities. The c/2a values are both very close to 1 and indicate potentially good thermoelectric performance according to a previous study.36 A ceramic composite containing the three individually synthesized compounds, Cu3SnS4, Cu2MgGeS4, and ZnS, is also shown in Figure 2a. The peaks are broad as three phases coexist. Although the main peaks of the three

Figure 2. XRD and EDX of sintered high-entropy sulfides and composite.

Table 1. Lattice Parameters of High Entropy Sulfides a [Å] experiment DFT calculation experiment DFT calculation Vegard’s lawa

Cu5SnMgGeZnS9 5.378 5.417 Cu3SnMgInZnS7 5.499 5.546 5.461

b [Å]

c [Å]

5.378 5.418

10.722 10.830

5.499 5.554 5.461

10.992 11.023 10.953

a

The lattice parameters used are a = 5.521 Å and c = 11.141 Å for CuInS2 from ICSD no. 186714, a = 5.427 Å and c = 10.85 Å for Cu2MgSnS4 from ref 44, a = 5.434 Å for ZnS from ICSD no. 77090.

phases overlap, some peaks can be identified for Cu2MgGeS4 as indicated by triangles. This also can be seen in the EDX results in the lowest panel of Figure 2b, where Mg and Ge have the same distribution pattern in the Cu3SnS4−Cu2MgGeS4− ZnS ceramic composite. For Cu 5 SnMgGeZnS 9 and Cu3SnMgInZnS7, the cations are homogeneously distributed (Figure 2b). Table 1 lists the DFT calculated lattice parameters of the high-entropy sulfides, which agree well with the experimental values with an error of about 1%. A slightly overestimation is typical when using PBE functional. The difference between the C

DOI: 10.1021/acs.inorgchem.8b02379 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry a and b lattice parameters is because that the SQS used in DFT calculations are not truly random and are just a local approximation.54 The lattice parameters were also calculated by considering Cu3SnMgInZnS7 as a solid solution, using the Vegard’s law and lattice parameters of Cu2MgSnS4, CuInS2, and ZnS. The calculated results agree well with experimental values. Validation of the Vegard’s law was also found in previous studies for high-entropy alloys, 9 while for Cu5SnMgGeZnS9, the Vegard’s law cannot be applied to because that Cu2MgGeS4 has a wurtzite derivative structure. To investigate the local structures of the high-entropy sulfides, Figure 3 shows the cation−sulfur bond length values,

respectively. The electrical conductivity was successfully reduced (Figure 4a), which resulted in an increased Seebeck coefficient. The electrical conductivities of the three samples all show metallic behavior above 523 K. Below 523 K, their behavior is quite different: Cu5SnMgGeZnS9 shows metallic behavior. With 10% additional Sn, Cu5Sn1.1MgGeZnS9 first shows metallic behavior, and the electrical conductivity shows a small maxima at 473 K. With 20% additional Sn, Cu5Sn1.2MgGeZnS9 shows semiconducting behavior. This can be understood by considering the localized states in these highly disordered systems. In Cu5SnMgGeZnS9, the carrier concentration is high and the Fermi level is in the valence band, above the localized states; therefore, in the whole temperature range it shows metallic behavior. With additional Sn, the carrier concentration is reduced and the Fermi level drops, so that carrier thermal activation now plays an important role, giving rise to the interesting behavior in Figure 4a. Because the composition is complex, at this stage it is difficult to quantify the effect of localized states, and further investigations are needed. The thermoelectric properties of the Cu 3 SnS 4 − Cu2MgGeS4−ZnS ceramic composite containing three individual phases are also shown in Figure 4a,b for comparison. The stability temperature improved by 100 K for the highentropy sulfides compared to that of the composite. The electrical conductivity of the composite is very low, probably because that the proportion of metallic phase Cu3SnS4 has not reached to the percolation threshold. The combination of XRD, EDX, and thermoelectric properties give strong evidence that single-phase solid solutions were formed for these highentropy sulfides. The power factor reaches 8 μW/cm K2 at 773 K for Cu5Sn1.2MgGeZnS9. This value is comparable to those of typical diamond-like Cu−S based thermoelectric materials, such as Cu2SnS3,52,58 Cu3SbS4,59,60 and Cu2CoSnS4.51 The c/ 2a value for this high-entropy compound was 0.997, that is, close to unity. From the point view of band structure, this means that the Γ5v and Γ4v bands converged near the valence band maximum, which gave rise to a high power factor. We used the c/2a structural descriptor rather than the DFT band structure because the band broadening61 resulting from disorder makes the band dispersion analysis intractable. The partial density of states of Cu5SnMgGeZn2S10 are shown in Figure S1. Although PBE+U failed to open a band gap for this system, it can still be seen that the density of states near the Fermi level was mainly composed of Cu 3d and S 3p orbitals. The thermal conductivities of the high-entropy sulfides are low and decrease with increasing temperature. The lattice thermal conductivity, calculated by subtracting the electronic part, reaches ∼0.4 W/m K at 773 K. This value is comparable to those of typical diamond-like Cu−S based thermoelectric materials, such as Cu 2 SnS 3 , 52,58 Cu 3 SbS 4 , 59,60 and Cu2CoSnS4.51 The reason for low lattice thermal conductivity is mainly due to weak Cu−S bonding. Furthermore, mechanical alloying plus SPS produce fine-grain-size ceramics, which further reduce the lattice thermal conductivity by interfacial phonon scattering. A zT value of 0.58 at 723 K was obtained for Cu5Sn1.2MgGeZnS9 (Figure 4d). The thermoelectric properties of high-entropy sulfides were similar to those of ternary or quaternary diamond-like sulfides. In other words, introducing disorder by incorporating more elements produced a marginal improvement in the thermo-

Figure 3. Box plot of cation−sulfur bond lengths in DFT relaxed supercells. For each plot, two short horizontal bars mean upper and lower bounds, and “□” are the mean values. The composition is slightly different to experimental ones due to the supercell size limit in DFT calculations. Bond length values calculated by BVM are also shown for comparison.

obtained from the SQS supercell structures optimized by DFT calculations. The bond length values calculated using BVM are also shown for comparison. It can be seen the average bond length values from DFT calculations, indicated by small squares, agree well with those from BVM. The average bond length value of each cation in the In containing compound is slightly higher than that in the Ge containing compounds, as In−S bond length (2.46 Å in BVM) is much larger than Ge− S(2.23 Å). This is also the reason why the lattice parameters of Cu 3 SnMgInZnS 7 are slightly larger than those of Cu5SnMgGeZnS9 (Table 1).The bond lengths in both compounds show large deviation in Figure 3, indicating strong local disorder. Thermoelectric Properties. Figure 4 shows the thermoelectric related properties of Cu5SnMgGeZnS9 and related compounds. As Cu3SnMgInZnS7 is a semiconductor and its electrical conductivity is very low, its thermoelectric properties are not reported. The electrical conductivity of Cu5SnMgGeZnS9 (Figure 4a) shows metallic behavior, and the values are higher than the typical values reported for Cu−S based thermoelectric compounds such as tetrahedrite. For example, the electrical conductivity is around 1000 S/cm at 623 K, compared with 770 S/cm for tetrahedrite.55,56 This results in a lower Seebeck coefficient; therefore, the carrier concentration should be reduced to optimize the power factor. It has been recently reported that the carrier concentration of Cu3SnS4 can be reduced by introducing additional Sn.57 Therefore, Cu5Sn1.1MgGeZnS9 and Cu5Sn1.2MgGeZnS9 ceramics were fabricated, with 10 and 20% additional Sn, D

DOI: 10.1021/acs.inorgchem.8b02379 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

Figure 4. Thermoelectric properties of high-entropy sulfides. Electrical conductivity and Seebeck coefficient of Cu3SnS4−Cu2MgGeS4−ZnS composite are also shown for comparison.

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electric properties of Cu−S based materials. The main reason is that the lattice thermal conductivity of Cu−S based materials is already very low, and it would be difficult to further reduce it. However, this does not rule out the possibility that the highentropy concept can be used to improve the thermoelectric properties of materials with intrinsic high thermal conductivity. The disorder in high-entropy compounds introduces mass and strain fluctuations that enhance phonon scattering, thus reducing lattice thermal conductivity. The disorder is likely to be beneficial in such systems,62 i.e., the reduction in carrier mobility due to electron scattering from disordered atoms is more than compensated for by the reduction in thermal conductivity from the same disorder.

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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/acs.inorgchem.8b02379. Bond length values and composition analysis of thermoelectric sulfides (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Rui-Zhi Zhang: 0000-0001-7229-769X CONCLUSION

Notes

The authors declare no competing financial interest.

Two high-entropy sulfides, Cu 5 SnMgGeZnS 9 and Cu3SnMgInZnS7, thermoelectric materials were designed. It was demonstrated that a simple data-driven approach, in which Cu−S containing diamond-like compounds in the Inorganic Crystal Structure Database (ICSD) were identified and the cation−sulfur bond lengths were analyzed, is effective in designing high-entropy compounds. This approach was supported by fabricating single-phase Cu5SnMgGeZnS9 and Cu3SnMgInZnS7 ceramics using mechanical alloying and spark plasma sintering. XRD, EDX, and thermoelectric transport properties measurement all support that single-phase solid solutions.

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ACKNOWLEDGMENTS This work was supported by Engineering and Physical Sciences Research Council (EPSRC) (Grant No. EP/N0227261/1), Designing Eco-Friendly and Cost efficient Materials (DEFCOM). R.Z. acknowledges the support from Natural Science Foundation of China (11674264) and thanks National Supercomputer Center in Jinan for making the first-principles calculations possible. F.G. was supported by European Community’s Horizon 2020 Programme through a Marie Skłodowska-Curie Innovative Training Network [g.a. no. 642557, CoACH-ETN]. We also would like to thank European Thermodynamics, Ltd., for its support. E

DOI: 10.1021/acs.inorgchem.8b02379 Inorg. Chem. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.inorgchem.8b02379 Inorg. Chem. XXXX, XXX, XXX−XXX