Computational Exploration of the Binary A1B1 Chemical Space for

Article pubs.acs.org/cm

Computational Exploration of the Binary A1B1 Chemical Space for Thermoelectric Performance Prashun Gorai,†,‡ Philip Parilla,‡ Eric S. Toberer,†,‡ and Vladan Stevanović*,†,‡ †

Colorado School of Mines, Golden, Colorado 80401, United States National Renewable Energy Laboratory, Golden, Colorado 80401, United States

‡

Downloaded by CENTRAL MICHIGAN UNIV on September 15, 2015 | http://pubs.acs.org Publication Date (Web): September 8, 2015 | doi: 10.1021/acs.chemmater.5b01179

S Supporting Information *

ABSTRACT: In spite of the emergence of chemically complex thermoelectric materials, compounds with simple binary A1B1 chemistry continue to dominate the highest zT thermoelectric materials. To understand the structure−property relations that drive this propensity, we employed a descriptor that combines ab initio calculations and modeled electron and phonon transport to offer a reliable assessment of the intrinsic material properties that govern the thermoelectric figure of merit zT. We evaluated the potential for thermoelectric performance of 518 A1B1 chemistries in 1508 different structures and found that good thermoelectric performance of A1B1 compounds originates mainly from low valent ions in combination with cubic and orthorhombic crystal structures, which primarily offer favorable charge carrier transport properties. Additionally, we have identified promising new A1B1 compounds, including their higher-energy polymorphs.

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INTRODUCTION Practical thermoelectric applications demand semiconductor materials that exhibit a large figure of merit zT =

α 2σT (κe + κL)

materials yet to be discovered within the well-studied A1B1 chemical space? To address these questions, we computationally assessed the potential for thermoelectric performance of the chemical space of known binary A1B1 metal-nonmetal compounds spanned across the main group and d-transition metals (excluding only Tc, Ru, Rh) as cations, and group V, VI, and VII elements (excluding Po, At) as anions. We screened 287 known A1B1 compositions reported in the Inorganic Crystal Structure Database (ICSD)17 including all reported crystal structures (polymorphs) for each composition in the ICSD. Additionally, 231 A1B1 compositions that are currently missing from the ICSD were considered assuming the hypothetical rocksalt structure. In total, we considered 518 A1B1 compositions in 1508 structures. To quantify the potential of materials for thermoelectric performance, we employed our previously developed metric βSE18 that can be evaluated directly from first-principles calculations. Details of βSE are provided in the next section. By employing βSE, we show that beyond rocksalts, the A1B1 compounds in cubic and orthorhombic structures are generally well-suited for p-type thermoelectric performance, primarily due to their beneficial charge carrier transport properties. The A1B1 stoichiometry in these two structure types naturally accommodates ions in the low oxidation state, which is beneficial for charge transport. Additionally, we identified promising new A1B1 compounds, including higher-energy polymorphs, that have not been previously considered for thermoelectric applications.

(1)

where α is the Seebeck coefficient, σ is the electronic conductivity, and κe and κL are the electronic and lattice components of thermal conductivity, respectively.1 Novel highperformance materials are needed for developing commercially viable technologies that would enable solar-thermal electricity generation,2 and a range of applications involving waste heat capture3 and compression-free refrigeration.4 However, inspection of eq 1 reveals that the need to simultaneously optimize both charge carrier and thermal transport properties is a fundamental challenge facing the rational design of new thermoelectric materials. The physics of thermal transport suggests that crystalline materials in relatively complex chemistries involving large number of atoms in the unit cell are desirable (enhanced phonon scattering and reduced phonon group velocities) for lowering κL.5 Interestingly, as shown in Figure 1, nearly 30% of good thermoelectric materials (10 out of 34) are in the simple binary A1B1 stoichiometry (blue circles, bar). Half of these A1B1 materials (5 out of 10) crystallize in the rocksalt structure (space group 225). All other stochiometries (orange circles, bar) are represented with three or fewer materials with relatively large reported zT values. The statistics from Figure 1 raise the following questions: (a) is there anything special about the A1B1 rocksalts that makes them particularly good thermoelectric materials or do the observations from Figure 1 suffer from historical biases toward more explored systems? and (b) are there new thermoelectric © XXXX American Chemical Society

Received: March 30, 2015 Revised: August 27, 2015

A

DOI: 10.1021/acs.chemmater.5b01179 Chem. Mater. XXXX, XXX, XXX−XXX

Article

Chemistry of Materials

throughput fashion. Motivated by the relationships describing electron−phonon scattering rates of band conductors, the intrinsic carrier mobility μ0 is modeled as μ0 = A 0(B)s (mb*)−t

(4)

where B is the bulk modulus that describes the elastic properties of the material and m*b the band effective mass. Four distinct electron−phonon scattering mechanisms are considered: (i) acoustic deformation potential scattering, (ii) optical deformation potential scattering, (iii) polar optical phonon scattering, and (iii) piezoelectric scattering. Fitting parameters A0, s, and t are taken from ref 18, while B and m*b are computed with first-principles methods. κL is modeled as


κL = A1

3 Mv vs ⎛ ̅ s 1 ⎞ ⎜1 − 2/3 ⎟ + A 2 2/3 2/3 1/3 V n V ⎝ n ⎠

(5)

where M is the average atomic mass, V the average volume per atom, vs the speed of sound, and n the number of atoms in the primitive cell. The model in eq 5 assumes a constant Grüneisen parameter (γ). To a first approximation, vs depends on B and

(

density d vs =

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THERMOELECTRIC PERFORMANCE METRIC Consideration of the Boltzmann transport equations for α, σ, and κe in the relaxation time approximation19 yields an expression uβ (vβ + 1)

(2)

where u and v depend on charge carrier chemical potential (η) and carrier scattering mechanisms, and β is a materialdependent parameter. Therefore, maximizing zT requires simultaneously optimizing the intrinsic material properties, contained within β, as well as doping. The parameter β is defined as 2 3/2 * 3/2 2e ⎛ kB ⎞ ⎛ kB ⎞ μ0 mDOS T 5/2 β = 3⎜ ⎟ ⎜ ⎟ κL ℏ ⎝ e ⎠ ⎝ 2π ⎠

). The first term on the right side of eq 5 is

the acoustic and the second term the optical component of κL. Here, A1 and A2 are fitting parameters that are taken from ref 18, while M, V, d, and B are obtained from calculations. To evaluate βSE, one needs to compute mDOS * , mb*, and B; M, V, and d are also directly accessible from the calculations. The band effective mass (m*b ) is evaluated from m*DOS and the band degeneracy (Nb) using the relation mDOS * = Nb2/3mb*, which strictly holds true for spherical and symmetry equivalent electron/hole pockets in the Brillouin zone. Nb is the total number of bands in all charge carrier pockets in the first Brillouin zone. Nb is calculated from the electronic structure using our previously developed algorithm.18 Density functional theory (DFT) calculations to compute Nb, m*DOS, and B were performed with plane-wave VASP code,20 with the exchange correlation in the Perdew Burke Ernzerhof (PBE) functional form within the projector augmented wave (PAW) formalism.21 For structure relaxations, a procedure similar to that employed in ref 22 was used, with plane wave cutoffs of 340−500 eV. A suitable on-site correction in the form of Hubbard U in the rotationally invariant form, introduced by Dudarev and co-workers,23 was applied for transition metals following the methodology in ref 22. In case of A1 B1 compounds containing transition metals, we performed a limited search for the magnetic ground state by enumerating over all possible magnetic configurations on a primitive unit cell. To determine the lowest energy magnetic state, the volume and ionic relaxations were performed with the magnetic moments initialized in all possible ways. Because the number of initial configurations scale as 2N with the number of magnetic atoms (N), we limited the total number of calculations. For all A1B1 compounds containing six or fewer transition metal atoms in the primitive unit cell, we considered all possible magnetic configurations (up to 32), while for those containing more than six, we randomly chose 32 different initial configurations. Higher-energy magnetic configurations were not included in the following analysis. Calculations of m*DOS and Nb were undertaken on a dense kpoint grid with a fixed number of k-points per atom, as determined by the equation Natoms × Nkpts = 8000, where Natoms is the number of atoms in the primitive cell and Nkpts the

Figure 1. (a) Scatter plot of zT values against the space group number for 34 known thermoelectric materials with zT ≥ 0.5.3,6−16 (b) More than 25% of known thermoelectric materials belong to the binary A1B1 stoichiometry (blue circles and bar, orange squares and bars are other stoichiometries). Half of the A1B1 materials with zT > 0.5 crystallize in the rocksalt structure.

zT =

B d

(3)

where μ0 is the intrinsic charge carrier mobility, m*DOS the density of states (DOS) effective mass, κL the lattice thermal conductivity, kB the Boltzmann constant, e the electronic charge, and ℏ the reduced Planck constant. For materials that were optimally doped to maximize zT, the β value was calculated from measured room temperature μ0, and mDOS * and κL were found to be good descriptors of the maximal achievable zT, as demonstrated in ref 18. To address the challenges associated with direct calculation of the transport properties entering eq 3, we have recently developed semiempirical models for μ0 and κL18 by combining first-principles calculations and a large body of measured room temperature μ0 and κL for a range of materials. By using these semiempirical models, β (now referred to as βSE) can be evaluated from first-principles calculations and in a highB


Article


Chemistry of Materials number of k-points. This k-point density is equivalent to a 14 × 14 × 14 k-mesh for diamond Si and provides sufficiently converged electronic structure properties. B is calculated by fitting the Birch−Murnaghan equation of state24 to a set of total energies computed at different volumes. m*DOS is determined from the electronic DOS within a parabolic band approximation such that the parabolic band reproduces the same number of states as the computed DOS within a 100 meV (adjustable) energy window from the relevant band edge. When the Fermi level lies close to the band edge, as in many thermoelectrics, the energy window is a measure of the extent to which the bands are populated with carriers at finite temperature. It is important to note that while βSE does not explicitly depend on the value of the band gap, the optimal working temperature of thermoelectric materials as well as its dopability does. Furthermore, we have included in our study all A1B1 compounds with DFT band gaps larger than 10 meV (computed on a dense k-point grid) because of the wellknown underestimation of band gaps in DFT methods. Previous notable attempts at computationally screening thermoelectric materials have focused on half-Heuslers,25 sintered materials,26 transition metal silicides,27 and ternary antimonides.28 Unlike these efforts, our approach does not rely on assumptions such as energy-independent charge carrier relaxation times or requirements such as morphological modifications (nanostructuring). These assumptions are typically used to overcome the difficulties associated with the direct calculation of charge carrier transport properties; the performance metrics are based on the power factor (α2σ) alone. The power factor-based metrics are used to rank materials, while the influence of κL is largely neglected. In contrast, the metric βSE (a) accounts for charge carrier transport beyond the constant (energy-independent) relaxation time approximation, and (b) includes the lattice thermal conductivity, which represents the dominant contribution to the thermal conductivity at low to moderate doping.

Figure 2. Calculated β SE values of all metal-nonmetal A 1 B 1 compositions (287) in all of their known structures reported in the ICSD, represented by the circle area for both (a) conduction (n-type) and (b) valence (p-type) band transport. Large βSE materials are dominated by the cubic (blue) and orthorhombic (orange) crystal systems.

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crystal systems, especially for valence band βSE (Figure 2b). A few tetragonal crystals (space group 75−142) in p-type (e.g., GeTe) and hexagonal crystals (space group 168−194) in n-type (e.g., InSe) also exhibit reasonably large βSE values. The dominance of cubic crystals is rather unsurprising because most known A1B1 thermoelectrics shown in Figure 1 are cubic crystals. The emergence of orthorhombic crystals as a promising structure space offers new guidance. It is important to note that not all cubic and orthorhombic crystals have large βSE values but that the majority of large βSE materials adopt the cubic and orthorhombic structures. The predicted inclination of good thermoelectrics to reside in the cubic or orthorhombic structures could be a result of the population statistics because the majority (∼60%) of A1B1 compounds that have nonzero calculated band gaps crystallize in these two crystal systems. To confirm the favorability of cubic and orthorhombic crystals such that population bias is minimized, we consider compounds that have at least one cubic or orthorhombic polymorph and at least one other that does not belong to those crystal systems, with at least one of the polymorphs with reasonably large βSE (⩾ 0.5 βSE,PbTe). Figure 3 shows the ratio of averaged βSE values of cubic and orthorhombic polymorphs to the βSE value averaged over non(cubic, orthorhombic) polymorphs for a given composition. A ratio of 1 implies that, on average, cubic and orthorhombic and non(cubic, orthorhombic) structures are predicted to have

A1B1 CHEMICAL SPACE: TRENDS IN TRANSPORT PROPERTIES Figure 2 shows the variation in βSE with μ0, κL as a function of the crystal system for all A1B1 metal-nonmetal compositions in all of their known crystal structures reported in the ICSD, provided the DFT-calculated band gap is larger than 10 meV. The circle area scales with βSE for conduction (Figure 2a) and valence (Figure 2b) band transport. The complete data set is provided in the Supporting Information (Table S1) and will be made available on our public database (www.tedesignlab.org). Known thermoelectric materials shown in Figure 1 are all correctly indentified as good thermoelectrics with relatively large βSE values in Figure 2. PbTe, PbS, PbSe, and SnTe are predicted to be good both as n- and p-type materials, consistent with the experimental literature.3,8,12−14,29−32 The SnSe Cmcm phase is predicted to outperform the room-temperature (Pnma) phase for p-type doping, which is again in agreement with recent experimental results.14 The trends in Figure 2 indicate that (a) cubic (blue) and orthorhombic (orange) crystal structures are dominant among the A1B1 materials with relatively large βSE, and (b) there is an intermediate optimal range of κL (∼1−10 Wm−1K−1) within which nearly all large βSE occur. Effects of Crystal Structure. Large βSE values in Figure 2 are dominated by cubic (blue) and orthorhombic (orange) C


Article

Chemistry of Materials ⎛ N ⎞⎛ β ⎞ βSE = ⎜ b ⎟⎜ SE ⎟ ⎝ mb* ⎠⎝ Nb/mb* ⎠

(7)


where the first and second bracket on the right-hand side still contain exclusively reciprocal and real space parameters, respectively. The positive linear dependence of βSE on the reciprocal space factor (Nb/m*b ) in Figure 4, panels a and c for n- and p-type

Figure 3. Ratio of averaged βSE values of cubic and orthorhombic (βSE, co ) to non(cubic, orthorhombic) (βSE, non−co) structures. Compositions that have at least one cubic, orthorhombic and at least one non(cubic, orthorhombic) polymorph and a βSE ≥ 0.5 βSE,PbTe are shown. A ratio larger than 1 indicates the favoribility of cubic and orthorhombic crystals.

similar thermoelectric performance, while a ratio larger than 1 suggests cubic and orthorhombic crystals perform better. It is evident from Figure 3, panel a, where 10 out of 14 compositions have ratios larger than 1, that cubic and orthorhombic crystals are especially favorable for valence band transport (assumed p-type doping) thermoelectricity. For n-type (Figure 3b), a similar number of compounds exhibit ratios larger than and smaller than 1, indicating no clear benefit of cubic and orthorhombic crystals. A closer look at Figure 3, panels a and b reveals that compounds containing ions in a low oxidation state (e.g., Pb2+, Ag+, Mn2+) exhibit ratios larger than 1 in both p- and n-type materials. As discussed in the Role of Low Valent Cations and Anions section, the oxidation state of the cation and anion in A1B1 materials also plays an important role in influencing transport properties besides the crystal structure. In Figure 3, for a given composition, the effects are purely structural in nature because the oxidation states of the ions are fixed. Effects of Key Transport Parameters. From eq 3, one would expect that large βSE results from maximizing μ0 and minimizing κL, that is, βSE should increase linearly with μ0 and 1 . However, this linearity is not satisfied (Figure S3 in

Figure 4. Linear correlation between βSE and (Nb/m*b ) in panels a and c suggests that reciprocal space parameters are the stronger drivers of thermoelectric performance in the A1B1 chemical space. The dependence is stronger in p-type materials (r2 = 0.82) compared to n-type (r2 = 0.67). The real space parameters lack any clear correlation with βSE.

materials, respectively, and the lack of any clear correlation between βSE and the real space parameters (βSE/(Nb/mb*)) suggest that the reciprocal space parameters are the “stronger” driver of thermoelectric performance in the A1B1 chemical space. Nb and m*b are the core parameters influencing charge carrier transport (eq 4). The real space parameters, which govern the thermal transport (eq 5), are the “weaker” driver of thermoelectric performance. While an optimal κL (1−10 Wm−1 K−1) is still necessary, it is not a sufficient condition to improve performance, as also suggested by Madsen28 previously. The fact that enhanced band degeneracy (Nb) and smaller band effective mass (m*b ) are beneficial for improving thermoelectric performance is well established,11,33 but the importance of these reciprocal space parameters in driving performance in the A1B1 chemical space provides new understanding. In other words, thermoelectric performance can be improved significantly by enhancing charge carrier transport when κL lies in an optimal range. Overall, orthorhombic crystals exhibit lower κL values than cubic crystals in Figure 2. As shown in Figure S1 (Supporting Information), this is due to the lower bulk modulus of orthorhombic structures. Structures belonging to the Pbca, Pnma, and Cmcm space groups, which comprise 60% of the

κL

Supporting Information) because of the natural interdependence between μ0 and κL, although there is a general increase in βSE with increasing μ0 and decreasing κL. There is an optimal κL range (∼1−10 Wm−1K−1) where larger μ0 yield relatively large βSE (Figure 2), with some exceptions in n-type materials, where large βSE is also found in the extremely low κL ≈ 0.1 Wm−1 K−1 regime. The interdependency warrants a closer examination of the more fundamental parameters affecting μ0 and κL and therefore βSE. By substituting the models for μ0 (eq 4) and κL (eq 5) in βSE (eq 3)18 and rearranging yields an expression for βSE becomes ⎞ ⎛ N ⎞⎛ A0 ⎟⎟ βSE ∝ ⎜ b ⎟⎜⎜ 2/3 1/3 3/2 1/2 2/3 2/3 1/2 1/2 − − − − − ⎝ mb* ⎠⎝ A1MV n d B + A 2V (1 − n )d B ⎠ ̅

(6)

where the terms in the first and second bracket on the righthand side are reciprocal (Nb, m*b ) and real space (M, V, n, d, B) parameters, respectively. A0, A1, and A2 are constants. By removing the proportionality, an exact expression for βSE can be written as D


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Role of Low Valent Cations and Anions. Cations in low oxidation state are prevalent in compounds predicted to be good n- and p-type thermoelectric materials (Figure 5). However, it is not immediately obvious how the enhancement of the reciprocal space factor (Nb/m*b ) in the cubic or orthorhombic structure is related to the low oxidation state of the ions and the characteristics of the valence and conduction band. In standard II−VI and III−V semiconductors that do not contain ions in low oxidation state, the chemical bond is formed by the interactions of the cation s and the anion p orbitals. As a result of the charge transfer, the valence band is predominantly of anion p character, while the conduction band is primarily composed of cation s orbitals. As illustrated in Figure 6, panel a

orthorhombic crystals in Figure 2, are layered materials with low B and therefore low κL. Consistent with these observations, orthorhombic crystals (orange) lie predominantly above the fitted straight line, while cubic crystals are below in Figure 4, panels a and c.


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COMPOSITION−STRUCTURE−PROPERTY RELATIONS From the previous sections, we infer that the reciprocal space factor (Nb/mb*) is the “stronger” driver of βSE, but large βSE values occur when simultaneously (Nb/m*b ) is large and κL is in the optimal range (1−10 Wm−1 K−1). Large (Nb/m*b ) ratios are predominantly found in cubic and orthorhombic crystals for valence band transport, whereas for conduction band transport, large (Nb/m*b ) is agnostic of structure type. In this section, we explore the chemical reasons for this observation. Inspection of the A1B1 materials predicted to have large βSE (⩾ 0.5 βSE,PbTe) reveals yet another commonality: an overwhelming majority of them contain elements in a low oxidation state (Figure 5). By

Figure 5. Variation of βSE (circle area) as a function of Nb and mb* for structures with βSE ⩾ 0.5βSE,PbTe. The predominant blue circles represent compounds containing cations or anions in a low oxidation state.

low oxidation state, we mean that the cation is partially ionized in the formal oxidation state, which is typical of elements with multiple valencies. For example, Pb2+ in PbTe is a low cation oxidation state with electronic configuration [Xe]4f145d104s2, while Pb4+ represents a fully ionized configuration [Xe]4f145d10. An analogous definition applies to anions. The binary A1B1 stoichiometry is one of the simplest chemistries that naturally accommodates ions in low oxidation states.

Figure 6. Electronic band structure and orbital-projected DOS for (a) InP (F43m), (b) PbTe (Fm3m), and (c) SnSe (Cmcm). The gray bands represent a 100 meV energy window within which Nb is calculated. The positions of E, A, and H for the orthorhombic Brillouin zone of SnSe (Cmcm) can be found in ref 18. E


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composed of ionically and covalently bonded atoms. As in Zintl compounds,38 the ionic cations donate electrons to covalently bonded anions, for example, [Sb2]−4 dimers in ZnSb. The valence band appears to be derived from the covalent anion p− p bonding interaction between the Sb dimer pair, with the VBM off of Γ (Nb = 2, 3 for ZnSb, CdSb) and relatively light mb* (0.08, 0.1 me for ZnSb, CdSb). The conduction band is derived from the antibonding orbital of cation s and anion p interaction with predominantly anion p character (see Figure S2 in Supporting Information for DOS). Because of the p character, the CBM occurs off of Γ, which enhances Nb (6 for ZnSb, CdSb). The cation s contribution to the CBM ensures dispersive bands with low mb*. Additionally, these orthorhombic structures benefit from the lower κL (Figure S1 in Supporting Information). Some of the transition metal compounds, such as the d3-(VTe), d5-(MnTe), and d10-(CuBr, AgBr, AgI) systems, exhibit band structure features similar to those observed in compounds containing cations in low oxidation state. This leads to larger band degeneracies (Nb) and smaller band effective masses (mb*), which are both beneficial for charge carrier transport. Validation in Hypothetical A1B1 Rocksalts. To further validate that a favorable combination of crystal structure (cubic or orthorhombic) and low oxidation state of the ions potentially improves thermoelectric performance, especially in p-type materials, we considered hypothetical A1B1 compounds in the rocksalt structure. Note that these hypothetical A1B1 rocksalts are used mainly for the purpose of testing our conclusions but are extremely unstable, as suggested by the energy offsets in Table S2 in the Supporting Information. We assessed the thermoelectric performance of hypothetical A1B1 rocksalts for (a) unknown A1B1 chemistries (231), and (b) known A1B1 chemistries but with no rocksalt polymorph (134). A large number of these hypothetical compounds contain ions in a low oxidation state. Out of the total 365 hypothetical structures, only 49 have finite DFT-calculated band gaps. βSE was calculated for these 49 structures. As expected, we find several promising p-type candidates (βSE ⩾ 0.5 βSE,PbTe) among the hypothetical A1B1 rocksalts, shown in Figure 7, panel a. All of these candidate compounds contain cations in a low oxidation state. Enhancement of valence band Nb and lowering of mb* leading to a large βSE are well demonstrated in the cases of p-type AlF, InF, PbO, and SnO. The favorable composition-structure properties that result in predicted good p-type thermoelectric performance do not offer similar benefits for n-type materials, a trend also observed in the previous section among known A1B1 compounds (Figures 3 and 5). The promising hypothetical candidates (refer to Table S1 in Supporting Information) will potentially outperform p-type PbTe, but phase stability, synthesizability, and doping are prerequisites for experimental realization of such compounds. Metrics such as energy offset from the ground state and formation enthalpies of the predicted top 10 most promising hypothetical structures are reported in Table S2 (Supporting Information) to gauge their stability. The candidate hypothetical A1B1 rocksalts are tens to hundreds of meV/atom higher in energy than the ground state A1B1 structure, which is larger than the typical standard deviation in DFT energies of 25 meV/atom,39 which makes them extremely challenging to synthesize. Nevertheless, this exercise serves its purpose of validating our hypothesis that in the binary A1B1 chemistry, favorable crystal structures (cubic or orthorhombic) combined

for a standard III−V semiconductor, InP (zinc blende), the valence band maximum (VBM) occurs at the Γ-point with three-fold degeneracy (Nb = 3) and relatively large DOS and band effective masses (mb* ≈ me) as evidenced by a large P(p) contribution to the valence band edge. The more dispersive conduction band minimum (CBM) is located at Γ and is nondegenerate. The features of this electronic structure are well understood and can be explained using relatively simple tightbinding models.34 If we compare the electronic structure of InP with PbTe (rocksalt), which contains a cation in a low oxidation state, the valence and conduction band features change both qualitatively and quantitatively. In PbTe, both cation s and p orbitals interact with the anion p forming multiple bands. The chemical bonding is established through the interactions of p orbitals on the cation and the anion. As a result of the p−p interactions, the conduction band is predominantly of the cation p character, unlike standard II−VI and III−V semiconductors. Furthermore, additional anion p-cation s interactions also exist; because both p and s channels are occupied by electrons, this interaction leads to the formation of two additional valence bands, of predominantly bonding and antibonding character, one of which appears near the top of the valence band. An example of this type of interaction is observed in the electronic DOS of PbTe (Figure 6b). Because of the symmetry properties of anion p and cation s orbitals that form the valence band, the VBM appears off of the Γ point, which increases the band degeneracy (Nb = 4). The CBM also appears off of Γ (Nb = 4) due to the p character of the conduction band. The presence of s orbitals close to the VBM affects the band dispersion; spatially extended 6s orbitals of Pb result in low m*b (0.07 me), which is an order of magnitude smaller than InP. The CBM is equally dispersive because of the spatially extended overlap of Pb(p) and Te(p) orbitals (mb* ≈ 0.06 me). Therefore, compounds with low oxidation state cations in the cubic structure will likely have large Nb and low m*b in the valence band as well as in the conduction band, which is beneficial for p- and n-type thermoelectric performance (Figure 4). In many compounds that contain low oxidation state cation, the on-site hybridization between the cation s and p electrons results in the formation of stereochemically active lone pairs,35−37 which break the cubic symmetry. This symmetry breaking typically leads to layered orthorhombic crystal structures. The electronic structure of such a material, SnSe (orthorhombic CmCm), is shown in Figure 6, panel c. The electronic structure exhibits features similar to the more symmetric version such as increased valence band Nb (4), s contribution to the VBM (m*b = 0.06me), and predominantly cation p character of the CBM. The anisotropy of the orthorhombic polymorph decreases B, which is accompanied by a corresponding decrease in κL (see Supporting Information for κL and B correlation). Although μ0 also depends on B, the reciprocal space parameters Nb and m*b are stronger drivers of μ0; consequently, the decrease in B does not significantly reduce μ0. Overall, the thermoelectric performance is improved. Therefore, compounds with low oxidation state cations in the orthorhombic structure, where anisotropy does not significantly degrade carrier mobilities, benefit not only from large valence and conduction band Nb and low mb*, but also lower κL. Anions in a low oxidation state occur in compounds, such as ZnSb and CdSb, that are predicted to be moderately good ptype and potentially best performing n-type thermoelectric materials in the orthorhombic structure. These compounds are F


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Table 1. Values of βSE Relative to PbTe of 15 Most Promising p- and n-type Candidates Predicted To Be Good Thermoelectric Materials. The Space Group Is Indicated in Parentheses. Note That This Table Includes Some of the Known Thermoelectric Materials in a Higher-Energy Polymorph or a Different Doping Type than Conventionally Achieved A1B1

βSE/βSE,PbTe (p)

A1B1

βSE/βSE,PbTe (n)

AgBr(225) AgI(225) InI(63) GeSe(225) CaTe(221) SnSe(225) MnSe(129) BaSe(221) CdAs(61) LaN(225) MnTe(62) SnS(225) NaSb(14) CdSb(61) GeSe(62)

5.6 3.3 2.5 1.8 1.7 1.4 1.3 1.3 1.3 1.3 1.2 1.2 1.1 1.1 1.1

ZnSb(61) CdSb(61) PdSe(135) InSe(12) GaTe(194) ZnAs(61) PbO(57) GaP(216) CdAs(61) AlSb(216) SnSe(62) InTe(140) InSe(194) SnO(36) KSb(14)

5.0 4.0 1.9 1.9 1.8 1.6 1.4 1.4 1.3 1.3 1.3 1.1 1.0 0.9 0.9

emerge as materials with the largest βSE values, primarily because of large valence band Nb. However, practical challenges associated with doping of these large band gap halides, potentially facile ionic diffusion, and water solubility pose obstacles in realizing the maximal zT in these materials. Group II-chalcogenides in the CsCl-structure and Mn-chalcogenides are predicted to be second-best p-type thermoelectrics after halides. Interestingly, our predictions suggest that SnS and GeSe in the higher-energy rocksalt structure are potentially good p-type thermoelectric materials. Orthorhombic arsenides and antimonides of Cd with low predicted κL ⩽ 5 Wm−1K−1 are the other prominent p-type candidates. Zintl-like compounds ZnSb, CdSb, ZnAs, and CdAs containing anion dimers are predicted to be the best n-type A1B1 thermoelectric materials. ZnSb is a well-known p-type thermoelectric material. Our predictions suggest that p-type ZnSb has the potential to be almost as good as p-type PbTe, but it is the n-type material that could remarkably outperform its p-doped counterpart and n-type PbTe. While ZnSb is natively p-type due to intrinsic defects,40 previous efforts to achieve n-doped ZnSb have been met with only limited success.41 Hexagonal InSe(194) is another known thermoelectric (Figure 1), but monoclinic InSe(12) can be expected to outperform as an n-type material. Recent reports14 have found that natively doped p-type high-temperature phase of SnSe(63) exhibits a high zT value, but the room-temperature phase SnSe(62) is not a good thermoelectric material. βSE predicts that the room-temperature phase may be a much better n-type thermoelectric, provided the material can be extrinsically doped to the desired type. Layered oxides such as PbO and SnO, owing to their low κL and dispersive CBM, also appear among the top n-type performers.

Figure 7. Variation of βSE (circle area) as a function of Nb and m*b for hypothetical A1B1 rocksalt structures with βSE ⩾ 0.5 βSE,PbTe. All of the hypothetical structures on this plot feature cations in a low oxidation state (blue circles). For comparison purposes, the data from Figure 5 are shown as gray circles.

with low oxidation state ions can be used to design Nb and m*b to improve p-type thermoelectric performance. It would be interesting to extend the design principles that we have developed here to other chemistries beyond A1B1. Therefore, the criteria to realize good thermoelectric performance in A1B1 materials and possibly other chemistries are (a) favorable crystal structure (cubic or orthorhombic) and (b) existence of ions in low oxidation state. In the context of Figure 1, we conclude that the predominance of cubic structures among the known good thermoelectric materials is due to their favorable charge carrier transport. The emergence of orthorhombic SnSe as a p-type thermoelectric with a zT of 2.414 offers some credence to the criteria set forth here.

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PROMISING A1B1 THERMOELECTRIC MATERIALS In addition to the known thermoelectric materials shown in Figure 1, screening of the A1B1 chemical space returns promising candidates that have not been previously considered including higher-energy polymorphs of known thermoelectric materials. The screening also reveals that certain known thermoelectric materials if doped differently (p- vs n-type) from what has been conventionally achieved could potentially result in higher zT values. Table 1 lists the 15 most promising p- and n-type candidates, where βSE is expressed relative to PbTe. For the complete list, please refer to the Supporting Information (Table S1). Among p-type candidates, A1B1 halides of relatively heavy cations (Ag, In) and less electronegative halogens (Br, I)

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CONCLUSIONS Motivated by a large fraction of A1B1 compounds among the known thermoelectric materials, we have herein computationally explored the A1B1 chemical space and found that the origin of their good thermoelectric performance is a favorable G


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combination of crystal structure (cubic or orthorhombic) and chemical composition (ions in a low oxidation state). While more chemically complex thermoelectric materials are emerging, simpler chemistries such as A1B1 offer rich grounds for discovering new structure−property relations that drive thermoelectric performance. On the basis of our screening, we have also proposed promising A1B1 compounds that have not yet been considered for thermoelectric applications.

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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.chemmater.5b01179. Raw data from screening of A1B1 chemical space (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the United States Department of Energy under Contract No. DE-AC3608GO28308 to NREL and through NREL’s LDRD program under Grant No. 06591403. We acknowledge support from National Science Foundation Division of Materials Research (NSF DMR) program, Grant No. 1334713. The research was performed using computational resources sponsored by the Department of Energy’s Office of Energy Efficiency and Renewable Energy and located at the National Renewable Energy Laboratory.

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Computational Exploration of the Binary A1B1 Chemical Space for

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