Bi2PdO4: A Promising Thermoelectric Oxide with High Power Factor

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Bi2PdO4: A Promising Thermoelectric Oxide with High Power Factor and Low Lattice Thermal Conductivity Jiangang He,† Shiqiang Hao,† Yi Xia,‡ S. Shahab Naghavi,† Vidvuds Ozoliņs,̌ ‡ and Chris Wolverton*,† †

Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208, United States Department of Materials Science and Engineering, University of California, Los Angeles, California 90095, United States

‡

S Supporting Information *

ABSTRACT: The search for new energy harvesting materials that directly convert (waste) heat into electricity has received increasing attention. Transition metal oxides are a promising class of thermoelectric (TE) materials that can operate at high temperature due to their chemical and thermal stability. However, the high lattice thermal conductivity, poor electrical conductivity, and low thermopower have significantly impeded their applications to date. Using first-principles calculations, we predict a known oxide Bi2PdO4 to be a highly efficient holedoped TE material with low lattice thermal conductivity and high power factor. These properties are due to (i) the strong anharmonicity stemming from Bi3+ 6s2 lone pair electrons (leading to low lattice thermal conductivity) and (ii) the flat-anddispersive valence band structure with high band degeneracy originating from the localized Pd2+ dz2 orbitals in the stacked square planar ligand field (leading to a large power factor). Our results highlight the possibility of oxides as potential TE materials and also afford a novel strategy of designing TE materials by synthesizing compounds which combine a lone pair active cation with a d8 cation in a stacked square planar ligand field.

T

clathrates,16 R-Heusler,17 and CsAg5Te318), anharmonicity (Cu12Sb4S1319 and SnSe4), and lone pair electrons.20,21 However, approaches for optimizing electrical performances are relatively limited due the complexity of the electronic structure. Recently, Bilc et al.22 demonstrated that the combination of flat (narrow carrier energy distribution, large effective mass) and dispersive (small effective mass) bands yields a high PF since S is proportional to the effective mass and σ is inversely proportional to the effective mass. Although the flat-and-dispersive band structure, which is energetically dispersive in some regions of the Brillouin zone and flat in others, is rare in materials, it has been observed in some full Heusler compounds.22 Oxides in general have high stability in air at high temperatures.23,24 Many oxides also are lightweight and environmentally friendly, which are desirable for commercial applications of energy harvesting devices. However, oxide thermoelectrics are often limited by high κL and low σ,25 leading to low ZT.26 Oxides with low κL have so far only been observed in complex crystal structures with a large number of atoms per primitive unit cell and low crystal symmetry, yielding a more tortuous path for phonon transport.6 A commonly used

hermoelectric materials, which directly interconvert heat and electricity, have important applications in the recovery of waste heat and refrigeration. However, although a long-term effort has been given to new TE material exploration and performance optimization,1 there are only very few materials with commercial applications. Commercial TE materials require high heat-electric conversion efficiency at a wide range of temperatures, stability (thermal, chemical, and mechanical) at high temperature and in air, and low cost. The figure of merit ZT of TE materials is defined as ZT = (S2σT)/ (κL + κe), where S, σ, κL, κe, and T are the Seebeck coefficient, electrical conductivity, lattice thermal conductivity, electron thermal conductivity, and temperature, respectively. Therefore, a high ZT material must possess the following combination of properties: high S and σ and low κL and κe. The power factor (PF, S2σ) of a compound mainly depends on its electronic structure: a large dispersive band (small effective mass) around the Fermi level gives rise to a large σ, while a sharp increase in the density of states (large effective mass) usually leads to large S.2 Owing to these requirements on material properties, TE materials with high PF and low κ (κL + κe) have, to date, mainly been discovered in the chalcogenide family, such as Bi2Te3, PbTe, SnSe, and AgSbTe2.3 For example, the ZT of the undoped SnSe bulk was reported to be 2.6 at 923 K,4 while Na doped SnSe has a high ZT in a broad temperature range.5 So far, many phonon-engineering strategies have been employed for reducing κL in semiconductors:6 nanostructuring (PbTe,7−11 half-Heusler12−14), rattling modes (skutterudites,15 © 2016 American Chemical Society

Special Issue: Computational Design of Functional Materials Received: October 4, 2016 Revised: December 22, 2016 Published: December 23, 2016 2529

DOI: 10.1021/acs.chemmater.6b04230 Chem. Mater. 2017, 29, 2529−2534

Article

Chemistry of Materials strategy of reducing κL in oxides is to employ the interfaces of layered oxides to scatter heat carrying phonons, such as NaCoO2,27 Ruddleson−Popper structures,28 and artificial superlattices.24 The main drawback of this method is the low σ through the interface due to the large inertial effective mass m*I .29 Although a high density of states effective mass (m*d ) is favorable for S,30 the band effective mass mb* is also high in these compounds due to the single-valley band structure and 31 low band degeneracy Nv since m*d = N2/3 v m* b . Large m* b leads τ to low electrical conductivity because σ ∝ m * (τ is the electron

octahedron connects with two neighboring BiO6 octahedra neighbors by edge-sharing along the c axis and six BiO6 octahedra by corner-sharing in the ab plane. Due to this connectivity and the strong distortion of the BiO6 octahedra, sizable tunnels are formed along the [001] and [110] directions. The large asymmetric distortion of the BiO6 octahedra also indicates the possibility of strong anharmonicity, which can significantly enhance heat carrying phonon scattering and reduce heat transport correspondingly20 (we will discuss κL later). The calculated phonon dispersion is shown in Figure 2. Three acoustic modes, which are largely responsible for heat

b

lifetime). On the basis of crystal field and crystal structure chemistry analysis, in this paper, we propose an alternative design strategy: we employ an oxide with asymmetrically distorted oxygen octahedra stemming from stereoactive lone pair electrons of the cation, Bi3+, and the electronic structure with a flat-and-dispersive band and high valley degeneracy originating from a d8 Pd2+ cation in a stacked square planar ligand field. This strategy is realized in a prototype compound, Bi2PdO4, which is predicted to be a promising p-type TE material with both low κL and high PF by means of firstprinciples calculations (see Supporting Information for computational details). Bi2PdO4 crystallizes in a tetragonal crystal structure (P4/ncc, No. 130), which is isostructural with Bi2CuO4. As shown in Figure 1, Pd2+ is coordinated in a square-planar geometry by

Figure 2. Phonon dispersion (left) and density of states (right) of Bi2PdO4. Inset is the first Brillouin zone.

transport, have zone-boundary frequencies around 30 cm−1 along the Γ−X (a, b axis) and Γ−M (diagonal of a and b axis) directions and 40 cm−1 along Γ−Z (c axis). The acoustic phonons in the ab plane (Γ−X and Γ−M) are softer than these along the c axis (Γ−Z). This softening is mainly due to the larger tunnel structure in the ab plane (i.e., tunnel along [001]) and the stereochemically active lone pair electron of Bi3+; see Figure 1. As shown in the phonon density of states (DOS) in Figure 2, these low frequency phonon modes have the largest contribution from the heavy Bi atoms. The three lowest optical modes at Γ are the polar modes A2u (38 cm−1) and Eu (39 cm−1). The lowest frequency modes at X, M, and Z points of the first Brillouin zone are X1 (27 cm−1), M1 (27 cm−1), and Z3Z4 (40 cm−1), respectively. All these low-frequency acoustic modes indicate small group velocities near the zone center (ΓX: 1520, 2400, and 2450 m/s; Γ-M: 840, 1480, 3280 m/s; Γ-Z: 1450, 1450, 4270 m/s) and low Debye temperatures, which facilitate a low κL (e.g., according to the Debye−Callaway model32,33). Accurate calculation of κL requires a full determination of anharmonic force constants. We use the recently developed first-principles compressive sensing lattice dynamics method34 and the first order perturbation theory with Boltzmann transport equation (BTE); see Supporting Information. The resulting lattice thermal conductivities, κL, are shown in Figure 3 as functions of temperature. The lattice thermal conductivities yy zz along the a (κxx L , or b, κL ) and c axes (κL ) are 2.2 and 2.8 W −1 −1 m K at 300 K, respectively, which are comparable with that of the high ZT chalcogenide material PbTe and is much lower

Figure 1. Crystal structure of Bi2PdO4 in top (a) and side view (b). The structure has tunnels along the c axis. (c) is the top view of the electron localization function (ELF) with isosurface level of 0.55. (d) is the distorted octahedra of BiO6 with ELF = 0.55. The stereoactive lone pair electrons of Bi3+ are clearly seen. The black lines indicate the unit cell.

four oxygen atoms, forming a PdO4 unit. The PdO4 units are stacked along the c axis, sharing two oxygens with the BiO6 octahedra that are asymmetrically distorted due to the stereoactive lone pair 6s2 electrons of Bi3+. The largest O−Bi−O angles in the BiO6 octahedra are 137° (in the ab plane) and 167° (along the c-axis). The corresponding Bi−O bond lengths are 2.765 and 2.376 Å, respectively. Each distorted BiO6 2530


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as indicated by the large charge density lobe in the [001] tunnel in Figure 1d. We also computed the Born effective charges (Z*). The Z* diagonal elements for the Bi3+ cation (3.78; 3.78; 4.76) and oxygen anion (−1.84; −2.82; −2.28) are significantly larger than their normal charge states +3 and −2, respectively. This anomalous Z* indicates a strong dynamic charge transfer associated with the change of Bi−O bond lengths and the deviation of quadratic relation between energy and atom displacement38,39 and, therefore, large anharmonicity, which results in low κL. On the other hand, the avoided crossing between the polar optical mode Eu and the acoustic modes is clearly seen along the Γ−X direction but absent in the Γ−Z direction. This avoided crossing is found in clathrate materials with rattling modes and is indicative of strong coupling between optical and acoustic modes.6,40 The large gap at the avoided crossing point indicates a high coupling strength, which significantly increases the phonon scattering rates, reduces acoustic mode velocities, and again contributes to the low κL.6,41 In Figure 5, we show the phonon mode scattering rates of three phonon interaction in the absorption (Γ+: λ + λ′ → λ″) and emission (Γ−: λ → λ′ + λ″) processes. The peaks in the scattering rates plot show the scattering magnitude of first phonon mode (λ) induced by the second phonon mode (λ′). In the absorption process, a low-frequency phonon mode combines with other low-frequency modes, giving rise to a high-frequency optical mode. In the emission process, the phonon mode is only allowed to decompose into a lowerfrequency mode, thus restricting the second phonon mode (λ′) in the right lower triangle. Both processes satisfy energy and crystal-momentum conservation. In Figure 5a, the scattering peaks centered around (ωλ ≈ 45 cm−1, ωλ′ ≈ 45 cm−1) indicate that acoustic modes, which carry the most heat, are dominantly scattered by the low-frequency (∼40 cm−1) optical modes near the avoided crossing, consistent with high coupling strength indicated by the avoided crossing. Phonon modes with ωλ > 100 cm−1 show considerable scattering in both absorption and emission processes as can be seen in Figure 5a,b. Therefore, the low κL is a combined effect of strong anharmonic phonon− phonon interaction and small group velocity, stemming from the stereochemically active lone pair electrons of Bi3+ 6s2 and the tunnel structure. In the square planar ligand field, d orbitals split into four energy levels, dxz/dyz, dz2, dxy, and dx2−y2 from low to high energy. However, the presence of weak interactions with ligands along the c-axis, i.e., the elongated octahedral ligand field, increases the energy level of the dz2 orbital. The amount of energy level shift directly depends on the interaction strength (or the distance between the center metal and its ligands along the c-

Figure 3. Lattice thermal conductivity of Bi2PdO4 as a function of temperature.

than most TE oxides including the layered oxides PbPdO2 (9 W m−1 K−1) and NaxCoO2−δ (19 W m−1 K−1).27,35,36 To understand the low κL, in Figure 4 we plot the third-order force

Figure 4. Norm of the calculated third-order IFCs.

constants Φmnl =

∂ 3E ∂um∂un∂ul

(E and u are the total energy and

atom displacement, respectively) for different atom species m, n, and l. Since phonon scattering rates are roughly proportional to |Φ|2,37 a high value of Φmnl suggests large anharmonicity. Both ΦBi3 (

∂ 3E ) ∂uBi ∂uBi ∂uBi

and ΦO3 (

∂ 3E ) ∂uO∂uO∂uO

play the most

important role, consistent with the large anharmonicity stemming from the stereochemically active Bi 6s2 lone pair,

Figure 5. Phonon scattering rates of the three phonon process in (a) absorption (Γ+: λ + λ′ → λ″) and (b) emission (Γ−: λ → λ′ + λ″) processes. 2531


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gaps of small band gap compounds,46,47 the band gap of Bi2PdO4 should be between them. As we discussed earlier, the top of valence band is composed mainly of the dz2 orbital states of the Pd2+ cation. As overlap of dz2 with the px and py orbitals of the in-plane oxygen ligands is negligible, a relatively flat band in the ab plane is expected. In fact, as seen in Figure 6, the valence band maximum along Γ− X−M−Γ is extremely flat, affording a high density of states (DOS) near the Fermi level. On the other hand, a proper overlap between Pd2+ dz2 orbitals along the c-axis leads to very dispersive bands along Γ−Z, X−R, and M−A (c-axis) directions, indicating small band effective masses and therefore high carrier mobility. To clearly see this effect, we applied uniaxial tensile strain along the c-axis to artificially increase the Pd−Pd distance from 3.083 to 3.43 Å. Figure S2 shows that the dz2 bandwidth and dz2/dxy band order are very sensitive to the Pd−Pd distance. Therefore, a proper Pd−Pd (square planar stacking) distance in Bi2PdO4 is very important to achieve such flat-and-dispersive band structure. As demonstrated by Bilc et al.,22 high PF along the dispersive band direction is expected once the dispersive and flat bands touch together, i.e., X and M in the case of Bi2PdO4; see Figure 6. Another advantage of the Bi2PdO4 band structure for a high PF is the high band degeneracy Nv, which is usually observed when multiple bands have similar energies at the same valley point (orbital degeneracy) or when the valley is located at a low symmetry point of the Brillouin zone of a high symmetry lattice (valley degeneracy). As we can see in Figure 6, the orbital degeneracy of the valence band along the X−M direction is twofold, and the valley degeneracies at M, X, and Y (between M and X) are 1, 2, and 4, respectively. Therefore, the band degeneracy at Y (Nv = 8) is comparable with the high Nv compounds usually only observed in cubic lattices, such as the half Heusler FeMSb (M = V and Nb) compound.49 In general, good TE materials with ZT > 1 almost always have Nv ≥ 6.50

axis). In the case of Bi2PdO4, the Pd−Pd distance between two stacked PdO4 square planar is 3.083 Å. Therefore, Pd2+ is effectively in an elongated octahedral ligand field, and the dz2 level switches order with dxy, becoming the top of the valence band. Since the ligand field splitting in 4d transition metals is large, the low spin state is always preferred. Consequently, the four low-energy levels are fully occupied by the eight electrons of the Pd2+ cation, with dz2 as the highest occupied orbital, resulting in an insulating ground state, as depicted in Figure 6.

Figure 6. DFT (PBE) band structure (left) and density of state (DOS) of Bi2PdO4. The inset is the decomposed charge density of the top of the valence band.

Therefore, Bi2PdO4 is a band semiconductor, as for the divalent Pd2+ cation in PbPdO2.36 The calculated DFT band gaps for PBE42 and HSE0643 exchange-correlation functionals are 0.15 and 1.41 eV, respectively, consistent with the semiconducting transport behavior observed in previous experimental measurements.44,45 Since the semilocal functionals such as PBE generally underestimate the band gap and HSE06 (25% Hartree−Fock exchange43) trends to overestimate the band

Figure 7. Seebeck coefficient S and |S| (a) and S2σ/τ (b) of Bi2PdO4 along the c-axis and SrTiO3 as a function of temperature and carrier concentration. Power factor (σS2) (c) and ZT (d) of Bi2PdO4 as function of chemical potential, compared with cubic SrTiO3. The absolute value of S is used for SrTiO3 as it is an n-type semiconductor. Electron relation time (τ) is assumed as 4.3 fs for SrTiO3 at 300 K. The experiment lattice thermal conductivity (κL = 10 W m−1 K−1 at 300 K, ref 48) of SrTiO3 is used. 2532


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Office of Science, Basic Energy Sciences, under Grant DEFG02-07ER46433. This research was supported in part through the computational resources and staff contributions provided for the Quest high performance computing facility at Northwestern University which is jointly supported by the Office of the Provost, the Office for Research, and Northwestern University Information Technology.

Electron transport properties of Bi2PdO4 were calculated using Boltzmann transport theory within relaxation time approximation as implemented in BoltzTraP code.51 The evolutions of S and S2σ/τ with respect to temperature (T) and carrier concentration (n) are shown in Figure 7a,b, respectively. Hole-doped Bi2PdO4 has a slightly higher Seebeck coefficient along the c-axis (Szz) than |S| (absolute value of S) of the n-type oxide SrTiO3 in wide ranges of T and n. SrTiO3 is well-known as a high-Seebeck n-type oxide.52 Combined with the higher value of σzz (smaller m* along Γ−Z direction), Bi2PdO4 shows two to four times higher S2zzσzz/τ than SrTiO3 at the same T and n as shown in Figure 7b. Figure 7c,d shows the PF and ZT as a function of relaxation time at T = 300 K. Bi2PdO4 has a much higher PF and ZT than SrTiO3 with the same relaxation time τ = 4.3 fs (which is adopted from ref 53), due to the higher σzz and lower κL. We note that previous experimental work on PbPdO2 has shown that p-type transport can be achieved by substituting Pd2+ with Li+ because Pd2+ has similar ionic radius with Li+.36 Since the Pd2+ cation in Bi2PdO4 has a coordination environment (stacked square planar) very similar to that in PbPdO2, we surmise that p-type Bi2PdO4 is achieved by substituting Pd2+ with Li+ as well.36 In this paper, a promising p-type TE oxide with high power factor and low lattice thermal conductivity is demonstrated by using first-principles lattice dynamic and electron Boltzmann transport theory within the relaxation time approximation. The yy zz low lattice thermal conductivity (κxx L = κL = 2.2 and κL = 2.8 W −1 −1 m K ) and high power factor of Bi2PdO4 not only suggest the possibility of using air-stable oxides as efficient TE materials but also offer new insights for discovering and designing highZT TE materials by combing stereochemically active lone pair electrons and d8 cations in a stacked square planar ligand field. The other strategies for reducing lattice thermal conductivity, such as nanostructuring, can be used to further enhance ZT in this system as well.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b04230. Computational details of the electrical transport, phonon dispersion, lattice thermal conductivity, HSE06 band structure, Fermi surface, and band structures under uniaxial strain (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*(C.W.) E-mail: [email protected]. ORCID

Jiangang He: 0000-0001-9643-3617 Chris Wolverton: 0000-0003-2248-474X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.H. acknowledges support via ONR STTR N00014-13-P-1056. S.H. acknowledges support by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Award Number DE-SC0014520. Y.X., S.S.N., V.O., and C.W. acknowledge support by the U.S. Department of Energy, 2533


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Bi2PdO4: A Promising Thermoelectric Oxide with High Power Factor

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