Review pubs.acs.org/CR
Rationally Designing High-Performance Bulk Thermoelectric Materials Gangjian Tan,† Li-Dong Zhao,*,‡ and Mercouri G. Kanatzidis*,† †
Department of Chemistry, Northwestern University, Evanston, Illinois 60208, United States School of Materials Science and Engineering, Beihang University, Beijing 100191, China
‡
ABSTRACT: There has been a renaissance of interest in exploring highly efficient thermoelectric materials as a possible route to address the worldwide energy generation, utilization, and management. This review describes the recent advances in designing high-performance bulk thermoelectric materials. We begin with the fundamental stratagem of achieving the greatest thermoelectric figure of merit ZT of a given material by carrier concentration engineering, including Fermi level regulation and optimum carrier density stabilization. We proceed to discuss ways of maximizing ZT at a constant doping level, such as increase of band degeneracy (crystal structure symmetry, band convergence), enhancement of band effective mass (resonant levels, band flattening), improvement of carrier mobility (modulation doping, texturing), and decrease of lattice thermal conductivity (synergistic alloying, second-phase nanostructuring, mesostructuring, and all-length-scale hierarchical architectures). We then highlight the decoupling of the electron and phonon transport through coherent interface, matrix/precipitate electronic bands alignment, and compositionally alloyed nanostructures. Finally, recent discoveries of new compounds with intrinsically low thermal conductivity are summarized, where SnSe, BiCuSeO, MgAgSb, complex copper and bismuth chalcogenides, pnicogen-group chalcogenides with lone-pair electrons, and tetrahedrites are given particular emphasis. Future possible strategies for further enhancing ZT are considered at the end of this review.
CONTENTS 1. Introduction 2. Basic Stratagem of Optimizing ZT: Carrier Concentration Engineering 3. Means of Increasing Maximum ZT 3.1. Enhancement of Carrier Effective Mass m* 3.1.1. Increasing the Number of Band Extrema NV 3.1.2. Increase of Carrier Effective Mass mb* 3.2. Modulation Doping and Carrier Mobility Improvement 3.3. Reducing Lattice Thermal Conductivity 3.3.1. Atomic Scale: Synergistic Alloying 3.2.2. Nanoscale: Nanostructuring with Second Phases 3.3.3. Mesoscale Structuring 3.3.4. All-Scale Hierarchical Architectures 4. Decoupling of Electron and Phonon Transport 4.1. Strained Endotaxial Nanostructuring 4.2. Matrix/Precipitate Band Alignment 4.3. Compositionally Alloyed Nanostructures 5. Discoveries of New Thermoelectric Materials with Intrinsically Low Thermal Conductivity 5.1. Layered SnSe 5.2. BiCuSeO Oxyselenides 5.3. Half-Heusler MgAgSb 5.4. Copper Chalcogenides 5.5. Complex Bismuth Chalcogenides © 2016 American Chemical Society
5.6. Chalcoantimonates with Lone-Pair Electrons 5.7. Tetrahedrites 6. Summary and Outlook Author Information Corresponding Authors Notes Biographies Acknowledgments References
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1. INTRODUCTION With more than two-thirds of the worldwide utilized energy being wasted as heat releasing to the atmosphere in vain, it is of great economic and environmental benefit to capture this largely untapped waste heat to generate emission-free renewable power. Thermoelectric materials that are capable of directly and reversibly converting heat into electricity have thus drawn increasing attention over the past several decades. The key of promoting this promising power generation technology into massive application is to increase the low conversion efficiency of current thermoelectric materials, which is technically evaluated by the dimensionless figure of merit ZT = S2σT/κ. A good thermoelectric material should have a large Seebeck coefficient (S) that is usually present in semi-
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Received: April 21, 2016 Published: August 31, 2016 12123
DOI: 10.1021/acs.chemrev.6b00255 Chem. Rev. 2016, 116, 12123−12149
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crystalline SnSe, a simple binary compound containing no toxic or scarce elements, displays an excitingly record high ZT of ∼2.6 at 923 K along the b axis of the room-temperature orthorhombic unit cell.40 This can be achieved because of the giant anharmonic and anisotropic bonding of SnSe which gives rise to an extremely low thermal conductivity.40 Thus, the search for new compounds with intriguing physical properties is a necessary activity to achieve high thermoelectric performance in addition to optimizing the known systems. Although in the past decade breakthroughs have been constantly made in the thermoelectric field, systematic and indepth analysis and new perspectives on the applied approaches and concepts are valuable. There were previously a few nice introductory reviews on thermoelectric materials, which could be a nice starting point for the readers who are interested in thermoelectrics. Typical examples are summarized by Wood,45 Disalvo,46 Snyder,47 and Kanatzidis.48 Interested readers are also encouraged to refer to some outstanding review articles that focus on some topics, e.g., nanostructuring,20,49,50 band structure engineering,26,51 or nanopolycrystalline composites,52,53 and some others that focus on several specific materials, such as clathrates,54 Zintl phase compounds,55 oxides,56,57 organic materials,58,59 and others.47,60−62 A recent review discusses issues of charge and phonon transport in thermoelectric compounds from the chemical bonding point of view.63 This review aims to summarize the most recent state-ofthe-art approaches of designing high-performance bulk thermoelectric materials which are most likely to enable the devices for large-scale power generation application. It covers all aspects, from improving the electrical properties in the manner of band structure and microstructure manipulations to decreasing the thermal conductivity by composition and microstructure designs and to decoupling the electron and phonon transport through matrix/precipitates band alignment and compositionally alloyed nanostructures. The advances in finding new compounds with intrinsically low thermal conductivity are also highlighted. Future potential strategies universally applicable to all compounds aimed at enhancing the performance are discussed. They can be a comprehensive guide to designing and exploring advanced bulk thermoelectric materials.
conductors, high electrical conductivity (σ) just like metals, and in the meantime poor thermal conductivity (κ) as in glasses. It is knotty to combine all of these features in a single material, enabling its high performance. Experimentally, to improve ZT, one can increase the numerator S2σ (also known as power factor) and/or decrease the denominator κ (thermal conductivity) by rational band structure and microstructure designs.1−7 Since the historic discoveries of thermoelectric phenomena by Seebeck and Peltier in the first half of the 19th century, many materials have been explored and considered useful to generate thermoelectricity, including metals,8−11 ceramics,12−14 and ultimately semiconductors.15−17 It needs to be emphasized that almost all these materials were initially obtained empirically through countless attempts based on personal experience. Therefore, the growth of the thermoelectric community was very slow in the beginning until the 1950s, the decade when the basic science of thermoelectric effects was established and heavily doped semiconductors were widely recognized as excellent thermoelectric materials.15−18 Since then the field of thermoelectrics advanced rapidly, especially in the past two decades, relying on the development of new concepts, better intuitive thinking and theoretical ideas relating to size effects,1−5,19−22 and band structuring engineering.3,23−28 Figure 1 shows the primary milestones achieved for ZT values of bulk materials over the last two decades as a function
2. BASIC STRATAGEM OF OPTIMIZING ZT: CARRIER CONCENTRATION ENGINEERING The fundamental challenge of designing high-ZT thermoelectric materials stems from the strong correlation of S, σ, and κ through carrier concentration n which can be adjusted by controlling the doping level. For a degenerated semiconductor with parabolic band dispersion, assuming that dopant does not change the scattering or band structure significantly, S is given by64
Figure 1. Current state-of-the-art bulk thermoelectric materials: the thermoelectric figure-of-merit ZT as a function of temperature and year illustrating important milestones. Green cylinders represent the ptype materials, while red cylinders represent the n-type ones. CsBi4Te6,29 BiSbTe,2 AgPbmSbTe2+m,1 Ba8Ga16Ge30,30 Tl−PbTe,23 In4Se3,31 CuxBiTeSe,32 (BaLaYb)xCo4Sb12,33 MgAgSb,34 BiSbTe+Te arrays,22 PbTe−SrTe,4 DDyFe3CoSb12,35 Mg2Si0.3Sn0.7,24 Cu2−xSe,36 Na2+xGa2+xSn4−x,37 GeTe−Bi2Te3,38 Pb(Te,Se,S),39 PbS−CdS,27 SnSe,40 Cu2−xS,41 PbTe−PbS,42 SnTe−CdS,43 and Pb1−xSbxSe.44
of both year and temperature. Great achievements have been achieved with both n- and p-type materials with the greatest ZTs around or above 2, especially since the year 2010.4,39,40,42 Traditional thermoelectric materials, namely, bismuth telluride2,22 and lead chalcogenides,1,3,4,23,25,27,39,42,44 remain the top performing ones in their respective working temperature region and attract strong attention. On the other hand, because of concerns of the scarceness of tellurium and the perceived toxicity of lead in lead chalcogenides, researchers also explore the possibility of Te- and Pb-free compounds, among which MgAgSb,34 skutterudites,33,35 and copper and tin chalcogenides36,40,41,43 appear as most promising. Particularly, single-
S=
⎛ π ⎞2/3 m*T ⎜ ⎟ ⎝ 3n ⎠ 3eh
8π 2kB2 2
(1)
where kB is the Boltzmann constant, e the electron charge, h the Plank constant, and m* the density of states effective mass of carriers. Apparently, high S is usually found in low-n semiconductors or insulators, and with increasing n, S drops rapidly, Figure 2a. On the contrary, to ensure a large σ, n should be as high as possible, see eq 2 and Figure 2a σ = neμ 12124
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orange line in Figure 2b and 2c. The consequence of this is that the theoretically maximum performance cannot be fully realized at every working temperature. One way to deal with this issue is to use functionally graded doping67−69 by integrating two or multiple segments with dissimilar n, see green lines in Figures 2b and 3c. One common approach developed in the late 2000s
Figure 2. (a) Schematic diagram showing how ZT and its related parameters (electrical conductivity σ, Seebeck coefficient S, power factor S2σ, electrical thermal conductivity κele, lattice thermal conductivity κlat, and total thermal conductivity κ) change as a function of carrier concentration n. (b) Strategies for stabilizing the optimal carrier concentration (n*, denoted by the red line, usually shows a (T)3/2 dependence66). For most conventional dopants, the resultant carrier concentration (denoted by orange dotted line) is almost temperature independent, functionally graded doping67−69 (green lines) by use of samples with dissimilar n, and use of temperature-dependent-solubility dopant,71,72 namely, n has a strong temperature dependence (purple line). (c) Comparison of different doping methods: (1) conventional doping, (2) graded doping, and (3) T-dependent doping. (d) Enhancement of ZT values over a broad temperature range through stabilizing n* in comparison to the conventional doping approach.69,71,75
Figure 3. (a) Band convergence effect by forming solid solution A1−xBxC between AC and BC: evolution of band structure with increasing doping fraction; Eg and ΔEL−Σ represent the band gap and energy separation between L and Σ bands, respectively. (b) Seebeck coefficient, (c) power factor, and (d) ZT values as a function of both temperature and doping fraction of Sn1−xMnxTe.89 The temperaturedependent Seebeck coefficient of SnTe-3%CdTe92 is included in b for comparison. (Inset of c) Reduction of lattice thermal conductivity with increasing Mn doping concentration.89
where μ is the carrier mobility. Only within the proper carrier concentration range (e.g., 1019−1020 cm−3 for most semiconductors47) can the power factors be maximized by balancing S and σ. The thermal conductivity κ comprises two major components: the electronic contribution κele and the lattice contribution κlat (among all ZT-related physical parameters, κlat is the only one with little dependence on n (Figure 2a) and potentially can be minimized to the amorphous limit through independent crystal structure and/or microstructure design4,55) κ = κele + κlat (3)
of preparing such a graded material is the so-called spark plasma sintering or hot pressing a compacted stack of powder layers, each of which has different carrier concentrations.67,69 However, after extended duration in service the initial carrier concentration gradient in the graded material may fade or vanish due to the diffusion-induced homogenization effect, thereby deteriorating the conversion efficiency.69,70 Alternatively, by making use of the temperature-dependent solubility71,72 of some specific dopants (Figure 2c), one can create a gradient of n within a single material controlled only by temperature and its gradient (see purple line in Figure 2b and 2c). A well-known example is that of Cu, Ag, and excess Pb, which have negligible solubility within PbTe around room temperature but are highly soluble at elevated temperatures.73,74 This temperature-dependent doping is reversible in the heating−cooling process and gets rid of the diffusion problem with graded doping, making it a better candidate for actual application.4,71 Figure 2d compares the temperature-dependent ZT values of n-type PbTe using different doping methods. The green and orange dotted lines represent A and B materials of conventional n-type PbTe with n = 5 × 1018 and 3 × 1018 cm−3, respectively, and the dotted purple line is for the graded doping by integrating the two components.69 A has small n and thus high ZT at low temperatures, while B with larger n has significantly higher ZT at high temperatures. Graded doping makes the ZT fall between A and B but can achieve a much larger average ZT in the entire working temperature range. The solid black line
and κele is influenced by n through the Wiedemann−Franz relation65
κele = LσT = LneμT
(4)
where L is the Lorenz number. Equation 4 links the electrical to thermal transport and makes the optimization of ZT even tougher: there is a trade-off between high σ and low κ (κele), Figure 2a. Nonetheless, as shown in Figure 2a, one can always achieve a maximum ZT at a given temperature by finely tuning n to an optimal level using an aliovalent substitution approach. However, the optimal carrier concentration (n*) of a thermoelectric semiconductor is not constant at all temperatures and usually increases rapidly with rising temperature, roughly obeying the power law of (T)3/2,66 as shown by the red line in Figure 2b. In the case of conventional doping, the carrier concentrations are generally irrelevant to temperature, see the 12125
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shows the theoretically optimal ZT for n-type PbTe.71 Conventional doping approaches, such as by heavy La doping75 in PbTe (solid navy line), can make the maximum ZT approach the optimal value around 750 K but cannot achieve high performance at all temperatures. The temperature-dependent solubility limit of Ag in the PbTe+Ag2Te composite (Tdependent doping, solid green line) enables an increase in n with increasing T and pushes ZT values close to the optimal levels over the entire temperature range. The T-dependent doping approach has also been successfully applied in many other systems including p-type Na-doped PbTe.4,42,72,76 It was demonstrated that the Na-rich precipitates residing at the grain boundaries at low temperature are redissolved into the PbTe matrix at T > 600 K.4,42 This gives rise to the enhancement of hole density, contributing to the increase of electrical conductivity and power factor and suppression of bipolar conduction at elevated temperature achieving superior performance. The modifications to the conventional doping method to include temperature-dependent doping behavior are helpful to acquire larger average ZT values which are especially important in technological applications.
noncubic lattice of either of the chalcopyrite compounds can be distorted to be cubic-like (c = 2a) on average. This reconstructed pseudocubic structure was perceived to be responsible for the lower energy-splitting parameter (or larger NV) and higher performance obtained in the solid solutions. More work is needed, however, in order to better understand just how much of the net ZT enhancement comes from the increase of NV since lattice thermal conductivity reduction through forming the solid solution is also contributing.82 Another attractive way to increase the effective NV is to converge different bands in the Brillouin zone within a few kBT in energy of each other. For example, both experimental and theoretical investigations suggest the presence of two valence bands in lead chalcogenides: one at the L point with NV = 4 and the other at the Σ point of the Brillouin zone with a much larger NV of 12.81 Normally, the two bands are separated by an energy ΔEL−Σ that is sufficiently large to make the Σ band irreverent to charge transport, Figure 3a. However, upon proper alloying with specific elements (for example, Mg,83 Cd,84 Sr,85 or Mn86 in PbTe; Sr in PbSe87), ΔEL−Σ can be significantly lowered, and the two valence bands become converged gradually. In that case, the effective NV becomes larger than 12, and higher performance can be achieved.25,26,87 Likewise, notable conduction band convergence was demonstrated to be effective in enhancing the n-type thermoelectric performance of Mg2Si by alloying with Sn at the Si site.24 We note that the mobility of carriers is nominally unaffected by NV, but there may be some reduction because of intervalley scattering.25 Recently, such a band convergence concept has also been extended to p-type SnTe,43,88−92 which is an analogue of lead chalcogenides but is supposed to be more environmental friendly. Pristine SnTe is not a good thermoelectric material because of high lattice thermal conductivity and the unavailability of its Σ valence band. Specifically, ΔEL−Σ is ∼0.35 eV for SnTe at 300 K,93 much larger than in PbTe (∼0.17 eV)94 or PbSe (∼0.24 eV).95 This means that a considerably larger amount of dopant is needed to produce the same band convergence effect as in PbTe or PbSe, because the doping-induced band convergence is dependent on the amount of dopant,96 Figure 3a. Cd43,92 and Hg90 are good alloying elements from the perspective of decreasing ΔEL−Σ in SnTe. However, because of their low solubility limit (∼3 mol %),90,92 the resultant ΔEL−Σ is still too high to reach the level of PbTe. For example, 3 mol % CdTe-alloyed SnTe92 has the highest Seebeck coefficient of ∼200 μV/K at ∼900 K, which is significantly larger than that of pristine SnTe but is far below that of p-type PbTe83 at the same hole concentration, Figure 3b. Most recently, Mn was explored as a valence band convergence producer in SnTe with a high solubility of >9 mol %.89,97,98 This gives rise to a much lower ΔEL−Σ that is comparable to that of PbTe.89 Correspondingly, the Seebeck coefficients and power factors of Sn1−xMnxTe are remarkably improved with increasing Mn doping fraction,89 Figure 3b and 3c. Notably, the 12 mol % Mn-doped SnTe89 displays the highest Seebeck coefficients (∼80 and ∼230 μV/K at 300 and 900 K, respectively), similar to PbTe83 with comparable hole densities, Figure 3b. Moreover, the higher doping fraction of Mn also facilitates the decrease of lattice thermal conductivity as a result of stronger point defect scattering,89 inset of Figure 3c. Concurrently, ZTs of SnTe are steadily improved upon Mn doping with a highest value approaching 1.3 at 900 K,89 a 120% increase over pristine SnTe. The above examples demonstrate
3. MEANS OF INCREASING MAXIMUM ZT Maximum performance of a given thermoelectric material is generally achieved by carrier concentration optimization, as we elaborated above. However, to increase the maximum ZT to much higher levels, one needs to carefully tailor the electronic structures and microstructures. Previous studies indicate that the dimensionless merit factor (β) of thermoelectric materials can be characterized by77,78 β=9
5/2 U ⎛ T ⎞ ⎜ ⎟ κlat ⎝ 300 ⎠
(5) 2
−1 −1
where U is the weighted mobility (in cm V s , a measure of the electrical properties) that can be written as79
U = (m*)3/2 μ
(6)
In eq 6, m* is the effective mass of carriers (in me, me is the free electron mass) and relates to the band effective mass mb* through the number of equivalent degenerated valleys of the band structure (NV)26,80 m* = (NV )2/3 mb*
(7)
Thus, to increase the maximum ZT, one needs to maximize NV, mb*, and μ and minimize κlat concurrently to achieve higher S and σ but lower κ at a constant n (according to eqs 1−4). Below we discuss the possible approaches. 3.1. Enhancement of Carrier Effective Mass m*
3.1.1. Increasing the Number of Band Extrema NV. Nv is closely related to the crystal structure symmetry and can be large when the crystal structures are highly symmetric. For example, PbTe with its cubic rocksalt structure has NV of 4 and 12 at the L and Σ points of the valence band, respectively.46,81 Other good thermoelectric materials, such as SiGe alloys, CoSb3, Mg2Si, and half-Heusler alloy, also feature NV > 1.26 Currently, strategies on how to increase the asymmetryrelated Nv are in their infancy. One illuminating attempt was recently carried out on tetragonal chalcopyrite compounds.82 By mixing two types of chalcopyrite compounds (c/2a > 1 for one but a) in a proper ratio to form solid solutions, the 12126
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1.8 × 1019 cm−3), the La-doped PbTe displays lower ZT value than that of I-doped samples.99 This is because despite the former’s larger mb* and higher Seebeck coefficient, there is a decline of μ leading to a net decrease of power factor. Nonetheless, at a higher doping level of n, La-doped PbTe samples can have comparable or even better power factors than I-doped PbTe samples, as demonstrated by both experimental results and theoretical predictions.99 Indeed, to make best use of the benefits of larger mb* through band flattening for power factor enhancement it generally requires a much higher optimal n to reach the same Fermi level as the one with smaller mb*. Figure 4b plots the power factor as a function of carrier concentration at 800 K for several state-of-the-art thermoelectric materials with different effective masses.107 It is clearly evident that the maximum power factor values of these heavy bands compounds (e.g., ntype CoSb3) are significantly higher than those with small mb* (for example, n-type PbTe). Moreover, the optimal n increases systematically with increasing mb*. Band flattening can increase not only mb* but also the band gap Eg, according to the Kane-band model.108 This model is widely accepted to describe the band dispersion of most excellent thermoelectric materials (for example, CoSb3109 and PbTe71,75)
the feasibility of turning poor thermoelectric materials into excellent ones by energetically converging multiple bands. 3.1.2. Increase of Carrier Effective Mass mb*. Physically, the effective mass mb* in a band is related to the curvature of the bands and can be modified by distorting the band. This can increase the density of states in the vicinity of Fermi level.23,51 Two commonly adopted approaches of enhancing mb* include band flattening99,100 and resonant levels23,91,101,102 through chemical doping, Figure 4a. It should be emphasized that in
⎛ ℏ2k 2 E⎞ = E⎜⎜1 + ⎟⎟ Eg ⎠ 2mb* ⎝
(9)
In eq 9, ℏ is the reduced Plank’s constant, k the crystal momentum, and E the energy of electron states. Intuitively, this additional band gap enlargement effect by band flattening can help to suppress the detrimental effect of bipolar diffusion on the thermoelectric properties.83,92 The concept of resonant levels was first proposed in metals in 1950s.110,111 Resonance levels originate from the coupling between electrons of a dilute impurity with those of the conduction or the valence band of the host solid. This creates excess density of states near the resonant energy and can give rise to improved mb* and enhanced Seebeck coefficient if the Fermi level can be brought close in energy.51 However, resonant levels are generally effective at low temperature, and their effect tends to diminish at high temperatures where the relaxation time of acoustic phonon scattering is much shorter than that of resonant impurity scattering.43,51 The most well-known examples of resonant levels are associated with the group-III impurities in IV−VI semiconductors. For example, Al was reported to form resonant levels in the conduction band of PbSe,102 while In43,91 and Tl23 create resonant levels in the valence bands of SnTe and PbTe, respectively. In addition to IV−VI semiconductors, resonant levels are also observed in Sn-doped Bi2Te3.101 Recently, the synergy of resonant levels and band convergence to strongly increase performance has been demonstrated in In- and Cd-codoped SnTe,43 Figure 4c and 4d. In forms resonant levels in the valence band of SnTe and therefore strongly improved the Seebeck coefficient and power factors of SnTe below 500 K. However, with increasing temperature, this enhancement becomes less significant because of the diminished resonant scattering at elevated temperatures. On the other hand, Cd substitution92 creates valence band convergence in SnTe that works most efficiently at higher temperatures where two valence bands approach each other, enabling a clear enhancement of the Seebeck coefficient, Figure
Figure 4. (a) Schematic representation of the density of states of a single valence band (blue line) contrasted to that of band flattening (purple line) and the introduction of resonant states (red line). (b) Power factors as a function of carrier concentrations for various of compounds (n-type PbTe, ZrNiSn, CoSb3 and p-type NbFeSb) with different effective masses (m*) at 800 K.107 (c) Seebeck coefficient, and (d) power factor as a function of temperature for SnTe with resonance levels by In doping and/or valence band convergence by alloying with Cd.43
most cases the increase of mb* will result in the decrease of carrier mobility and through it the electrical conductivity, according to the relationship46 eτ μ= ml* (8) where ml* is the inertial mass along the transport direction (and equal to mb* for an isotropic band) and τ is the scattering time which decreases with increasing mb* so long as the carriers are scattered predominately by phonons.26 Band flattening effects can be achieved through the adoption of dopants containing highly localized orbitals which can decrease orbital overlap. For instance, both theoretical and experimental studies suggest that La103−106 or Nd103,106 substitution for Sr significantly flattens the conduction band of SrTiO3 perovskites for largely improved density of states effective mass of electrons, thereby leading to higher power factors and thermoelectric figure of merits. Likewise, in Ladoped PbTe,99,100 because of the hybridization between La f states (or d states if f states are fully localized) and Pb p states, the conduction band at the L point can be affected, contributing to the increase of mb* by band flattening.100 In comparison, iodine-doped n-type PbTe shows negligible changes in the conduction band structure, consistent with the rather broad I d states.100 For equal carrier concentrations (n = 12127
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4c. The introduction of Cd does not extinguish the favorable resonance effect of In below 500 K but improves the Seebeck coefficients and power factors over the entire temperature range. We believe this codoping concept can improve the average ZT over a broad temperature range for many thermoelectric materials. In summary, as indicated by eq 7, the effective mass (m*) can be enhanced by increasing the valley number (NV) or by increasing local DOS effective mass (mb*) through distorting DOS. It is well known that the carrier mobility is inversely proportional to the effective mass, but the carrier mobility will be less deteriorated by increasing valley number (NV) than by increasing the local effective mass (mb*).86 3.2. Modulation Doping and Carrier Mobility Improvement
Most state-of-the-art thermoelectric materials are heavily doped semiconductors with the carrier concentrations on the order of 1019−1021 cm−3, Figure 2a. The high population of free carriers in these heavily doped semiconductors leads to a decrease of carrier mobility with respect to the lightly doped or undoped ones, because of the increased ionized impurity scattering. For example, Hilsum112 found that at room temperature, the mobility is inversely proportional to [1 + (nD/1017)1/2] for a number of important semiconductors, where nD is the donor concentration (in cm−3). Three-dimensional (3D) modulation doping has been recently demonstrated to be effective in increasing the ZT values of several important thermoelectric materials by carrier mobility enhancement.113−116 Modulation-doped samples (Figure 5b) actually are two-phase composites made of undoped (Figure 5a) and heavily doped (Figure 5c) counterparts. The undoped pristine sample has low carrier concentration but high carrier mobilities, while the uniformly and heavily doped sample has high carrier concentrations but low carrier mobilities. The Fermi level of the undoped sample usually locates at the middle of the energy gap and would move deep into the conduction band (n-type doping, Figure 5d) or the valence band (p-type doping, Figure 5e) in the case of heavily doped sample. Because of the Fermi level imbalance between the undoped and the heavily doped phases, the carriers in the modulation-doped sample spill over from the heavily doped region to the undoped region (Figure 5d and 5e). This process results in carrier mobility enhancements relative to uniform doping because of avoidance of ionized impurity scattering. The spatial separation of carriers and impurity scattering centers in 3D modulation doping enables higher carrier mobility without deteriorating the Seebeck coefficient, Figure 5b. For example, under the same carrier concentrations, the 3D modulation-doped p-type SiGe alloys113 and BiCuSeO compounds116 possess considerably larger carrier mobilities and power factors than the uniformly doped materials, Figure 5f. Recently, this 3D modulation doping approach has also been successfully applied to several other bulk thermoelectric systems (e.g., p-type ZnSb117 and n-type FeSb2118) with largely improved thermoelectric performance. One concern of modulation-doped structures is that they may functionally fail when operating at high temperature for long periods of time, due to element diffusion and thermodynamic equilibration. Therefore, modulation doping could be more promising at relatively lower temperatures. Aside from modulation doping, texturing could be another feasible approach to increase the carrier mobility, especially for
Figure 5. Schematic representation of (a) nondoped semiconductor, (b) heavily doped semiconductor where dopants are uniformly dispersed in the host matrix, and (c) modulation doping where two types of grains consisting of nondoped and heavily doped semiconductors are spatially separated. Red arrows show how carriers are scattered when mobilizing across the material. Fermi level positions in undoped, uniformly doped, and modulation-doped semiconductors: (d) n-type doping and (e) p-type doping. The Fermi level imbalance between the undoped and the heavily doped grains prompts the carriers to diffuse from the latter to the former. (f) Comparison of power factors of p-type SiGe alloys113 and p-type BiCuSeO116 in the cases of uniform doping and modulation doping, respectively. At comparable carrier concentration, materials with modulation doping clearly show much higher power factors than those by uniform doping, due to the much larger carrier mobilities.
materials with anisotropic structures. In these anisotropic compounds, carrier mobility may be higher in certain crystallographic directions. In polycrystalline sample, the random orientation of grains weakens the anisotropy of carrier transport and the carrier mobility is a statistical mean value along different crystallographic directions. To take advantage of the anisotropy and maximize carrier mobilities, it is desirable to produce grains that orient along a certain direction, so as to approach the character of the single crystals. For instance, single crystals of SnSe40 feature a high carrier mobility of ∼250 cm2 V−1 s−1 at 300 K, along the b axis of the orthorhombic unit cell, which is about 5 times larger than in its polycrystalline119 form with equal hole concentrations. The significantly higher mobility of SnSe single crystal is the main reason for its much superior thermoelectric performance as compared with its polycrystalline samples. However, as single-crystal growth is highly dependent on the equipment and is time consuming, simpler methods to realize highly oriented polycrystalline samples by hot deformation (thermoforging) technique are being developed.120 Such methods have been extensively utilized to improve the thermoelectric performance of many 12128
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layer structured materials; for example, Bi 2 Te 3 , 121,122 Ca3Co4O9,123,124 and BiCuSeO.116 Texturing is not sensitive to temperature, so it can be applied to high-temperature thermoelectric materials. 3.3. Reducing Lattice Thermal Conductivity
In solids, the interaction between atoms creates displacements from their equilibrium positions leading to a set of vibrational waves with various wavelengths, so-called phonons. These phonons are heat carriers that propagate through the lattice, contributing to the lattice thermal conductivity κlat. At crystal defects (e.g., point defects, dislocations, interfaces, precipitates, etc.), phonon waves can be scattered, giving rise to additional thermal resistance and a reduction of κlat. For example, atomic point defects formed by elemental substitution and nanoscaled precipitates created by second-phase nucleation and growth can significantly scatter the short- and medium-wavelength phonons, respectively. Mesoscaled grains can also scatter phonons but are more effective for long-wavelength phonons.4,125 Below we will elaborate on these mechanisms. 3.3.1. Atomic Scale: Synergistic Alloying. Introduction of lattice imperfections (point defects, at the length scale of angstroms) in the host lattice (by doping or alloying) is a wellestablished approach of decreasing the lattice thermal conductivity. According to the thermal conductivity model developed by Klemens126 and Callaway,127,128 this reduction of κlat is a result of combination of mass contrast and strain field fluctuations. The degree of reduction can be evaluated by the scattering parameter (Γ) that is written as129 ⎡ ⎛ adisorder − a pure ⎞2 ⎤ ⎛ ΔM ⎞2 ⎢ ⎟⎟ ⎥ ⎟ + ε⎜ Γ = x(1 − x) ⎜ ⎜ ⎢⎝ M ⎠ a ⎝ ⎠ ⎥⎦ pure ⎣
Figure 6. Schematic representation of various types of point defects: (a) single doping, (b) cross-substitution, and (c) lattice vacancy formation. (d) Comparison of lattice thermal conductivities as a function of temperature for SnTe with different point defects.43,140,141
one Fe2+ and one Te2− concurrently, thus forming an isoelectronic compound FeSb2Te.130−132 Cross-substituted compound can have a significantly larger solubility limit of dopants than by single doping, and one could expect a much lower κlat, according to eq 10. It should be noted that crosssubstitution not only considerably impacts the phonon transport but may modify the electronic structure (band gap mostly),131,133 providing other avenues to tune the thermoelectric properties of the host material. Because only when the two aliovalent elements are present together in a specific ratio do they enter the matrix in larger amounts (than each alone can) we refer to this effect as synergistic alloying. In addition to a high doping fraction, increasing the atomic mass contrast between the guest and the host atoms can lead to low lattice thermal conductivity. However, the maximum mass contrast (ΔM/M = 1) seems unattainable by conventional doping but is possible when the guest or host atom represents a disordered vacancy, Figure 6c. For instance, in partially filled skutterudites FyCo4Sb12 (F and y represent the filler atom and filling fraction, respectively; y < 1), the lattice thermal conductivity is unexpectedly low, which has been rationally explained by the strong point defect scattering between the filler F in fully filled FCo4Sb12 and the structural vacancy □ in unfilled □Co4Sb12, a 100% mass difference.134 Other examples include clathrate compounds135 with void cages, La3−δTe4 materials136,137 with intrinsically high concentration of cationic vacancies, and InSb/GeTe/SnTe−In2Te3 solid solutions138−140 (note: one-third of the cationic sites are vacant in In2Te3) where very low lattice thermal conductivity is observed. Figure 6d compares the temperature-dependent lattice thermal conductivities of SnTe with different types of point defects: (A) single In doping,43 (B) cross-substitution by Ag and Bi,141 and (C) formation of lattice vacancies by introduction of In2Te3.140 It is clear to see that crosssubstitution and vacancy formation are superior ways of frustrating the phonon propagation in SnTe compared to single doping, as we discussed above. This synergistic alloying approach to thermal conductivity reduction is applicable to most kinds of thermoelectric materials.
(10)
where x is the doping fraction, ΔM/M is the rate of change of atomic mass, adisorder and apure represent the lattice constants of disordered and pure alloys, respectively, and ε is an elastic properties related adjusting parameter.129 From eq 10, one can conclude that to maximize Γ and achieve the lowest κlat it is necessary to have (1) a high doping fraction x, (2) a large mass difference between the dopant and the host element (ΔM/M) creating disorder in the lattice, and (3) a significant lattice mismatch between the disordered phase and the host phase (adisorder/apure). Requirements 1 and 3 can be conflicting in many cases, since large lattice and size mismatch generally renders the dopant insoluble. Figures 6a−c schematically represent the typical doping approaches frequently used in thermoelectric materials research, namely, single-element doping, cross-substitution, and formation of lattice vacancies. In the case of single doping, the dopant could be either isovalent with the host element to generate lattice disorder or aliovalent to control the carrier concentration, Figure 6a. However, due to charge imbalance, singly aliovalent doping is limited by the low doping fraction possible which prevents the further decrease of κlat. To promote a large solubility limit of aliovalent elements, cross-substitution is used. Cross substitution means replacing one or more of the host elements by pairs from other groups of the Periodic Table while keeping the overall valence electron counts constant, Figure 6b. For example, in PbTe, when the divalent Pb is simultaneously substituted by half monovalent Ag and half trivalent Sb, one could obtain AgPbmSbTe2+m, also known as LAST.1 In CoSb3, one Co3+ and one Sb1− can be replaced by 12129
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3.2.2. Nanoscale: Nanostructuring with Second Phases. Nanoscaled defects in crystals help scatter the phonons with wavelengths on the nanometer scale. To make this scattering effective, the geometric length of the nanoscaled defects should be small enough, typically on the order of several to dozens of nanometers, and the nanostructures should be uniformly distributed for maximal interface density over a large material volume.3,4,142 There are several approaches to achieving nanoscale inhomogeneity, including ex-situ additions of guest phase by mechanical or chemical mixing143,144 and in-situ second-phase precipitation through thermodynamically/kinetically driven processes.1,3,4,145,146 While both have been reported to create nanostructures in thermoelectric materials, the latter is more favorable for charge transport because they can afford better dispersion and yield coherent interfaces between precipitate and matrix.3,4 Nucleation and growth of a second phase is the most common in-situ approach of producing nanostructures in bulk crystals,147 and its mechanism is schematically presented in Figure 7a. This works well when the second phase is completely
This nanostructuring approach has been successfully applied to numerous thermoelectric materials with a great reduction of lattice thermal conductivity. Typical examples include PbTe− MTe (M = Ag, Ca, Sr, Ba, Cd, and Hg),3,4,71,75,148,149 PbSe− MSe (M = Ca, Sr, Ba, Zn, Cd, Sb, and Bi),28,44,150 PbS−MS (M = Bi, Sb, Ca, Sr, Zn, and Cd),27,151,152 SnTe−MS (M = Cd and Zn),43,92 CoSb3−MSb (M = In, Ga, and Zn),153−156 and Bi2Te3−M (M = Cu, Zn, and Te).22,32 A specific example is shown in Figure 7c. When only ∼4% (mole fraction) of strontium chalcogenides is added as second phase to the parent lead chalcogenides, the lattice thermal conductivities are strongly decreased. Unlike point defect scattering where high alloying fraction is always pursued to achieve the lowest thermal conductivity, in the case of nanostructuring, a relatively low volume fraction of the second phase (usually a few moles %) is optimal to achieve the strongest phonon scattering. In fact, at higher fractions, the nanostructures can aggregate or coalesce into larger structures with lower interface area, weakening their scattering efficiency.130,151 Despite the numerous successes described above, we must note that nanostructuring is not always successful in scattering the heat-carrying phonons. As an example, Pb and Bi nanostructures appear to exert little influence on the lattice thermal conductivity of PbTe.157 In fact, the phonon propagation inside the nanostructures is rather complicated and usually unpredictable. One should always bear this in mind when designing materials. Moreover, at elevated temperatures where diffusion becomes more active, nanoscale precipitates may coarsen and grow, reducing their effectiveness. This challenge needs to be overcome and will require further investigations in this direction, and new insights and techniques already employed in preparing metallurgical nanostructured alloys.158 3.3.3. Mesoscale Structuring. Low- and medium-wavelength phonons carry most of the heat and can be effectively scattered by point defects and second-phase nanostructures, respectively. There are still many long-wavelength phonons remaining, however, and they also contribute to the lattice thermal conductivity. To scatter more of these phonons as well, crystal defects and structure features at the length scale of micrometers or submicrometers is necessary. This is the socalled mesoscale, and it can be engineered into materials through careful powder processing. Typically, the single crystals or cast ingots (Figure 8a) have grains that are rather large (typically > 10 μm in geometric size). A mesoscale sample typically has grain sizes from 0.1 to 3 micrometers, Figure 8b. Rowe et al.159 investigated the thermal conductivities of SiGe alloys with different grain sizes and compared them with that of their single crystals, Figure 8c. They showed that large grain sizes (light blue region where cast ingots locate) are ineffective in decreasing the thermal conductivities. Only grains with relatively small sizes (5 μm and below, light red area where the polycrystalline samples locate) could scatter phonons strongly (∼20% reduction of thermal conductivity with respect to the single crystal). This work highlights the importance of mesoscale grains in impeding the phonon transport of bulk materials and points to further research to better understand mesoscale effects. To fabricate polycrystalline bulk thermoelectric materials, one usually needs to first produce mesoscopic particles and then densify them by either hot pressing or spark plasma sintering. There are two general routes of obtaining the mesoscopic particles, namely, top-down and bottom-up ap-
Figure 7. (a) Schematic ternary diagram, which indicates a strong temperature-dependent solubility of the second-phase B within the matrix A. (b) Typical TEM image that shows B nanostructures embedding in the A matrix, as grown by the nucleation and growth mechanism. (c) Comparison of lattice thermal conductivities between pristine and nanostructured lead chalcogenides.4,27,150 Strong reduction of lattice thermal conductivity is achieved through nanostructuring.
soluble in the parent material when molten (region I) but has very low solubility in the solid state (region II). When the molten mixture (region I) is rapidly cooled to form a solid, the second phase precipitates (region III) since the solid solution limit is exceeded. Moreover, to ensure a fine distribution and good thermal stability, the second phase should have a comparable or higher melting point than the host material. Figure 7b displays typical nanostructuring created by the nucleation and growth mechanism under the observation of transmission electron microscopy (TEM). The sample is PbTe−SrTe composite and features ubiquitous nanocrystals of second-phase SrTe coherently dispersed in the host material of PbTe. This good interface originates from the homogeneous dispersion of SrTe in PbTe enabled by fast cooling as well as their very small lattice mismatch. 12130
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Figure 8. Schematic diagrams of microstructures of (a) single crystals or cast ingots without grain boundaries or with rather coarse grains (>10 μm in size) and (b) polycrystalline samples with mesoscale grains (hundreds of nanometers to several microns). (c) Experimental study of the thermal conductivity of SiGe alloys (green circles) with different grain sizes as compared to the single crystal.159 Solid line is a guide to the eyes. Light blue and red areas denote where the grain sizes of cast ingot and polycrystalline samples locate, respectively.
Figure 9. Schematic diagram of the integration of multisized defects: (a) atomic-scale point defects, (b) nanoscale precipitates, and (c) mesoscale grains in one single material for all-scale hierarchical architectures of phonon scattering.4 (d) Contributions of phonons with different mean free paths to the cumulative κlat value for PbTe.125 (e) Temperature dependence of lattice thermal conductivity for the all-scale hierarchical architecture SnTe system.88,92 Green color depicts the mesostructuring, red color depicts the approach of solid solution point defects, and blue line depicts the approach of nanostructuring.
proaches.160 In the top-down approach, the mesoscopic particles are acquired by pulverizing the coarse-grained crystals to fine powders with the aid of hand grinding, mechanical alloying, etc. Alternately, as developed by Tang’s group, using one-pot melt spinning or self-propagation high-temperature synthesis (SHS), one could obtain the products with fine grains or small particle size. This has proven to be particularly effective in producing high-performance bulk thermoelectric materials in a very short period.161−164 Inversely, the bottom-up approach means direct control of the mesoscopic particles growth by, such as, solution chemistry methods including hydro- and solvothermal synthesis,165 electrochemical deposition,166 sonochemical synthesis,167 and so on. These solution chemistry methods have been widely used to synthesize a wide variety of thermoelectric semiconductors (e.g., skutterudites,168 metal chalcogenides,167 zinc antimonides169) with controllable size and morphology. 3.3.4. All-Scale Hierarchical Architectures. When point defects, nanostructuring, and mesoscale structuring are all combined into a single thermoelectric material, we call this as an all-scale hierarchical architecture.4 While the thermal conductivity in crystalline materials is limited by the Umklapp scattering process, it can be decreased by defects at different length scales with a broad range of wavelengths and mean free paths (MFP, defined as the average distance traveled by phonons between successive scatterings). Theoretical calculations125 suggest that, in PbTe, over 50% of the κlat value comes from the contribution by phonons with MFP less than 1 nm, which can be ascribed to scattering by atomic-scale point defects, Figure 9c. The remaining contribution to κlat is almost equally divided between phonon modes with MFP of 1−10 nm and phonon modes with MFP 10−1000 nm, Figure 9c), which can be notably impeded by nanoscale precipitates and mesoscale grains, respectively. Similar trends are found in PbTe1−xSex170 and Si.171 All-scale hierarchical architectures achieve the strongest phonon scattering,83,148,155,172 see Figure 9a. All-scale hierarchical architectures were successfully created in lead chalcogenides, have led to significantly enhanced thermoelectric performance, and now have been applied to other lead-free
materials, including SnTe, 43,92 GeTe, 38 AgSbSe 2 , 173 AgCrSe2,174 CoSb3,155,164 Bi2Te3,175 and In2O3.176 Figure 9e shows a comparison of the lattice thermal conductivity of SnTe samples with different defects: mesoscale grains by SPS treatment,88,92 atomic-scale point defects of Cd substitution for Sn,92 and nanoscale CdS precipitates.92 It is apparent that mesostructuring lowers the lattice thermal conductivity of SnTe ingot by about 22% at room temperature, from ∼2.7 to ∼2.1 W m−1 K−1. The atomic point defects and nanoscale precipitates contribute additional phonon scattering, leading to further reduction of κlat by ∼25% and ∼20%, respectively. In all, a total reduction of κlat by more than 50% is achieved by all-scale hierarchical architectures of phonon scattering.
4. DECOUPLING OF ELECTRON AND PHONON TRANSPORT We highlighted above that nanostructuring in bulk materials dramatically reduces the thermal conductivity. However, simultaneously it can also increase the charge carrier scattering due to the additional energy barrier caused by crystallographic mismatch and/or electronic bands misalignment at the interfaces.4,43,83 This has detrimental effects on the carrier mobility and power factor. Therefore, to avoid the mobility loss in nanostructured thermoelectric materials, both coherent interfaces (endotaxy) and energy-matched electronic bands are required. To some extent this situation achieves a decoupling of electron and phonon transport. Below we discuss approaches of decoupling electron and phonon transport in nanostructured bulk thermoelectric materials. 4.1. Strained Endotaxial Nanostructuring
In a high-performing nanostructured thermoelectric material, the phonons should be scattered as much as possible by the nanoprecipitates while the electrons should flow across the interfaces without much scattering, Figure 10a. The electron and phonon scattering are strongly affected by the interface (endotaxy), which is usually determined by the degree of lattice misfit (ε) between the nanoprecipitates and the matrix.157 12131
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demonstrated, including PbTe−GeTe,38 PbTe−PbS,42 PbTe− MTe (M = Mg, Ca, Sr, Ba),3,4,83,148 PbSe−MSe (M = Ca, Sr, Ba),150 and SnTe−MnTe.89,97 Figure 10 c−f show strained endotaxial nanostructuring present in the PbTe−SrTe system. Figure 10c is a typical phase contrast high-resolution TEM image showing several 2−4 nm SrTe precipitates (depicted by the white arrows, marked as i, ii, iii, and iv, respectively) within the PbTe matrix. An enlarged high-resolution TEM image of precipitate (i) shown in Figure 10d clearly suggests the absence of any dislocations at the boundary highlighted by the dotted line. In Figure 10e, the inverse first Fourier transform reconstructed image of the precipitate (i) depicts a perfect interface endotaxy (coherency) between the precipitate and the matrix. The shear strain map profiles based on geometric phase analysis conducted on the four nanoprecipitates shown in Figure 10c are displayed in Figure 10f.3 Elastic strain is pervasive in and around all precipitates, and there is also plastic strain around the dislocation cores in precipitates iii and iv. The coherent but strained interfaces between the matrix and the nanoprecipitates lead to strong phonon scattering but minimal electron scattering. Strained endotaxial nanostructuring is now becoming a popular approach of designing high-performance bulk thermoelectric materials. 4.2. Matrix/Precipitate Band Alignment
Figure 10. Schematic diagram of electron and phonon transport decoupling in nanostructured bulk materials: phonons (depicted by blue arrows) are strongly scattered by nanoprecipitates, while the electrons (depicted by red arrows) travel across the interfaces without restriction. (b) Schematic of phonons scattered by three possible types of interfaces (coherent, semicoherent, and incoherent) between matrix and nanoprecipitates. Reprinted with permission from ref 157. Copyright 2010 American Chemical Society. (c) High-resolution TEM phase contrast image of several SrTe nanoprecipitates (i, ii, iii, and iv) embedded in the PbTe matrix. (d) Enlarged image of nanoprecipitate i showing coherency at the boundary highlighted by the dotted line. (e) Inverse first Fourier transform image of precipitate i, indicating the absence of dislocations at the grain boundary. (f) Shear strain map profiles for the four nanoprecipitates shown in d. There are elastic strains at and around all precipitates and also plastic strain at and around dislocation cores in precipitates iii and iv. (c−f) Reprinted with permission from ref 3. Copyright 2011 Nature Publishing Group.
Though the scattering of electrons can be minimized by improving the interface coherency in nanostructured materials, the additional energy barrier from misalignment of electronic bands can hinder electron flow. Previous studies on GaAs/InAs (001) heterojunctions indicated that charge carriers can transmit freely when the band offsets are minimal.182 Recently, a similar approach has been developed in three-dimensional bulk nanostructured thermoelectric materials by minimizing the energy offsets of electronic bands between the nanoprecipitates and the matrix.3,4,27,28 The concept of electronic band alignment is illustrated in Figure 11a. The dotted lines depict the energies of the conduction band minimum (CBM) and the valence band maximum (VBM) of two different second phases and a host matrix. Phase A has good valence band alignment with the matrix (an energy difference that is comparable to the magnitude of thermal energy at elevated temperatures of kBT is considered band alignment). Therefore, the matrix/A system
There are generally three types of precipitate−matrix interfaces in light of their coherency: coherent (ε < 1%), semicoherent (1% < ε < 25%), and incoherent (ε > 50%).157,177 These three scenarios embody different atomic configurations and associated local interfacial relaxation mechanisms,157 Figure 10b. In the case of semicoherent or incoherent interfaces, the surrounding atomic order is strongly disrupted, leading to significant scattering of both electrons and phonons. The direct consequence is limited ZT improvement. When the nanoprecipitates and the matrix are coherently (endotaxially) connected but have a certain degree of strain around their interfaces, we call it strained endotaxial nanostructuring. This interface is supposed to facilitate charge transport across it but strongly block/scatter phonon propagation. The presence of strained endotaxial interfaces has been observed in a number of nanostructured materials. In pioneering work by Hsu et al.,1 coherent nanostructured bulk thermoelectric materials LAST were synthesized with a measured ZT of ∼1.7 at 700 K. They contained Ag−Sb-rich nanoprecipitates embedded within the PbTe matrix. Subsequently, the nature of the LAST materials was analyzed in detail by several groups.178−181 Later, other examples were
Figure 11. (a) Schematic representation of the alignment of the valence band (VB) and conduction band (CB) energies of A and B second phase in the matrix. ΔEC and ΔEV denote the energy offsets of CB and VB between the second phase and the matrix, respectively. The small band offsets allow seamless carrier transmission. (b) Temperature dependence of carrier mobilities and lattice thermal conductivity for the PbTe−SrTe system doped with 2% Na.3,4 All samples have similar doping level. The endotaxially nanostructured SrTe with small valence band offsets has negligible effect on the hole mobility while blocking heat-carrying phonons at the matrix/ nanostructure interface. 12132
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is expected to enable seamless hole transmission across the interface. Likewise, phase B has negligible energy difference of CBM with that of the matrix, and it is expected to allow facile electron transmission. p-Type PbTe embedded with well-dispersed SrTe nanocrystals is a well-known example of valence band alignment.3,4 As shown in Figure 11b, the lattice thermal conductivity of PbTe is remarkably decreased upon the addition of SrTe second phase but the hole mobility is largely unaffected. Specifically, under similar hole doping, the room-temperature lattice thermal conductivity of the control sample (containing no SrTe) is ∼1.8 W m−1 K−1, and it is decreased to ∼1.5 and ∼1.3 W m−1 K−1 by introducing 1% and 2% SrTe, respectively. In contrast, the carrier mobility is almost constant in this process, stabilizing between 340 and 350 cm2 V−1 s−1 at room temperature. The reason for this is 2-fold:3 (1) endotaxial alignment of SrTe and PbTe phases with coherent interfaces, as we elaborated in the previous section, and (2) the alignment of the energies of the two valence bands in the two materials where the band offset is very small at T > 300 K. Actually, the generality of the matrix/precipitate band alignment concept is also evident in the PbS system nanostructured with various metal sulfides (CdS, ZnS, CaS, and SrS).27 Though all these nanostructures are equally effective in achieving a very low lattice thermal conductivity (∼0.6 W m−1 K−1 at 923 K), only CdS helps maintain a high hole mobility due to its smallest valence energy offsets with PbS (∼0.13 eV at 0 K). This is the main reason for the superior ZT of the CdS-containing samples (∼1.3 at 923 K in 2.5% Nadoped PbS with 3% CdS), a record value for PbS.27
Figure 12. (a) Schematic representation of how compositionally alloyed nanostructures can achieve aligned electronic bands. (b) Valence band alignment by compositionally alloyed nanostructuring in p-type PbSe system.28 (c) Room-temperature carrier mobility of 2% Na-doped PbSe nanostructured with CdSe, ZnSe, CdS, and ZnS as a function of second-phase mole fraction.28 (d) Temperature-dependent lattice thermal conductivity of 2% Na-doped PbSe nanostructured with 3% CdSe, ZnSe, CdS, and ZnS.28
These happen via an interfacial reaction between the selenide matrix and the sulfide second phase and are confirmed by the chemical composition analysis using high-resolution energydispersive spectroscopy (EDS).28 The compositionally alloyed new phases CdS1−xSex and ZnS1−xSex then have different band energies and can be employed to create minimal energy offsets with VBM of PbSe, Figure 12b. Because of the good band alignment the compositionally alloyed nanostructures have almost no detrimental effect on the carrier mobility, Figure 12c. In contrast, a decreasing trend of mobility with increasing second-phase fraction is observed for the CdSe- or ZnSe-containing PbSe samples due to incorrect band alignment with PbSe, Figure 12b. Of course, the embedded nanostructures continue to scatter phonons to produce large reductions in lattice thermal conductivity, Figure 12d. Therefore, the compositionally alloyed nanostructuring samples feature superior performance, e.g., Pb0.98Na0.02Se−3% CdS has ZT of ∼1.6 at 923 K, the highest value ever reported for PbSe.28
4.3. Compositionally Alloyed Nanostructures
The ideal nanostructuring case is when the electronic bands of matrix and the second phase are perfectly aligned in energy. In practice it is not easy to find such an appropriate combination of second phases. The CBM or VBM of the possible candidates lie either higher or lower in energy with respect to those of the matrix. In this case we can use the concept of “compositionally alloyed nanostructures”28 to achieve electronic band alignment. The concept is schematically presented in Figure 12a. The CBM of the second phases AB and AC is too high or too low with respect to the matrix to achieve effective conduction band alignment on their own. However, if one could mix them in a proper ratio to form a solid solution (AB1−xCx) then this alloy may have minimal energy offsets with the matrix. Similarly, valence band alignment can be achieved by alloying a proper amount of second-phase XZ in XY as nanostructures (XY1−mZm). In this regard, compositionally alloyed nanostructure is a universal concept of matrix/precipitate band alignment. A good example of applying this idea is p-type PbSe compositionally alloyed with CdS or ZnS.28 As shown in Figure 12b, based on the theoretical band calculation results, the VBMs of CdS (∼0.27 eV) and ZnS (∼0.30 eV) are far below that of PbSe, while those of CdSe (∼0.06 eV) and ZnSe (∼0.13 eV) are higher than that of PbSe. Therefore, none of them could be directly used to align the valence bands. However, when CdS or ZnS is added to PbSe, the following alloying reactions are expected to occur PbSe + CdS → PbSe1 − xSx + CdS1 − x Sex
(11)
PbSe + ZnS → PbSe1 − xSx + ZnS1 − x Sex
(12)
5. DISCOVERIES OF NEW THERMOELECTRIC MATERIALS WITH INTRINSICALLY LOW THERMAL CONDUCTIVITY From the above it is apparent that a number of useful concepts have emerged, which can be integrated in a synergistic manner in bulk materials to greatly enhance thermoelectric performance.183 Clearly, we are in a new era for thermoelectric materials research. In a very special group of materials, high thermoelectric performance can be found in pristine compounds with intrinsically low thermal conductivity. The intrinsically low thermal conductivity means that the most complex approaches to reduce thermal conductivity could be avoided. Below we introduce some promising thermoelectric materials with intrinsically low thermal conductivity, which may arise from an anharmonic and anisotropic bonding,40,56 lattice vibra12133
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tions,184,185 atomic disorders induced by ion migrations,185 copper ion liquid-like behaviors, 36,186 large molecular weight,55,187 complex crystal structure,188 lone-pair electrons,189,190 etc.
moderate ZT value of approximately 0.8 was measured along the a axis, Figure 13b. These high ZT values observed in SnSe single crystals are not observed in polycrystalline samples of SnSe, which exhibit a ZT peak of ∼1.2 at 973 K. The reason is the big differences in carrier mobility and thermal conductivity between SnSe single- and polycrystalline samples where the three different crystallographic directions are averaged but in a difficult to control manner because of the varying degrees of preferential orientation, Figure 14a.
5.1. Layered SnSe
Recently, a record high ZT of 2.6 in a single binary crystal of SnSe was observed.40 SnSe has an unusual layered structure that derives from a three-dimensional distortion of the NaCl structure. SnSe has two-atom-thick SnSe slabs (along the b-c plane) with strong Sn−Se bonding within the plane of the slabs, which are then linked with weaker Sn−Se bonding along the a direction, see Figure 13a. The two-atom-thick SnSe slabs
Figure 13. (a) SnSe crystal structure viewed along the b axis: gray, Sn atoms; red, Se atoms. Blue box represents a unit cell. (b) ZT values as a function of temperature for SnSe single crystals along different axial directions and polycrystalline SnSe pellets along radial and axial directions.40
Figure 14. (a) Carrier mobility and (b) power factor as a function of temperature for undoped SnSe single crystals40 along different axial directions and polycrystalline SnSe pellets119 along radial and axial directions. (c) Thermal conductivities as a function of temperature of undoped SnSe single crystals40 and polycrystalline SnSe prepared in air and a glovebox.192
are corrugated, creating a zigzag accordion-like projection along the b axis. The easy cleavage in this system is along the (l00) planes.40 The special crystal structure results in impressively low thermal conductivities of 0.7 (300 K) and 0.4 W m−1 K−1 (700 K) for SnSe crystals (b axis). To probe the origin of the intrinsically low thermal conductivity of SnSe, the phonon and Grüneisen dispersions, which reflect an anharmonicity of chemical bonds, have been calculated using first-principles density-functional theory (DFT). The results show that the average Grüneisen parameters along the a, b, and c axes are 4.1, 2.1, and 2.3, respectively. Along the a axis, the maximum longitudinal acoustic Grüneisen parameter is extraordinarily high at ∼7.2. In contrast, the Grüneisen parameters for known low thermal conductivity materials is 2.05 for AgSbTe2,191 3.5 for AgSbSe2,189 and 1.45 for PbTe.191 These materials have lattice thermal conductivities at room temperature of 0.68, 0.48, and 2.4 W m−1 K−1, respectively. The anomalously high Grüneisen parameter of SnSe is a reflection of its crystal structure which contains much distorted SnSe7 polyhedra (due to the lone pair of Sn2+) and the zigzag accordion-like geometry of slabs in the b-c plane. This implies a very soft lattice, in which if mechanically stressed along the b and c directions would not directly change the Sn−Se bond lengths, but instead the zigzag and geometry would allow it to be deformed like a retractable spring. In addition, along the a direction the weaker bonding between SnSe slabs makes it a good stress buffer or a “cushion”, thus dissipating phonon transport laterally. The anomalously high Grüneisen parameter is therefore a consequence of “soft” bonding in SnSe, which presumably leads to the very low thermal conductivity and the surprising thermoelectric performance of the single crystals.40 Single crystals of SnSe show a ZT value of approximately 2.6 at 923 K along the b axis and 2.3 along the c axis, whereas a
The carrier mobility along the b axis for SnSe single crystals is 10 times higher than along the a axis. This strong anisotropic character diminishes the carrier mobility in polycrystalline SnSe, as also observed by Chen et al.119 For example, at room temperature, the hole mobility of polycrystalline SnSe is ∼50 cm2 V−1 s−1 with a carrier density of 3 × 1017 cm−3;119 however, the hole mobility in single crystals is about 250 cm2 V−1 s−1 (at similar carrier density of 3 × 1017 cm−3). At 750 K, at the carrier density of 4 × 1018 cm−3, the hole mobility of polycrystalline SnSe sample is about 10 cm2 V−1 s−1, which is only one-fifth of ∼50 cm2 V−1 s−1 for the SnSe single crystals.40 The low carrier mobility of polycrystalline SnSe results in an electrical conductivity that is five times lower than that of SnSe single crystals. This results in a one-fifth of the power factor (Figure 14b) and lower ZT values (Figure 13b). We expect this number to change from report to report and from sample to sample since the degree of polycrystalline orientation may vary across samples and laboratories. For this reason we suggest such reports of transport properties of polycrystalline SnSe to be accompanied with detailed X-ray and microscopic characterization of the degree of preferential orientation. Very recently, Zhang et al.192 reported a similar thermal conductivity in polycrystalline SnSe to that of SnSe single crystals.40 The maximum power factor in polycrystalline SnSe achieved to date is ∼4 μW cm−1 K−2 at 773 K and a ZT of 1.0.192 Correspondingly, the maximum power factor is ∼6 μW cm−1 K−2 at 773 K, resulting in a ZT of 1.5 at 773 K in undoped SnSe single crystals.40 It should be noted that both these reports have samples of similar carrier concentration and Seebeck coefficient. Therefore, the differences in power factor 12134
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and ZTs come from the carrier mobility and from the strong anisotropic character of the SnSe crystal structure. Apart from the carrier mobility in some reports,90,119,193−196 the ZT differences between SnSe single crystals and polycrystalline SnSe samples also come from thermal conductivity deviations. Indeed, the explanations of strong anharmonic chemical bonding given for the low thermal conductivity of SnSe single crystals also apply to polycrystalline SnSe samples.40,107 However, accurately measuring the thermal conductivity of SnSe even in single-crystal samples seems to be a challenge. It has been found that polycrystalline samples are more difficult to work with because of surface oxidation and preferential orientation. It is possible that the surface oxidation yields SnO2 second phase, which has a thermal conductivity of ∼98 W m−1 K−1, about 140 times higher than SnSe.197 If the polycrystalline samples are prepared or handled in air this could give higher thermal conductivity values. In our experience polycrystalline samples protected from oxidation have low thermal conductivities similar to single-crystal samples.192 Recently, He et al. gave the same explanation for the thermal conductivity issue.198 They found that the thermal conductivity of polycrystalline SnSe will decrease when the SnSe powders are processed in a glovebox and will closely approach the 0.30 W m−1 K−1 value at 773 K, which is comparable to 0.30 (c axis) and 0.35 W m−1 K−1 (b axis) of SnSe single crystals.40 This oxidation could lead to a thin layer of tin oxides on the surface of the micrometer-sized powders. Indeed, a similar low thermal conductivity of 0.30 W m−1 K−1 at 773 K was observed in polycrystalline SnSe strictly prepared in a glovebox,192 as shown in Figure 14c. To investigate this hypothesis, a series of control experiments was carried out. We find that the thermal conductivity of polycrystalline SnSe is very low when the SnSe powders are processed in a glovebox compared to processing in air and closely approaches the 0.36 W m−1 K−1 value at 773 K, which is comparable to 0.30−0.35 W m−1 K−1 of SnSe single crystals.40 Interestingly, when we processed the SnSe powders with a small added amount of SnO2 (e.g., the SnO2 addition ranged from 0.0038 to 0.02 g of SnO2 per 5 g of SnSe, 0.1−0.6% by weight), the thermal conductivities of the polycrystalline SnSe samples showed a significant increase even though the powders were processed in a glovebox. Besides the preparation conditions, stoichiometric composition is also crucial to the thermal conductivity of SnSe. Serrano-Sanchez et al. confirmed the intrinsically low thermal conductivity of SnSe and provided insights into the stoichiometric ratio and the sample processing conditions.199 The microscopic neutron powder diffraction analysis demonstrated a nearly ideal stoichiometry and a high amount of anharmonicity of the chemical bonds of SnSe, and the lowest thermal conductivity value is close to 0.1 W m−1 K−1 at room temperature for the polycrystalline SnSe.199 As an analogue of SnSe, the thermoelectric properties of SnS are also receiving attention. Experimentally, Tan et al. reported that the low thermal conductivity falls below 0.5 W m−1 K−1 at 873 K and leads to a high ZT of 0.6 in Ag-doped polycrystalline SnS, pointing out that the low-cost SnS is a promising candidate for thermoelectric investigations.200,201 The experimental results are well supported by first-principles theoretical calculations, which indicate that SnS could possess a high Seebeck coefficient and a very low thermal conductivity.202 Bera et al. suggested that SnS is potentially a good thermoelectric material if it can be suitably doped.203 Considering the poor electrical transport properties of SnS, a
high thermoelectric performance could be expected in perfect SnS single crystals with heavy doping. Apart from the intrinsically low thermal conductivity of SnSe, the electronic band structure is also very impressive. It is well known that the Seebeck coefficients could be enhanced through manipulating multiple valence or conduction bands, which are highly sought features in thermoelectric materials. Figure 15a
Figure 15. (a) Schematic of the electronic band structure of SnSe indicating nonparabolic, complex multiband valence states. The Fermi level (green dash line) is moving into the multiband structure after heavily doping. Electrical transport properties as a function of temperature for undoped SnSe and hole-doped SnSe along different crystallographic directions: (b) electrical conductivity; (c) Seebeck coefficients (inset shows the room-temperature Seebeck coefficients comparisons for the lead and tin chalcogenides with similar carrier concentration of ∼4 × 1019 cm−3); (d) power factors including those of the optimized Bi2−xSbxTe3 and PbTe−4SrTe−2Na plotted for comparison.2,4
shows multiple valence bands for SnSe, and it is rare to find a system that exhibits this enhancement while also exhibiting extremely low thermal conductivity and a high electrical conductivity.204,205 Hole doping increases the electrical conductivity from ∼12 to ∼1500 S cm−1 as the carrier concentration increases from ∼1017 to ∼1019 cm−3 at 300 K, as shown in Figure 15b. Meanwhile, the Seebeck coefficient decreases from ∼+500 μV K−1 for undoped SnSe to ∼+160 μV K−1 at 300 K in doped while still keeping a large value of ∼+300 μVK−1 at 773 K. The inset of Figure 15c indicates that the Seebeck coefficient for hole-doped SnSe is clearly much higher than ∼+70 μV K−1 for PbTe,206 ∼+60 μV K−1 for PbSe,207 ∼+50 μV K−1 for PbS,27 and ∼+25 μV K−1 for SnTe92 at similar doping levels. The observed Seebeck coefficient enhancements of hole-doped SnSe can be attributed to the multiband character of the electronic structure.204,205 The combination of vastly increased electrical conductivity and high Seebeck coefficient results in a large power factor of ∼40 μW cm−1 K−2 for hole-doped SnSe (b axis) at 300 K, Figure 15d. The power factors obtained in hole-doped SnSe are as high as those of optimized Bi2−xSbxTe3 materials2 near room temperature and are higher than those of the high-performance hierarchically architectured p-type PbTe−SrTe system in the range of 300−500 K.4 The temperature dependence of total thermal conductivities (κtot) for undoped and hole-doped SnSe are shown in Figure 16a. At room temperature, the values of κtot for undoped SnSe are ∼0.46, 0.70, and 0.68 W m−1 K−1 along the a, b, and c axis 12135
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Figure 17. BiCuSeO crystal structure and ZT values. (a) Crystal structure along the a axis: yellow, Cu atoms; red, Se atoms; purple, Bi atoms; blue, O atoms. Blue box represents a unit cell. (b) Dimensionless figure-of-merit ZT vs temperature of selected typical current thermoelectric materials: CsBi 4 Te 6 , 29 Bi−Sb−Te, 2 AgPbmSbTem+2 (LAST),1 Mg2SiSn,24 PbTe−SrTe−Na,4 skutterudite,33 BiCuSeO,116,213 half-Heusler,214 SiGe,6 and Zintl phase.55,187 Green lines are p-type, blue lines are n-type materials, and thick red line is BiCuSeO.
Figure 16. (a) Total thermal conductivities, (b) lattice thermal conductivities and (c) ZT values as a function of temperature for undoped SnSe and hole-doped SnSe along different crystallographic directions; (d) ZT values comparisons of hole doped SnSe (b axis) and the current state-of-the-art p-type thermoelectrics, BiSbTe, 2 MgAgSb,34 NaPbmSbTem+2 (SALT),208 PbTe-4SrTe-2Na4 and SnSe (b axis).40
BiCuSeO exceeds 1.0 above 650 K and monotonously increases up to 1.4 at 923 K.116,212,213 The average ZT, quantitatively represented by the area under the ZT vs temperature curve, is the property used to estimate the performance in real application conditions. It can be seen that the average ZT of BiCuSeO outperforms several conventional thermoelectric materials. Moreover, compared to conventional heavy-metalbased thermoelectric materials,5,50,56,96 BiCuSeO oxyselenides are earth abundant and can thus be regarded as promising candidates for vehicle waste heat recovery and solar thermal engine replacement. The promising ZT of the oxyseleneide compound BiCuSeO is mainly due to its intrinsically low thermal conductivity.215−218 Ding et al. calculated the thermal conductivity of BiCuSeO using the lattice thermal conductivity obtained by the Grüneisen parameter and the electronic thermal conductivity using the Wiedemann−Franz relation.185 As shown in Figure 18a, at low temperature the experimental data are far below the calculated results, even after the addition of scattering contributions from the defects. This indicates an extra mechanism may be responsible for the low thermal conductivity of BiCuSeO. Figure 18b shows the heat capacity of BiCuSeO as a function of temperature; the heat capacity at room temperature shows good agreement with the Dulong− Petit law. Saha184 proposed an atomic displacement pattern for the respective lowest frequency optical mode of BiCuSeO, as shown in Figure 18c. In this pattern the arrows are proportional to the amplitude of the atomic motions, since the Bi atoms exhibit a significantly large displacement, indicating higher anharmonic effects.184 Assuming the heat is conducted only by acoustic and quasiacoustic phonons via umklapp scattering processes, the calculations suggest an average Grüneisen parameter of 2.9. Additionally, the calculated thermal conductivity in the out-of-plane direction of BiCuSeO is about two times smaller than that in-plane one, indicating that BiCuSeO has an large anisotropy of heat flow between the inplane and the out-of-plane directions.184 Ding et al. also calculated the phonon spectrum and mode Grüneisen parameters of BiCuSeO.185 First-principles calculations provide direct evidence of the structural in-layer and interlayer off-phase vibration modes, which contribute to the anharmonic vibrations and structural scattering of phonons and
directions, respectively. These already low values continue to decrease with rising temperature, and all fall in the range 0.25− 0.28 W m−1 K−1 at 773 K. After hole doping, the total thermal conductivities are higher due to a large contribution from electronic thermal conductivities. To derive the lattice thermal conductivity, the Lorenz number of 1.5 × 10−8 V2 K−2 was used for the undoped SnSe since it is a nondegenerate semiconductor. To more accurately obtain an estimate of the lattice thermal conductivity of hole-doped SnSe, the Lorenz number L has to be calculated based on a multiband model. Using more appropriate Lorenz numbers, one can see that the lattice thermal conductivity of hole-doped SnSe is comparable to or even lower than undoped SnSe, Figure 16 b. After hole doping, one can find a vast increase in ZT from 0.1-undoped to 0.7hole-doped along the b axis at 300 K while obtaining the ZTmax of 2.0 at 773 K, Figure 16 c. The hole-doped SnSe (b axis) outperforms most of current state-of-the-art p-type materials at 300−773 K, such as Bi2−xSbxTe3,2 MgAgSb,34 NaPbmSbTem+2 (SALT),208 PbTe−4SrTe−2Na4 and SnSe (b axis),40 as shown in Figure 16 d. 5.2. BiCuSeO Oxyselenides
Since BiCuSeO oxyselenides have been reported as potential thermoelectric materials in 2010 by Zhao et al.,209 they have attracted everincreasing attention and have been extensively studied. BiCuSeO crystallizes in a layered ZrCuSiAs structure type, with the tetragonal unit cell a = b = 3.9273 Å, c = 8.9293 Å, Z = 2, and the space group P4/nmm (No.129, PDF 450296).56 Figure 17a shows that BiCuSeO exhibits a twodimensional structure containing fluorite-like Bi2O2 layers alternatively stacked with Cu2Se2 layers along the c axis. The coordination of Bi can also be considered as a distorted square antiprism with four O atoms in one base and four Se atoms in the other. The Bi−Se bond length ∼3.2 Å is longer than the Bi−O bond length ∼2.33 Å, which implies its layered feature. The Cu2Se2 layers consist of slightly distorted CuSe4 tetrahedra with shared Se−Se edges. The Cu2Se2 layer could be considered as a reversed version of Bi2O2 layer, because Cu atoms occupy the Bi sites while Se atoms occupy the O sites.210,211 As shown in Figure 17b, the maximum ZT of 12136
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Figure 19. (a) α-MgAgSb crystal structure: light blue, Ag atoms; red, Sb atoms; light purple, Mg atoms. (b) ZT values as a function of temperature for doped samples of MgAgSb.34,223
axis, with one-half of the Mg−Sb pseudocubes filled with Ag. The unit cell of the α-MgAgSb phase is doubled (distorted Mg−Sb rocksalt lattice) along both axes to accommodate a different ordering of the Ag atoms. In the pattern of filling of the Mg−Sb cubes (distorted Mg−Sb rocksalt lattice), the Agfilled sites form one-dimensional chains, running in all three primary directions. The presence of complicated phase transitions makes it difficult to obtain pure α-MgAgSb phase when the samples are cooled from 1250 K to room temperature and the impurities degrade the thermoelectric performance. For example, a αMgAgSb sample with high content of secondary phase of Ag3Sb (∼19%) shows a maximum ZT of only ∼0.5 at 425 K.221 To eliminate the impurity phase, Ying et al. carried out a 2-week annealing treatment at 553 K,222 which led to a maximum ZT of ∼0.8 at 525 K. After optimizing the carrier density using In doping on the Sb site, a maximum ZT value of ∼1.1 was achieved at 525 K at an optimized carrier density of 8−9 × 1019 cm−3, Figure 19b. Compared with conventional melting techniques, mechanical alloying has been widely used in the thermoelectric field to nanostructuring grain sizes and purifying material phases.2 Zhao et al. recently used a two-step mechanical alloying method and successfully obtained α-MgAgSb single phase, which shows a ZT of ∼0.9 at 450 K.34 Figure 19b shows that the thermoelectric performance of α-MgAgSb can be significantly enhanced through doping, namely, the maximum ZT values can be achieved ∼1.2, ∼1.4, ∼1.3, and ∼1.3 for MgAg0.97Sb0.99,34 MgAg 0.965 Ni 0.005 Sb 0.99 , 34 MgAg 0.963 Cu 0.007 Sb 0.99 , 223 and Mg0.9925Na0.0075Ag0.97Sb0.99,223 respectively. Experimentally, a high thermoelectric conversion efficiency of 8.5% was reported with a single leg based on α-MgAgSb-based compound operating between 300 and 520 K. Within the temperature range of 300−450 K, the efficiency of a MgAgSb-based device can match that of a Bi2Te3-based device.224 Considering the abundantly available constituent elements, α-MgAgSb is promising for power generation at 300−550 K. The promising thermoelectric properties of MgAgSb are ascribed to the low thermal conductivity. As shown in Figure 20a, the thermal conductivities show a decreasing trend up to 400 K and then increase with rising temperature because of bipolar diffusion. The minimum thermal conductivities at ∼373 K are ∼0.98 and ∼0.95 W m−1 K−1 for MgAgSb and MgAg0.97Sb0.99In0.01, respectively, and can be further reduced by point defects scattering through doping,222 namely, the minimum thermal conductivities at ∼373 K are ∼0.74, ∼0.66, ∼0.71, and ∼0.77 W m −1 K −1 for MgAg 0.97 Sb 0.99 , 34 MgAg 0.965 Ni 0.005 Sb 0.99 , 34 MgAg 0.963 Cu 0.007 Sb 0.99 , 223 and Mg0.9925Na0.0075Ag0.97Sb0.99,223 respectively.
Figure 18. (a) Thermal conductivity as a function of temperature for pristine BiCuSeO, the blue line is the calculated total thermal conductivity, and the black line the experimental data.185,215 (b) Heat capacity as a function of temperature for BiCuSeO; the red line is the data based on the Dulong−Petit law.215,216 (c) Atomic displacement patterns for BiCuSeO; arrows are proportional to the amplitude of the atomic motions.184 (d) Mode Grüneisen parameters of BiCuSeO. Red squares correspond to the mode Grüneisen parameters of acoustic branches, black circles correspond to the frequencies between 2.5 and 6 THz, and the blue diamond represents the phonon modes of O above 6 THz.185
result in a low thermal conductivity for BiCuSeO. As shown in Figure 18d, the mode Grüneisen parameters vary between 0.08 and 6.74. The average Grüneisen parameter is approximately 2.5, which is considerably larger than the experimental value of 1.5 estimated from the average sound velocity in polycrystalline BiCuSeO.219 It is believed that the presence of the heavy element Bi contributes to the large Grüneisen parameter due to its large valence shell formed by lone-pair electrons.56,219 As can be seen from Figure 18 d, the Grüneisen parameters of the lowfrequency modes are very large, which indicates the strong interaction between acoustic phonons and optical phonons.185 These phonon−phonon Umklapp processes can significantly scatter acoustic phonons carrying heat and reduce the lattice thermal conductivity. The anomalously high Grüneisen parameters of BiCuSeO also reflect its crystal structure, which contains distorted edge-sharing CuSe4 tetrahedra and a layered structure with zigzag geometry. This implies a soft lattice, which can scatter phonons easily. 5.3. Half-Heusler MgAgSb
Materials with the half-Heusler structure can possess excellent electrical transport properties that make them of strong interest for thermoelectric applications.220 MgAgSb is compositionally and structurally related to many other half-Heusler materials, whose thermoelectric properties along with ab initio determination of crystal structures were extensively investigated.221 MgAgSb exists in three different crystal structures at 300−700 K, taking the half-Heusler structure at 630−700 K (γ-phase with space group F4̅3m), a Cu2Sb-related structure at 560−630 K (β-phase with space group P4/nmm), and a tetragonal structure at 300−560 K (α-phase with space group I4̅c2). The low Seebeck coefficient of ∼70 μV/K and high electrical conductivity of ∼2.5× 104 S/cm indicate that β-MgAgSb shows a metallic transport behavior; therefore, most reports focus on the thermoelectric properties at 300−560 K of α-MgAgSb. As shown in Figure 19a, the α-MgAgSb phase consists of a distorted Mg−Sb rocksalt lattice, rotated by 45° about the c 12137
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disordered throughout the structure, and the disordered Cu ions are superionic mobile.231 Figure 21b shows the temperature dependence of ZT values for copper chalcogenides. Yu et al. described Cu2Se as a thermoelectric material with an ordered selenium layer and a disordered copper layer, with a maximum ZT value of ∼1.6 at 973 K.229 Liu et al. described Cu2Se a copper ion liquid-like thermoelectric material with a maximum ZT value of ∼1.5 at 1000 K.36 Following these reports, Zhong et al.232 supposed that Cu1.94Al0.02Se would show anisotropic transport properties and created a highly aligned large lamellae in bulk Cu1.94Al0.02Se using the direct-current hot-pressing process. A high ZT of 2.62 at ∼1030 K was reported in Cu1.94Al0.02Se with lamellar structure, supposing that the superionic properties were concentrated on one direction, and a ZT of 1.4 at ∼1030 K along the direction perpendicular to lamellar structure was reported. Meanwhile, Zhong et al. mentioned that a big spread of ZT values among 50 samples raised concerns about repeatability.232 Surprisingly, Cu1.97S also exhibits an impressive high ZT of 1.7 at 1000 K,41 which was further enhanced to ZT of 2.1 at 1000 K in Cu2S0.52Te0.48.233 The high ZT obtained in Cu2S0.52Te0.48 is attributed to a special microstructure involving mosaic crystals which exhibit the good electrical properties of single crystals and the low thermal conductivity of polycrystalline or nanocrystalline samples. Unlike the random orientation in ordinary polycrystalline materials, blocks in a so-called mosaic crystal exhibit a nearly identical orientation; thereby the bulk appears like a single crystal from a macroscale point of view but contains a number of small angle boundaries. The apparent high performance in copper chalcogenides mainly comes from the intriguing thermal transport properties, especially in the thermal conductivity. As shown in Figure 22a,
Figure 20. (a) Thermal conductivity as a function of temperature for samples of MgAgSb.34,223 (b) Ag+ migration model from Ag site to Mg vacancy and (c) Mg2+ migration model from Mg site to Ag vacancy in α-MgAgSb.185 (b and c) Reprinted with permission from Li et al. Adv. Funct. Mater. 2015, 25, 6478−6488. Copyright 2015 WILEY Publishing.
Li et al. found that unique Ag and Mg ion migrations in αMgAg0.97Sb0.99 cause significant local atomic disorder which is believed to be the main origin of the low thermal conductivity.185 DFT calculations indicate that the activation energy for Ag+ migration from the Ag2 site to the Mg vacancy is ∼0.202 eV, as shown in Figure 20b. The respective activation for Mg2+ migration from the Mg site to the Ag2 vacancy is ∼0.485 eV, as shown in Figure 20c. This reveals a unique type of ion migration between the Ag site and the Mg site in αMgAg0.97Sb0.99, which weakens the chemical bonds, consistent with the softening transverse phonon modes, the low Debye temperature (160 K), and the low mean phonon velocity of 1276 ms−1. 5.4. Copper Chalcogenides
Copper sulfides and selenides have been recognized as interesting thermoelectric materials. The history of copper chalcogenides goes back 1827, when Becquerel observed that burning some sulfur powder atop the copper wire significantly enhanced the generation of electricity.225,226 They were also studied in the 1960s;227 then the general interest waned only to re-emerge in recent years. Ge et al. reported a maximum ZT value 0.5 at 673 K for polycrystalline Cu1.8S fabricated using a combined process of mechanical alloying and spark plasma sintering,228 and then Liu et al.36 and Yu et al.229 independently reported high ZT values of 1.5−1.6 at ∼1000 K for Cu2Se. Interested readers are encouraged to refer to a relevant review by Dennler et al.,186 summarizing the long history of copper chalcogenides as thermoelectric materials. Cu2Se undergoes a phase transition at ∼400 K, where during the cooling process β-Cu2Se turns into α-Cu2Se and this transition is reversible.230 Figure 21a shows the β-Cu2Se crystal structure, where the Se atoms are in a simple face-centeredcubic packing in the space group Fm3̅m, but the Cu ions are
Figure 22. (a) High-temperature thermal conductivity of Cu2Se as a function of temperature.36,41,229,232,233 (b) Specific heat capacity as a function of temperature for copper chalcogenides.36 Dashed blue line shows the expected value of the specific heat at constant pressure Cp in a solid crystal Cu2Se without liquid-like properties, which is usually beyond the Dulong−Petit limit at high temperatures owing to the extra contributions by carriers (Ce) and lattice thermal expansion. B is the bulk modulus, V is the volume per atom, and α is the thermal expansion coefficient.
the thermal conductivities are ultralow at high temperatures, namely, the minimum thermal conductivities at ∼1000 K can reach as low as ∼0.71, ∼0.60 , ∼0.48, and ∼0.39 W m−1 K−1 for Cu2Se,36,229 Cu1.94Al0.02Se,232 Cu1.97S,41 and Cu2S0.52Te0.48,233 respectively. Figure 22b shows that these materials exhibit an unusual heat capacity.36 The theoretical value (Dulong−Petit law) for the high-temperature specific heat at constant volume Cv is 3NkB in a solid crystal, where N is the number of particles and kB is the Boltzmann constant. The lowest Cv theoretical value in a liquid is 2NkB. Cu2Se shows a reduced Cv, approaching 2NkB at high temperatures, which is a typical ion liquid-like behavior,36 as in an ionic battery.234 However, the
Figure 21. (a) β-Cu2Se crystal structure: yellow, Cu atoms; red, Se atoms. (b) ZT values as a function of temperature for copper chalcogenides.36,41,229,232,233 12138
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physical explanation of this ion liquid-like behavior phenomenon is not clear yet. In an ion liquid-like semiconductor, the lattice thermal conductivity can be reduced below that of a glass by reducing not only the mean free path of phonons but also eliminating lattice vibrations. The idea of using the liquid-like behavior of superionic conductors may be considered an extension of the phonon-glass electron-crystal concept, and such materials could be considered phonon-liquid electron-crystal (PLEC) thermoelectrics. The very property that makes copper chalcogenides exhibit good thermoelectric performance may also be its Achilles heel when it comes to moving these materials to device fabrication and ultimate technological applications, namely, the very low thermal conductivity achievable in these systems is due to the very high mobility of Cu ions in the lattice causing great disorder and strong phonon scattering. Because thermoelectric devices are low-voltage high-current devices operating in a dc model, massive and rapid migration of Cu ions from one end of the sample to the other and severe Se/S vaporization will cause decomposition and massive polarization issues rendering the materials unstable for application. The realization is likely the reason that these materials were not pursued further in the first phase of their investigation in the 1960s. Incidentally, in the photovoltaic field the same issue of strong Cu ion migration and rapid instability during device operation caused the promising and good photovoltaic properties of Cu2S to be abandoned. These issues have been reviewed and comprehensively discussed in recent publications.186,235
centers form Bi−Bi bonds of 3.238 Å. The compound has a lamellar structure with slabs of [Bi4Te6]− alternating with layers of Cs+ ions, Figure 23b. Complex bismuth chalcogenides show very low thermal conductivities. Compared to the state-of-the-art thermoelectric Bi−Sb−Te241 and Bi−Sb,242 it can be readily seen that the thermal conductivity of β-K2Bi8Se13 is low, ranging from 1.0 to 1.5 W m−1 K−1, at temperatures below room temperature. The thermal conductivity of CsBi4Te6 decreases with rising temperature and reaches ∼1.5 W m−1 K−1 at room temperature, Figure 24a. No reports are available that deal rigorously
Figure 24. (a) Thermal conductivity comparisons of complex bismuth chalcogenides, and current state-of-the-art low-temperature thermoelectrics.29,236,240−242 (b) ZT values comparisons of complex bismuth chalcogenides, and current state-of-the-art low-temperature thermoelectrics.29,236,240−242
with origins of the intrinsically low thermal conductivity of these complex bismuth chalcogenides. Clarke reported materials selection guidelines for low thermal conductivity thermal barrier coatings.243 According to those guidelines, a material will have a low thermal conductivity if it satisfies these principal conditions: A large molecular weight, a complex crystal structure, nondirectional bonding, and a large number of different atoms per molecule. Complex bismuth chalcogenides fulfill these conditions. Electrical transport properties and thermal conductivity measurements on β-K2Bi8Se13 single crystals showed a relatively high power factor (∼10 μW cm−1 K−2) at room temperature, giving ZT of 0.22 at room temperature,240 Figure 24b. Extensive doping experiments on CsBi4Te6 give high values of power factor (>30 μW cm−1 K−2) at 100−220 K. The highest power factors of 40−60 μW cm−1 K−2 at 150−180 K were obtained through doping with Sb, Bi, SbI3, and BiI3. A ZT value of 0.8 at 225 K was obtained for 0.06% SbI3-doped CsBi4Te6, which is record high at a temperature gap of 150−275 K.29
5.5. Complex Bismuth Chalcogenides
Since the solid solutions of Bi−Sb−Te−Se were established as the leading thermoelectric materials near room temperature,66,79 there have been continuing efforts to find better thermoelectric materials with these elements, and ternary alkali metal−bismuth−chalcogenides are typical ones that have been found.29,236−240 Compared to Bi−Sb−Te−Se solid solutions, ternary alkali metal−bismuth−chalcogenides possess more complex crystal structures such as β-K2Bi8Se13 and CsBi4Te6. As shown in Figure 23a, β-K2Bi8Se13 has a low-symmetry
5.6. Chalcoantimonates with Lone-Pair Electrons
Just as the so-called lone pair of electrons in Pb2+, Sn2+, Ge2+, Bi3+ and Sb3+ plays a role in defining the thermoelectric properties of the various materials described above (and particularly the thermal conductivity), so do they define the properties of the compounds in the Cu/Sb/Se system. In this class we have three members which allow one to more clearly appreciate the role of the lone pair of electrons on the thermal conductivity, Cu3SbSe4, Cu3SnSe3, and CuSbSe2. The first member is a Sb5+ species and has no lone pair of electrons, while the latter two contain Sb3+ with an active lone pairs of electrons. As shown in Figure 25a, Cu3SbSe4 shows a tetragonal structure with the space group I42m. It derives from the diamond structure in which all atoms have tetrahedral coordination geometry.244 CuSbSe2 has an orthorhombic structure with the space group Pnma190,245 and Cu3SbSe3 a
Figure 23. (a) β-K2Bi8Se13 crystal structure: blue, Bi atoms; pink, Se atoms; gray, Ag atoms. Red box represents a unit cell. (b) Typical CsBi4Te6 crystal structure: blue, Bi atoms; pink, Cs atoms; dark reddish, Te atoms. Red box represents a unit cell.
monoclinic structure that consists of two Bi/Se building blocks (NaCl type and Bi2Se3 type) connected at the K/Bi mixed site (blue); the K atoms are in the channels. These two Bi/Se blocks are infinitely extended along the crystallographic b axis and connected to each other at special mixed-occupancy K/Bi sites. It has a highly anisotropic structure, and it grows along the b axis with a needle or columnar structure.240 CsBi4Te6 features a strong anisotropic structure that contains both formally Bi3+ and Bi2+centers.29 The unusual reduced Bi2+ 12139
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Figure 25. Typical crystal structures for (a) Cu3SbSe4, (b) CuSbSe2, and (c) Cu3SbSe3: yellow, Cu atoms; red, Se atoms; gray, Sb atoms. Schematic representation of the local atomic environment of Sb in (d) Cu3SbSe4, (e) CuSbSe2, and (f) Cu3SbSe3. Shaded lines represent Sb− Se bonds; dashed lines illustrate the approximate morphology of the Sb lone-pair 5s electron orbital.
Figure 26. (a) Temperature dependence of the thermal conductivity of Cu3SbSe4, CuSbSe2, and Cu3SbSe3.190 (b) Temperature dependence of the thermal conductivity of two I−V−VI2 cubic semiconductors AgSbTe2 and AgBiSe2, of single-crystal PbTe, and of the chalcopyrite compound AgInTe2.191 Electronic contributions to the thermal conductivity are negligible in all samples; thus, the data shown represent the lattice thermal conductivity. Solid line represents the calculated minimum thermal conductivity for AgSbTe2. (c) Temperature dependence of ZT values for Cu3SbSe4 and Cu3SbSe3.249−251 (d) Temperature dependence of ZT values for I−V−VI2 cubic semiconductors.233,253−257
different orthorhombic structure with the space group Pnma,244 Figure 25b and 25c. In Cu3SbSe4, the Sb5+ centers are coordinated by 4 Se atoms with tetrahedral Se−Sb−Se bond angles of 109.5°, Figure 25d, suggesting sp3 hybridization of the Sb valence electron orbitals. In CuSbSe2, however, Sb is in a 3+ formal oxidation state and coordinated by 3 Se atoms in a trigonal pyramidal geometry and an average Se−Sb−Se bond angle of 95.24°, as shown in Figure 25e. In this arrangement only the Sb 5p electrons form bonds with Se, leaving the Sb 5s2 electrons “free” to orient along the missing vertex of the tetrahedron. The configuration is similar for Cu3SbSe3 except the average Se−Sb−Se bond angle is 99.42°. Once again the Sb 5s2 lone pair helps the Sb3+ to form an imperfect tetrahedron if we consider that is occupies the fourth coordination site, Figure 25f. From a structural point of view, one may expect these three compounds to have similar thermal conductivity since their average atomic masses are nearly the same and none of them possess an overly complex crystal structure; this however is not the case. As shown in Figure 26a, Cu3SbSe4, CuSbSe2, and Cu3SbSe3 possess vastly different thermal conductivity.190 In Cu3SbSe4, the thermal conductivity decreases rapidly with rising temperature due to strong phonon−phonon interactions (typical for a crystalline material). In CuSbSe2, thermal conductivity shows the same decreasing trend with temperature, but it is only one-half that of Cu3SbSe4. Remarkably, Cu3SbSe3 has a very low and temperature-independent thermal conductivity even at cryogenic temperatures. The reason for the large thermal conductivity differences is the different intrinsic phonon scattering mechanisms acting in Cu3SbSe4, CuSbSe2, and Cu3SbSe3. These mechanisms are related to the role of the lone pair of s electrons in the Sb3+ centers in CuSbSe2 to Cu3SbSe3. The nature of the lone pair in heavy main group atoms and its chemical and physical properties have been the subject of much study and debate over many decades and remains topical today.246−248 We can say that understanding the behavior of these lone pairs and how they influence the electronic properties is still incomplete. The relationship between lonepair electrons and low thermal conductivity involves the enhancement of anharmonicity in the lattice by the overlapping
wave functions of the lone-pair electrons and nearby valence electrons which induces nonlinear repulsive electrostatic forces. This is well supported by the density functional theory calculations by Zhang et al.,245 showing that Cu3SbSe3 has larger Grüneisen parameters, smaller Debye temperatures, and lower phonon velocities than Cu3SbSe4. The highest degree of anharmonicity should thus be achieved when the lone-pair electron is far removed from the Sb nucleus and not participating in bonding. Therefore, it is reasonable that the thermal conductivity of CuSbSe2 is higher than that of Cu3SbSe3, since the lone electron pair is farther removed from the Sb nucleus in Cu3SbSe3. Another interesting comparison is the case of AgInTe2 versus AgSbTe2,191 where the thermal conductivity of AgInTe2 (lacking lone pair of electrons) is “normal” while that of AgSbTe2 (Sb3+ 5s2 pair) is glasslike, approaching the calculated minimum thermal conductivity value, Figure 26b. Wei et al.249,250 extensively investigated the electrical and thermal transport properties of Cu3SbSe4 between 300 and 673 K. They found that the maximum ZT at 673 K increases from 0.4 for undoped Cu3SbSe4 to 0.7 when Sn doping is used on the Sb site, Figure 26c. For Cu3SbSe3 an extremely low thermal conductivity (0.25−0.30 W m−1 K−1) was observed, a maximum ZT of 0.25 was obtained at 650 K.251 AgSbTe 2 is well known for its very low thermal conductivity.190,191,252 Wang et al.253 investigated the polycrystalline AgSbTe2, which was fabricated using a combined process of mechanical alloying and spark plasma sintering. It was found that stoichiometric AgSbTe2 is a promising thermoelectric material, whose ZT reaches 1.6 at 673 K, benefiting from its extremely low thermal conductivity of 0.30 W m−1 K−1, Figure 26 d. Nielsen et al.189 reported that lonepair electrons also could minimize the lattice thermal conductivity of AgSbSe2, as in AgSbTe2, since the Grüneisen parameter (3.5) of AgSbSe2 is much larger than that (2.05) of 12140
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AgSbTe2; however, it was found that the electrical transport properties of AgSbSe2 are inferior to AgSbTe2. By improving the electrical transport properties, the ZT values have been enhanced from ∼0.4 for undoped AgSbSe2 to ∼1.0 through introducing Sb vacancies,254 Na doping,233 and Pb doping.255 As an analogue of AgSbSe2, AgBiSe2 is a n-type semiconductor and exhibits very low thermal conductivity; ZT values could be achieved in 0.9−1.0 through Nb doping on the Ag site256 and I doping on the Se site.257
Figure 28. (a) Thermal conductivity as a function of temperature for samples of tetrahedrite Cu12Sb4S13. (b) Sb[CuS3]Sb trigonal bipyramid. (c) Valence electron density map projected onto a (101) plane showing the coordination of Cu12e, Sb, S2a, and S24g atoms. Space group of Cu12Sb4S13 is I-43m and features two Cu sites (12d and 12e), two S sites (2a and 24g), and one Sb site (8c), blue for Cu12e, green for S2a, yellow for S24g, and brown for Sb.251 (b and c) Reprinted with permission from ref 251. Copyright 2015 WILEY Publishing.
5.7. Tetrahedrites
Recently, some natural mineral tetrahedrites were reported as a possible direct source of thermoelectric materials, led by the independent groups of Morelli and Suekuni.258−260 The tetrahedrite phase with general formula Cu12Sb4S13 is one of the most widespread sulfosalt minerals on Earth. It can accommodate a variety of substitutions onto Cu and Sb sites; thus, natural tetrahedrite is commonly written as (Cu, Ag)10(Cu, Zn, Fe, Co, Ni, Cd, Hg)2(Sb, Te, Bi, As)4(S, Se)13. Interest in studying the thermoelectric properties of tetrahedrites has surged because they consist of environmentally benign elements copper and sulfur.261 Figure 27a shows the
drites may result from the synergistic effects of local bonding asymmetry and anharmonic rattling modes.251 As shown in Figure 28 b, a strong local bonding asymmetry is identified inside a Sb[CuS3]Sb atomic cage, in which Cu (blue) forms strong covalent bonding with S (green and yellow) and weak covalent bonding with one of the Sb atoms (brown). The bonding asymmetry of Cu12e causes the low thermal conductivity of tetrahedrites, as indicated in Figure 28c. In addition, the localized anharmonic rattling modes enabled by the lone-pair electrons of Sb also can contribute to resonant scattering of phonons, which is the as same to that of pnicogengroup chalcogenides with lone-pair electrons. Skoug and Morelli identified a correlation between minimal thermal conductivity and the existence of an Sb lone s2 pair in Sbcontaining ternary semiconductors.190 Lone-pair electrons of Sb induce strong lattice anharmonicity;191 the “crescent-moon” shape around Sb is a clear indicator of the existence of electron lone pairs, as shown in Figure 28c.
Figure 27. (a) Crystal structure of tetrahedrite Cu12Sb4S13; (b) ZT values as a function of temperature for doped samples of tetrahedrite Cu12Sb4S13.258,262−265
crystal structure of tetrahedrite Cu12Sb4S13. It possesses a cubic sphalerite-like structure of I-43m symmetry with 6 of the 12 Cu atoms occupying trigonal planar 12e sites and the remaining Cu atoms distributed on tetrahedral 12d sites. The Sb atoms also occupy a tetrahedral site but are bonded to only three S atoms, leading to a void in the structure presumably occupied by the lone pair of electrons. In terms of a simple crystal chemical formula, 4 of the 6 tetrahedral sites are thought to be occupied by monovalent Cu while the other 2 are occupied by Cu2+ ions; the trigonal planar sites are occupied solely by monovalent Cu. Lu et al. found that pure synthetic Cu12Sb4S13 exhibits a ZT value of 0.56 at 673 K,258 as shown in Figure 27b. After optimizing and substituting on Cu or Sb sites, the ZT at 723 K could be further increased to 0.76 for Cu10.5Ni1.5Sb4S13, 0.90 for Cu12Sb3Te4S13, 0.92 for Cu11.5Zn0.5Sb4S13, and 1.1 for Cu10.5Ni1.0Zn0.5Sb4S13.262−265 The promising thermoelectric performance of Cu12Sb4S13 is ascribed to the intrinsically low thermal conductivity. As shown in Figure 28a, the thermal conductivity of Cu12Sb4S13 shows an increasing trend up to 723 K. After doping and alloying, the thermal conductivities are reduced in the entire temperature range; some samples even show the glass-like and temperatureindependent thermal transport behaviors. It seems that the phonon mean free path approaches one interatomic spacing, and the thermal transport reaches the “minimal” thermal conductivity, namely, the thermal conductivity ranges from 0.40 W m−1 K−1 at 300 K to 0.45 W m−1 K−1 at 723 K for Cu10.5Ni1.5Sb4S13.265 The low thermal conductivity of tetrahe-
6. SUMMARY AND OUTLOOK The past two decades have witnessed the rapid growth and several exciting conceptual and performance breakthroughs in thermoelectric research. The development of better and more accessible physical property and thermoelectric measurement techniques and commercially available robust instrumentation especially for reliable high-temperature measurements have played an important role in facilitating in the growth of the thermoelectric community. Furthermore, the power of synthetic solid state chemistry in its ability to deliver new materials and new processing techniques has been critical in this regard. New concepts make it possible to invent new strategies on how to decouple the strong interrelation of thermoelectric transport parameters, raising the ZT values steadily from the historical threshold of around unity to well above 2. As there are no theoretical or thermodynamic limits to the maximum value of ZT, much higher performance can be anticipated for the next generation of thermoelectric devices. Given the many materials yet to be investigated, there is certainly much work ahead and promise for developing higher efficiency thermoelectric materials and devices. As we discussed above, there are generally two main directions to achieving high-performance thermoelectrics: (1) optimizing the known materials by band structure and microstructure manipulation and (2) exploring new compounds with peculiar physical properties that may lead to 12141
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unexpectedly high ZTs. For the former it is highly desirable to integrate all advanced performance-enhancing concepts in one single material. The latter is also appealing given the power of intuitive thinking63 and the elements of surprising discoveries. In principle, the materials selection process can be accelerated using high-throughput computational techniques to perform initial screenings of the search space and identify the best candidates to be investigated experimentally, namely, the socalled materials genome approach. The materials with intrinsically very low thermal conductivity are also of strong interest, especially when they simultaneously feature unique band structures (for example, the conducting bands are composed of multicarrier pockets) that allow high power factors. Of course, considering the complexity of thermoelectric materials, their future development would benefit greatly from close collaborations between chemists, physicists, and materials scientists. Given the need for alternative energy technologies and materials to ultimately replace the shrinking supply of fossil fuels or extend its duration, energy-related research and the study of clean and reliable thermoelectric energy conversion technology will play an important role.
postdoctoral research fellow at the University of Michigan and Northwestern University. He holds a Charles E. and Emma H. Morrison Professor Chair at Northwestern University.
ACKNOWLEDGMENTS This work was supported in part by a Department of Energy grant to the Revolutionary Materials for Solid State Energy Conversion, an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Sciences under Award Number DE-SC0001054. Currently, work at Northwestern is supported by the Department of Energy, Office of Science Basic Energy Sciences grant DE-SC0014520. We also acknowledge the use of the transmission electron microscope from the NUANCE Center at Northwestern University. This work was also supported by the “Zhuoyue” program of Beihang University, the Recruitment Program for Young Professionals, and NSFC under Grant No. 51571007 (L.D.Z). We thank especially Professors C. Uher, C. Wolverton, and V. P. Dravid, whose collaboration has been critical to our understanding of many aspects of our novel materials in our laboratory. We also thank Professors D. N. Seidman, T. P. Hogan, J. P. Heremans, E. D. Case, X. F. Tang, H. B. Xu, S. K. Gong, J. Q. He, and Y. L. Pei for plentiful discussions and fruitful collaborations. Of course, most of all, we are grateful to the numerous dedicated graduate students and postdoctoral fellows who have contributed to our thermoelectric research efforts. Their names appear in the various publications cited in this article.
AUTHOR INFORMATION Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
REFERENCES
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Gangjian Tan received in 2013 his Ph.D. degree in Materials Science from Wuhan University of Technology, China, under the supervision of Professor Xinfeng Tang, with a focus on nanostructured skutterudite compounds as advanced thermoelectric materials by melt spinning. In June of 2013, he joined Professor Mercouri Kanatzidis’s group at Northwestern University as a postdoctoral research fellow, where his research extends to the development of new thermoelectric chalcogenides. He is interested in the understanding of charge and phonon transport behavior in solids associated with thermoelectric effects. Li-Dong Zhao is a Professor of Materials Science and Engineering at Beihang University, China. He received his B.E. and M.E. degrees in Materials Science from the Liaoning Technical University and his Ph.D. degree in Materials Science from the University of Science and Technology Beijing, China, in 2009. He was a postdoctoral research fellow in the LEMHE-ICMMO (CNRS-UMR 8182) at the University of Paris-Sud from 2009 to 2011 and continued as a postdoctoral research fellow in the Department of Chemistry at Northwestern University from 2011 to 2014. He holds the fellowship of “Recruitment Program for Young Professionals”. His research interests include thermoelectric materials, superconductors, and thermal barrier coatings. Mercouri G. Kanatzidis is a Professor of Chemistry and of Materials Science and Engineering at Northwestern University in Evanston, IL. He also has a senior scientist appointment at Argonne National Laboratory. His interests include the design and synthesis of new materials with emphasis on systems with highly unusual structural/ physical characteristics or those capable of energy conversion, energy detection, environmental remediation, and catalysis. After obtaining his B.Sc. degree from Aristotle University in Greece, he received his Ph.D. degree in Chemistry from the University of Iowa and was a 12142
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