High thermoelectric performance of α-MgAgSb for power generation

Abstract

Solid-state thermoelectric devices enable the conversion of waste heat and solar energy into electricity, providing an alternative route for energy harvesting to tackle the challenges of energy sustainability. α-MgAgSb-based materials have recently gained popular attention as a new promising p-type candidate for low-temperature (between room temperature and 550 K) applications. A high figure of merit (ZT) of 1.2–1.4 at 550 K was achieved, along with experimental demonstration of a record high conversion efficiency of ∼8.5% under a cold- and hot-side temperature difference of 225 K, which holds the realistic prospect for power generation. In this review, we summarize the recent progress in both material-level understanding and device-level measurement of the α-MgAgSb system. First, the phase transitions and common fabrication methods are briefly introduced. Then, the origin of the “phonon glass electron crystal” behavior of α-MgAgSb is thoroughly elucidated with regard to some critical factors, such as the crystal structure, lattice dynamic properties, defect chemistry, microstructure, and band structure. Afterwards, the effective strategies to further enhance the ZT are illustrated, including optimizing the carrier concentration and intrinsic defect engineering. In addition, other feasible methods in theory are also presented. Finally, the conversion efficiency on a single-leg device is presented. In the outlook section, the currently unsolved questions as well as future directions and challenges for this material system are discussed.

---

Zihang Liu

Zihang Liu is a postdoctoral fellow in the Department of Physics and TcSUH at the University of Houston, USA. He obtained his PhD degree from Harbin Institute of Technology in March, 2017. He received his Bachelor's degree from Inner Mongolia University of Technology in July 2012. His current research interests are mainly focused on the microscopic mechanism of phonon and electron transport in nanostructured thermoelectric materials.

Jun Mao

Jun Mao is currently a PhD candidate at the Department of Mechanical Engineering at the University of Houston, USA. He received his Bachelor's and Master's degrees from Thermal and Power Engineering at Northeastern University, China. His current research is mainly focused on identifying novel thermoelectric materials.

Jiehe Sui

Jiehe Sui is currently the Head of Material Physics and Chemistry at Harbin Institute of Technology. He received his Master's and PhD degrees in Materials Science and Engineering from Harbin Institute of Technology, China. He was a senior visiting scholar in the lab of Dr. Zhifeng Ren at the University of Houston from May, 2013 to April, 2015. He received the National Natural Science Foundation of China (NSFC) Excellent Young Scientist Fellowship in 2016. His current research is mainly focused on thermoelectric materials and devices.

Zhifeng Ren

Zhifeng Ren, PhD, is an M.D. Anderson Chair Professor in the Department of Physics and TcSUH at the University of Houston, USA. He is experienced in materials synthesis, physics, and applications and has made seminar contributions to high temperature superconductors, carbon nanotubes, ZnO nanowires, thermoelectric materials, nano-biomaterials and sensors, flexible transparent electrodes, hydrogen and oxygen evolution reactions and water splitting, 2D nanosheets for enhanced oil recovery, etc. He has published ∼400 journal papers and has 38 issued patents. He received the 2008 R&D 100 Award and the 2014 Edith and Peter O’Donnell Award. He is an elected APS fellow, AAAS fellow, and NAI fellow.

---

Broader context

For broader real applications in low-grade waste heat recovery or solar energy harvesting, promising thermoelectric materials should possess some critical attributes, including a high average ZT (for high conversion efficiency), a high average PF (for a large output power density), superior mechanical properties, and good thermal stability (for reliable long-term service) as well as non-toxic and earth-abundant matrix elements (for a low cost of raw materials). Since 2012, α-MgAgSb-based materials have received intensive interest as a promising p-type candidate for low to medium temperature power generation. A record high conversion efficiency of 8.5% for a single leg was experimentally demonstrated at an operating temperature difference of 225 K. In this perspective, we summarize the recent progress in both a material-level understanding and device-level measurement of the α-MgAgSb system, including phase transition and the fabrication method, the “phonon glass electron crystal” (PGEC) behavior, current strategies to enhance the thermoelectric performance, and the mechanical properties as well as device fabrication and efficiency measurements. Finally, the currently unsolved questions as well as future directions and challenges are also pointed out.

1. Introduction

The International Energy Agency (IEA) has predicted a 37% increase in global energy demand by 2040, while the Paris Agreement on climate change aims to keep the world average temperature “well below” 2 K above preindustrial levels, with this target coming into effect on November, 2016.^1,2 In the context of the accelerated global energy demand and increasing pressure to reduce greenhouse-gas emissions, the efficient utilization of clean and renewable energy has attracted extensive interest over the last decade,³ including wind power,⁴ solar energy,⁵ hydropower, and biofuels.^6,7 Meanwhile, in 2016 more than half (∼66.4%) of the primary energy was ultimately rejected to the environment throughout the United States,⁸ resulting in various potential heat sources. Thermoelectric power generation (TEG) is capable of directly converting waste heat into electricity based on the Seebeck effect and would play a vital role in future energy harvesting.^9,10 The solar thermoelectric generator (STEG) is also an attractive candidate for converting solar energy into electricity,^11,12 which has achieved a high system efficiency of 7.4% as demonstrated very recently by Kraemer et al.¹³ Thermoelectric devices, with unique advantages of no moving parts, no pollutants, light weight, high reliability, and simplicity, have long been used for powering the spacecrafts used in most NASA deep-space missions in the form of the radioisotope thermoelectric generator (RTG).^14–16 However, TEG falls short of realizing the hopes and expectations placed upon it in a wide range of applications in commercial markets, primarily due to its relatively low conversion efficiency in thermoelectric devices compared with conventional heat engines. The conversion efficiency is dominated by the Carnot efficiency and the material's dimensionless thermoelectric figure of merit (ZT), ZT = (S²σ/(κ_lat + κ_ele))T, where S, σ, κ_lat, κ_ele, and T are the Seebeck coefficient, the electrical conductivity, the lattice thermal conductivity, the electronic thermal conductivity, and the absolute temperature, respectively. Since the fundamental theory of the thermoelectric effect was first established by Ioffe in the 1950s,¹⁷ pursuing a higher ZT has been a key topic for the thermoelectric community. Due to the intertwined or even contradictory fundamental parameters,^18,19 a ZT above unity was originally regarded as a benchmark for bulk thermoelectric materials.^17,20,21 However, over the past two decades, band structure engineering and microstructure engineering have been theoretically proposed and experimentally demonstrated as effective methods to enhance the power factor (PF = S²σ) and suppress κ_lat for traditional thermoelectric materials,^22–37 respectively. Simultaneously, the new concept of the “phonon glass electron crystal” (PGEC), proposed by Slack in 1995, has changed the thinking about thermoelectric materials research and led to the design of new high performance materials,¹⁴ especially cage-like compounds^38–41 and superionic conductors.^42–46 Interested readers are encouraged to refer to some excellent review articles that also cover electron and phonon transport,^{18,19,47–51} band structure engineering,^52,53 nanostructuring,^54–56 panoscopic approach,^57–59 thermoelectric power generators,^60–62 and specific material systems, such as Bi₂Te₃,^63,64 PbTe,⁶⁵ Zn₄Sb₃,⁶⁶ clathrates,⁴¹ Zintl phase,^67,68 half-Heusler,^69,70 oxide,^71,72 and others.^73–76

In fact, remarkable progress in enhancing ZT has been achieved over the last decade; consequently promoting the active consideration of thermoelectric devices for waste heat recovery in industry and/or automobiles.^15,77Fig. 1(a) and (b) show the temperature-dependent ZT of the state-of-the-art n-type and p-type bulk thermoelectric materials,^{24,27,78–90} respectively. It seems to be a record-breaking time for thermoelectric materials to achieve peak ZT values. In real applications, however, a high peak ZT does not guarantee a high conversion efficiency for power generation. Conventionally, the peak ZT, relating to the theoretical efficiency, is the only target for the thermoelectric community. However, in practical applications, on a materials level, the average ZT determines the efficiency, and a high PF is equally important to a high average ZT, or even more important when the heat source is unlimited or free,^91,92 because a high PF leads to a large output power density for given working boundary conditions. The mechanical strength of thermoelectric materials should be good enough to realize a high performance, otherwise the manufacturing will be difficult and reliable operation of the TEG devices will be almost impossible. In addition, the toxicity, abundance, and price of the constituent raw materials are also critical factors for facilitating widespread applications. For module and system assembly, a low contact resistance, simple fabrication and assembling procedure, cost-effectiveness, and good reliability are distinguishing attributes that require special attention.

Fig. 1 (a) and (b) Temperature-dependent ZT of the state of the art of bulk advanced n-type and p-type thermoelectric materials,^27,78–90 respectively.

It is well known that Bi–Sb–Te alloys are unique promising p-type thermoelectric materials for applications around room temperature,^24,63,93,94 but the strong bipolar effect severely degrades their performance above 373 K.⁶³ Furthermore, tellurium (Te) is an extremely scarce element in the earth's crust, and its earth abundance (0.001 ppm) is even much lower than that of gold (Au) ∼0.004 ppm.⁹⁵ Therefore, the search for a better alternative without Te operating at higher temperature is necessary and important in thermoelectric material research. Several new p-type Te-free thermoelectric materials with a relatively high ZT have been discovered in the last decade, such as Zn₄Sb₃,^96–98 AgSbSe₂,^99–101 BiCuSeO,^102–104 Cu₁₂Sb₄Sb₁₃,^105,106 and SnSe (single crystal)-based materials.^88,107,108 Among these, Na-doped SnSe single crystal (b axis) has shown a high room temperature PF (∼40 μW cm⁻¹ K⁻²) and a high ZT (∼0.7) due to the combination of multiple electronic valence bands and high anharmonic bonding.⁸⁸ This seems to suggest it would be a good candidate for power generation. However, the very poor mechanical properties of the layered structure prevent its practical applications. Other compounds show relatively low PFs and maximum values below 573 K of only around 15 μW cm⁻¹ K⁻².^{98,100,103,106} Thus, it is still imperative to discover more really promising candidates for low-temperature power generation.

Recently, α-MgAgSb has been demonstrated as a promising p-type candidate for power generation below 550 K.^109–120 α-MgAgSb shows the typical degenerate semiconductor behavior and satisfies the PGEC criteria, and consequently it has received intensive attention since 2012.^{109–116,118–126} It has a high average ZT over the whole measured temperature range, coupled with a relatively high PF and good mechanical properties.^111,118 Moreover, a record high conversion efficiency of 8.5% for a single leg was experimentally demonstrated at an operating temperature difference of 225 K in combination with a simple fabrication process.¹¹¹ In this review, we first introduce the phase transition and fabrication methods. Then, the origin of the PGEC behavior of the pristine compound is discussed and current strategies to further enhance the TE performance are presented. Finally, the single-leg device fabrication and conversion efficiency measurements are highlighted.

2. Phase transition and fabrication method

As first reported by Kirkham et al.,¹⁰⁹ MgAgSb has complicated phase transitions from the room-temperature α phase to the intermediate-temperature β phase and finally to the high-temperature γ phase. α-MgAgSb and β-MgAgSb have a tetragonal distorted structure, while γ-MgAgSb has a cubic half-Heusler structure. The main difference in the three MgAgSb structures lies in the filling pattern of the Ag atom in the Mg–Sb cubes.¹⁰⁹ α-MgAgSb can be described as a distorted Mg–Sb rocksalt sublattice rotated by 45° along the c axis (Fig. 2a). With increasing the temperature, a tendency of increasing structural symmetry can be observed. β-MgAgSb exhibits a similar structure with the Cu₂Sb compound, where each Ag and Mg atom replaces one of the two Cu atoms (Fig. 2b). However, the actual composition largely deviates from the nominal stoichiometric ratio, probably containing a high concentration of Ag and Sb vacancies.¹²⁷ Based on the maximum entropy method (MEM) analysis and experimental results, γ-MgAgSb tends to have the MgAgAs structure (Fig. 2c),¹²⁷ rather than the first proposed MgCuSb structure.¹⁰⁹ γ-MgAgSb has a highly disordered structure, where the Sb sublattice forms an anion framework with the mixed sites of Mg and Ag as well as vacancies, but it will continuously decompose at high temperatures.¹²⁷ Due to the fact that α-MgAgSb has shown promising low-temperature thermoelectric performance, in the following parts we only discuss its related details, spanning from a material-level understanding to device-efficiency measurements.

Fig. 2 (a) Crystal structure of the room-temperature α-MgAgSb phase, looking along the (left) 〈001〉 and (right) 〈110〉 directions; (b) and (c) crystal structure of the β-MgAgSb phase and the high-temperature γ-MgAgSb phase, respectively. All the figures are drawn to include atoms outside the unit cell in order to emphasize the distorted rocksalt lattice of Mg and Sb atoms, with Mg shown in dark blue, Sb in light tan, and Ag in silver inside the polyhedra.¹⁰⁹ Reproduced with permission from ref. 109. Copyright 2012 American Physical Society.

Since α-MgAgSb undergoes complicated phase transitions, it is a big challenge to obtain the pure phase using the traditional method. Kirkham et al. first tried to prepare α-MgAgSb using a vacuum-melting and hot-pressing method.¹⁰⁹ However, the high content of secondary phases, namely Sb and Ag₃Sb, could be detected in their specimens (Fig. 3a). Ying et al. applied a long-time annealing process that could reduce the content of the impurity phases to a mass fraction around 2% (Fig. 3b).¹¹⁴ Meanwhile, the maximum ZT could be enhanced somewhat from 0.56 at 423 K to 0.83 at 525 K.^109,114 Zhao et al. employed a simple and novel two-step ball milling method in combination with a quick hot-pressing process, which allowed them to finely tune the composition from MgAgSb to MgAg_0.97Sb_0.99 and to successfully fabricate nanostructured α-MgAgSb without any detectable impurity phases within the detection limit of XRD analysis (Fig. 3c).¹¹⁰ The corresponding maximum ZT was around 1.2 at 548 K (Fig. 3d),¹¹⁰ which is much higher than other results,^109,114 which could be attributed to the typical PGEC features.

Fig. 3 (a) Non-ambient X-ray diffraction (XRD) data collected on MgAgSb over two cycles of heating and cooling between 300 K and 693 K (Kirkham et al.).¹⁰⁹ Reproduced with permission from ref. 109. Copyright 2012 American Physical Society. (b) Back scattering electron image of the α-MgAgSb_0.99In_0.01 sample (Ying et al.).¹¹⁴ Reproduced with permission from ref. 114. Copyright 2015 American Chemical Society. (c) XRD pattern with the corresponding Rietveld refinement of the hot-pressed nanostructured α-MgAg_0.97Sb_0.99 alloy (Zhao et al.),¹¹⁸ Reproduced with permission from ref. 118. Copyright 2017 Elsevier B.V. (d) Comparison of the ZT-dependent temperature for the above-mentioned three samples.^109,110,114

3. “Phonon glass electron crystal” behavior

In 1957, Ioffe first defined the quantity “Z” to evaluate the thermoelectric performance.¹⁷ Meanwhile, there was a shift in thermoelectric research from metals to narrow-gap semiconductors at that time.^{17,21,128–130} Promising thermoelectric materials should possess good electronic properties and also low thermal conductivity, following the PGEC design concept.^14,131 At the microscale level, this means that the phonon's mean free path should be as small as possible and the electron's mean free path should be as large as possible. As expected, highly degenerative semiconductors can be designed to enable the efficient transmission of charge carriers (high PF), while largely impeding the flow of phonons by the lattice or defects (low κ_lat). Fig. 4 presents the PF dependence of κ_lat at room temperature for advanced thermoelectric materials.^{29,42,82,85,88,90,91,98,102,132–139} It seems that materials with a high (or low) PF usually exhibit a high (or low) κ_lat. Clearly, α-MgAgSb showed a relatively high PF in combination with a low κ_lat. In the next section, we describe its PGEC behavior and discuss the corresponding origin.

Fig. 4 The lattice thermal conductivity κ_latversus the power factor PF for the state of the art of bulk advanced n-type (solid blue square) and p-type (open blue square) thermoelectric materials.^{29,42,82,85,88,90,91,98,102,132–139}

3.1 Low lattice thermal conductivity-phonon glass

An in-depth understanding of the phonon transport behavior is considered to be a prerequisite for developing high thermoelectric performance materials. In fact, Slack's proposal (PGEC) originally focused on the “glass-like” thermal conductivity,¹⁴ which was soon realized in filled skutterudites and intermetallic clathrates with rattling atoms in the host framework.^39,40 In addition, some noncaged compounds, such as Zn₄Sb₃,^96,97 CdSb, and α-MgAgSb,^110,140 also exhibit the PGEC behavior with low κ_lat. Generally, a low κ_lat is strongly associated with intrinsic features of a crystal's structure, microstructural defects, or lattice dynamic properties. Next, we discuss the microscopic origin of the low κ_lat of α-MgAgSb in regard to the above-mentioned critical aspects.

3.1.1 Complex crystal structure. It is generally assumed that compounds with a large number of atoms (N) in the primitive unit cell will exhibit low κ_lat due to the large quantities of optical branches (3N − 3). Optical branches have small or negligible contributions to κ_lat in bulk materials as a result of their low phonon velocities, leading to the fact that only a fraction of the heat energy can be transported by the limited acoustic branches. Toberer et al. found that the κ_lat of Zintl antimonides is inversely dependent on the primitive cell volume, namely the atom numbers.⁴⁸ α-MgAgSb has a complex crystal structure with a large primitive cell volume of ∼535 ų and contains a large number of atoms N ∼ 24.¹⁰⁹ Thus, there will be 3 acoustic branches and 69 optical branches in the crystal. Half-Heusler alloys with only 3 atoms in the primitive cell result in high κ_lat, e.g., 11.1 W m⁻¹ K⁻¹ for ZrNiSn and 12.2 W m⁻¹ K⁻¹ for VFeSb at 300 K,^141,142 while a large number of atoms in α-MgAgSb are beneficial to achieving a low κ_lat. Similarly, several complex Zintl compounds, such as Yb₁₄MnSb₁₁ (N = 104, κ_lat = 0.6 W m⁻¹ K⁻¹ at 300 K) and Yb₁₁InSb₉ (N = 42, κ_lat = 0.8 W m⁻¹ K⁻¹ at 300 K),^78,143 have intrinsically low κ_lat values mainly due to the large number of atoms in the primitive cell.

3.1.2 Lattice dynamics properties. In general, κ_lat can be expressed as the following relationship according to the kinetic theory and Boltzmann transport equation:¹⁴⁴where C_v is the specific heat, ω is the phonon frequency, v is the phonon group velocity, and l is the phonon mean free path (MFP). The C_v of most solid crystalline substances above Debye temperature is around 3R per mole of substance, based on the Dulong–Petit law, where R is the gas constant 8.314 J K⁻¹ mol⁻¹. Thus, v and l are the remaining decisive factors in the heat transport process. Fig. 5 shows the average sound velocity v_ave dependent room-temperature κ_lat for typical thermoelectric materials,^{87,121,145–155} where the phonon group velocity reaches the sound velocity in a crystal at the long wavelength limit. It is obvious that κ_lat exhibits an approximately linear relationship with v_ave and hence materials with a low κ_lat must possess a low v_ave. α-MgAgSb has an extremely low v_ave of ∼1276 m s⁻¹,¹²¹ which is even comparable with complex thallium compounds such as Ag₉TlTe₅ ∼1203 m s⁻¹.¹⁴⁶ Generally, a low v_ave has a close relationship with weak chemical bonding. The elastic modulus and lattice dynamics properties reflect the strength of chemical bonding on the macroscopic and microscopic level, respectively. The low elastic modulus of α-MgAgSb revealed by nanoindentation experiments (∼55.0 GPa) and theoretical calculations (∼43.5 GPa) demonstrates the weak chemical bonding.^118,126Fig. 6 presents the phonon and Grüneisen dispersions of α-MgAgSb along the high symmetry directions within the Brillouin zone, which were calculated using density-functional theory (DFT) phonon calculations within the quasi-harmonic approximation.¹²⁰ The saturated frequencies of acoustic branches responsible for phonon transport merely reach around 20–35 cm⁻¹, even lower than SnSe and PbTe.^107,156 Hence, these anomalously low acoustic-branch frequencies also demonstrate the intrinsically weak chemical bonding in α-MgAgSb. The weak chemical bonding is also related to the peculiar behavior of the Ag atom. First, Ag has an abnormal occupied site in the crystal structure. Ag atoms fill half of the Sb tetrahedrons, but the radius of the Sb tetrahedron is about 1.01 Å, which is much smaller than that of the ionic radius of Ag⁺ (∼1.26 Å).^109,121 This filled structure is considered to be unstable to a certain extent, leading to the weak Ag–Sb bonding. Second, first-principles calculations revealed the low defect formation energy of Ag vacancies, indicating the existence of weak Ag bonding.¹¹⁵ Third, Ying et al. assumed that the weak chemical bonding is relevant to the lack of d–d and (s, p-hybridized)–d interactions due to the deep non-interactive 4d¹⁰ electronic configuration of the center atoms of Ag.¹²⁶ Thus, the valence electron count (VEC) of α-MgAgSb is only eight per formula unit, with s and p electrons contributing to the electronic states around the Fermi level, in contrast with normal half-Heusler alloys with VEC = 18 and strong d–d and (s, p-hybridized)–d interactions.¹⁵⁷

Fig. 5 The average sound velocity ν_aveversus the lattice thermal conductivity κ_lat conductivity for typical thermoelectric materials.^{87,121,145–155}

Fig. 6 (a) Phonon dispersions and (b) the corresponding Grüneisen dispersions of MgAgSb. The thick lines and thin lines in the top panel represent the phonon dispersions at the DFT equilibrium volume and the expansion cell (+4%), respectively. The red, green, blue, and orange lines highlight the TA, TA′, LA, and LO phonon branches, respectively. The inset is the first Brillouin zones of MgAgSb with the high-symmetry points (red points) considered in our current calculations.¹²⁰ Reproduced with permission from ref. 120. Copyright 2017 Elsevier B.V.

Except for the low-lying acoustic branches, one extremely anomalous longitudinal optical (LO) branch (orange) can be also observed in Fig. 6. The boundary frequency of the LO branch at the Γ point is extremely low (∼17 cm⁻¹), lower than most of the thermoelectric materials.^107,156 The existence of a low-lying LO branch can be also reflected by the Einstein modes fitting the low-temperature heat capacity.¹²⁶ Except for this abnormal LO branch, the other optical branches also have low frequencies, which is related with the multicenter bonding interactions caused by the lattice distortion.^140,158 The Mg–Ag–Sb forms a close-packed three-center bonding scheme in α-MgAgSb (Fig. 7a) and the charge density difference of α-MgAgSb shows that the maximum charge density accumulation of the three-center bond is located within the triangle (Fig. 7b), in contrast with two-center bonding and the non-interacting Mg–Sb in the half-Heusler γ-MgAgSb (Fig. 7c and d).¹²⁶

Fig. 7 (a) and (b) The structural unit and related charge density differences for α-MgAgSb, respectively; (c) and (d) the structural unit and related charge density differences for γ-MgAgSb, respectively.¹²⁶ Reproduced with permission from ref. 126. Copyright 2017 Wiley-VCH.

Umklapp scattering, known as the U-process, dominates the phonon MFP of solids at high temperature, where the Grüneisen parameter γ is the decisive factor for the anharmonic scattering strength. Both the LA and LO branches possess much higher Grüneisen parameters, compared with those of the two TA branches (Fig. 6b). Specifically, the maximum Grüneisen parameter of the LO branch around the Γ point is extraordinarily high at ∼5.8. The average corresponding Grüneisen parameters ([small gamma, Greek, macron]) of the three acoustic branches were calculated based on . The [small gamma, Greek, macron] of the LA branch is about 1.9, surpassing that of the TA (∼0.8) and TA′ (∼0.6) branches by a factor of 2. Besides, the sudden change of Grüneisen parameters as well as phonon dispersion around the Γ point for the LA and LO branches demonstrate the “avoided-crossing” interaction, which was also observed in PbTe and Cu₃SbSe₃.^159,160 It was reported that the strong anharmonic coupling between the transverse optical (TO) and longitudinal acoustic (LA) branches play a pronounced role in the low κ_lat in PbTe, as found using a combination of inelastic neutron scattering measurements and first-principles computation.¹⁵⁹ Tian et al. further demonstrated that the contributions of optical phonons remained about 25% for PbSe and 22% for PbTe over the whole temperature range (300–700 K).¹⁵⁶ However, given the complex crystal structure of α-MgAgSb, it is rather difficult to quantitatively calculate the contribution of this LO branch.

3.1.3 Intrinsic Ag vacancy. Since real materials are always not perfect, intrinsic point defects in crystals significantly affect the phonon MFP due to the effective scattering of short-wavelength phonons.^{97,115,161,162} Detailed calculations on the intrinsic defect physics revealed that the Ag vacancy is the dominant intrinsic point defect in α-MgAgSb.¹¹⁵ Herein, the formation energy of various defects was first calculated, depending on the chemical potentials of the atomic species. Fig. 8a shows the calculated range of the chemical potentials of Ag and Sb in α-MgAgSb, namely the stability area of the Mg–Ag–Sb system in the two-dimensional (2D) range (μ_Sb, μ_Ag), while α-MgAgSb can only be stable in a narrow Sb-poor–Ag-rich or Sb-rich–Ag-poor region (the blue area). Fig. 8b and c indicate that the formation of a Ag vacancy is always much easier than that of a Sb vacancy, no matter how the defect concentrations change in both Ag-rich–Sb-poor and Ag-poor–Sb-rich environments, especially under a Ag-poor–Sb-rich condition. Since the crystal structure formation enthalpy is independent of the chemical potentials that can be interpreted in terms of the crystal structure stability, Fig. 8d shows the crystal structure formation enthalpy dependence of the different defect types and concentrations in α-MgAgSb. It is obvious that an appropriate content of Ag vacancies significantly increases the stability, compared with other defects. Both types of calculation results indicated that a Ag vacancy is much easier to form in α-MgAgSb as the main intrinsic point defect. Feng et al. also found that the Ag vacancy has the lowest formation energy under Mg rich conditions, as the dominant type of acceptor.¹⁶³ Pang et al. calculated the concentration of defects with charged states, where the Ag vacancies (neutral state or charged state −1) still have the highest concentration over the whole temperature range.¹⁶⁴

Fig. 8 (a) Calculated range of the chemical potentials of Ag and Sb (μ_Ag and μ_Sb) in α-MgAgSb, namely the stability area of the Mg–Ag–Sb systems in the two-dimensional (μ_Ag, μ_Sb) diagram; (b) defect formation energies in the Ag-rich and Sb-poor environments. V_Ag represents the formation energies of a Ag vacancy with different concentrations; V_Sb-max and V_Sb-min represent the formation energies of a Sb vacancy with different concentrations for the maximum and minimum μ_Sb, respectively; (c) defect formation energies in the Ag-poor and Sb-rich environments. V_Ag-max and V_Ag-min represent the formation energies of a Ag vacancy with different concentrations for the maximum and minimum μ_Ag, respectively; V_Sb represents the formation energies of a Sb vacancy with different concentrations; (d) crystal formation enthalpy of α-MgAgSb with different defect types and concentrations.¹¹⁵ Reproduced with permission from ref. 115. Copyright 2016 Royal Society of Chemistry.

There are three types of Ag atoms in α-MgAgSb: Ag1 atoms on the corners of the lattice, Ag2 atoms on the lattice edges of the c′ axis, and Ag3 atoms on the lattice edges of the a′ and b′ axes, where a′, b′, and c′ are the unit cell lattice parameters of the tetragonal sublattice (Fig. 9a). Recently, Mi et al. used the Rietveld refinement in high-resolution synchrotron radiation powder X-ray diffraction and revealed the much larger atomic displacement parameters (ADPs) of the Ag1 atoms at the 4a position compared with that of the other atoms (Fig. 9b), which indicated a possible strong atomic disorder of Ag atoms in α-MgAgSb.¹²⁷ The formation of Ag vacancies is primarily related to the weak Ag–X chemical bonding. Vacancies cause a larger mass difference and strain fluctuation than normal doping or substituting, which is more effective for scattering phonons with a short wavelength, which thereby largely reduces κ_lat, as already demonstrated in various systems.^165–170 Therefore, a certain concentration of Ag vacancies in the crystal is also responsible for the intrinsically low κ_lat of α-MgAgSb.

Fig. 9 (a) Tetragonal sublattice showing a Mg₄Sb₄ distorted hexahedron located in the cage formed by the Ag atoms; (b) temperature dependence of isotropic atomic displacement parameters ADPs (U_iso) for different atoms of α-MgAgSb.¹²⁷ Reproduced with permission from ref. 127. Copyright 2017 American Chemical Society.

3.1.4 Multiscale microstructure. It is widely acknowledged that nanostructuring is an effective strategy to suppress κ_lat in thermoelectrics,^54,55 due to the existence of high density of micro–nanoscale boundaries and interfaces as scattering centers for phonons. α-MgAgSb with coarse grains has a room-temperature κ_lat around 0.82 W m⁻¹ K⁻¹,¹¹⁴ over 20% higher than that of a nanostructured sample (0.67 W m⁻¹ K⁻¹).¹¹⁷ This suppression could be ascribed to the strong phonon scattering through the multiscale microstructure, including a high density of dislocations and stacking faults, nanoscale precipitates, and microscale grain boundaries (Fig. 10).¹¹⁷ The typical grain size ranges from 100 to 200 nm with high crystallinity (Fig. 10a and b), significantly smaller than other nanostructured thermoelectric materials.^55,69 Ubiquitous in situ nanoprecipitates around 10 nm can be also observed (Fig. 10c). A high density of nanoscale stacking faults about three layers of the lattice in width and 20 nm in length can be found in some grains (Fig. 10d and e), which was also confirmed by the corresponding fast Fourier transformation (FFT) image (Fig. 10f). In addition, the inverse FFT (IFFT) image shows that a large quantity of dislocations can be clearly observed inside the grain rather than along the grain boundary (Fig. 10g and h). To study the surrounding strain field around the dislocation cores, the high-quality HRTEM image was analyzed via geometric phase analysis (GPA), and the result present as the inset in Fig. 10h,^171,172 which shows the maximum tensile and compressive stresses of around 3% and 5%, respectively.

Fig. 10 Typical microstructures for nanostructured α-MgAgSb. (a) Medium magnification TEM image showing the mesoscale grains; (b) high-magnification TEM image of the grain boundary showing good crystallization; the inset corresponds to the fast Fourier transformation (FFT) image along the C zone axis direction; (c) high-magnification TEM image showing nanoinclusions; (d) high-magnification TEM image showing high density stacking faults; (e) high-magnification TEM image showing the specific morphology of a stacking fault; (f) FFT image along the [021] direction; (g) high-magnification TEM image showing a large quantity of dislocations inside the grain; (h) corresponding inverse FFT (IFFT) images showing a high density of dislocations with the enlarged dislocations and GPA analysis images as insets.¹¹⁷ Reproduced with permission from ref. 117. Copyright 2016 Wiley-VCH.

Microstructural defects with different dimensions are targeted to scatter phonons with a comparable size.^173,174 Generally, the effective scattering rate τ_eff⁻¹ can be evaluated by Matthiessen's rule: , where τ_I⁻¹ represents the relaxation times of a specified type of defect. Grain boundaries have a phonon scattering rate given by: τ_GB⁻¹ ∼ ω⁰, independent of the phonon frequency, which has a stronger interaction with low-frequency phonons. Nanoprecipitates can scatter phonons in a wider range of frequencies, based on τ_NP⁻¹ ∼ ω⁰ + ω⁴. The dislocations are displayed as the scattering centers targets for mid-frequency phonons, where the phonon scattering rate arising from the dislocation core and the strain field are given by τ_DC⁻¹ ∼ ω³ and τ_DS⁻¹ ∼ ω, respectively. Combined with the above-mentioned Ag vacancies, which are preferable to scatter phonons with high frequencies with τ_PD⁻¹ ∼ ω⁴, this hierarchical microstructure could further suppress the thermal conductivity of α-MgAgSb in comparison with the perfect crystal due to scattering of the broad-frequency phonons. Due to the fact that a high density of boundaries and interfaces as well as defects could effectively block phonon transport (much lower lattice thermal conductivity) with little deterioration of the charge carrier mobility (comparable mobility), nanostructured α-MgAgSb has a much higher ZT (1.2 at 550 K) than that of α-MgAgSb with coarse grains (0.8 at 550 K).^114,119

3.2 High power factor-electron crystal

In thermoelectric science, it is relatively easy to identify low thermal conductivity materials according to some effective material selection guidelines, such as a heavy atomic mass, complex unit cell, weak chemical bonding, anharmonic bonding.^175,176 In contrast, it is difficult to discover high power factor materials due to a lack of intuitively valid strategies.

For a given scattering mechanism and optimal carrier concentration, the weighted mobility U = μ(m*/m₀)^3/2 determines the maximum power factor, where μ is the carrier mobility, m* is the total density-of-states effective mass, and m₀ is the free electron mass.⁹ In the classical approximation, however, there is a negative correlation between the carrier mobility and effective mass for common scattering mechanisms; for example, for ionized impurity scattering μ ∝ (m*)^−1/2 and acoustic phonon scattering μ ∝ (m_b*)^−3/2(m_I*)⁻¹, where m_b* is the density-of-states effective mass for each pocket and m_I* is the inertial mass of the carriers along the conducting direction (m_I* is equal to m_b* for an isotropic band). Thus, it is imperative to rationally balance μ and m* to design high PF materials. Generally, heavy (light) carriers diffuse with low (high) velocities, but α-MgAgSb exhibits a large m* coupled with a high μ. Next, we discuss the effect of those two decisive parameters on the electrical transport properties.

3.2.1 Large total density-of-states effective mass. Previous first-principles calculations have clearly shown the flat feature of the valence band of α-MgAgSb,^{114,115,121–125,163,164,177} indicating the potential of a large m*. In addition, the calculated room-temperature m* of MgAgSb is around 2.3m₀ based on the single parabolic model with the acoustic phonon scattering mechanism,¹¹⁷ consistent with the aforementioned band structure. The high m* results in a high weighted mobility U and thus a high PF, such as for Mg₂X (X = Si, Sn, Ge, and Pb),^{28,91,178,179} filled skutterudites,^83,180 and half-Heusler alloys, like NbFeSb, and ZrNiSn.^70,138,181

A large m* could be a consequence of either a high band degeneracy N_v or a heavy m_b* via m* = N_v^2/3m_b*. Here, it should be mentioned that the initial results show the valence band maximum (VBM) of α-MgAgSb locating at point X, which results in a low N_v of ∼2.^{114,115,124,125} Subsequent work pointed out a high N_v of 8 for the VBM located between Z and A (Fig. 11a).^{122,163,164,177}Fig. 11b and c show the Fermi surface near the conduction band minimum (CBM) and valence band maximum (VBM),¹⁷⁷ respectively. Clearly, there is only one electron pocket, whereas the number of hole pockets is eight. In fact, N_v is usually below 4 for the majority of thermoelectric materials and a high N_v is a general sign of a high PF for advanced thermoelectric materials,⁵²e.g., 6 for Bi_0.4Sb_1.6Te₃,¹⁸² 6 for Mg₂Si_0.3Sn_0.7,²⁸ 6 for n-type Mg₃Sb₂,¹⁸³ 8 for p-type MFeSb (M = V, Nb),¹⁸⁴ 12 or more for p-type PbTe_0.85Se_0.15,²⁷ and 12 or more for n-type Yb_xCo₄Sb₁₂.³²

Fig. 11 (a) Calculated band structure for α-MgAgSb by using PBE and mBJ functionals; and the Fermi surface highlighting (b) the electron pocket and (c) the hole pockets in the Brillouin zone.¹⁷⁶ Reproduced with permission from ref. 176. Copyright 2017 Wiley-VCH.

3.2.2 High carrier mobility. Qualitatively, for high purity and perfect crystals, a small band gap leads to a high carrier mobility μ, especially for intrinsic semiconductors. The electronic band structure at 0 K is easily calculated based on first-principles calculations, but the reported results are somewhat different for α-MgAgSb.^{114,115,121–126,163,164,177} The majority of works show the existence of a narrow band gap of ∼0.1–0.3 eV,^{114,115,121,124–126,163,164,177} while others show the characteristics of a semimetal.^{122–124,177} Ying et al. first calculated the band structure of α-MgAgSb using the local density approximation (LDA) exchange–correlation function implemented in the Vienna ab-initio simulation package (VASP) and showed that α-MgAgSb was a narrow-gap semiconductor with an indirect gap energy of 0.1 eV (Fig. 12a).¹¹⁴ However, Miao et al. showed that α-MgAgSb is semi-metallic, overlapping between the VBM at the Z–A line and the conduction band minimum (CBM) at the Γ point using three independent calculated methods, including Perdew–Burke–Ernzerhof generalized gradient approximation (GGA-PBE), LDA, and GGA-PBE sol functions implemented in the VASP (Fig. 12b).¹²² Very recently, based on Tran–Blaha modified Becke–Johnson (TB-mBJ) implemented in WIEN2k, Feng et al. and Pang et al. showed that α-MgAgSb was a semiconductor with a band gap of 0.32 eV, where the CBM was near the Γ point and the VBM between Z and A (Fig. 12c).^163,164 The differently calculated results were due to the different exchange–correlation functions used and the calculated path within the primitive Brillouin zone. First, standard density-functional theory (DFT) calculation models, like LDA and GGA, usually underestimate the band gap of semiconductors by about 30–40% because of the existence of a derivative discontinuity of the energy concerning the number of electrons.^10,185 Second, the works of Ying et al., Li et al., and Sheng et al. were restricted to a limited path within the primitive Brillouin zone that may not cross the hole pockets,^114,121,124 whereas the others adopted a distinct calculated path,^122,163,164 where the VBM was located between Z and A. However, the actual band structure needs to be further clarified by measurement of the optical properties. α-MgAgSb is compositionally and structurally associated with half-Heusler alloys, which usually exhibit a semiconductor behavior resulting from a strong hybridization of the d states of the transition metal atoms.^70,157 However, Ying et al. highlighted a deep non-interactive 4d¹⁰ electronic configuration of Ag for α-MgAgSb.¹²⁶ This is why α-MgAgSb has a relatively smaller band gap compared with most common half-Heusler alloys.

Fig. 12 (a)–(c) Calculated band structure for α-MgAgSb by using the LDA functional implemented in VASP (Ying et al.),¹¹⁴ GGA-PBE functional implemented in VASP (Miao et al.)¹²² and TB-mBJ functional implemented in WIEN2k (Feng et al.),¹⁶² respectively. Reproduced with permission from ref. 114. Copyright 2015 Wiley-VCH, ref. 122. Copyright 2015 American Chemical Society and ref. 162. Copyright 2017 Nature Publishing Group.

Generally, the mobility is hardly affected by the high N_v in semiconductors if the intervalley scattering is negligible. Considering the high N_v = 8 for α-MgAgSb, a relatively heavy band m_b* = 0.6m₀ can be obtained, which is much lower than that of half-Heusler alloys with strong d–d and (s, p-hybridized)–d interactions.¹⁵⁷ Since the mobility is inversely proportional to the inertial mass m_I* according to μ = τe/m_I*, where τ is the relaxation time and e is the electron charge, a lower m_b* results in a higher mobility for α-MgAgSb in comparison with half-Heusler alloys.¹⁵⁷

4. Strategies to enhance thermoelectric performance

4.1 Optimizing carrier concentration to increase power factor

As previously discussed, α-MgAgSb has a large m* that requires a high optimal carrier concentration n_opt to achieve good electrical transport properties due to the relationship of n_opt ∝ (m*T)^3/2.⁵² The calculated room-temperature n_opt is about 9 × 10¹⁹ cm⁻³ based on the single parabolic band model with acoustic phonon scattering as the dominant carrier scattering mechanism. However, pristine α-MgAgSb has a relatively low carrier concentration n of around 2.7 × 10¹⁹ cm⁻³ at room temperature. Thus, various dopants have been utilized to increase the carrier concentration and then to enhance the power factor, including alkali metals (Li and Na) and divalent metals (Ca and Yb) doping on the Mg site, as well as by tuning the Sb content.^{112,116,119,120} In addition, doping on the Sb site has also been studied to compare the role of doping at cation and anion sites on the carrier transport behavior.¹¹⁹ It should be mentioned that the doping effect of isoelectronic elements is possibly caused by the change in the bandgap or intrinsic defect formation energy.^186,187 In this section, we summarize the electrical transport properties and discuss the principles behind doping.

It is obvious that Li is the most effective dopant to supply holes, compared with other dopants (Fig. 13a).^{112,113,116,117,119,120} The maximum carrier concentration in Li-doping is around 1.2 × 10²⁰ cm⁻³, more than 5 times higher than that of the pristine α-MgAgSb. This may be caused by the small difference in ionic radius between Li (60 pm) and Mg (66 pm). Fig. 13b–d show the electrical transport properties for the optimum composition for different dopants.^{112,113,116,117,119,120} Due to the increased carrier concentration upon doping, the electrical resistivity is decreased somewhat (Fig. 13b). As expected, the Li-doped sample has the lowest electrical resistivity, around 1.3 × 10⁻⁵ Ω m at room temperature. In addition, the electrical resistivity of all the samples fitted the temperature dependence of T^3/2 before the intrinsic excitation, indicating that the carrier transport mechanism is mainly dominated by acoustic phonon scattering in the low-temperature range. Concurrently, the decreased electrical resistivity also leads to a decreased Seebeck coefficient (Fig. 13c). In addition, a strong bipolar effect leads to the appearance of a peak Seebeck coefficient below 400 K owing to the very small band gap or semimetal characteristics. Finally, the power factor could be enhanced by about 20–30% over the entire temperature range upon doping, and the highest almost constant PF of ∼25 μW cm⁻¹ K⁻² from 300 to 548 K could be achieved by Li-doping (Fig. 13d). Theoretically, Miao et al. and Sheng et al. predicted that the power factor could be enhanced via hole-doping using first-principles simulations and the Boltzmann transport theory within the constant relaxation time approximation.^122,124 The experimental results for tuning the carrier concentration to enhance the power factor were consistent with the aforementioned prediction. Since doping on the Sb site shows some different but interesting behaviors, herein we separately discuss the corresponding underlying mechanism.

Fig. 13 Thermoelectric properties of α-MgAgSb-based materials, including Li-, Na-, Cu-, Ca-, and Yb-doping as well as tuning the Sb content. (a) Doping-concentration-dependent carrier concentration; temperature-dependent (b) electrical resistivity ρ, (c) Seebeck coefficient S and (d) power factor PF for the above-mentioned optimized composition.^{112,113,117,119,120}

In order to quantitatively clarify the effect of the carrier concentration and doping site on the electrical transport properties, theoretical calculations were performed based on the single parabolic band model with acoustic phonon scattering (Fig. 14).¹¹⁹ Here the solid and open symbols represent the room-temperature experimental data, including Li-, Ca-, and Yb-doping at the Mg site as well as As-, Bi-, Sn-, and Pb-doping at the Sb site.^119,120Fig. 14a shows that the carrier mobility reduction by doping at the Mg site matches well with the theoretical model. In contrast, dopants at the Sb site give rise to a lower carrier mobility. Therefore, doping at the Mg site could realize a lower electrical resistivity, compared with doping at the Sb site (Fig. 14b). All the experimental data (Seebeck coefficient vs. carrier concentration) fall nearly on the calculated Pisarenko plot with m* = 2.4m₀ (Fig. 14c). This illustrates that the doping can be described in the framework of a rigid band model that only changes the Fermi energy and tunes the carrier concentration. Therefore, the band structure is almost unchanged upon doping and the doping site is irrelevant. Finally, the power factor of doping at the Mg site is basically in accordance with the theoretical model, but obviously higher than that from doping at the Sb site (Fig. 14d).

Fig. 14 Carrier-concentration-dependent electrical transport properties of α-MgAgSb-based materials, including the dopants Li, Ca, Yb, As, Bi, Sn, and Pb. (a) Carrier mobility μ, (b) electrical resistivity ρ, (c) Seebeck coefficient S, and (d) power factor PF. The dashed lines are calculated based on the single parabolic band model with the acoustic phonon scattering mechanism.^117,119,120

The critical difference in the carrier transport behavior of doping at the Mg site and Sb site can be attributed to the introduced perturbation to the valence band when doping at the Sb site, which is somehow analogous to low-temperature Anderson localization.¹⁸⁸ In general, the valence band maximum is mainly dominated by anion atomic orbitals, while the conduction band minimum is mainly dominated by cation atomic orbitals.¹⁸⁹ Due to the fact that the high total DOS of the heavy valence band is predominantly decided by the p orbital of Sb,¹¹⁴ doping at the Sb site would introduce perturbation to the valence band, while doping at the Mg site will have less extra influence on the valence band. Therefore, doping at the site that has less influence on the charge-conducting band should be a critical doping principle in the thermoelectric field.

Except for tuning the carrier concentration upon doping, the associated point defect scattering could generate additional phonon scattering and reduce the lattice thermal conductivity κ_lat due to the mass fluctuation and surrounding strain field fluctuation based on the Rayleigh-type scattering mechanism.^141,190,191 The calculated phonon mean free path l of α-MgAgSb was around 0.53 nm, indicating that phonon scattering by point defects is an effective strategy to further reduce κ_lat for α-MgAgSb. Yb-doping plays a more effective role in suppressing κ_lat, compared with other doping (Fig. 15a).^117,119,120 Due to the enhanced power factor and significantly suppressed κ_lat, Yb-doping exhibited a higher ZT over the whole measured temperature range.^117,119,120 Specifically, the average ZT was improved from 1.0 for pristine α-MgAgSb to 1.1 (Li-doping),¹¹⁷ 1.1 (Ca-doping),¹¹⁹ and 1.2 (Yb-doping) (Fig. 15b).¹²⁰

Fig. 15 (a) Temperature-dependent lattice thermal conductivity κ_lat and (b) average ZT from 300 K to 548 K for Li-, Ca-, and Yb-doped α-MgAgSb.^117,119,120

4.2 Intrinsic Ag vacancy engineering to suppress lattice thermal conductivity

Intrinsic point defects engineering to optimize the thermoelectric performance has been reported in some thermoelectric systems, e.g., (Bi, Sb)₂(Te, Se)₃¹⁹² and Mg₂(Si, Sn).¹⁹³ Previous calculations have demonstrated that a Ag vacancy is the dominant intrinsic point defect in α-MgAgSb. Controlling the hot-press temperature could manipulate the Ag vacancy concentration due to the recovery effect, which is generally assumed as the thermal relaxation process to counter the native defects or donor-like effect in semiconductors.^64,115 It is noted that earlier researchers were mainly concerned about the consolidation aspect for powder metallurgy technology,⁹ but a few reports focused on the manipulation of intrinsic lattice defects for semiconductors.^194–196

Fig. 16a shows that the carrier concentration decreases from 4 × 10¹⁹ cm⁻³ to 2.7 × 10¹⁹ cm⁻³ and then increases up to 4.1 × 10¹⁹ cm⁻³ by simply varying the hot-press temperature.¹¹⁵ The reduction in the carrier concentration is mainly related to the recovery effect under the hot-press process while the increment is caused by the appearance of a second phase when hot pressed at 593 K and 613 K. The carrier mobility monotonically increases with hot-pressing temperature as a result of a weaker scattering of charge carrier from Ag vacancies and a sharp grain growth related with the phase transformation (Fig. 16a). The power factor decreases somewhat with increasing the hot-pressing temperature from 533 K to 573 K, while a higher temperature-independent power factor could be achieved at a higher hot-press temperature owing to the concurrent increased carrier concentration and mobility (Fig. 16b).

Fig. 16 Thermoelectric properties of α-MgAgSb hot-pressed at different temperatures. (a) Doping-concentration-dependent carrier concentration and mobility; temperature-dependent (b) power factor PF, (c) lattice thermal conductivity κ_lat and (d) ZT.¹¹⁵ Reproduced with permission from ref. 115. Copyright 2016 Royal Society of Chemistry.

Controlling Ag vacancies has a more profound effect on the phonon transport process, whereby κ_L gradually decreases with the decreased hot temperature (Fig. 16c). For example, the room-temperature κ_lat decreases from 0.66 W m⁻¹ K⁻¹ (573 K) to 0.54 W m⁻¹ K⁻¹ (533 K) due to the increased Ag vacancy concentration, which is even lower than that of Yb-doping (∼0.59 W m⁻¹ K⁻¹).¹²⁰ Since a vacancy would cause a larger mass difference and strain fluctuation than normal doping or substituting, it would maximize the mass and strain fluctuations. Thus, a vacancy could more effectively scatter the phonons with high frequencies, enabling a significant suppression of κ_lat. Benefiting from the sharply reduced κ_lat, a high peak ZT of ∼1.3 and an average ZT of ∼1.1 could be realized when hot pressed at 533 K (Fig. 16d).

4.3 Other feasible approaches in theory

Miao et al. performed theoretical calculations for the volume dependence of S and PF for α-MgAgSb along both the xx and zz directions using first-principles simulations and Boltzmann transport theory within the constant relaxation time approximation.¹²² A volume compression of 2% resulted in an increment of S of about 25% along both directions at the optimal chemical potential. Meanwhile, it enhanced the value of PF/τ around 10% at the chemical potential of −0.1 eV, where τ is the relaxation time. In the same way, they also reported that the thermoelectric properties of α-MgAgSb could be dramatically improved with the applied hydrostatic pressure, which was attributed to the pressure-induced semimetal-to-semiconductor transition.

Recently, Tan et al. pointed out that band engineering may improve the thermoelectric performance of α-MgAgSb.¹⁷⁷ Based on a careful analysis of the Fermi surface, they showed that the number of degenerate valleys in α-MgAgSb could be largely enhanced by tuning the Mg-s or Ag-d orbitals, e.g., Mg_1−xZn_xAgSb and MgAg_1−xPd_xSb, and finally a high ZT of 2.0 was predicted, which would be interesting if it could be experimentally demonstrated. Similarly, Feng et al. reported that control of the Ag–Mg antisite defects could significantly increase the thermoelectric performance of α-MgAgSb by increasing the number of band valleys near the Fermi level.¹⁶³

5. Mechanical properties

Since thermoelectric materials usually work under a cyclic temperature gradient, sometimes even under severe mechanical vibration, poor mechanical properties could lead to crack generation and consequently a deterioration in performance under thermal stress.^15,60 A material's mechanical robustness should be good enough to realize a high thermoelectric performance as well as reliable operation. Besides, poor mechanical properties increase the difficulty of the machining, manufacturing, and assembling processes. Fig. 17 shows the mechanical properties of nanostructured α-MgAgSb in comparison with other promising p-type thermoelectric materials working at a low to medium temperature range.^{94,118,197–207} Because of the global weak bonding of α-MgAgSb, its Young's modulus is about 55.0 GPa, comparable with BiSbTe and II–VI (II = Pb or Sn, VI = Te or Se) compounds,^197–200 but much lower than that of p-type nanostructured filled skutterudite (Fig. 17a).²⁰⁴ In contrast, the hardness (3.3 GPa), compressive strength (389.6 MPa), and fracture toughness (1.1 MPa m^1/2) of α-MgAgSb are almost comparable with that of p-type skutterudite (Fig. 17b–d),^203,204 which is possibly related with the boundaries and interfaces hardening and toughening effect,^208–211 benefiting from the multiscale microstructure of nanostructured α-MgAgSb. In real applications, the relatively good mechanical properties of nanostructured α-MgAgSb could enable the realization of a high theoretical conversion efficiency for devices.

Fig. 17 Comparison of the mechanical properties of nanostructured α-MgAgSb with other promising p-type thermoelectric materials working at a low to medium temperature range. (a) Young's modulus, (b) hardness, (c) compressive strength and (d) fracture toughness.¹¹⁸ Reproduced with permission from ref. 118. Copyright 2017 Elsevier B.V.

6. Single-leg device fabrication and conversion efficiency

In real applications, good electrical and thermal contacts are necessary for a thermoelectric module to realize its expected efficiency potential. Generally, a metallized contact layer is designed between thermoelectric materials and interconnects to act as an elemental diffusion barrier.^60,61 Conventional methods to fabricate the contact layer primarily conclude with sputtering or electroplating/chemical vapor deposition methods.⁶¹ However, sputtering is not a promising scalable method for mass production due to its both costly and time-consuming features, especially for high operating temperatures that need relatively thick contact layers.^60,61 The electrochemical deposition process sometimes can result in a weak bonding strength.⁶⁰ Kraemer et al. adopts a simple one-step hot-press technique to fabricate the single α-MgAgSb leg with a silver pad on the top and bottom surfaces with low resistance and high mechanical strength (Fig. 18a),¹¹¹ which eliminates the typically required sample metallization process. The sample for the efficiency measurements was about 3 mm × 3 mm × 5 mm, with silver contact pads between 0.25 and 0.35 mm thick (Fig. 18b). A clean and well-defined interface between the α-MgAgSb-based compound and the Ag contact pad could be clearly observed after the fabrication process (Fig. 18c). The contact resistance below 10 μΩ cm² was measured by a home-made scanning voltage probe with a typical current of 0.1 A (Fig. 18d). The reasons for choosing a silver contact were threefold: first, silver has a high electrical and thermal conductivity and is also easy to solder because of its softness; Second, the thermal expansion coefficient of silver (19.5 × 10⁻⁶ K⁻¹) is well-matched with that of α-MgAgSb (20 × 10⁻⁶ K⁻¹),¹¹¹ which could avoid the severe interface stress; Third, silver is one of the component elements that can reduce elemental diffusion due to a smaller concentration gradient. All these attributes contribute to obtaining a mechanically strong and thermally stable bond with low electrical interface resistance.

Fig. 18 Thermoelectric sample fabrication with electrical contact pads using a hot-press technique. (a) Thermoelectric material powder (1) is sandwiched between electrical contact pad materials (2) inside the graphite die (3) of the hot-press. While a graphite piston (4) applies pressure, the current flowing through the piston, die, and materials increases the hot-press temperature; (b) α-MgAgSb sample as fabricated with a three-step process (ball milling, hot-pressing, cutting) with silver contact pads with a thickness of 0.25–0.35 mm on each end; (c) SEM pictures showing a clean and well-defined interface between α-MgAgSb and the silver contact pad; (d) the measured contact resistance between α-MgAgSb and the silver contact pad.¹¹¹ Reproduced with permission from ref. 111. Copyright 2015 Royal Society of Chemistry.

The measured single thermoelectric leg was soldered with its electrical contact pads in between a hot junction copper heater assembly and a cold junction copper electrode (Fig. 19a). The heated radiation shields were designed to minimize the parasitic heat losses from the heater. However, the detailed design principles and measurement methods are beyond the scope of this review and so are not covered further.¹¹¹ The measured single-leg thermoelectric conversion efficiency reached 8.5% operating between 293 K and 518 K (Fig. 19b). At a high operating temperature above 425 K, the conversion efficiency of the α-MgAgSb leg obviously outperformed the reference sample, which was a p-type Bi₂Te₃-based material. The high conversion efficiency was also demonstrated with a power output of 46.2 mW (power density ∼5.14 kW m⁻²) at a current of 1.48 A (current density ∼16.4 A cm⁻²).¹¹¹ At the imposed temperature difference of 225 K, the efficiency of the α-MgAgSb leg was significantly higher than the previously reported efficiency, including Bi₂Te₃, skutterudite, PbTe, half-Heusler alloys, the Zintl system, and segmented legs (PbTe/Bi₂Te₃, and skutterudite/Bi₂Te₃) (Fig. 19c).^{87,138,212–221} An efficiency exceeding 10% could be expected at a temperature difference of 548 K, which was only reported at almost twice the temperature difference with the segmented legs. The demonstration of a high conversion efficiency of ∼8.5% at a much lower operating temperature difference of 225 K in combination with a simple fabrication process highlighted the promising prospects for the large-scale deployment of α-MgAgSb thermoelectric devices for low-temperature applications.

Fig. 19 (a) Fabricated single thermoelectric leg device with the sample soldered to the copper heater assembly (also acting as the hot-junction electrode) and the copper cold junction electrode. The device is soldered onto a thermoelectric cooler (TEC), which is mounted onto a liquid-cooled cold plate and surrounded by a heated radiation shield;¹¹¹ (b) efficiency results of a single thermoelectric leg device based on the α-MgAgSb sample (blue circles) compared to a device based on a commercial p-type-doped bismuth telluride sample (red squares). Solid lines correspond to the simulation results obtained with the iterative method based on the temperature-dependent material properties extracted from the average measured material properties;¹¹¹ (c) efficiency comparison between the α-MgAgSb samples (solid diamond) with the reported maximum thermoelectric device efficiencies (open diamond) as a function of the hot-junction temperature.^{87,138,194–203} Reproduced with permission from ref. 111. Copyright 2015 Royal Society of Chemistry.

7. Summary and outlook

In this prospective, we mainly discussed the phase transition, synthesis method, thermoelectric properties, and effective strategies to enhance ZT, as well as the efficiency measurements of α-MgAgSb. In particular, the origins of the “phonon glass electron crystal” behaviors, including the unique crystal and structural features, beneficial lattice dynamics properties, and band structure as well as the multiscale microstructure, were emphasized, which led to a combination of a relatively high power factor and intrinsically low lattice thermal conductivity. As a result, a record high conversion efficiency of ∼8.5% for a single leg at a much lower operating temperature difference of 225 K was achieved, which highlighted the promising prospects for low-temperature power generation. However, since research on the α-MgAgSb-based materials is still at an early stage, more and more attention should be paid to this promising system. Some currently unsolved questions as well as future directions and challenges are summarized in the following:

(1) At the material level: first, the strong bipolar effect seems to be beneficial for the thermoelectric performance, which contradicts the conventional knowledge; so what is the underlying reason for this interesting behavior? Second, does band engineering to increase the number of degenerate valleys and thus to enhance ZT really work in this system? Third, how about the long-term thermal stability of the multiscale microstructure and the thermoelectric properties of nanostructured α-MgAgSb?

(2) At the device level: first, it may be possible to further decrease the contact resistance by optimizing the fabrication process or by designing a new contact layer because the current contact resistance of ∼10 μΩ cm² is still too high, and should be reduced to less than 1 μΩ cm². Second, in terms of real applications, since it is highly beneficial to fabricate a pair of n-type and p-type thermoelectric materials based on one parent compound, how to develop the n-type α-MgAgSb becomes an imperative task. If not, it is necessary to discover and design the n-type counterpart of α-MgAgSb with comparable thermoelectric and mechanical properties. Under such conditions, the high conversion efficiency of thermoelectric devices for power generation could be highly promising, which should speed up their real applications for energy harvesting.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the U.S. Department of Energy under award number DE-SC0010831, and was also supported by the National Natural Science Foundation of China (no. 51471061, 51622101 and 51771065). We thank Dr Gang Chen, Dr Wei Cai, Dr Huiyuan Geng, Dr Yumei Wang, Dr Yongsheng Zhang, Dr Huaizhou Zhao, Dr Jing Shuai, Dr Daniel Kraemer and Dr Weihong Gao for the plentiful discussions and fruitful collaborations.

References

1. R. Mohtadi and S.-I. Orimo, Nat. Rev. Mater., 2016, 2, 16091.
2. D. Gielen, Nat. Mater., 2016, 15, 117–120.
3. S. Chu and A. Majumdar, Nature, 2012, 488, 294–303.
4. H. R. Zhao, Q. W. Wu, S. J. Hu, H. H. Xu and C. N. Rasmussen, Appl. Energy, 2015, 137, 545–553.
5. N. Kannan and D. Vakeesan, Renewable Sustainable Energy Rev., 2016, 62, 1092–1105.
6. D. K. Okot, Renewable Sustainable Energy Rev., 2013, 26, 515–520.
7. R. A. Voloshin, M. V. Rodionova, S. K. Zharmukhamedov, T. N. Veziroglu and S. I. Allakhverdiev, Int. J. Hydrogen Energy, 2016, 41, 17257–17273.
8. Energy Flow Charts, http://https://flowcharts.llnl.gov/commodities/energy, 2017.
9. H. J. Goldsmid, Introduction to thermoelectricity, Springer Science & Business Media, New York, 2009.
10. M. Zebarjadi, K. Esfarjani, M. S. Dresselhaus, Z. F. Ren and G. Chen, Energy Environ. Sci., 2012, 5, 5147–5162.
11. D. Kraemer, B. Poudel, H.-P. Feng, J. C. Caylor, B. Yu, X. Yan, Y. Ma, X. W. Wang, D. Z. Wang, A. Muto, K. McEnaney, M. Chiesa, Z. F. Ren and G. Chen, Nat. Mater., 2011, 10, 532–538.
12. L. L. Baranowski, G. J. Snyder and E. S. Toberer, Energy Environ. Sci., 2012, 5, 9055–9067.
13. D. Kraemer, Q. Jie, K. McEnaney, F. Cao, W. S. Liu, L. A. Weinstein, J. Loomis, Z. F. Ren and G. Chen, Nat. Energy, 2016, 1, 16153.
14. D. M. Rowe, CRC handbook of thermoelectrics, CRC press, New York, 1995.
15. J. H. Yang and T. Caillat, MRS Bull., 2006, 31, 224–229.
16. W. S. Liu, J. Z. Hu, S. M. Zhang, M. J. Deng, C. G. Han and Y. Liu, Mater. Today Phys., 2017, 1, 50–60.
17. A. F. Ioffe, Phys. Today, 1957, 12, 42.
18. G. J. Snyder and E. S. Toberer, Nat. Mater., 2008, 7, 105–114.
19. T. J. Zhu, Y. T. Liu, C. G. Fu, J. P. Heremans, J. G. Snyder and X. B. Zhao, Adv. Mater., 2017, 29, 1605884.
20. C. H. Champness, P. T. Chiang and P. Parekh, Can. J. Phys., 1965, 43, 653–669.
21. H. J. Goldsmid and R. W. Douglas, Br. J. Appl. Phys., 1954, 5, 386.
22. T. Koga, X. Sun, S. B. Cronin and M. S. Dresselhaus, MRS Online Proc. Libr., 1998, 73, 2950–2952.
23. K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis and M. G. Kanatzidis, Science, 2004, 303, 818–821.
24. B. Poudel, Q. Hao, Y. Ma, Y. C. Lan, A. Minnich, B. Yu, X. Yan, D. Z. Wang, A. Muto, D. Vashaee, X. Y. Chen, J. M. Liu, M. S. Dresselhaus, G. Chen and Z. F. Ren, Science, 2008, 320, 634–638.
25. Q. Zhang, J. He, T. Zhu, S. Zhang, X. Zhao and T. M. Tritt, Appl. Phys. Lett., 2008, 93, 102109.
26. D. L. Medlin and G. J. Snyder, Curr. Opin. Colloid Interface Sci., 2009, 14, 226–235.
27. Y. Z. Pei, X. Y. Shi, A. LaLonde, H. Wang, L. Chen and G. J. Snyder, Nature, 2011, 473, 66–69.
28. W. Liu, X. J. Tan, K. Yin, H. J. Liu, X. F. Tang, J. Shi, Q. J. Zhang and C. Uher, Phys. Rev. Lett., 2012, 108, 166601.
29. K. Biswas, J. Q. He, I. D. Blum, C.-I. Wu, T. P. Hogan, D. N. Seidman, V. P. Dravid and M. G. Kanatzidis, Nature, 2012, 489, 414–418.
30. Q. Zhang, F. Cao, W. Liu, K. Lukas, B. Yu, S. Chen, C. Opeil, D. Broido, G. Chen and Z. Ren, J. Am. Chem. Soc., 2012, 134, 10031–10038.
31. G. J. Tan, L. D. Zhao, F. Y. Shi, J. W. Doak, S.-H. Lo, H. Sun, C. Wolverton, V. P. Dravid, C. Uher and M. G. Kanatzidis, J. Am. Chem. Soc., 2014, 136, 7006–7017.
32. Y. L. Tang, Z. M. Gibbs, L. A. Agapito, G. D. Li, H.-S. Kim, M. B. Nardelli, S. Curtarolo and G. J. Snyder, Nat. Mater., 2015, 14, 1223–1228.
33. S. I. Kim, K. H. Lee, H. A. Mun, H. S. Kim, S. W. Hwang, J. W. Roh, D. J. Yang, W. H. Shin, X. S. Li, Y. H. Lee, G. J. Snyder and S. W. Kim, Science, 2015, 348, 109–114.
34. J. W. Zhang, L. R. Song, G. K. H. Madsen, K. F. F. Fischer, W. Q. Zhang, X. Shi and B. B. Iversen, Nat. Commun., 2016, 7, 10892.
35. R. He, H. T. Zhu, J. Y. Sun, J. Mao, H. Reith, S. Chen, G. Schierning, K. Nielsch and Z. F. Ren, Mater. Today Phys., 2017, 1, 24–30.
36. J. W. Zhang, R. H. Liu, N. Cheng, Y. B. Zhang, J. H. Yang, C. Uher, X. Shi, L. D. Chen and W. Q. Zhang, Adv. Mater., 2014, 26, 3848–3853.
37. J. Shuai, J. Mao, S. W. Song, Q. Y. Zhang, G. Chen and Z. F. Ren, Mater. Today Phys., 2017, 1, 74–95.
38. B. C. Sales, D. Mandrus and R. K. Williams, Science, 1996, 272, 1325.
39. G. S. Nolas, G. A. Slack and S. B. Schujman, Semicond. Semimetals, 2001, 69, 255–300.
40. G. S. Nolas, D. T. Morelli and T. M. Tritt, Annu. Rev. Mater. Res., 2003, 29, 89–116.
41. T. Takabatake, K. Suekuni, T. Nakayama and E. Kaneshita, Rev. Mod. Phys., 2014, 86, 669–716.
42. H. L. Liu, X. Shi, F. F. Xu, L. L. Zhang, W. Q. Zhang, L. D. Chen, Q. Li, C. Uher, T. Day and G. J. Snyder, Nat. Mater., 2012, 11, 422–425.
43. A. A. Olvera, N. A. Moroz, P. Sahoo, P. Ren, T. P. Bailey, A. A. Page, C. Uher and P. F. P. Poudeu, Energy Environ. Sci., 2017, 10, 1668–1676.
44. S. D. Kang, J.-H. Pöhls, U. Aydemir, P. F. Qiu, C. C. Stoumpos, R. Hanus, M. A. White, X. Shi, L. D. Chen, M. G. Kanatzidis and G. J. Snyder, Mater. Today Phys., 2017, 1, 7–13.
45. R. Nunna, P. F. Qiu, M. J. Yin, H. Y. Chen, R. Hanus, Q. F. Song, T. S. Zhang, M.-Y. Chou, M. T. Agne, J. Q. He, G. J. Snyder, X. Shi and L. D. Chen, Energy Environ. Sci., 2017, 10, 1928–1935.
46. K. P. Zhao, P. F. Qiu, Q. F. Song, A. B. Blichfeld, E. Eikeland, D. Ren, B. H. Ge, B. B. Iversen, X. Shi and L. D. Chen, Mater. Today Phys., 2017, 1, 14–23.
47. Z. T. Tian, S. Lee and G. Chen, J. Heat Transfer, 2013, 135, 061605.
48. E. S. Toberer, A. Zevalkink and G. J. Snyder, J. Mater. Chem., 2011, 21, 15843–15852.
49. B. L. Liao and G. Chen, MRS Bull., 2015, 40, 746–752.
50. J. Yang, L. L. Xi, W. J. Qiu, L. H. Wu, X. Shi, L. D. Chen, J. H. Yang, W. Q. Zhang, C. Uher and D. J. Singh, npj Comput. Mater., 2016, 2, 15015.
51. K. Vandaele, S. J. Watzman, B. Flebus, A. Prakash, Y. H. Zheng, S. R. Boona and J. P. Heremans, Mater. Today Phys., 2017, 1, 39–49.
52. Y. Z. Pei, H. Wang and G. J. Snyder, Adv. Mater., 2012, 24, 6125–6135.
53. A. M. Dehkordi, M. Zebarjadi, J. He and T. M. Tritt, Mater. Sci. Eng., R, 2015, 97, 1–22.
54. A. J. Minnich, M. S. Dresselhaus, Z. F. Ren and G. Chen, Energy Environ. Sci., 2009, 2, 466–479.
55. Y. C. Lan, A. J. Minnich, G. Chen and Z. F. Ren, Adv. Funct. Mater., 2010, 20, 357–376.
56. J. F. Li, W. S. Liu, L. D. Zhao and M. Zhou, NPG Asia Mater., 2010, 2, 152–158.
57. J. He, M. G. Kanatzidis and V. P. Dravid, Mater. Today, 2013, 16, 166–176.
58. L. D. Zhao, V. P. Dravid and M. G. Kanatzidis, Energy Environ. Sci., 2014, 7, 251–268.
59. M. G. Kanatzidis, MRS Bull., 2015, 40, 687–695.
60. W. S. Liu, Q. Jie, H. S. Kim and Z. F. Ren, Acta Mater., 2015, 87, 357–376.
61. Q. H. Zhang, X. Y. Huang, S. Q. Bai, X. Shi, C. Uher and L. D. Chen, Adv. Eng. Mater., 2016, 18, 194–213.
62. H. S. Kim, W. S. Liu and Z. F. Ren, Energy Environ. Sci., 2017, 10, 69–85.
63. H. J. Goldsmid, Materials, 2014, 7, 2577–2592.
64. T. J. Zhu, L. P. Hu, X. B. Zhao and J. He, Adv. Sci., 2016, 3, 1600004.
65. A. D. LaLonde, Y. Z. Pei, H. Wang and G. J. Snyder, Mater. Today, 2011, 14, 526–532.
66. B. B. Iversen, J. Mater. Chem., 2010, 20, 10778–10787.
67. S. M. Kauzlarich, S. R. Brown and G. J. Snyder, Dalton Trans., 2007, 2099–2107.
68. E. S. Toberer, A. F. May and G. J. Snyder, Chem. Mater., 2009, 22, 624–634.
69. S. Chen and Z. F. Ren, Mater. Today, 2013, 16, 387–395.
70. T. J. Zhu, C. G. Fu, H. H. Xie, Y. T. Liu and X. B. Zhao, Adv. Energy Mater., 2015, 5, 1500588.
71. S. Walia, S. Balendhran, H. Nili, S. Zhuiykov, G. Rosengarten, Q. H. Wang, M. Bhaskaran, S. Sriram, M. S. Strano and K. Kalantar-zadeh, Prog. Mater. Sci., 2013, 58, 1443–1489.
72. L. D. Zhao, J. He, D. Berardan, Y. Lin, J. F. Li, C. W. Nan and N. Dragoe, Energy Environ. Sci., 2014, 7, 2900–2924.
73. W. S. Liu, X. Yan, G. Chen and Z. F. Ren, Nano Energy, 2012, 1, 42–56.
74. X. Shi, L. Chen and C. Uher, Int. Mater. Rev., 2016, 61, 379–415.
75. G. J. Tan, L. D. Zhao and M. G. Kanatzidis, Chem. Rev., 2016, 116, 12123–12149.
76. X. L. Su, P. Wei, H. Li, W. Liu, Y. G. Yan, P. Li, C. Q. Su, C. J. Xie, W. Y. Zhao, P. C. Zhai, Q. J. Zhang, X. F. Tang and C. Uher, Adv. Mater., 2017, 29, 1602013.
77. H. T. Ma, L. H. Yin, X. P. Shen, W. Lu, Y. X. Sun, Y. F. Zhang and N. Deng, Appl. Energy, 2016, 169, 177–186.
78. S. R. Brown, S. M. Kauzlarich, F. Gascoin and G. J. Snyder, Chem. Mater., 2006, 18, 1873–1877.
79. X. W. Wang, H. Lee, Y. C. Lan, G. H. Zhu, G. Joshi, D. Z. Wang, J. Yang, A. J. Muto, M. Y. Tang, J. Klatsky, S. Song, M. S. Dresselhaus, G. Chen and Z. F. Ren, Appl. Phys. Lett., 2008, 93, 193121.
80. G. Joshi, H. Lee, Y. C. Lan, X. W. Wang, G. H. Zhu, D. Z. Wang, R. W. Gould, D. C. Cuff, M. Y. Tang and M. S. Dresselhaus, Nano Lett., 2008, 8, 4670–4674.
81. X. Yan, B. Poudel, Y. Ma, W. S. Liu, G. Joshi, H. Wang, Y. C. Lan, D. Z. Wang, G. Chen and Z. F. Ren, Nano Lett., 2010, 10, 3373–3378.
82. W. S. Liu, Q. Y. Zhang, Y. C. Lan, S. Chen, X. Yan, Q. Zhang, H. Wang, D. Z. Wang, G. Chen and Z. F. Ren, Adv. Energy Mater., 2011, 1, 577–587.
83. X. Shi, J. Yang, J. R. Salvador, M. F. Chi, J. Y. Cho, H. Wang, S. Q. Bai, J. H. Yang, W. Q. Zhang and L. D. Chen, J. Am. Chem. Soc., 2011, 133, 7837.
84. A. D. LaLonde, Y. Z. Pei and G. J. Snyder, Energy Environ. Sci., 2011, 4, 2090–2096.
85. S. Chen, K. C. Lukas, W. S. Liu, C. P. Opeil, G. Chen and Z. F. Ren, Adv. Energy Mater., 2013, 3, 1210–1214.
86. Q. Jie, H. Z. Wang, W. S. Liu, H. Wang, G. Chen and Z. F. Ren, Phys. Chem. Chem. Phys., 2013, 15, 6809–6816.
87. C. G. Fu, S. Q. Bai, Y. T. Liu, Y. S. Tang, L. D. Chen, X. B. Zhao and T. J. Zhu, Nat. Commun., 2015, 6, 8144.
88. L. D. Zhao, G. J. Tan, S. Q. Hao, J. Q. He, Y. L. Pei, H. Chi, H. Wang, S. K. Gong, H. B. Xu, V. P. Dravid, C. Uher, G. J. Snyder, C. Wolverton and M. G. Kanatzidis, Science, 2016, 351, 141–144.
89. J. Shuai, J. Mao, S. W. Song, Q. Zhu, J. F. Sun, Y. M. Wang, R. He, J. W. Zhou, G. Chen, D. J. Singh and Z. F. Ren, Energy Environ. Sci., 2017, 10, 799–807.
90. X. F. Meng, Z. H. Liu, B. Cui, D. D. Qin, H. Y. Geng, W. Cai, L. W. Fu, J. Q. He, Z. F. Ren and J. H. Sui, Adv. Energy Mater., 2017, 7, 1602582.
91. W. S. Liu, H. S. Kim, S. Chen, Q. Jie, B. Lv, M. L. Yao, Z. S. Ren, C. P. Opeil, S. Wilson, C.-W. Chu and Z. F. Ren, Proc. Natl. Acad. Sci. U. S. A., 2015, 112, 3269–3274.
92. W. S. Liu, H. S. Kim, Q. Jie and Z. F. Ren, Scr. Mater., 2016, 111, 3–9.
93. L.-P. Hu, T.-J. Zhu, Y.-G. Wang, H.-H. Xie, Z.-J. Xu and X.-B. Zhao, NPG Asia Mater., 2014, 6, e88.
94. Y. Zheng, Q. Zhang, X. L. Su, H. Y. Xie, S. C. Shu, T. L. Chen, G. J. Tan, Y. G. Yan, X. F. Tang and C. Uher, Adv. Energy Mater., 2015, 5, 1401391.
95. J. Emsley, Nature's building blocks: an AZ guide to the elements, Oxford University Press, New York, 2011.
96. T. Caillat, J. P. Fleurial and A. Borshchevsky, J. Phys. Chem. Solids, 1997, 58, 1119–1125.
97. G. J. Snyder, M. Christensen, E. Nishibori, T. Caillat and B. B. Iversen, Nat. Mater., 2004, 3, 458–463.
98. S. Y. Wang, X. J. Tan, G. J. Tan, X. Y. She, W. Liu, H. Li, H. J. Liu and X. F. Tang, J. Mater. Chem., 2012, 22, 13977–13985.
99. S. N. Guin, A. Chatterjee, D. S. Negi, R. Datta and K. Biswas, Energy Environ. Sci., 2013, 6, 2603–2608.
100. Z. H. Liu, J. Shuai, H. Y. Geng, J. Mao, Y. Feng, X. Zhao, X. F. Meng, R. He, W. Cai and J. H. Sui, ACS Appl. Mater. Interfaces, 2015, 7, 23047–23055.
101. S. T. Cai, Z. H. Liu, J. Y. Sun, R. Li, W. D. Fei and J. H. Sui, Dalton Trans., 2015, 44, 1046–1051.
102. J. Li, J. H. Sui, Y. L. Pei, C. Barreteau, D. Berardan, N. Dragoe, W. Cai, J. Q. He and L. D. Zhao, Energy Environ. Sci., 2012, 5, 8543–8547.
103. J. H. Sui, J. Li, J. Q. He, Y. L. Pei, D. Berardan, H. J. Wu, N. Dragoe, W. Cai and L. D. Zhao, Energy Environ. Sci., 2013, 6, 2916–2920.
104. Y. Liu, L.-D. Zhao, Y. C. Zhu, Y. C. Liu, F. Li, M. J. Yu, D. B. Liu, W. Xu, Y. H. Lin and C. W. Nan, Adv. Energy Mater., 2016, 6, 1502423.
105. X. Lu, D. T. Morelli, Y. Xia, F. Zhou, V. Ozolins, H. Chi, X. Y. Zhou and C. Uher, Adv. Energy Mater., 2013, 3, 342–348.
106. X. Lu, D. T. Morelli, Y. Xia and V. Ozolins, Chem. Mater., 2015, 27, 408–413.
107. L. D. Zhao, S.-H. Lo, Y. S. Zhang, H. Sun, G. J. Tan, C. Uher, C. Wolverton, V. P. Dravid and M. G. Kanatzidis, Nature, 2014, 508, 373–377.
108. K. L. Peng, X. Lu, H. Zhan, S. Hui, X. D. Tang, G. W. Wang, J. Dai, C. Uher, G. Y. Wang and X. Y. Zhou, Energy Environ. Sci., 2016, 9, 454–460.
109. M. J. Kirkham, A. M. dos Santos, C. J. Rawn, E. Lara-Curzio, J. W. Sharp and A. J. Thompson, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 85, 144120.
110. H. Z. Zhao, J. H. Sui, Z. J. Tang, Y. C. Lan, Q. Jie, D. Kraemer, K. McEnaney, A. Guloy, G. Chen and Z. F. Ren, Nano Energy, 2014, 7, 97–103.
111. D. Kraemer, J. H. Sui, K. McEnaney, H. Z. Zhao, Q. Jie, Z. F. Ren and G. Chen, Energy Environ. Sci., 2015, 8, 1299–1308.
112. J. Shuai, H. S. Kim, Y. C. Lan, S. Chen, Y. Liu, H. Z. Zhao, J. H. Sui and Z. F. Ren, Nano Energy, 2015, 11, 640–646.
113. J. H. Sui, J. Shuai, Y. C. Lan, Y. Liu, R. He, D. Z. Wang, Q. Jie and Z. F. Ren, Acta Mater., 2015, 87, 266–272.
114. P. J. Ying, X. H. Liu, C. G. Fu, X. Q. Yue, H. H. Xie, X. B. Zhao, W. Q. Zhang and T. J. Zhu, Chem. Mater., 2015, 27, 909–913.
115. Z. H. Liu, H. Y. Geng, J. Mao, S. Jing, R. He, C. Wang, W. Cai, J. H. Sui and Z. F. Ren, J. Mater. Chem. A, 2016, 4, 16834–16840.
116. Z. H. Liu, J. Shuai, J. Mao, Y. M. Wang, Z. Y. Wang, W. Cai, J. H. Sui and Z. F. Ren, Acta Mater., 2016, 102, 17–23.
117. Z. H. Liu, Y. M. Wang, J. Mao, H. Y. Geng, J. Shuai, Y. X. Wang, R. He, W. Cai, J. H. Sui and Z. F. Ren, Adv. Energy Mater., 2016, 6, 1502269.
118. Z. H. Liu, W. H. Gao, X. F. Meng, X. B. Li, J. Mao, Y. M. Wang, J. Shuai, W. Cai, Z. F. Ren and J. H. Sui, Scr. Mater., 2017, 127, 72–75.
119. Z. H. Liu, Y. M. Wang, W. H. Gao, J. Mao, H. Y. Geng, J. Shuai, W. Cai, J. H. Sui and Z. F. Ren, Nano Energy, 2017, 31, 194–200.
120. Z. H. Liu, Y. S. Zhang, J. Mao, W. H. Gao, Y. M. Wang, J. Shuai, W. Cai, J. H. Sui and Z. F. Ren, Acta Mater., 2017, 128, 227–234.
121. D. D. Li, H. Z. Zhao, S. M. Li, B. P. Wei, J. Shuai, C. L. Shi, X. K. Xi, P. J. Sun, S. Meng, L. Gu, Z. F. Ren and X. L. Chen, Adv. Funct. Mater., 2015, 25, 6478–6488.
122. N. H. Miao and P. Ghosez, J. Phys. Chem. C, 2015, 119, 14017–14022.
123. N. H. Miao, J. Zhou, B. S. Sa, B. Xu and Z. M. Sun, Appl. Phys. Lett., 2016, 108, 213902.
124. C. Y. Sheng, H. J. Liu, D. D. Fan, L. Cheng, J. Zhang, J. Wei, J. H. Liang, P. H. Jiang and J. Shi, J. Appl. Phys., 2016, 119, 195101.
125. J. F. Wang, X. N. Fu, X. D. Zhang, J. T. Wang, X. D. Li and Z. Y. Jiang, Chin. Phys. B, 2016, 25, 086302.
126. P. J. Ying, X. Li, Y. C. Wang, J. Yang, C. G. Fu, W. Q. Zhang, X. B. Zhao and T. J. Zhu, Adv. Funct. Mater., 2017, 27, 1604145.
127. J. L. Mi, P. J. Ying, M. Sist, H. Reardon, P. Zhang, T. J. Zhu, X. B. Zhao and B. B. Iversen, Chem. Mater., 2017, 29, 6378–6388.
128. R. G. Morris, R. D. Redin and G. C. Danielson, Phys. Rev., 1958, 109, 1909–1915.
129. R. Bowers, R. W. Ure, J. E. Bauerle and A. J. Cornish, J. Appl. Phys., 1959, 30, 930–934.
130. D. A. Wright, Int. Mater. Rev., 1970, 147–160.
131. M. Beekman, D. T. Morelli and G. S. Nolas, Nat. Mater., 2015, 14, 1182–1185.
132. Z. H. Liu, Y. L. Pei, H. Y. Geng, J. C. Zhou, X. F. Meng, W. Cai, W. S. Liu and J. H. Sui, Nano Energy, 2015, 13, 554–562.
133. M. Zhou, J. F. Li and T. Kita, J. Am. Chem. Soc., 2008, 130, 4527–4532.
134. L. D. Zhao, X. Zhang, H. J. Wu, G. J. Tan, Y. L. Pei, Y. Xiao, C. Chang, D. Wu, H. Chi, L. Zheng, S. K. Gong, C. Uher, J. Q. He and M. G. Kanatzidis, J. Am. Chem. Soc., 2016, 138, 2366.
135. Q. Y. Zhang, H. Wang, W. S. Liu, H. Z. Wang, B. Yu, Q. Zhang, Z. T. Tian, G. Ni, S. Lee, K. Esfarjani, G. Chen and Z. F. Ren, Energy Environ. Sci., 2012, 5, 5246–5251.
136. X. Yan, W. S. Liu, H. Wang, S. Chen, J. Shiomi, K. Esfarjani, H. Z. Wang, D. Z. Wang, G. Chen and Z. F. Ren, Energy Environ. Sci., 2012, 5, 7543–7548.
137. J. Mao, Y. M. Wang, H. S. Kim, Z. H. Liu, U. Saparamadu, F. Tian, K. Dahal, J. Y. Sun, S. Chen and W. S. Liu, Nano Energy, 2015, 17, 279–289.
138. R. He, D. Kraemer, J. Mao, L. P. Zeng, Q. Jie, Y. C. Lan, C. H. Li, J. Shuai, H. S. Kim, Y. Liu, D. Broido, C.-W. Chu, G. Chen and Z. F. Ren, Proc. Natl. Acad. Sci. U. S. A., 2016, 113, 13576–13581.
139. D. Q. He, W. Y. Zhao, X. Mu, H. Y. Zhou and Q. J. Zhang, J. Electron. Mater., 2015, 44, 1919–1925.
140. S. Y. Wang, J. Yang, L. H. Wu, P. Wei, J. Yang, W. Q. Zhang and Y. Grin, Chem. Mater., 2015, 27, 1071–1081.
141. J. Yang, G. Meisner and L. Chen, Appl. Phys. Lett., 2004, 85, 1140.
142. C. G. Fu, H. H. Xie, T. J. Zhu, J. Xie and X. B. Zhao, J. Appl. Phys., 2012, 112, 66.
143. T. H. Yi, C. A. Cox, E. S. Toberer, G. J. Snyder and S. M. Kauzlarich, Chem. Mater., 2010, 22, 935–941.
144. T. M. Tritt, Thermal conductivity: theory, properties, and applications, Springer Science & Business Media, New York, 2005.
145. W. Li, S. Q. Lin, B. H. Ge, J. Yang, W. Q. Zhang and Y. Z. Pei, Adv. Sci., 2016, 3, 1600196.
146. K. Kurosaki, A. Kosuga, H. Muta, M. Uno and S. Yamanaka, Appl. Phys. Lett., 2005, 87, 061919.
147. Y. Z. Pei, N. A. Heinz and G. J. Snyder, J. Mater. Chem., 2011, 21, 18256–18260.
148. O. Madelung, Semiconductors: Data Handbook, Springer Berlin Heidelberg, New York, 2004.
149. S. Q. Lin, L. Wen, Z. W. Chen, J. W. Shen, B. H. Ge and Y. Z. Pei, Nat. Commun., 2016, 7, 10287.
150. H. Wang, E. Schechtel, Y. Z. Pei and G. J. Snyder, Adv. Energy Mater., 2013, 3, 488–495.
151. J. W. Shen, Z. W. Chen, L. L. Zheng, W. Li and Y. Z. Pei, J. Mater. Chem. C, 2016, 4, 209–214.
152. X. Shi, S. Q. Bai, L. L. Xi, J. Yang, W. Zhang, L. D. Chen and J. H. Yang, J. Mater. Res., 2011, 26, 1745–1754.
153. S. Bhattacharya, M. J. Skove, M. Russell, T. M. Tritt, Y. Xia, V. Ponnambalam, S. J. Poon and N. Thadhani, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 998–1002.
154. A. F. May, J.-P. Fleurial and G. J. Snyder, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 78, 125205.
155. S. K. Bux, R. G. Blair, P. K. Gogna, H. Lee, G. Chen, M. S. Dresselhaus, R. B. Kaner and J. P. Fleurial, Adv. Funct. Mater., 2009, 19, 2445–2452.
156. Z. T. Tian, J. Garg, K. Esfarjani, T. Shiga, J. Shiomi and G. Chen, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 85, 184303.
157. W. G. Zeier, J. Schmitt, G. Hautier, U. Aydemir, Z. M. Gibbs, C. Felser and G. J. Snyder, Nat. Rev. Mater., 2016, 16032.
158. A. Fischer, E. W. Scheidt, W. Scherer, D. E. Benson, Y. Wu, D. Eklöf and U. Häussermann, Phys. Rev. B: Condens. Matter Mater. Phys., 2015, 91, 224309.
159. O. Delaire, J. Ma, K. Marty, A. F. May, M. A. McGuire, M. H. Du, D. J. Singh, A. Podlesnyak, G. Ehlers, M. Lumsden and B. C. Sales, Nat. Mater., 2011, 10, 614–619.
160. Y. S. Zhang, E. Skoug, J. Cain, V. Ozoliņš, D. Morelli and C. Wolverton, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 85, 054306.
161. T. Dasgupta, C. Stiewe, R. Hassdorf, A. J. Zhou, L. Boettcher and E. Mueller, Phys. Rev. B: Condens. Matter Mater. Phys., 2011, 83, 235207.
162. X. H. Liu, L. L. Xi, W. J. Qiu, J. Yang, T. J. Zhu, X. B. Zhao and W. Q. Zhang, Adv. Electron. Mater., 2015, 2, 1500284.
163. Z. Z. Feng, J. H. Zhang, Y. L. Yan, G. B. Zhang, C. Wang, C. X. Peng, F. Z. Ren, Y. X. Wang and Z. X. Cheng, Sci. Rep., 2017, 7, 2572.
164. Z. Y. Pang, X. W. Zhang and C. Wang, Curr. Appl. Phys., 2017, 17, 1279–1287.
165. K. Kurosaki, H. Matsumoto, A. Charoenphakdee, S. Yamanaka, M. Ishimaru and Y. Hirotsu, Appl. Phys. Lett., 2008, 93, 12101.
166. O. Delaire, A. F. May, M. A. McGuire, W. D. Porter, M. S. Lucas, M. B. Stone, D. L. Abernathy, V. A. Ravi, S. A. Firdosy and G. J. Snyder, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 184302.
167. C. Yu, M. L. Scullin, M. Huijben, R. Ramesh and A. Majumdar, Appl. Phys. Lett., 2008, 92, 191911.
168. W. Li, S. Q. Lin, X. Y. Zhang, Z. W. Chen, X. F. Xu and Y. Z. Pei, Chem. Mater., 2016, 28, 6227–6232.
169. Y. Z. Pei and D. T. Morelli, Appl. Phys. Lett., 2009, 94, 122112.
170. G. J. Tan, W. G. Zeier, F. Y. Shi, P. L. Wang, G. J. Snyder, V. P. Dravid and M. G. Kanatzidis, Chem. Mater., 2015, 27, 7801–7811.
171. M. Hÿtch, E. Snoeck and R. Kilaas, Ultramicroscopy, 1998, 74, 131–146.
172. J. Q. He, J. R. Sootsman, S. N. Girard, J. C. Zheng, J. G. Wen, Y. M. Zhu, M. G. Kanatzidis and V. P. Dravid, J. Am. Chem. Soc., 2010, 132, 8669–8675.
173. P. G. Klemens, Proc. Phys. Soc., London, Sect. A, 1955, 68, 1113.
174. J. Callaway, Phys. Rev., 1959, 113, 1046.
175. X. Zhang and L. D. Zhao, J. Materiomics, 2015, 1, 92–105.
176. D. R. Clarke, Surf. Coat. Technol., 2003, 163, 67–74.
177. X. J. Tan, L. Wang, H. Z. Shao, S. Yue, J. T. Xu, G. Q. Liu, H. C. Jiang and J. Jiang, Adv. Energy Mater., 2017, 1700076.
178. J. Mao, H. S. Kim, J. Shuai, Z. H. Liu, R. He, U. Saparamadu, F. Tian, W. S. Liu and Z. F. Ren, Acta Mater., 2016, 103, 633–642.
179. J. Mao, Y. M. Wang, B. H. Ge, Q. Jie, Z. H. Liu, U. Saparamadu, W. S. Liu and Z. F. Ren, Phys. Chem. Chem. Phys., 2016, 18, 20726–20737.
180. S. Y. Wang, J. R. Salvador, J. Yang, P. Wei, B. Duan and J. H. Yang, NPG Asia Mater., 2016, 8, e825.
181. H. H. Xie, H. Wang, Y. Z. Pei, C. G. Fu, X. H. Liu, G. J. Snyder, X. B. Zhao and T. J. Zhu, Adv. Funct. Mater., 2013, 23, 5123–5130.
182. H. Goldsmid, Thermoelectric refrigeration, Springer, New York, 2013.
183. J. w. Zhang, L. r. Song, S. H. Pedersen, H. Yin, L. T. Hung and B. B. Iversen, Nat. Commun., 2017, 8, 13901.
184. C. G. Fu, T. J. Zhu, Y. Z. Pei, H. H. Xie, H. Wang, G. J. Snyder, Y. Liu, Y. T. Liu and X. B. Zhao, Adv. Energy Mater., 2014, 4, 1400600.
185. H. Xiao, J. Tahir-Kheli and W. A. Goddard, J. Phys. Chem. Lett., 2011, 2, 212–217.
186. J. Wang, X.-C. Liu, S.-Q. Xia and X.-T. Tao, J. Am. Chem. Soc., 2013, 135, 11840–11848.
187. G. S. Pomrehn, A. Zevalkink, W. G. Zeier, A. van de Walle and G. J. Snyder, Angew. Chem., Int. Ed., 2014, 53, 3422–3426.
188. R. Abouchacra, D. J. Thouless and P. W. Anderson, J. Phys. C, 2002, 96, 1734.
189. A. F. Ioffe, Semiconductor thermoelements, and thermoelectric cooling, Infosearch, Ltd, 1957.
190. J. Callaway and H. C. von Baeyer, Phys. Rev., 1960, 120, 1149.
191. B. Abeles, Phys. Rev., 1963, 131, 1906.
192. L. P. Hu, T. J. Zhu, X. H. Liu and X. B. Zhao, Adv. Funct. Mater., 2014, 24, 5211–5218.
193. G. Y. Jiang, J. He, T. J. Zhu, C. G. Fu, X. H. Liu, L. P. Hu and X. B. Zhao, Adv. Funct. Mater., 2014, 24, 3776–3781.
194. L. P. Hu, H. L. Gao, X. H. Liu, H. H. Xie, J. J. Shen, T. J. Zhu and X. B. Zhao, J. Mater. Chem., 2012, 22, 16484–16490.
195. L. Chen, S. Gao, X. Zeng, A. M. Dehkordi, T. M. Tritt and S. J. Poon, Appl. Phys. Lett., 2015, 107, 041902.
196. Y. Pan and J. F. Li, NPG Asia Mater., 2016, 8, e275.
197. G. Li, K. Gadelrab, T. Souier, P. L. Potapov, G. Chen and M. Chiesa, Nanotechnology, 2012, 23, 065703.
198. B. Li, P. Xie, S. Y. Zhang and D. Q. Liu, J. Mater. Sci., 2011, 46, 4000–4004.
199. R. D. Schmidt, E. D. Case, J. E. Ni, R. M. Trejo, E. Lara-Curzio, R. J. Korkosz and M. G. Kanatzidis, J. Mater. Sci., 2013, 48, 8244–8258.
200. R. D. Schmidt, E. D. Case, L.-D. Zhao and M. G. Kanatzidis, J. Mater. Sci., 2015, 50, 1770–1782.
201. Y. Gelbstein, G. Gotesman, Y. Lishzinker, Z. Dashevsky and M. Dariel, Scr. Mater., 2008, 58, 251–254.
202. K. Tyagi, B. Gahtori, S. Bathula, M. Jayasimhadri, S. Sharma, N. K. Singh, D. Haranath, A. Srivastava and A. Dhar, Solid State Commun., 2015, 207, 21–25.
203. G. Rogl and P. Rogl, Sci. Adv. Mater., 2011, 3, 517–538.
204. T. Dahal, S. Gahlawat, Q. Jie, K. Dahal, Y. Lan, K. White and Z. Ren, J. Appl. Phys., 2015, 117, 055101.
205. F. Tseng, S. Li, C. Wu, Y. Pan and L. Li, J. Mater. Sci., 2016, 51, 5271–5280.
206. K. Ueno, A. Yamamoto, T. Noguchi, T. Inoue, S. Sodeoka and H. Obara, J. Alloys Compd., 2005, 388, 118–121.
207. J. E. Ni, E. D. Case, K. N. Khabir, R. C. Stewart, C.-I. Wu, T. P. Hogan, E. J. Timm, S. N. Girard and M. G. Kanatzidis, Mater. Sci. Eng., B, 2010, 170, 58–66.
208. N. Petch, J. Iron Steel Inst., London, 1953, 174, 25–28.
209. E. Hall, Proc. Phys. Soc., London, Sect. B, 1951, 64, 747.
210. P. F. Becher, J. Am. Ceram. Soc., 1991, 74, 255–269.
211. W. H. Gao, X. Y. Yi, B. Sun, X. L. Meng, W. Cai and L. C. Zhao, Acta Mater., 2017, 132, 405–415.
212. M. Telkes, J. Appl. Phys., 1954, 25, 765–777.
213. E. Groß, M. Riffel and U. Stöhrer, J. Mater. Res., 1995, 10, 34–40.
214. T. Caillat, J. P. Fleurial, G. J. Snyder and A. Borshchevsky, Proceedings of 20th International Conference on Thermoelectrics, Cat. no. 01TH8589, 2001, pp. 282–285.
215. A. Muto, D. Kraemer, Q. Hao, Z. F. Ren and G. Chen, Rev. Sci. Instrum., 2009, 80, 093901.
216. A. Muto, J. Yang, B. Poudel, Z. F. Ren and G. Chen, Adv. Energy Mater., 2012, 3, 245–251.
217. J. R. Salvador, J. Y. Cho, Z. Ye, J. E. Moczygemba, A. J. Thompson, J. W. Sharp, J. D. Koenig, R. Maloney, T. Thompson, J. Sakamoto, H. Wang and A. A. Wereszczak, Phys. Chem. Chem. Phys., 2014, 16, 12510–12520.
218. J. Q. Guo, H. Y. Geng, T. Ochi, S. Suzuki, M. Kikuchi, Y. Yamaguchi and S. Ito, J. Electron. Mater., 2012, 41, 1036–1042.
219. X. K. Hu, P. Jood, M. Ohta, M. Kunii, K. Nagase, H. Nishiate, M. G. Kanatzidis and A. Yamamoto, Energy Environ. Sci., 2016, 9, 517–529.
220. Q. H. Zhang, J. C. Liao, Y. S. Tang, M. Gu, C. Ming, P. F. Qiu, S. Q. Bai, X. Shi, C. Uher and L. D. Chen, Energy Environ. Sci., 2017, 10, 956–963.
221. P. A. Zong, R. Hanus, M. Dylla, Y. S. Tang, J. C. Liao, Q. H. Zhang, G. J. Snyder and L. D. Chen, Energy Environ. Sci., 2017, 10, 183–191.

---