Thermoelectric Compounds

Thermoelectricity has been recognized as an environmentally friendly energy conversion technology due to its ability to directly achieve conversion between heat and electricity for a long time. β-Zn4Sb3 has attracted considerable interest as promising thermoelectric material in the moderate temperature range (500K–900K), which is the temperature range of most industrial waste heat sources. In this paper, first we present the structure of β-Zn4Sb3 and the traditional doping strategy used to enhance its performance. Next, we review the details of some new methods utilized for improving the thermoelectric properties of β-Zn4Sb3 and its thermal stability as well as reliability. Finally, the review finishes with highlighting some promising strategies for future research directions in the material.


Introduction
During the last decade, due to their ability to convert heat into electricity directly as well as without moving parts or greenhouse emissions, thermoelectric materials have drawn much attention because of the energy crisis and the environmental concerns of fossil fuel use [1,2].When a temperature gradient is applied to a thermoelectric couple consisting of n-type and p-type materials, the charge carriers at the hot side will diffuse to the cold side, producing a thermoelectric voltage.This characteristic is the basis of thermoelectric power generation, known as the Seebeck effect.Conversely, when a voltage is applied to a thermoelectric couple, a temperature difference will be created.This characteristic is the basis of thermoelectric electronic refrigeration, known as the Peltier effect.The conversion efficiency of a thermoelectric material is qualified by the dimensionless figure of merit, , defined as  = ( 2 /), where , , , and  are the Seebeck coefficient, electrical resistivity, thermal conductivity (including the lattice thermal conductivity   , and the carrier thermal conductivity   ), and absolute temperature, respectively [3,4].A good thermoelectric material should possess a high power factor PF (= 2 /) and low thermal conductivity.Typically, there are two strategies to improve the  of thermoelectric materials: one is to lower the thermal conductivity  and the other is to boost the PF.
Thermoelectric materials are normally classified into four categories depending on their temperature range of application: (1) cryogenic temperature range: from 4 K to 250 K; (2) near room-temperature range: from 250 K to 500 K; (3) intermediate temperature range: from 500 K to 900 K; and (4) high temperature range: beyond 900 K.As intermediate temperature range is just the temperature range of most industrial waste heat sources, it is very important to research high  intermediate thermoelectrics.Among the wide variety of intermediate temperature materials, -Zn 4 Sb 3 compounds with low thermal conductivity and made of relatively cheap and nontoxic elements are pointed out as one kind of most promising thermoelectric materials [5][6][7].
The ideal thermoelectric material should be a "phononglass and electron crystal" material, which possesses electronic properties similar to a good semiconductor single crystal but has thermal properties associated with amorphous materials [8][9][10][11][12].-Zn 4 Sb 3 , the p-type intermetallic compound which is most suitable for use as a state-of-theart material at moderate temperatures, is one of the three modifications of Zn 4 Sb 3 .Zn 4 Sb 3 is known to have three structural phases, namely, -, -, and -Zn 4 Sb 3 , which are stable below 263 K, between 263 K and 765 K, and above 765 K, respectively [13].The highest  value reported for -Zn 4 Sb 3 is 1.40 at 675 K [13][14][15].The power factor in -Zn 4 Sb 3 is reasonably high (∼13 W m −1 K −2 at 675 K) while it possesses a remarkable "phonon-glass" behavior, characterized by an unusually low thermal conductivity of ∼0.9 Wm −1 K −1 at 300 K, comparable to that of a glass [13], as shown in Figure 1.
The organization of the review is as follows.First, we would like to provide some important backgrounds by introducing the structure of -Zn 4 Sb 3 and highlight traditional doping method previously used in order to enhance the thermoelectric properties of -Zn 4 Sb 3 .We then will review the recent progress in -Zn 4 Sb 3 in details, including the energy filtering effect, distortion of the electronic density of states, in situ nanostructures, and its thermal stability.Finally, we identify strategies and research directions which could lead to further research in the material.

Structure of 𝛽-Zn 4 Sb 3 and
Traditional Doping Strategy to Enhance ZT for -Zn 4 Sb 3 The detailed crystal structure of -Zn 4 Sb 3 has been determined by using both single-crystal and powder X-ray diffraction methods coupled with maximum entropy analysis [16,27].The -Zn 4 Sb 3 has the hexagonal rhombohedral crystal structure and lattice constants are  = 12.231 Å and  = 12.428 Å with a R-3c space group [28].To date, there are mainly two different models (Mayer model [29] and threeinterstitial model [16]) to explain the crystal structure of -Zn 4 Sb 3 unit cell.In the three-interstitial model, the mass density and composition of the crystal structure are reported to be in agreement with measurements [30,31].In the experimentally determined -Zn 4 Sb 3 unit cell, it contains 30 Sb atoms, but there are four in equilibrium Zn positions with partial occupations: a deficiency of Zn1 site with ∼90% occupancy and interstitial Zn2, Zn3, and Zn4 sites with ∼5% occupancy to balance the stoichiometry; thus, the number of Zn in the unit cell is 39 [16,29].From the experimental crystal structure analysis, the stoichiometry of -Zn 4 Sb 3 is actually Zn 39 Sb 30 or Zn 13 Sb 10 , as shown in Figure 2 [17,27].As the Zn interstitials exhibit large thermal displacements, the glass-like interstitials are mainly responsible for the phonon damping that suppresses the lattice thermal conductivity.
There is apparently Sb disorder along the -axis that can contribute to the glass-like thermal conductivity.Electronic structure and transport calculations using the crystal structure obtained have identified the compound as a p-type semiconductor [27], which is in agreement with experimental findings of the doping trend.It is demonstrated that the Zn interstitial atoms play a dual role as electron donors and thermopower enhancers.First-principles calculations of electronic structure and thermoelectric properties have also been performed [32].The band structure results reveal the covalent tendency of the compound, consistent with the good carrier mobility measured.It is believed that the Zn disorder in the structure and the three interstitial partially occupied Zn sites attribute to its low thermal conductivity.
And the high Seebeck coefficient can be attributed to the strong energy-dependence of the Fermi surface topology near band-filling [32].
Although -Zn 4 Sb 3 has been identified as an excellent thermoelectric material with glass-like thermal conductivity, further improvements of thermoelectric performance are of importance to practical applications.It is well known that the power factor has an optimum versus the carrier concentration.Doping is an effective approach to optimize the thermoelectric properties by adjusting the carrier concentration.In recent years, enhanced power factors through doping optimization are achieved in -Zn 4 Sb 3 .Conventional doping such as the substitutions of Pb [33,34], Bi [35], Nb [36], Mg [37], Cu [38], Cd [39,40], Sn [33,41], In [33,34,42,43], Al [42,44], Ga [42,44], Ag [38,45], Hg [46], Fe [47], Te [48],  and Se [49] for -Zn 4 Sb 3 have been investigated.As listed in Table 1, the composition, Seebeck coefficient , total thermal conductivity , and maximum   reported in some typical literatures are given.The results show that the doping causes a limited improvement of its thermoelectric performance.And it is also found that doping in -Zn 4 Sb 3 is not always beneficial.Liu et al. [34] and Tsutsui et al. [43] investigated the effects of Al, Ga, and In doping on the thermoelectric properties of -Zn 4 Sb 3 , respectively.They found that the substitutions increase both the electrical resistivity and the Seebeck coefficient, resulting in a reduction in  finally.Pedersen et al. [46] investigated the thermoelectric properties of Hg 0.04 Zn 3.96 Sb 3 , which shows that the Hg doping has a minor influence on the transport properties of -Zn 4 Sb 3 and  remains unchanged for both the undoped and the Hgdoped samples.

New Strategies to Enhance ZT for 𝛽-Zn 4 Sb 3
Recently some special physical ideas related to band structure engineering are introduced in thermoelectric research, such as energy filtering effect (EFE) in PbTe-based nanocomposites embedded with Pb nanoparticles [50,51], distortion of the electronic density of states (DOS) in Tl doped PbTe [52], and nanostructure approach.In the following we will discuss these new methods in both theory and experiments in the sphere of -Zn 4 Sb 3 based thermoelectric materials.

Through Energy Filtering to Enhance Thermoelectric
with carrier mobility () = / * , where  is the electrical conductivity,  the carrier charge,  the energy, () and () energy dependent carrier density and mobility,   the Boltzmann constant,  * the effective mass, and   the Fermi energy.Assuming relaxation time  has power law relation to scattering parameter , that is,  =  0  −1/2 (where  0 means an energy-independent constant) [53], increasing the scattering time's energy-dependence, ()/, can result in an increase in the energy-dependence of the mobility ()/ through preferentially scattering electrons depending on their energy.In a nanocomposite system, the obvious scattering mechanism to increase the scattering parameter is grain boundary scattering and interface scattering, which can reduce the carrier mobility and preferentially scatters carriers with energies lower than the barrier height [54].As shown in Figure 3, Minnich et al. calculated the normalized Seebeck distribution versus energy for heavily doped bulk n-type Si 80 Ge 20 and the results show that low energy electrons will reduce the thermopower because this portion of the Seebeck distribution of low energy electrons is negative [18].EFE is a good example of how nanostructured materials can be used to improve electrical transport properties by scattering low energy charge carriers while still maintaining low thermal conductivity [55][56][57].
In metal-based InGaAs/InGaAlAs superlattices, Vashaee and Shakouri's work shows that metal-based superlattices with tall barriers can achieve a large  (>5) at room temperature through a detailed calculation [58].Faleev and Léonard used perturbation theory and partial wave method to investigate PbTe based composites dispersed with Pb nanoparticles, and they assume that the electron scattering on spherically symmetrical interface potentials is independent of other scattering mechanisms.The calculated thermopower they got is larger than that of bulk PbTe matrix [59].Yang and Qin have first proposed a concept of "synergetic scattering" of carriers in a semiconductor matrix dispersed with metallic nanoinclusions [19,60].They calculated the scattering parameter and thermopower in both single scattering and synergetic scattering of the interface potential barriers and wells formed because of the dispersed nanoinclusions in the matrix.The results indicate that the synergetic scattering of electrons at ionized impurities and the interface potential barriers or wells can produce great scattering parameter and enhanced thermopower.The effects of nanoinclusion radius and energy dispersion relations on the scattering parameter are given in Figure 4.
Theoretically if different types of semiconductors dispersed in a semiconductor matrix to form nanocomposites, two kinds of heterojunctions (nN type and Nn type) will be configured.In principle, the potential energies for carriers in the heterojunctions can be derived by the Thomas-Fermi approximation and depletion layer approximation.The calculation results indicate that scattering parameters depend on temperature , radii of spheres , and electron concentrations and  0 = 10 nm (I), 20 nm (△), 30 nm (◊), and 40 nm (f).The upper curves are for single scattering; the lower curves correspond to synergetic scattering.Reproduced with permission from [20].
. Seebeck coefficients calculated for synergetic scattering are enhanced compared to those for the single scattering, as shown in Figure 5 [20].The results demonstrate that heterojunction potentials in semiconductor-based nanocomposites with semiconducting inclusions can give rise to enhanced EFE, which can boost thermopower and thermoelectric performance of the nanocomposite systems.
with Fermi integral of order : where ℎ is the Planck constant,   is the reduced Fermi level   /(  ),  is the carrier density,  is electron charge,  is scattering parameters, and   is the Boltzmann constant.The calculation results are shown in Figure 6.
In the experiment, increased PF comes from both enhanced Seebeck coefficient because of intensified EFE caused by potential barriers formed at phase boundary between -Zn 4 Sb 3 matrix and nanoscale Cu 3 SbSe 4 inclusions and moderate reduction of hall carrier mobility due to hierarchical structures of the nanoscale inclusions, as shown in Figure 7.At room temperature, the band gap   of dispersed phase Cu 3 SbSe 4 is 0.3-0.4eV [63,68], which is larger than that (0.26 eV) of matrix -Zn 4 Sb 3 [17].When they contact each other, due to band bending (the schematic at the bottom in Figure 7(b)) caused by the transfer of holes from dispersed phase Cu 3 SbSe 4 to the matrix -Zn 4 Sb 3 to guarantee the equal chemical potentials on both sides, valence band offset appears at heterojunction interfaces (Figure 7(a)) and p-p type heterojunction barriers form at the interface in the nanocomposites.Due to significant increase in PF and drastic reduction in thermal conductivity,  reaches 1.37 at 648 K in the composite system with 5 vol.% of nanophase Cu 3 SbSe 4 .Present results demonstrate that simultaneous enhancement of power factor and phonon blocking can be achieved via proper design of a material system and its microstructures, resulting in large increase in  of a material system.

Concept and Theory.
From (1), the second approach to enhance the Seebeck coefficient is the introduction of resonant distortion of electrical density of states near the Fermi level (  ) reflected by increased effective mass  * .The use of impurity band energy levels to increase the thermopower has resulted in an obvious increase in  value [52,69].Previously resonant impurity is a concept introduced in solid state physics for metals [70][71][72].Theoretically Hicks  and  are the chemical potentials for the inclusions, matrix, and the composite system, respectively.Reproduced with permission from [21].
Copyright 2014, American Institute of Physics.
and Dresselhaus [73] and Mahan and Sofo [74] predict an enhancement in thermoelectric properties due to an increase in the electronic density of states first.The resonant level can be regarded as a bound level with an energy that falls above the conduction band edge or below the valence band edge [22], creating a local maximum in the density of states, as shown in Figure 8.The figure represents schematically the case for In:PbTe, where the resonant states are in the conduction band.Band structure calculations show that not only impurities create sharp DOS peaks close to the Fermi level, but also those peaks should be of the similar character as the host band structure.Results show that d-or even f-state impurities are useful to improve the thermopower of metals, but s-or p-state resonance levels are more suited to improve thermoelectric properties of semiconductors [75][76][77].( = 0, 0.001, 0.002, and 0.003) at the temperatures from 300 K to 615 K [23,78].The results indicate that Sm doping and Pr doping can cause the resonant distortion of density of states of -Zn 4 Sb 3 and result in about a 2-fold increase in effective mass  *  of -Zn 4 Sb 3 in these two compounds.Sm doping and Pr doping result in ∼50% and ∼65% increases of the Seebeck coefficient for the doped samples, compared with that (∼75 V/K) of the undoped sample.Furthermore, thermal conductivity decreases substantially by Sm doping and Pr doping.

Experiments
They observed an interesting phenomenon that the thermopower of nanocomposites increases minorly compared with that of the pure -Zn 4 Sb 3 , as shown in Figure 9.The obtained effective mass  *  /  (where   is the free electron mass) as functions of temperature in the temperature range of 300 K to 615 K is shown in Figure 10(a).The solid line in Figure 10(b) is carrier concentration dependence of thermopower for the undoped -Zn 4 Sb 3 , which is calculated by using formulae (2) for  *  = 1.47   .And this resonant distortion of DOS results in obvious increase in thermopower for the doped compounds at room temperature, as shown in Figure 10(b).The larger effective masses indicate that there is strong resonant distortion of DOS around the Fermi level.These data are above the black line, including the experimentally measured Seebeck coefficient of the Sm doped at room temperature in Figure 10(b), indicating strong DOS resonant distortion effect achieved.Finally,  value of -(Zn 1−x Sm x ) 4 Sb 3 ( = 0.002) is about 53% larger than that of the undoped sample and reaches 1.10 at 615 K in the study.

Through Melt Spinning-Spark Plasma Sintering (MS-SPS)
to Get In Situ Nanostructures.Over the past decade, one successful strategy that has been used to boost the performance is nanostructure in several thermoelectric materials, and the nanostructure approach significantly enhances the  values by drastically reducing the lattice thermal conductivity [73][74][75][76][77][78][79][80][81][82][83][84].Recently, it is reported that, in addition to the reduction of the lattice thermal conductivity, nanostructure can also increase the power factor in some nanocomposites [85][86][87].In other words, it is possible that in some material systems the three interrelated thermoelectric properties can be uncoupled by introducing nanostructures.High-energy ball milling [88] and melt spinning (MS) [80,81,[89][90][91][92][93][94] techniques have been utilized to produce nanostructured bulk materials (nanosize powders or precursors containing nanoinclusions) for commercial applications, and the corresponding bulk compacted materials with nanoinclusions show notably improved  values.
Wang et al. used MS-SPS (melt spinning-spark plasma sintering) technique to prepare nanostructured -Zn 4 Sb 3 compounds with minute Cd-doping [24].As shown in Figure 11(a), each ribbon is composed of two different surfaces: one is contact surface which directly contacts the copper roller and the other is the free surface.Figure 11(c) displays the morphology of the free surface and Figure 11(d) displays the corresponding high-resolution picture for MS ribbon.Many flower-like clusters of nanosheets or nanoneedles are distributed on the free surface, and these ∼10 nm nanosheets or nanoneedles grow perpendicular to the surface.These ∼1 m flower-like clusters are adhered to the surface of ribbon.
The MS-SPS technique generates multiscale nanostructures in the ribbon-shape samples and the compacted bulk materials.Figure 12 shows the microstructures of the undoped MS-SPS bulk sample.These unique multiple nanostructures result in reductions in lattice thermal conductivities, particularly for samples with some ZnSb nanodots with sizes of 10-30 nm, as displayed in Figure 12(a).These nanostructures originate from the multiscale nanostructures in melt spinning ribbons, as well as the subsequent chemical reactions during the following spark plasma sintering process [28].High-resolution transmission electron microscopy observations were used on the undoped MS-SPS bulk sample and are presented in Figures 12(b)-12(d).
In the MS-SPS experiments, Cd-doping affects the electrical properties by minorly reducing the electrical conductivity and distinctly increasing the thermopower.As a result, the nonstructural strategy combined with the Cd-doping remarkably improves the final figure of merit.A peak  value of 1.30 is achieved for (Zn 0.99 Cd 0.01 ) 4 Sb 3 sample at 700 K, which is ∼13% and ∼23% larger than the undoped MS-SPS sample and the 1% Cd-doped melt ingot at the same temperature.

Recent Research about Stability and Reliability of 𝛽-Zn 4 Sb 3 for Commercialization
Stability and reliability are very important requirements for a candidate thermoelectric material to practical application.Several studies have focused on the thermal stability and decomposition process of -Zn 4 Sb 3 [95][96][97][98].Ab initio calculations [99,100] and multitemperature synchrotron powder X-ray diffraction measurements [101] suggest a decomposition process: Zn 4 Sb 3 → 3ZnSb + Zn.Some studies have proposed a starting temperature of 500 K for decomposition of -Zn 4 Sb 3 into ZnSb and Zn [102][103][104] while some research reported instabilities of -Zn 4 Sb 3 that have also happened below 500 K [105,106].On the other hand, there are experimental reports of an outstanding  of about 1.30 at around 670 K for pure -Zn 4 Sb 3 [107,108].In the following we will show two typical studies about stability and reliability of -Zn 4 Sb 3 .When the temperature reaches 565 K, Zn begins to react with ZnSb above the second transition temperature again.-Zn 4 Sb 3 becomes thermodynamically stable and the damage caused by decomposition can be recovered as well.This is the reason for its state-of-the-art thermoelectric performance at high temperature: the maximum  value reaches 1.40 at 748 K. Since the thermal stability is a prerequisite for thermoelectric application, the study provides insight into the search of new high-temperature thermoelectric materials.

Conclusion and Outlook
In this paper, we have briefly reviewed the recent progress and advances in -Zn 4 Sb 3 based thermoelectric materials.The thermoelectric properties are enhanced significantly by band structure engineering (DOS distortion) and nanostructuring (EFE and phonon scattering).However, bipolar effect, which is not thermoelectric favorable, will be very obvious at high temperature [61,110,111].The bipolar effect derives from the truth that there are two types of carriers, electrons and holes.At high temperature some electrons are thermally excited from the valence band to the conduction band, resulting in an equal number of holes.As holes and electrons have opposite charges, the thermopower will be suppressed if electrons and holes are both present.Thus, reducing the bipolar effect can improve the figure of merit of -Zn 4 Sb 3 by creating a nanostructure which scatters minority carriers preferentially [18].Even though both the resonant distortion of density of states of electron and the energy filtering effect can enhance the Seebeck coefficient or , successful joining of the two approaches to improve the thermoelectric performance is still elusive.If we can join the two effects in one system to enhance its thermopower and thermoelectric properties, then we may provide a new mechanism to prepare high performance thermoelectric materials.

Figure 1 :
Figure 1: (a) Thermoelectric figure of merit and (b) thermal conductivity of -Zn 4 Sb 3 compared with other materials.Reproduced with permission from [16].Copyright 2004, Nature Publishing Group.

Figure 2 :
Figure 2: Crystal structure of (a) -Zn 4 Sb 3 in space group R-3c with all atoms in full occupancy, the interstitial Zn atoms are presented in smaller spheres, and (b) the Zn 13 Sb 10 model with occupancy close to the experimental value.Reproduced with permission from [17].Copyright 2010, American Physical Society.

Figure 3 :
Figure 3: Calculated normalized Seebeck distribution versus energy for heavily doped bulk n-type Si 80 Ge 20 .Reproduced with permission from [18].Copyright 2009, Royal Society of Chemistry.

Figure 4 :
Figure 4: (a) Dependences of  0 on radius of the metal sphere and the barrier height for synergetic scattering at ionized impurities and the interface potential barriers.(b) Variations in  0 with well depth and radius of spherical Pb particles for synergetic scattering at interface potential wells in n-type PbTe/Pb nanocomposites at 300 K. Reproduced with permission from [19].Copyright 2010, American Institute of Physics.

Figure 7 :
Figure7: Cross sectional schematics of (a) the energy bands for Cu 3 SbSe 4 (band gap   1 ) and -Zn 4 Sb 3 matrix (band gap   2 ) before contact (where   1 and   2 are the conduction band bottoms and  V 1 and  V 2 are the valence band tops), and (b) p-p type interface potential barriers (lower schematic) with an effective barrier height   eff formed from band bending, where the upper schematic shows the corresponding Cu 3 SbSe 4 particle with hierarchical nanostructures embedded in -Zn 4 Sb 3 matrix, where  is the particle size of Cu 3 SbSe 4 , and  1 ,  2 , and  are the chemical potentials for the inclusions, matrix, and the composite system, respectively.Reproduced with permission from[21].Copyright 2014, American Institute of Physics.

Figure 11 :
Figure 11: (a) Sketch of the MS process; (b) photograph of the MS ribbons; (c)-(f) FESEM images and the corresponding high-resolution images for MS ribbon; (c, d) showing the free surface and (e, f) the contact surface.Reproduced with permission from [24].Copyright 2011, Elsevier Ltd.

Figure 13 :
Figure 13: (a) Refined weight fractions of -Zn 4 Sb 3 phase as a function of temperature during the first heating cycle.Data for a pure sample are shown for comparison.(b) Refined weight fraction of -Zn 4 Sb 3 phase for all nanocomposites during thermal cycles.Data for a pure sample are shown for comparison.Reproduced by permission from [25].Copyright 2013, Royal Society of Chemistry.

Figure 14 :
Figure 14: (a) Schematic of the time-temperature-transformation curve for -Zn 4 Sb 3 and (b) microstructure of after different heat treatments following rapid cooling.Reproduced with permission from [26].Copyright 2013, American Chemistry Society.

Table 1 :
List of composition, Seebeck coefficient , total thermal conductivity , and maximum   obtained from the literatures. is Seebeck coefficient; b  is total thermal conductivity; c   is the maximum  value. a [13][63][64][65][66][67]ed in -Zn 4 Sb 3 Based Nanocompounds.Experimentally, Zou et al. found that EFE can boost the Seebeck coefficient in ((Bi 2 Te 3 ) 0.2 (Sb 2 Te 3 ) 0.8 )/-Zn 4 Sb 3 Sb 3 -Cu 3 SbSe 4 .Through coprecipitation method they got nanoscale inclusions Cu 3 SbSe 4 .Cu 3 SbSe 4 is another important thermoelectric material with large effective mass and small band gap in intermediate temperature range[62][63][64][65][66][67].Normally if carrier concentration is enhanced, electronic conductivity will be increased and the Seebeck coefficient should be decreased.However, they observed that the thermopower of nanocomposites increases compared with that of the pure -Zn 4 Sb 3 while electronic conductivity increases obviously compared with that of the pure -Zn 4 Sb 3 .They calculated  by using a single parabolic band model, in which effective masses  *  and  can be expressed as[13] [21,61]0.5, 1, and 2 vol.%) nanocompounds and (Cu 3 SbSe 4 )/ -Zn 4 Sb 3 ( = 0, 1, 3, 5, and 6 vol.%) nanocompounds[21,61], especially in hierarchical nanostructured -Zn 4 [22]matic energy versus distance diagram where the spheres on the bottom represent atoms.The periodic potential of the host atoms of the solid is experienced by conduction electrons and results in the formation of conduction and valence bands, extended states available to the nearly-free electrons.Reproduced by permission from[22].Copyright 2012, Royal Society of Chemistry.