Hierarchical Architecturing for Layered Thermoelectric Sulfides and Chalcogenides

Sulfides are promising candidates for environment-friendly and cost-effective thermoelectric materials. In this article, we review the recent progress in all-length-scale hierarchical architecturing for sulfides and chalcogenides, highlighting the key strategies used to enhance their thermoelectric performance. We primarily focus on TiS2-based layered sulfides, misfit layered sulfides, homologous chalcogenides, accordion-like layered Sn chalcogenides, and thermoelectric minerals. CS2 sulfurization is an appropriate method for preparing sulfide thermoelectric materials. At the atomic scale, the intercalation of guest atoms/layers into host crystal layers, crystal-structural evolution enabled by the homologous series, and low-energy atomic vibration effectively scatter phonons, resulting in a reduced lattice thermal conductivity. At the nanoscale, stacking faults further reduce the lattice thermal conductivity. At the microscale, the highly oriented microtexture allows high carrier mobility in the in-plane direction, leading to a high thermoelectric power factor.


Introduction
The growing demand for energy throughout the world is causing an energy crisis and aggravating environmental burden. However, more than 50% of the primary energy supplied is not utilized and is wasted in the form of heat. Solid-state devices based on thermoelectrics can directly convert the waste heat generated from various sources into useful electrical energy and can thus provide a new approach to improving energy management and sustainability while reducing greenhouse-gas emissions [1][2][3][4][5]. Currently, thermoelectric devices are found only in niche applications because thermoelectric materials show low efficiency and mainly consist of toxic and scarce (expensive) elements. Therefore, extensive efforts have been devoted to develop high-efficiency, environment-friendly, and cost-effective thermoelectric materials for large-scale practical applications, such as waste-heat recovery in vehicles and industries.
The thermoelectric figure of merit (ZT) expresses the efficiency of thermoelectric materials and is defined as ZT = (S 2 /ρκtotal)T, where S, ρ, κtotal, and T are the Seebeck coefficient, electrical resistivity, total thermal conductivity, and absolute temperature, respectively. An increase in the quantity S 2 /ρ, which is known as the thermoelectric power factor, leads to an increase in the electrical performance. The S 2 /ρ is typically optimized by tuning the carrier concentration of materials. The κtotal is the sum of two parts: the charge carriers transporting heat (i.e., electronic thermal conductivity, κel) and phonons traveling through the lattice (i.e., lattice thermal conductivity, κlat). Therefore, κtotal = κel + κlat. The former is directly related to ρ and can be estimated using the Wiedemann-Franz law: κel = LT/ρ, where L is the Lorenz number. Therefore, one way to reduce the κtotal is to minimize κlat, which is a carrier-independent parameter. In order to increase S 2 /ρ and reduce κlat, thermoelectric materials have been strategically developed with the phonon glass-electron crystal (PGEC) concept proposed by Slack [6]. A PGEC system consists of an electron crystal region and a phonon glass region. The electron crystal region allows carrier transmission, resulting in high carrier mobility and high S 2 /ρ. The phonon glass region effectively scatters phonons, resulting in low κlat. The PGEC concept has been realized using three methods: nanoblock integration, a nano-and meso-structuring/panoscopic approach, and rattling/low-energy atomic vibration.
Layered cobaltite oxides such as NaxCoO and Ca-Co-O have been demonstrated to be promising high-temperature thermoelectric materials [7][8][9][10][11][12][13]. An important advantage of thermoelectric oxides is their high chemical stability in air over a wide temperature range of 300-1200 K. The high ZT of these oxides originates from the integration of physical properties of the metallic electron-crystal nanoblock layer and disordered phonon-glass nanoblock layer. While the metallic Co-O nanoblock layers provide a high S 2 /ρ, the disordered Na and Ca-Co-O nanoblock layers scatter phonons and reduce κlat [10][11][12][13]. The impact of layered oxides has generated considerable interest in layered compounds, particularly layered sulfides and chalcogenides. The covalency generally increases when moving from oxides to sulfides and chalcogenides; therefore, the layered sulfides and chalcogenides show lower ρ and higher S 2 /ρ [14].
PbTe-based materials represent one of the most successful examples of nano-and meso-structuring [15][16][17][18][19][20][21]. The insertion of endotaxial nanostructures in PbTe bulk materials causes the effective scattering of short-mean-free-path phonons without affecting the carrier mobility. Moreover, long-mean-free-path phonons are scattered at grain boundaries by controlling and fine-tuning the mesoscale architecture of nanostructured materials. As a result, the all-length-scale hierarchical architecture (panoscopic approach) in PbTe bulk thermoelectric materials causes a significant reduction in κlat and dramatically increases ZT to an exceptionally high value of 2.2 at 915 K [17].
Skutterudites and clathrates are highly promising for practical thermoelectric devices operating in the intermediate temperature range of 573-973 K [22][23][24][25][26][27][28]. These systems contain large cages of host atoms in their crystal structures. Filling the large cages with guest atoms reduces κlat because the guest atoms rattle at low energy inside the cages and effectively scatter phonons. A very high ZT of 1.9 at 835 K was achieved in the skutterudite Sr0.09Ba0.11Yb0.05Co4Sb12 [27], and a conversion efficiency of 7% was demonstrated in a skutterudite-based thermoelectric module [28].

CS 2 Sulfurization and Pressurized Sintering
We first discuss the synthesis and processing of thermoelectric sulfides, which drastically affects their properties. In the case of TiS2-based layered sulfides, a single crystal can be grown using the chemical-vapor-transport method with I2 as the transport agent [38][39][40][41]. Polycrystalline TiS2-based layered sulfides have been commonly prepared by melting stoichiometric amounts of the constituent elements in evacuated and sealed quartz tubes at 905-1273 K, followed by pressurized sintering at 873-1173 K [30,[42][43][44][45][46][47]. However, these methods are difficult to apply because of the large difference in vapor pressure between metals and sulfur; consequently, there is less motivation for researchers in the thermoelectric community to investigate thermoelectric sulfides further. In this review, we focused on CS2 sulfurization, which is a low-temperature preparation method for thermoelectric sulfides [29,[48][49][50][51][52][53].
The temperature dependence of the standard free-energy change (ΔG°) for the sulfurization of TiO2, La2O3, CeO2, and Pr6O11 with CS2 and H2S gases, calculated from thermodynamic data [54,55], is shown in Figure 2 [29,51,52]. The value of ΔG° for CS2 sulfurization is lower than that for H2S sulfurization in the temperature range of 600-1300 K. For example, the values of ΔG° at 1100 K for the sulfurization of La2O3 with CS2 and H2S are −126 and −26 kJ·mol −1 , respectively, which implies that CS2 gas is a powerful sulfurizing agent for oxides, allowing the low-temperature formation of sulfides.
A schematic diagram of the experimental apparatus used for CS2 sulfurization is shown in Figure 3. The apparatus was referenced previously in a report by Hirai et al. [51]. The starting oxide powders were placed in quartz boats and set in a quartz reaction tube. The quartz tube was evacuated and purged with Ar gas. The powders were heated to 573 K under Ar gas flow. A mixture of CS2 and Ar gases was introduced into the quartz tube as soon as the powders reached 573 K. The CS2 gas was obtained by bubbling Ar carrier gas through CS2 liquid. Single phases of TiS2, [LaS]1.20CrS2, and [LaS]1.14NbS2 were successfully prepared through CS2 sulfurization at 1073 K for 4-12 h [29,32].
Powders of layered thermoelectric sulfides and chalcogenides were sintered under uniaxial pressure to obtain high-density compacts. Figure 4 shows scanning electron microscopy (SEM) micrographs of the fractured section of sintered compacts of Ti1.008S2 [29], [LaS]1.20CrS2 [32], and Pb5Bi6Se14 [34] that were fractured parallel to the pressure direction. The micrographs reveal a dense structure and well-organized microtexture, indicating that the pressurized sintering promotes densification and grain orientation. The XRD patterns show that the crystalline c-axis is preferentially oriented along the pressing (out-of-plane) direction [29,32,34]. A centrifugal heating technique also provides the dense samples with highly oriented microtexture [56]. The highly oriented microtextures allow high carrier mobility in the in-plane direction, leading to a high thermoelectric power factor.   [32]; and (c) Pb5Bi6Se14 [34].
To interpret the thermoelectric properties of TiS2, we used the following formulas for approximations of electrical resistivity ρ, carrier mobility μ, κlat, and Seebeck coefficient S [71][72][73]: where n, e, τe, m*, Cv, va, lp, kB, and h are the carrier concentration, electronic charge, relaxation time of charge carriers, effective mass, heat capacity at constant pressure, average sound velocity, mean free path of phonons, Boltzmann constant, and Planck's constant, respectively. These relationships are derived from the parabolic band model and energy-independent scattering time for metals and degenerate semiconductors. The layered crystal structure results in highly anisotropic electrical and thermal transport properties [29,40,43]. Table 1 lists S, ρ, μ, S 2 /ρ, κlat, and ZT at room temperature in the in-plane (ab-plane) and out-of-plane (c-axis) directions for a single crystal of nearly stoichiometric TiS2 [40] and polycrystalline Ti1.008S2 [29]. The polycrystalline sample possesses a well-organized microtexture ( Figure 4a) with the crystalline ab-plane preferentially oriented along the in-plane direction. The room-temperature n of the single crystal and polycrystalline samples are ~2.8 × 10 20 cm −3 and ~4.5 × 10 21 cm −3 , respectively. For single crystal, the out-of-plane ρ (~13,000 μΩ·m) is nearly 750 times higher than the in-plane ρ (~17 μΩ·m), and the out-of-plane μ (~0.017 cm 2 ·V −1 ·s −1 ) is significantly lower than the in-plane μ (~15 cm 2 ·V −1 ·s −1 ) at 300 K. Moreover, the out-of-plane κlat (~4.21 W K −1 ·m −1 ) is slightly lower than the in-plane κlat (~6.35 W·K −1 ·m −1 ) at 300 K. The highly oriented polycrystalline sample also exhibits lower ρ, higher μ, and higher κlat in the in-plane direction. The high value of the out-of-plane ρ and low value of the out-of-plane κlat are principally due to the reduced relaxation time (reduced mean free path) resulting from the significant electron and phonon scatterings, respectively, at the interfaces between the TiS2 layers (see Equations (1)-(3)). The sign of S is negative for both samples, confirming n-type carrier transport. Unlike ρ and κlat, S was found to be insensitive to the crystal orientation in the sintered compacts; as there is no relationship between S and τ in Equation (1), S is nearly isotropic. The in-plane S (~−80 μV·K −1 ) is nearly the same as the out-of-plane S (~−84 μV·K −1 ) at 300 K. The higher S 2 /ρ (~1030 μW·K −2 ·m −1 ) and higher ZT (~0.12) in the in-plane direction at 300 K for polycrystalline Ti1.008S2 is due to the lower in-plane ρ and insensitivity of S to the crystal orientation.
The reduction in κlat through intercalation and substitution is limited; therefore, ZT is below 0.5. Future work should aim to develop new methods for a dramatic reduction in κlat to achieve ZT enhancement in TiS2-based layered sulfides. Recently, Koumoto et al. [64,66] have demonstrated that the stacking faults in the layers can be tuned to reduce the thermal conductivity. We believe that well-organized stacking faults can ideally reduce κlat and enhance ZT beyond 0.5.

Misfit Layered Sulfides [MS] 1+m [TS 2 ] n
TiS2-based layered sulfides are a part of a large family of misfit layered sulfides with a general formula [MS]1+m[TS2]n, where M = Sn, Pb, Sb, Bi, and rare-earth metals; T = Ti, V, Cr, Nb, and Ta; and n = 1, 2, 3 [78]. These compounds consist of alternating MS and TS2 layers, which belong to separate subgroups; therefore, these compounds lack three-dimensional periodicity. The crystal-structure analysis of rare-earth misfit compound (MS)1+mNbS2 has been performed using different subgroups including the (3+1)-dimensional superspace group [31,79,80], and different structural variants depending upon the intercalation layer were proposed. Miyazaki et al. [81] have reported a significant variation in the c-axis depending on the ionic radius of the rare-earth element. Previous results have shown that NbS2 [32,53,81,82], TaS2 [83,84], and TiS2 [42,43,65,66] sandwich structures show metallic conductivity, whereas CrS2 [32,85] and VS2 [78,85] sandwich structures show semiconducting properties. The crystal structure and physical properties of this misfit family were extensively studied in the 1990s [78]; however, not many reports on their thermoelectric properties exist to date. In recent years, the misfit layered sulfides have gained interest in the thermoelectric community for their PGEC behavior, where the intercalated NaCl-type MS layer is primarily responsible for the disorder (reduction in κlat) and the CdI2-type TS2 layer behaves as a charge-carrier pathway [86,87]. The entire crystal structure is stabilized through charge transfer from the MS layer to the TS2 layer [78,88]. Through the concept of bond valences, it is established that the interlayer La-S bond valences are much larger than the interlayer M-S bond valences with M = Sn or Bi [88][89][90], which makes the LnS-based misfit layered compounds (Ln = rare-earth metals) much more mechanically hard (due to strong interlayer bonding) than the SnS-, PbS-, BiS-, and SbS-based systems [88].
Thus far, only [MS]1+mNbS2 with M = rare-earth elements [32,53,81]; [LaS]1.2CrS2 [32]; and [MS]1+mTiS2 with M = Sn, Pb, or Bi [42,43,[64][65][66] (discussed in the previous section) have been studied in depth for their thermoelectric properties. The thermoelectric properties of [MS]1+mTS2 (M = La, Yb; T = Cr, Nb) in the in-plane (ab-plane) and out-of-plane (c-axis) directions are summarized in Table 2. The NbS2 systems show p-type S, whereas CrS2 systems show n-type S. Among all compounds in the LnS-based series, [Yb2S2]0.62NbS2 shows the highest ZT of ~0.10 at 300 K because it shows the highest S 2 /ρ [81]. The S of the Yb sample is ~35%-60% higher than those of samples consisting of the other elements in the lanthanide series at 300 K. This is due to its slightly lower n (~5 × 10 20 cm −3 ), the reason for which is not very well understood and requires further study. At 300 K, a very low κlat ~0.41 W·K −1 ·m −1 is achievable for [Yb2S2]0.62NbS2, which reduces even further (~0.18 W·K −1 ·m −1 ) with the removal of ~5% Yb and S from the [Yb2S2] layer, slightly enhancing the room-temperature ZT to ~0.11. This is due to the high phonon scattering originating from the highly modulated structure and atomic deficiency. Further improvements in ZT are expected at higher temperatures. Table 2. Seebeck coefficient (S); electrical resistivity (ρ); total thermal conductivity (κtotal); lattice thermal conductivity (κlat); power factor (S 2 /ρ); and thermoelectric figure of merit (ZT) in the in-plane (ab-plane) and out-of-plane (c-axis) directions of state-of-the-art misfit layered sulfides: [MS]1+mTS2 (M = La, Yb; T = Cr, Nb) [32,81].

Sample
Direction T As seen from Table 2, misfit compounds are highly sensitive to microstructural variations because of the anisotropic nature of their atomic bonds. Therefore, one strategy to enhance ZT is tuning the microstructure. Microstructure control was achieved in (LaS)1+mTS2 (T = Nb, Cr) [32] by varying the sulfurization duration from 6 to 12 h, followed by pressure-assisted sintering to obtain samples with randomly and highly oriented textures. Extended sulfurization (for 12 h) resulted in higher carbon content in the samples, which impeded grain growth [91]. On the other hand, the grains in the sample sulfurized for 6 h grew to >20 μm and self-arranged into a layered structure after sintering (Figure 4b). Large anisotropy was observed in thermoelectric properties for both the systems (Table 2). Both systems show low total thermal conductivity κtotal, especially in the out-of-plane direction, and the lowest κtotal was observed for highly oriented (LaS)1.2CrS2 (~0.92 W·K −1 ·m −1 ) and (LaS)1.14NbS2 (~1.34 W·K −1 ·m −1 ), which mainly results from the very low κlat ~0.84 W·K −1 ·m −1 and ~0.52 W·K −1 ·m −1 , respectively, at 950 K. The low κlat is attributed to the fact that the interfaces between the host TS2 and guest MS layers act as effective phonon scatterers. Similar to ρ and κlat, S was found to be highly anisotropic for the highly oriented NbS2 misfit compounds. For instance, the in-plane and out-of-plane S values were ~83 μV·K −1 and ~56 μV·K −1 , respectively, for (LaS)1.14NbS2 at 950 K. The anisotropy in S may have originated from the anisotropic band structure. Band-structure calculations showed that strong intralayer energy dispersions (~1.0 eV) occur near the Fermi level, while smaller dispersions of 0.01-0.05 eV occur in the interlayer direction [79,88].
Defects such as the presence of extra bright contrast planes are observed in the HRTEM image (indicated by white arrows) and ED patterns (streaks along the c-axis) of the CrS2 system (Figure 8), which exhibits coherent stacking-fault-induced intergrowth of CrS2 layers [32]. With proper manipulation, these crystal defects can help improve the thermoelectric properties. These nanoscale defects, along with the phonon scattering at the atomic scale (layer interfaces, dopants, and point defects) and micro scale (microstructure control) make these compounds good candidates for ZT enhancement through all-length-scale hierarchical architecturing [17,18,20]. The highly oriented texture provided the highest ZT ~0.14 at 950 K in (LaS)1.2CrS2, while the sample with weakly oriented texture had the highest ZT ~0.15 at 950 K among the (LaS)1.14NbS2 samples [32]. Carrier mobility (μ) is quite low in these misfit compounds with μ ~ 0.5-1.6 cm 2 ·V −1 ·s −1 for the CrS2 system and μ ~ 7-11 cm 2 ·V −1 ·s −1 for the NbS2 system at 300 K. The carrier concentrations at 300 K are n ~ 3 × 10 20 cm −3 for the CrS2 system and n ~ 1 × 10 21 cm −3 for the NbS2 system; these values need to be optimized further for enhancing S 2 /ρ. The ZT can, therefore, be further improved through appropriate doping and substitutions not only to optimize n but also to tune the stacking faults, as reported for the TiS2 misfit system [64,66]. These misfit layered sulfides are promising candidates for high-temperature thermoelectric applications as they are environmentally benign, nontoxic, and stable at high temperature; further, they provide tremendous opportunities for enhancing ZT.

Homologous Chalcogenides
A structure of the homologous series is built on the same structural principle with certain module(s) expanding in various dimension(s) by regular increments [92][93][94][95][96]. For example, the crystal structure of the cannizzarite homologous series consists of alternating infinite PbSe-and Bi2Se3-type layers [33,95,97], as shown in Figures 1c and 9. The two layers are stacked alternately along the c-axis, resulting in a three-dimensional structure with varying thicknesses that form different members in the homology. The thermoelectric properties of homologous compounds can be tuned by modifying the size and shape of the structural module(s); therefore, the homologous compounds are good platforms for developing new thermoelectric materials [34,94,[98][99][100][101][102][103][104][105][106][107][108][109].  Figure 10 shows the κlat, ZT, and crystal structure of CsBi4Te6, a member of the Cs4[Bi2n+4Te3n+6] homologous series [99,102]; SnBi2Te4, a member of the [SnTe]n[Bi2Te3]m homologous series [106,107]; Pb5Bi6Se14, a member of the cannizzarite homologous series [34]; PbBi2S4, a member of the galenobismuthite homologous series [34]; and Pb7Bi4Se13, a member of lillianite homologous series [109]. CsBi4Te6 and SnBi2Te4 show p-type behavior, while Pb5Bi6Se14, PbBi2S4, and Pb7Bi4Se13 show n-type behavior. The complex crystal structures yield low κlat in the range of 0.15 to 1.15 W·K −1 ·m −1 over the temperature range of 100 K to 763 K, leading to high ZT. A record-high ZT of ~0.8 at 225 K and a high ZT of ~0.9 at 775 K were found in CsBi4Te6 and Pb7Bi4Se13, respectively.
As shown in Figure 4c, the scanning electron microscope images of the fractured section of sintered compacts of Pb5Bi6Se14 reveal that the crystal grains were preferentially grown in the direction perpendicular to the pressure applied during sintering, forming needle-like grains with a mean length of ~30 μm. The XRD patterns show that the crystalline c-axis is preferentially oriented along the pressing (out-of-plane) direction [34]. Figure 11 shows the temperature dependence of the S, ρ, κtotal, κlat, and ZT for sintered compacts of the cannizzarite homologous series member Pb5Bi6Se14 in the in-plane and out-of-plane directions. The room-temperature carrier concentration of the system is ~4.8 × 10 19 cm −3 . As in TiS2, S was observed to be insensitive to the crystal orientation ( Figure 11a); for example, at 705 K, the in-plane S value (~210 μV·K −1 ) is in rough agreement with the out-of-plane S value (~230 μV·K −1 ). On the other hand, the interfaces between the PbSe layer and the Bi2Se3 layer effectively scatter the charge carriers and heat-carrying phonons, leading to highly anisotropic ρ and κlat. For example, at 705 K, the in-plane ρ value (~130 μΩ·m) is 60% lower than the out-of-plane ρ value (~320 μΩ·m) (Figure 11b), and the in-plane κlat value (~0.39 W·K −1 ·m −1 ) is slightly higher than the out-of-plane κlat value (~0.31 W·K −1 ·m −1 ) (Figure 11c). The lower ρ in the in-plane direction and the insensitivity of S to crystal orientation results in a higher S 2 /ρ of 320 μW·K −2 ·m −1 and higher ZT of 0.46 in the in-plane direction at 705 K (Figure 11d).  [106,107]; Pb5Bi6Se14, a member of the cannizzarite homologous series [34]; PbBi2S4, a member of the galenobismuthite homologous series [34]; and Pb7Bi4Se13, a member of the lillianite homologous series [109].  One way to enhance the ZT of homologous compounds is the tuning of carrier concentration n through doping for optimizing S 2 /ρ. Another way is to reduce κlat further by increasing the complexity of the crystal structure using crystal-structural evolution enabled by the homologous series ( Figure 9). Table 3 lists the room-temperature thermoelectric properties of three members of the cannizzarite homologous series, Pb5Bi6Se14, Pb5Bi12Se23, and Pb5Bi18Se32 [103]. An important result here is that κlat systematically reduces from 0.72 W·K −1 ·m −1 for Pb5Bi6Se14 (m = 1, n = 1) to 0.49 W·K −1 ·m −1 for Pb5Bi18Se32 (m = 1, n = 3), demonstrating the reduction in κlat through crystal-structural evolution at the atomic scale. Table 3. Seebeck coefficient (S), electrical resistivity (ρ), carrier concentration (n), carrier mobility (μ), power factor (S 2 /ρ), lattice thermal conductivity (κlat), and thermoelectric figure of merit (ZT) at room temperature in three members of the cannizzarite homologous series, Pb5Bi6Se14, Pb5Bi12Se23, and Pb5Bi18Se32 [103].

Accordion-Like Layered SnQ (Q = S, Se)
The major strategies for achieving good thermoelectric performance have mostly involved the use of heavy elements (often toxic elements such as Pb), nanostructuring (which requires precise control of synthesis procedures) [15][16][17][18][19][20][21], and complex unit cells such as skutterudites [22][23][24][25][26][27] and zintl phases [110]. SnSe, however, possesses a very simple crystal structure with light, earth-abundant elements ( Figure 1d) and exhibits an intrinsically ultra-low thermal conductivity [35]. SnSe has a layered orthorhombic crystal structure with zigzag (accordion-like) atomic chains (space group Pnma) below ~750 K [111]; at ~750 K, it undergoes a phase transition towards its higher-symmetry phase (space group Cmcm) [112,113]. SnSe, which has been ignored by the thermoelectric community in the past, has attracted tremendous interest after the very recent report by Kanatzidis et al. [35], which demonstrates a record-high ZT of ~2.62 at 923 K along the b-axis, high ZT of ~2.3 along the c-axis, and moderate ZT of ~0.8 along the a-axis in single-crystal SnSe. The lighter analogous sulfide SnS has also received attention in the thermoelectric community [114][115][116]. Figure 12 shows a comparison of the thermoelectric properties of single-crystal [35], polycrystalline [117], and Ag-alloyed SnSe [118]. There are no significant differences observed S between the a-, b-, and c-axis for single-crystal SnSe. S decreases at the transition temperature of ~750 K but retains a high value (Figure 12a). For example, the b-axis S for single crystals decreases from ~570 μV·K −1 at 573 K to ~340 μV·K −1 at 823 K. Unlike S, a large anisotropy in ρ can be seen for the single crystal, where ρ along the b-and c-axis is much smaller than that along the a-axis (Figure 12b). This is because the carrier mobilities μ ~ 250 cm 2 ·V −1 ·s −1 in the b-axis direction and μ ~ 130 cm 2 ·V −1 ·s −1 in the c-axis direction at 300 K are higher within the plane of the slab than in the inter-slab direction. The in-plane and out-of-plane ρ of the polycrystalline samples yielded similar observations. The value of ρ dramatically decreases at ~750 K and consequently increases S 2 /ρ. In the case of single crystals, the b-axis ρ decreases from ~2000 μΩ·m at 573 K to ~120 μΩ·m at 823 K. With Ag alloying of polycrystalline SnSe, the room-temperature carrier concentration increases from 2 × 10 17 cm −3 for a pure system to 9 × 10 18 cm −3 for a 7% Ag system [118]. The 1% Ag-alloyed SnSe system produces the highest ZT of ~0.6 at 750 K, in contrast to the pure SnSe system, which has a ZT of ~0.3 at the same temperature and ~0.5 at 820 K (Figure 12d).  measured along the a-, b-, and c-axis [35], polycrystalline (PC) SnSe in the in-plane (crystalline bc-plane) and out-of-plane (crystalline a-axis) directions [117], and 1% Ag-alloyed polycrystalline SnSe in the in-plane direction [118].
One would expect the κtotal (κlat) of polycrystalline samples to be less than that of single-crystal samples because of increased phonon scattering from grain boundaries in polycrystalline samples; however, the opposite is observed for SnSe (Figure 12c). For instance, in-plane κtotal values of ~0.6 W·K −1 ·m −1 (at 850 K) and ~0.7 W·K −1 ·m −1 (at 750 K) were obtained for pure polycrystalline and Ag-alloyed SnSe, respectively. However, very low κtotal values of ~0.23 W·K −1 ·m −1 (a-axis), ~0.34 W·K −1 ·m −1 (b-axis), and ~0.29 W·K −1 ·m −1 (c-axis) were obtained for the single-crystal sample at 973 K. Ab initio studies suggest a strong anisotropy between all the crystallographic axes with the conductivity in the b-axis direction (κlat ~ 1.4 W·K −1 ·m −1 ) higher than that in the c-axis direction (κlat ~ 0.7 W·K −1 ·m −1 ) at 300 K [119]. This theoretical study relates quite well with the polycrystalline samples but differs markedly from the values for single-crystal samples, in which κlat values along b and c axis are reported to be similar (~0.7 W·K −1 ·m −1 at 300 K). As data for only two directions (i.e., parallel and perpendicular to the pressing direction) are available for polycrystalline samples, it is difficult to draw conclusions. Furthermore, the room-temperature κtotal of the single crystal differs markedly from the earlier reported work on SnSe system [120] and therefore, further verification is warranted. Very recent investigations on Te-substituted SnSe [121] and non-stoichiometric SnSe [118] have indicated that n-type conductivity in SnSe is feasible.
The lighter analog SnS is also gaining increased interest, backed up by theoretical work [122,123] supporting the good thermoelectric properties of this compound. SnS also has an accordion-like layered structure and is environmentally compatible and cost-effective. Among the few reports on the thermoelectric properties of SnS [114][115][116], the Ag-doped system demonstrates the highest ZT of ~0.6 at 973 K [116]. There is a big scope for improvement in ZT through improved doping and an all-length-scale hierarchical architecture approach.
In 2012, Suekuni et al. [127] first reported a notable S 2 /ρ and low κlat at room temperature in tetrahedrite systems. Since then, many efforts have been devoted to enhance the ZT of tetrahedrite systems [36,37,124,125] and to find new mineral-based thermoelectric materials [126,128]. As shown in Figure 13, mineral-based sulfide systems show extremely low κlat, resulting in high ZT. In the case of the tetrahedrites, the low κlat is due to the low-energy vibration of the Cu atom out of the [CuS3] trigonal planar unit, which appears similar to the rattling in skutterudites and clathrates (Figure 1e) [36]. The κlat of both systems ranges from ~0.1 W·K −1 ·m −1 to ~0.7 W·K −1 ·m −1 over the temperature range of 300 to 730 K (Figure 13b). The value of S 2 /ρ can be increased by tuning the carrier concentration by substituting Tr = Mn [125,127], Fe [124,127], Co [127], Ni [36,37,127], and Zn [37,124,127] at the Cu sites in Cu12−xTrxSb4S13. For example, the value of S 2 /ρ at 660 K was slightly boosted through Ni doping from 1170 μW·K −2 ·m −1 for Cu12Sb4S13 to 1210 μW·K −2 ·m −1 for Cu11.5Ni0.5Sb4S13. A ZT of 1.03 at 723 K was achieved for Cu10.5Ni1.0Zn0.5Sb4S13 (Figure 13a) [37]. Recently, the structural stability and purity of synthetic Cu12Sb4S13 and Cu10.4Ni1.6Sb4S13 were also reported [129]. These high-ZT sulfide minerals may help realize feasible methods for environment-friendly and cost-effective thermoelectric waste heat recovery.

Conclusions and Insights
The decoupling of the interdependent thermoelectric properties of a material has always been a challenge in the development of high-efficiency thermoelectric materials. A layered structure not only provides vast opportunities for enhancing the thermoelectric figure of merit ZT through appropriate optimizations at all length scales but also provides methods for individual tuning of thermal and electron transports. Ultra-low lattice thermal conductivities below 0.5 W·K −1 ·m −1 have been obtained through intercalation, crystal-structural evolution, or the formation of stacking faults in layered sulfides. Future work must consider scattering centers on all relevant length scales in a hierarchical manner, i.e., from atomic-scale lattice disorders (layer interfaces, substitution sites, and structural evolution) to nano-scale disorders (stacking faults) and microscale grain boundaries (through microtexturing), to achieve the maximum reduction in lattice thermal conductivity. Higher ZT is expected with further work to optimize the carrier concentrations in this new category of materials.