Hierarchical Architecturing for Layered Thermoelectric Sulfides and Chalcogenides

Abstract

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.

1. 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 = (S²/ρκ_total)T, where S, ρ, κ_total, and T are the Seebeck coefficient, electrical resistivity, total thermal conductivity, and absolute temperature, respectively. An increase in the quantity S²/ρ, which is known as the thermoelectric power factor, leads to an increase in the electrical performance. The S²/ρ is typically optimized by tuning the carrier concentration of materials. The κ_total is the sum of two parts: the charge carriers transporting heat (i.e., electronic thermal conductivity, κ_el) and phonons traveling through the lattice (i.e., lattice thermal conductivity, κ_lat). Therefore, κ_total = κ_el + κ_lat. The former is directly related to ρ and can be estimated using the Wiedemann-Franz law: κ_el = LT/ρ, where L is the Lorenz number. Therefore, one way to reduce the κ_total is to minimize κ_lat, which is a carrier-independent parameter. In order to increase S²/ρ and reduce κ_lat, 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 S²/ρ. The phonon glass region effectively scatters phonons, resulting in low κ_lat. 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 Na_xCoO 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 S²/ρ, the disordered Na and Ca–Co–O nanoblock layers scatter phonons and reduce κ_lat [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 S²/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 κ_lat 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 κ_lat 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 Sr_0.09Ba_0.11Yb_0.05Co₄Sb₁₂ [27], and a conversion efficiency of 7% was demonstrated in a skutterudite-based thermoelectric module [28].

This review discusses recent progress in an intriguing new class of thermoelectric materials, layered chalcogenides. Among the layered chalcogenides, we primarily focus on the sulfide systems because sulfur is an environment-friendly and cost-effective element. Figure 1 shows the crystal structures of the thermoelectric sulfides and chalcogenides addressed in this article, including layered sulfide TiS₂, misfit layered sulfide [LaS]_1.14NbS₂, a member of cannizzarite homologous series Pb₅Bi₆Se₁₄, accordion-like layered selenide SnSe, and thermoelectric mineral Cu₁₂Sb₄S₁₃. The nanoblock integration, nano- and meso-structuring/panoscopic approach, and rattling/low-energy atomic vibration to layered sulfides and chalcogenides are important guidance for ZT enhancement through all-length-scale hierarchical architecture.

Figure 1. Crystal structures of the thermoelectric sulfides and chalcogenides addressed in this article: (a) TiS₂ [29,30]; (b) [LaS]_1.14NbS₂ [31,32]; (c) Pb₅Bi₆Se₁₄ [33,34]; (d) SnSe [35]; and (e) Cu₁₂Sb₄S₁₃ [36,37]. Sizes of atoms in this figure are arbitrary.

Figure 1. Crystal structures of the thermoelectric sulfides and chalcogenides addressed in this article: (a) TiS₂ [29,30]; (b) [LaS]_1.14NbS₂ [31,32]; (c) Pb₅Bi₆Se₁₄ [33,34]; (d) SnSe [35]; and (e) Cu₁₂Sb₄S₁₃ [36,37]. Sizes of atoms in this figure are arbitrary.

2. CS₂ 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.

Figure 2. Temperature dependence of the standard free-energy change (ΔG°) for the sulfurization of TiO₂ [29], La₂O₃, CeO₂ [51], and Pr₆O₁₁ [52] with CS₂ and H₂S.

Figure 2. Temperature dependence of the standard free-energy change (ΔG°) for the sulfurization of TiO₂ [29], La₂O₃, CeO₂ [51], and Pr₆O₁₁ [52] with CS₂ and H₂S.

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 Ti_1.008S₂ [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.

Figure 3. Schematic diagram of the experimental apparatus used for CS₂ sulfurization. The apparatus was referenced previously in a report by Hirai et al. [51].

Figure 3. Schematic diagram of the experimental apparatus used for CS₂ sulfurization. The apparatus was referenced previously in a report by Hirai et al. [51].

Figure 4. Scanning electron micrographs of the fractured section of sintered compacts of (a) Ti_1.008S₂ [29]; (b) [LaS]_1.20CrS₂ [32]; and (c) Pb₅Bi₆Se₁₄ [34].

Figure 4. Scanning electron micrographs of the fractured section of sintered compacts of (a) Ti_1.008S₂ [29]; (b) [LaS]_1.20CrS₂ [32]; and (c) Pb₅Bi₆Se₁₄ [34].

3. TiS₂-Based Layered Sulfides

Because TiS₂-based layered sulfides are primarily composed of earth-abundant, low-toxicity, and light elements, they will pave the way for environment-friendly, cost-effective, and lightweight thermoelectric devices [29,30,39,40,41,42,43,44,45,46,47,56,57,58,59,60,61,62,63,64,65,66]. The two-dimensional crystal structure of these systems is a great example in which the thermoelectric performance can be improved through nanoblock integration and hierarchical architecturing. The recently developed TiS₂-based sulfides with high thermoelectric figure of merit (ZT) are summarized in Figure 5. In 2001, Imai et al. [40] demonstrated a high power factor (S²/ρ) of ~3710 μW·K⁻²·m⁻¹ at 300 K in a single crystal of near-stoichiometric TiS₂, which is comparable to that of commercially available thermoelectric materials such as Bi₂Te₃. However, the single crystal shows a high lattice thermal conductivity κ_lat of ~6.35 W·K⁻¹·m⁻¹, which limits the ZT to ~0.16 at 300 K (Table 1). Recently, the intercalation of guest atoms and guest layers into TiS₂ layers was found to reduce the κ_lat of these systems, similar to layered cobaltite oxides [7,8,9,10,11,12,13]. For example, Cu intercalation reduces κ_lat and enhances ZT to ~0.5 at 823 K [44].

Figure 5. Current state-of-the-art TiS₂-based layered sulfides. Temperature dependence of the thermoelectric figure of merit (ZT) in the in-plane (ab-plane) direction for single-crystal TiS₂ [40] and polycrystalline Ti_1.008S₂ [29], Ti_1.025S₂ [30], Cu_0.1TiS₂ [44], TiS_1.5Se_0.5 [45], Ti_0.95Ta_0.05S₂ [46], [BiS]_1.2[TiS₂]₂ [42], [PbS]_1.18[TiS₂]₂ [42], [SnS]_1.2[TiS₂]₂ [43], and [BiS]_1.2[Ti_0.95Cr_0.05S₂]₂ [66].

Figure 5. Current state-of-the-art TiS₂-based layered sulfides. Temperature dependence of the thermoelectric figure of merit (ZT) in the in-plane (ab-plane) direction for single-crystal TiS₂ [40] and polycrystalline Ti_1.008S₂ [29], Ti_1.025S₂ [30], Cu_0.1TiS₂ [44], TiS_1.5Se_0.5 [45], Ti_0.95Ta_0.05S₂ [46], [BiS]_1.2[TiS₂]₂ [42], [PbS]_1.18[TiS₂]₂ [42], [SnS]_1.2[TiS₂]₂ [43], and [BiS]_1.2[Ti_0.95Cr_0.05S₂]₂ [66].

Table 1. Seebeck coefficient (S), electrical resistivity (ρ), carrier mobility (μ), power factor (S²/ρ), lattice thermal conductivity (κ_lat), and thermoelectric figure of merit (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 Ti_1.008S₂ [29].

Sample	Direction	S (μV·K−1)	ρ (μΩ·m)	μ (cm2·V−1·s−1)	S2/ρ (μW·K−2·m−1)	κlat (W·K−1·m−1)	ZT
Single crystal	In-plane	−251	17	15	3710	6.35	0.16
Single crystal	Out-of-plane	-	13,000	0.017	-	4.21	-
Polycrystalline	In-plane	−80	6.2	2.3	1030	1.5	0.12
Polycrystalline	Out-of-plane	−84	11	1.2	630	1.3	0.10

Table 1. Seebeck coefficient (S), electrical resistivity (ρ), carrier mobility (μ), power factor (S²/ρ), lattice thermal conductivity (κ_lat), and thermoelectric figure of merit (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 Ti_1.008S₂ [29].

Sample	Direction	S (μV·K−1)	ρ (μΩ·m)	μ (cm2·V−1·s−1)	S2/ρ (μW·K−2·m−1)	κlat (W·K−1·m−1)	ZT
Single crystal	In-plane	−251	17	15	3710	6.35	0.16
Single crystal	Out-of-plane	-	13,000	0.017	-	4.21	-
Polycrystalline	In-plane	−80	6.2	2.3	1030	1.5	0.12
Polycrystalline	Out-of-plane	−84	11	1.2	630	1.3	0.10

The crystal structure of TiS₂ consists of a stacked CdI₂-type layer along the crystalline c-axis and is shown in Figure 1a. The TiS₂ phase has a wide range of chemical compositions ranging from stoichiometric to Ti-rich: Ti_1+xS₂ with 0 ≤ x < 0.1 [67,68,69]. Because the TiS₂ layer is weakly stacked through van der Waals forces, the excess Ti atoms occupy the space between TiS₂ layers. The lattice parameter a monotonically increases from 0.3405 nm for Ti_1.001S₂ to 0.3412 nm for Ti_1.093S₂, and c increases from 0.5691 nm for Ti_1.001S₂ to 0.5711 nm for Ti_1.093S₂ [70].

To interpret the thermoelectric properties of TiS₂, we used the following formulas for approximations of electrical resistivity ρ, carrier mobility μ, κ_lat, and Seebeck coefficient S [71,72,73]:

$$\frac{1}{\mathrm{\rho }}=ne\mathrm{\mu }$$

(1)

$$\mathrm{\mu }=\frac{e{\mathrm{\tau }}_{\mathrm{e}}}{m^{*}}$$

(2)

$${\kappa }_{\mathrm{lat}}=\frac{1}{3}{C}_{\mathrm{v}}{v}_{\mathrm{a}}{l}_{\mathrm{p}}$$

(3)

$$S=\frac{8{\mathrm{\pi }}^2{k}_{\mathrm{B}}^2}{3e{h}^2}{m}^{*}T{\left(\frac{\mathrm{\pi }}{3n}\right)}^{2/3}$$

(4)

where n, e, τ_e, m*, C_v, v_a, l_p, k_B, 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, S²/ρ, κ_lat, 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 Ti_1.008S₂ [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 × 10²⁰ cm⁻³ and ~4.5 × 10²¹ 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 cm²·V⁻¹·s⁻¹) is significantly lower than the in-plane μ (~15 cm²·V⁻¹·s⁻¹) at 300 K. Moreover, the out-of-plane κ_lat (~4.21 W K⁻¹·m⁻¹) is slightly lower than the in-plane κ_lat (~6.35 W·K⁻¹·m⁻¹) at 300 K. The highly oriented polycrystalline sample also exhibits lower ρ, higher μ, and higher κ_lat in the in-plane direction. The high value of the out-of-plane ρ and low value of the out-of-plane κ_lat 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 κ_lat, 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 S²/ρ (~1030 μW·K⁻²·m⁻¹) and higher ZT (~0.12) in the in-plane direction at 300 K for polycrystalline Ti_1.008S₂ is due to the lower in-plane ρ and insensitivity of S to the crystal orientation.

The intercalated Ti provides n-type carriers to the system; therefore, n can be tuned to optimize S²/ρ by self-intercalation. Figure 6 shows the room-temperature S, ρ, and S²/ρ plotted against n. The solid line in Figure 6a represents the values calculated using Equation (4) with m^*/m₀ (m₀ is the free electron mass) equal to 2.88 when n is greater than 5 × 10²⁰ cm⁻³ [74,75,76]. The measured values fall on this calculated line. An increase in Ti content results in an increase in n and, hence, a decrease in S and ρ. The S²/ρ peaks around n ~ 2.8 × 10²¹ cm⁻³ in Ti_1+xS₂ and reaches a value of ~3700 μW·K⁻²·m⁻¹.

Figure 6. (a) Seebeck coefficient (S); (b) electrical resistivity (ρ); and (c) power factor (S²/ρ) plotted against the carrier concentration (n) at 300 K in the in-plane (ab-plane) direction for Ti_1+xS₂ [29,30,41,43,44,75,76,77]. The solid line in (a) represents the values calculated using Equation (4) with m^*/m₀ (m₀ is the free electron mass) equal to 2.88 when n is greater than 5 × 10²⁰ cm⁻³ [74,75,76].

Figure 6. (a) Seebeck coefficient (S); (b) electrical resistivity (ρ); and (c) power factor (S²/ρ) plotted against the carrier concentration (n) at 300 K in the in-plane (ab-plane) direction for Ti_1+xS₂ [29,30,41,43,44,75,76,77]. The solid line in (a) represents the values calculated using Equation (4) with m^*/m₀ (m₀ is the free electron mass) equal to 2.88 when n is greater than 5 × 10²⁰ cm⁻³ [74,75,76].

One way to reduce κ_lat is the intercalation of guest atoms and guest layers into the host TiS₂ layer [42,43,44,65,66]. For example, Cu intercalation reduces κ_lat from ~2.0 W·K⁻¹·m⁻¹ for TiS₂ to ~1.7 W·K⁻¹·m⁻¹ for Cu_0.1TiS₂, and SnS intercalation dramatically reduces κ_lat to ~1.0 W·K⁻¹·m⁻¹ for [SnS]_1.2[TiS₂]₂ at 300 K (Figure 7a). Substitution is another way to reduce κ_lat [45,46,47]; for example, the substitution of Ti by Ta slightly reduces κ_lat to ~1.8 W·K⁻¹·m⁻¹ for Ti_0.95Ta_0.05S₂ at 300 K (Figure 7b).

Figure 7. Temperature dependence of the lattice thermal conductivity (κ_lat) in the in-plane (ab-plane) direction for Ti_1.008S₂ [29]: (a) intercalated systems [BiS]_1.2[TiS₂]₂ [42], [PbS]_1.18[TiS₂]₂ [42], [SnS]_1.2[TiS₂]₂ [43], and Cu_0.1TiS₂ [44]; (b) substituted systems TiS_1.5Se_0.5 [45] and Ti_0.95Ta_0.05S₂ [46].

Figure 7. Temperature dependence of the lattice thermal conductivity (κ_lat) in the in-plane (ab-plane) direction for Ti_1.008S₂ [29]: (a) intercalated systems [BiS]_1.2[TiS₂]₂ [42], [PbS]_1.18[TiS₂]₂ [42], [SnS]_1.2[TiS₂]₂ [43], and Cu_0.1TiS₂ [44]; (b) substituted systems TiS_1.5Se_0.5 [45] and Ti_0.95Ta_0.05S₂ [46].

The reduction in κ_lat 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 κ_lat 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 κ_lat and enhance ZT beyond 0.5.

4. Misfit Layered Sulfides [MS]_1+m[TS₂]_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 κ_lat) 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 S²/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 × 10²⁰ cm⁻³), the reason for which is not very well understood and requires further study. At 300 K, a very low κ_lat ~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 (κ_total); lattice thermal conductivity (κ_lat); power factor (S²/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 (K)	ρ (μΩ·m)	S (μV·K−1)	κtotal (W·K−1·m−1)	κlat (W·K−1·m−1)	S2/ρ (μW·K−2·m−1)	ZT	Reference
(Yb2S2)0.62NbS2	In-plane	300	19.0	60	0.80	0.41	200	0.1	[81]
(La2S2)0.62NbS2	In-plane	300	11.5	22	-	-	50	-	[81]
(LaS)1.14NbS2 a	In-plane	300	7.6	37	2.50	1.50	177	0.02	[32]
		950	22.0	83	2.00	0.93	316	0.15
	Out-of-plane	300	13.3	25	2.04	1.48	49	0.01
		950	32.1	72	1.62	0.88	162	0.09
(LaS)1.14NbS2 b	In-plane	300	5.2	35	4.88	3.45	233	0.02	[32]
		950	16.9	83	3.25	1.86	405	0.15
	Out-of-plane	300	9.3	25	1.56	0.75	70	0.01
		950	28.5	56	1.34	0.52	111	0.09
(LaS)1.2CrS2 a	In-plane	950	207	−172	1.16	1.04	143	0.12	[32]
	Out-of-plane	950	223	−174	1.02	0.91	137	0.13
(LaS)1.2CrS2 b	In-plane	950	171	−172	1.25	1.11	174	0.13	[32]
	Out-of-plane	950	278	−154	0.92	0.84	84	0.08

^a Small grains (~1 μm), weak/random orientation of grains; ^b Large grains (>20 μm), strong orientation of grains perpendicular to the pressing direction.

Table 2. Seebeck coefficient (S); electrical resistivity (ρ); total thermal conductivity (κ_total); lattice thermal conductivity (κ_lat); power factor (S²/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 (K)	ρ (μΩ·m)	S (μV·K−1)	κtotal (W·K−1·m−1)	κlat (W·K−1·m−1)	S2/ρ (μW·K−2·m−1)	ZT	Reference
(Yb2S2)0.62NbS2	In-plane	300	19.0	60	0.80	0.41	200	0.1	[81]
(La2S2)0.62NbS2	In-plane	300	11.5	22	-	-	50	-	[81]
(LaS)1.14NbS2 a	In-plane	300	7.6	37	2.50	1.50	177	0.02	[32]
		950	22.0	83	2.00	0.93	316	0.15
	Out-of-plane	300	13.3	25	2.04	1.48	49	0.01
		950	32.1	72	1.62	0.88	162	0.09
(LaS)1.14NbS2 b	In-plane	300	5.2	35	4.88	3.45	233	0.02	[32]
		950	16.9	83	3.25	1.86	405	0.15
	Out-of-plane	300	9.3	25	1.56	0.75	70	0.01
		950	28.5	56	1.34	0.52	111	0.09
(LaS)1.2CrS2 a	In-plane	950	207	−172	1.16	1.04	143	0.12	[32]
	Out-of-plane	950	223	−174	1.02	0.91	137	0.13
(LaS)1.2CrS2 b	In-plane	950	171	−172	1.25	1.11	174	0.13	[32]
	Out-of-plane	950	278	−154	0.92	0.84	84	0.08

^a Small grains (~1 μm), weak/random orientation of grains; ^b Large grains (>20 μm), strong orientation of grains perpendicular to the pressing direction.

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 κ_total, especially in the out-of-plane direction, and the lowest κ_total 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 κ_lat ~0.84 W·K⁻¹·m⁻¹ and ~0.52 W·K⁻¹·m⁻¹, respectively, at 950 K. The low κ_lat 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 κ_lat, 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].

Figure 8. High-resolution transmission electron microscopy (HRTEM) image of (LaS)_1.2CrS₂ and corresponding electron diffraction pattern. The structural model superimposed on the enlarged HRTEM image is given as inset in the bottom-left corner of the figure. La, Cr, and S are represented by blue, red, and yellow, respectively. White arrows indicate stacking faults/defects (taken with permission from reference [32]).

Figure 8. High-resolution transmission electron microscopy (HRTEM) image of (LaS)_1.2CrS₂ and corresponding electron diffraction pattern. The structural model superimposed on the enlarged HRTEM image is given as inset in the bottom-left corner of the figure. La, Cr, and S are represented by blue, red, and yellow, respectively. White arrows indicate stacking faults/defects (taken with permission from reference [32]).

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 cm²·V⁻¹·s⁻¹ for the CrS₂ system and μ ~ 7–11 cm²·V⁻¹·s⁻¹ for the NbS₂ system at 300 K. The carrier concentrations at 300 K are n ~ 3 × 10²⁰ cm⁻³ for the CrS₂ system and n ~ 1 × 10²¹ cm⁻³ for the NbS₂ system; these values need to be optimized further for enhancing S²/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.

5. 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 Figure 1c and Figure 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 9. Structural evolution in the cannizzarite homologous series [(PbSe)₅]_m[(Bi₂Se₃)₃]_n: (a) Pb₅Bi₆Se₁₄ (m = 1, n = 1); (b) Pb₅Bi₁₂Se₂₃ (m = 1, n = 2); (c) Pb₅Bi₁₈Se₃₂ (m = 1, n = 3); and (d) Pb₅Bi₂₄Se₄₁ (m = 1, n = 4) [33,95,97]. The sizes of atoms in this figure are arbitrary.

Figure 9. Structural evolution in the cannizzarite homologous series [(PbSe)₅]_m[(Bi₂Se₃)₃]_n: (a) Pb₅Bi₆Se₁₄ (m = 1, n = 1); (b) Pb₅Bi₁₂Se₂₃ (m = 1, n = 2); (c) Pb₅Bi₁₈Se₃₂ (m = 1, n = 3); and (d) Pb₅Bi₂₄Se₄₁ (m = 1, n = 4) [33,95,97]. The sizes of atoms in this figure are arbitrary.

Figure 10 shows the κ_lat, ZT, and crystal structure of CsBi₄Te₆, a member of the Cs₄[Bi_2n+4Te_3n+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 κ_lat 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, κ_total, κ_lat, 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 × 10¹⁹ 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 κ_lat. 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 κ_lat value (~0.39 W·K⁻¹·m⁻¹) is slightly higher than the out-of-plane κ_lat 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 S²/ρ of 320 μW·K⁻²·m⁻¹ and higher ZT of 0.46 in the in-plane direction at 705 K (Figure 11d).

Figure 10. Temperature dependence of the (a) lattice thermal conductivity (κ_lat); (b) thermoelectric figure of merit (ZT); and (c) crystal structure of CsBi₄Te₆, a member of the Cs₄[Bi_2n+4Te_3n+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 the lillianite homologous series [109].

Figure 10. Temperature dependence of the (a) lattice thermal conductivity (κ_lat); (b) thermoelectric figure of merit (ZT); and (c) crystal structure of CsBi₄Te₆, a member of the Cs₄[Bi_2n+4Te_3n+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 the lillianite homologous series [109].

Figure 11. Temperature dependence of the (a) Seebeck coefficient (S), (b) electrical resistivity (ρ), (c) total thermal conductivity (κ_total) and lattice thermal conductivity (κ_lat), and (d) thermoelectric figure of merit (ZT) for sintered compacts of the cannizzarite homologous member Pb₅Bi₆Se₁₄ in the in-plane (ab-plane) and out-of-plane (c-axis) directions [34].

Figure 11. Temperature dependence of the (a) Seebeck coefficient (S), (b) electrical resistivity (ρ), (c) total thermal conductivity (κ_total) and lattice thermal conductivity (κ_lat), and (d) thermoelectric figure of merit (ZT) for sintered compacts of the cannizzarite homologous member Pb₅Bi₆Se₁₄ in the in-plane (ab-plane) and out-of-plane (c-axis) directions [34].

One way to enhance the ZT of homologous compounds is the tuning of carrier concentration n through doping for optimizing S²/ρ. Another way is to reduce κ_lat 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 κ_lat 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 κ_lat through crystal-structural evolution at the atomic scale.

Table 3. Seebeck coefficient (S), electrical resistivity (ρ), carrier concentration (n), carrier mobility (μ), power factor (S²/ρ), lattice thermal conductivity (κ_lat), and thermoelectric figure of merit (ZT) at room temperature in three members of the cannizzarite homologous series, Pb₅Bi₆Se₁₄, Pb₅Bi₁₂Se₂₃, and Pb₅Bi₁₈Se₃₂ [103].

Sample	S (μV·K−1)	ρ (μΩ·m)	n (cm−3)	μ (cm2·V−1·s−1)	S2/ρ (μW·K−2·m−1)	κlat (W·K−1·m−1)	ZT
Pb5Bi6Se14	−28	22	0.86 × 10−20	33	36	0.72	0.01
Pb5Bi12Se23	−27	27	1.15 × 10−20	20	27	0.59	0.01
Pb5Bi18Se32	−52	39	1.19 × 10−20	14	69	0.49	0.03

Table 3. Seebeck coefficient (S), electrical resistivity (ρ), carrier concentration (n), carrier mobility (μ), power factor (S²/ρ), lattice thermal conductivity (κ_lat), and thermoelectric figure of merit (ZT) at room temperature in three members of the cannizzarite homologous series, Pb₅Bi₆Se₁₄, Pb₅Bi₁₂Se₂₃, and Pb₅Bi₁₈Se₃₂ [103].

Sample	S (μV·K−1)	ρ (μΩ·m)	n (cm−3)	μ (cm2·V−1·s−1)	S2/ρ (μW·K−2·m−1)	κlat (W·K−1·m−1)	ZT
Pb5Bi6Se14	−28	22	0.86 × 10−20	33	36	0.72	0.01
Pb5Bi12Se23	−27	27	1.15 × 10−20	20	27	0.59	0.01
Pb5Bi18Se32	−52	39	1.19 × 10−20	14	69	0.49	0.03

6. 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 cm²·V⁻¹·s⁻¹ in the b-axis direction and μ ~ 130 cm²·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 S²/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 × 10¹⁷ cm⁻³ for a pure system to 9 × 10¹⁸ 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).

Figure 12. Temperature dependence of the (a) Seebeck coefficient (S); (b) electrical resistivity (ρ); (c) total thermal conductivity (κ_total); and (d) thermoelectric figure of merit (ZT) for single-crystal (SC) SnSe 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].

Figure 12. Temperature dependence of the (a) Seebeck coefficient (S); (b) electrical resistivity (ρ); (c) total thermal conductivity (κ_total); and (d) thermoelectric figure of merit (ZT) for single-crystal (SC) SnSe 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].

The performance of SnSe surpasses that of other materials, especially above the transition temperature of ~750 K, where the single-crystal κ_lat less than 0.25 W·K⁻¹·m⁻¹ is achieved along all crystallographic axes (Figure 12c) [35]. This value is significantly lower than the κ_lat obtained for all-length-scale hierarchically architectured PbTe (PbTe-4 mol% SrTe-2 mol% Na has κ_lat ~ 0.5 W·K⁻¹·m⁻¹ and ZT ~ 2.2 at 900 K) [17] and skutterudites exhibiting rattling (for example, LaFe₃CoSb₁₂ has κ_lat ~ 1 W·K⁻¹·m⁻¹ and ZT ~ 0.9 at 750 K) [22].

One would expect the κ_total (κ_lat) 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 κ_total 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 κ_total 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 (κ_lat ~ 1.4 W·K⁻¹·m⁻¹) higher than that in the c-axis direction (κ_lat ~ 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 κ_lat 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 κ_total 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.

7. Thermoelectric Minerals

The thermoelectric minerals tetrahedrites (Cu₁₂Sb₄S₁₃) and colusites (Cu₂₆V₂M₆S₃₂; M = Ge, Sn) include no layers in their crystal structures. However, the p-type ZT demonstrated in these mineral-based sulfide systems is among the highest achieved in Pb-free thermoelectric sulfides (Figure 13) and is therefore worth mentioning [36,37,124,125,126].

The terms “tetrahedrite” and “colusite” are derived from naturally occurring minerals (Cu,Fe,Ag,Zn)₁₂Sb₄S₁₃ and Cu_24–26V₂(As,Sn,Sb)₆S₃₂, respectively, which are mainly composed of the earth-abundant and low-toxicity elements Cu and S. The tetrahedrites possess a cubic structure of $I\overline{4}3m$ symmetry with SbS₃ pyramids, CuS₄ tetrahedra, and CuS₃ triangles. The colusites crystallize in a cubic structure of $P\overline{4}3n$ symmetry with CuS₄ tetrahedra and VS₄ tetrahedra.

Figure 13. Temperature dependence of (a) thermoelectric figure of merit (ZT) (p-type); and (b) lattice thermal conductivity (κ_lat) for the tetrahedrites Cu_10.5Ni_1.5Sb₄S₁₃ [36], Cu_11.5Zn_0.5Sb₄S₁₃ [124], Cu_11.6Mn_0.4Sb₄S₁₃ [125], and Cu_10.5Ni_1.0Zn_0.5Sb₄S₁₃ [37] and the colusite Cu₂₆V₂Ge₆S₃₂ [126].

Figure 13. Temperature dependence of (a) thermoelectric figure of merit (ZT) (p-type); and (b) lattice thermal conductivity (κ_lat) for the tetrahedrites Cu_10.5Ni_1.5Sb₄S₁₃ [36], Cu_11.5Zn_0.5Sb₄S₁₃ [124], Cu_11.6Mn_0.4Sb₄S₁₃ [125], and Cu_10.5Ni_1.0Zn_0.5Sb₄S₁₃ [37] and the colusite Cu₂₆V₂Ge₆S₃₂ [126].

In 2012, Suekuni et al. [127] first reported a notable S²/ρ and low κ_lat 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 κ_lat, resulting in high ZT. In the case of the tetrahedrites, the low κ_lat 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 κ_lat 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 S²/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 Cu_12−xTr_xSb₄S₁₃. For example, the value of S²/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 Cu_11.5Ni_0.5Sb₄S₁₃. A ZT of 1.03 at 723 K was achieved for Cu_10.5Ni_1.0Zn_0.5Sb₄S₁₃ (Figure 13a) [37]. Recently, the structural stability and purity of synthetic Cu₁₂Sb₄S₁₃ and Cu_10.4Ni_1.6Sb₄S₁₃ were also reported [129]. These high-ZT sulfide minerals may help realize feasible methods for environment-friendly and cost-effective thermoelectric waste heat recovery.

8. 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.