Improved Thermoelectric Performance through Double Substitution in Shandite-Type Mixed-Metal Sulfides.

Substitution of tin by indium in shandite-type phases, A3Sn2S2 with mixed Co/Fe occupancy of the A-sites is used to tune the Fermi level within a region of the density of states in which there are sharp, narrow bands of predominantly metal d-character. Materials of general formula Co2.5+x Fe0.5-x Sn2--yIn y S2 (x = 0, 0.167; 0.0 ≤ y ≤ 0.7) have been prepared by solid-state reaction and the products characterized by powder X-ray diffraction. Electrical-transport property data reveal that the progressive depopulation of the upper conduction band as tin is replaced by indium increases the electrical resistivity, and the weakly temperature-dependent ρ(T) becomes more semiconducting in character. Concomitant changes in the negative Seebeck coefficient, the temperature dependence of which becomes increasingly linear, suggests the more highly substituted materials are n-type degenerate semiconductors. The power factors of the substituted phases, while increased, exhibit a weak temperature dependence. The observed reductions in thermal conductivity are principally due to reductions in the charge-carrier contribution on hole doping. A maximum figure-of-merit of (ZT)max = 0.29 is obtained for the composition Co2.667Fe0.333Sn1.6In0.4S2 at 573 K: among the highest values for an n-type sulfide at this temperature.

Introduction

The ability of thermoelectric devices to convert thermal energy directly into electrical energy offers considerable scope for improving the efficiency of industrial processes through the harvesting of waste heat. Device performance is determined principally by that of the constituent materials, commonly expressed in terms of a thermoelectric figure-of-merit, ZT = S2σT/κ encompassing the Seebeck coefficient (S), electrical conductivity (σ), and thermal conductivity (κ), the last having contributions from lattice vibrations (κL) and charge carriers (κe).

Commercial thermoelectric devices are constructed from bismuth telluride, appropriately doped to produce the n- and p-type variants. However, the low abundance (1 ppb) and availability of tellurium[1,2] presents a barrier to the use of telluride-based devices in large-volume applications. Moreover, bismuth telluride exhibits its highest performance close to room temperature. Performance falls off at higher temperatures, making such devices unsuitable for applications at elevated temperatures, including the region 373 ≤ T/K ≤ 573, where it has been estimated that ca. 80% of industrial waste heat is released.[3]

The search for new high-performance alternatives to bismuth telluride has led to the emergence of a number of design strategies. These include effecting reductions in thermal conductivity through the introduction of species with low-energy localized vibrational modes (the phonon–glass electron crystal (PGEC) approach),[4] the manipulation of interface scattering of phonons through grain-boundary engineering,[5] the introduction of nanoinclusions[6] or the formation of nanocomposites with a second phase,[7] or bringing about a liquid-like state of one sublattice in a crystalline material (the phonon–liquid electron crystal (PLEC) approach).[8] Similarly, electronic properties have been targeted through band structure modifications including the creation of resonant states,[9] energy filtering,[10] increasing the carrier effective mass through magnetic interactions,[11] enhancing the power factor through spin fluctuations of itinerant electrons,[12] or exploiting low dimensionality to enhance the Seebeck coefficient.[13]

Much of the recent interest in the development of alternatives to bismuth telluride has focused on sulfides due in part to the high abundance of sulfur (350,000 ppb).[1] A number of recent reviews[14−18] of sulfide thermoelectrics underline the significant advances achieved in p-type materials. Figures-of-merit which approach unity at elevated temperatures have been achieved in derivatives of tetrahedrite (ZT ≈ 1.0 at 723 K)[19] and colusite (ZT ≈ 0.93 at 675 K),[20] while the copper-deficient binary phases, Cu2–S show even higher performance (ZT = 1.7 at 1000 K).[21]

Progress in n-type materials has generally been less marked. Compared to their p-type counterparts, the figures-of-merit of n-type materials are more modest. The n-type materials such as Bi2S3 (ZT = 0.6 at 760 K),[22] MnBi4S7 (ZT = 0.21 at 700 K),[23] and chalcopyrite-related phases (ZT = 0.33 at 700 K),[24] are among those with the highest figures-of-merit.

In the search for new n-type materials, we have sought to exploit the highly structured density of states N(E) that result from low dimensionality in materials with the shandite structure. Shandite-type phases, A3M2S2 (A = Ni, Co, Rh, Pd; M = Pb, In, Sn, Tl), adopt a structure[25] containing a kagome-like network of corner-sharing A3 triangles, with M atoms located in sites of 6-fold coordination by A (Figure ). Each A3 triangle is capped by a sulfur atom. Additional M atoms are located in trigonal antiprismatic interlayer sites, linking kagome layers into a three-dimensional structure. In addition to fundamental studies to characterize the formal oxidation states in shandites,[26−29] materials in this family have attracted considerable interest for their electronic structure and properties[27,30−32] and magnetic properties[33−35] including the recent observation of more exotic phenomena such as Weyl semi-metal- and skyrmion-type behaviors.[36−39]

Figure 1

Shandite structure adopted by Co3Sn2S2. Cobalt-centered trigonal antiprisms are shown as blue polyhedra; cobalt, tin, and sulfur atoms, as blue, magenta, and yellow circles.

The low-dimensional character of the kagome layers is reflected in a density-of-states N(E) that in the vicinity of the Fermi level, EF, exhibits sharp, narrow bands, which band structure calculations reveal to be of predominantly Co d-character with small contributions from Sn 5p and S 3p states.[40] Since the Seebeck coefficient is proportional to the derivative of N(E) at EF, through the Mott relation,[41] tuning EF to a sharp discontinuity in N(E) may offer a means of increasing the Seebeck coefficient.[42] Indeed the resulting sharp peak in N(E) of Co3Sn2S2 at EF may contribute to the relatively high Seebeck coefficient of the ternary phase.[43]

We have recently shown the applicability of such an approach by demonstrating that enhancements in thermoelectric performance can be realized by tuning EF through the substitution of tin by indium in the series Co3Sn2–InS2.[44] This produces an almost 3-fold improvement in the room-temperature figure-of-merit in Co3Sn1.15In0.85S2 (ZT = 0.2) over that of the end-member phase Co3Sn2S2.[40]

In a complementary approach to the tuning of electronic properties through manipulation of the position of EF, we have explored chemical substitution at the transition-metal site (A-site).[45] While electron doping through nickel substitution in Co3–NiSn2S2 (0 ≤ x ≤ 3) leads to loss of thermoelectric performance, as materials become more metallic, hole doping through the partial replacement of cobalt by iron in Co3–FeSn2S2 (0 ≤ x ≤ 0.6) leads to performance enhancements. The power factor of Co2.4Fe0.6Sn2S2 reaches 10.3 μW cm–1 K–2 close to room temperature and ZT = 0.2 is achieved at 523 K in Co2.6Fe0.4Sn2S2. Given the comparative dearth of n-type sulfide thermoelectrics,[14] we have sought to achieve further enhancements in thermoelectric performance through substitution of tin by indium in n-type iron-substituted (x ≤ 0.5) phases, Co3–FeSn2–InS2. Here we report that this strategy results in n-type materials with figures-of-merit that approach ZT = 0.3 at temperatures in the critical 373 ≤ T/K ≤ 573 region.

Experimental Section

Materials of composition Co2.5+Fe0.5–Sn2–InS2 (x = 0, 0.167; 0.0 ≤ y ≤ 0.7) were prepared by high-temperature synthesis from the powdered elements. Mixtures of cobalt (Alfa Aesar, powder, 99.8%), iron (Sigma-Aldrich, powder, 99.9%), tin (Sigma-Aldrich, powder, ≥99%), indium (350 mesh, Alfa, 99.99%), and sulfur (Sigma-Aldrich, flakes, 99.99%) of appropriate stoichiometry were ground in an agate pestle and mortar, prior to sealing into evacuated (10–4 mbar) fused-silica tubes. Mixtures were fired initially for 48 h at 773 K and subsequently, following an intermediate regrinding, at 973 K for a further 48 h. A heating/cooling rate of 0.5 K min–1 was used.

Powder X-ray diffraction data for the products were collected using a Bruker D8 Advance diffractometer, operating with Ge-monochromated Cu Kα1 radiation (λ = 1.5406 Å) and equipped with a LynxEye linear detector. Diffraction data were collected over the angular range 10 ≤ 2θ/° ≤ 120, counting for 3.6 s at each increment of 2θ = 0.018° in detector angle. Powder X-ray diffraction data were analyzed by the Rietveld method, as implemented in the General Structure Analysis System (GSAS) program.[46]

Powder samples were consolidated into pellets by hot pressing for 25 min in graphite molds at 973 K and 60 bar under a nitrogen atmosphere, using equipment constructed in-house. The resulting pellets have a diameter of ca. 12.7 mm and a thickness of ca. 2 mm. The density of the consolidated pellets was determined by the Archimedes method using an AE Adam PW 184 balance. Densities in excess of 98% of the crystallographic value were achieved for all materials.

Electrical resistivity and Seebeck coefficient data were collected simultaneously using a Linseis LSR3-800 system. Data were collected in 10 K intervals over the temperature range 303 ≤ T/K ≤ 673. A current of 100 mA was used for the four-probe resistivity measurements and a temperature gradient of 50 K applied for the determination of Seebeck coefficients. Thermal diffusivity data in the temperature range 300 ≤ T/K ≤ 575 were obtained using a Netzsch LFA 447 Nanoflash instrument. Data were collected in 25 K increments on circular pellets coated with graphite. The thermal conductivity was calculated using values of the heat capacity (0.365–0.368 J g–1 K–1, depending on composition) obtained by application of the Dulong–Petit law. A recent round-robin exercise suggests uncertainties in measured resistivities, Seebeck coefficients, and thermal conductivities of 8%, 6%, and 11%, respectively, leading to a 19% uncertainty in ZT.[47]

Results and Discussion

Powder X-ray diffraction data for compositions Co2.5Fe0.5Sn2–InS2 reveal that the shandite structure is adopted throughout the composition range 0 ≤ y ≤ 0.6. Similar behavior is observed in materials with higher cobalt content, Co2.667Fe0.333Sn2–InS2, over the composition range 0.0 ≤ y ≤ 0.7. The previously refined structures of the corresponding indium-free materials Co2.5+Fe0.5–Sn2S2 (x = 0.0, 0.2)[45] were used to provide the initial structural models for Co2.5+Fe0.5Sn2–InS2 phases, described in the space group R3̅m. Similar atomic numbers of tin and indium prevent discrimination between these two elements by X-ray methods. However, a previous investigation of Co2Sn2–InS2 (0 ≤ y ≤ 2) by neutron diffraction and DFT has revealed that indium shows a preference for trigonal prismatic, interlayer sites over those in the kagome layer.[40] Site occupancy factors for the two main-group elements were therefore set according to the corresponding distribution in the iron-free materials. Thermal parameters of all elements were constrained to be equivalent and site occupancy factors fixed at those corresponding to the nominal compositions. Refinement proceeded smoothly, resulting in Rwp values of 2.8–3.1% and χ2 in the range 1.26–1.47. Representative profiles appear in Figure , with the remaining provided as Supporting Information, while final refined parameters are presented in Table .

Figure 2

Final observed (crosses), calculated (full line), and difference (lower full line) X-ray profiles for Co2.667Fe0.333Sn1.4In0.6S2. Reflection positions for the shandite phase are indicated by the upper set of vertical markers, while the lower set of markers refers to the SnIn4S4 impurity phase (ca. 4.4 wt %).

Table 1

Refined Parameters from Rietveld Analysisa of Powder X-ray Diffraction Data for (a) Co2.667Fe0.333Sn2–InS2 (0.2 ≤ y ≤ 0.7) and (b) Co2.5Fe0.5Sn2–InS2 (0.2 ≤ y ≤ 0.6)

y	a/Å	c/Å	V/Å3	S(z)	Uiso/Å2	Rwp/%	χ2
(a) Co2.667Fe0.333Sn2–yInyS2
0.2	5.35723(3)	13.2450(1)	329.203(5)	0.2833(3)	0.51(4)	3.0	1.41
0.3	5.35086(3)	13.2755(1)	329.17(1)	0.2828(3)	0.49(4)	2.8	1.25
0.4	5.34507(9)	13.3102(2)	329.32(1)	0.2829(3)	0.14(4)	3.0	1.26
0.5	5.33903(4)	13.3451(1)	329.441(6)	0.2820(3)	0.57(4)	3.0	1.37
0.6	5.33310(4)	13.3779(1)	329.516(6)	0.2819(3)	0.63(3)	2.8	1.28
0.7	5.32931(4)	13.4098(1)	329.833(6)	0.2817(3)	0.18(4)	3.1	1.47
(b) Co2.5Fe0.5Sn2–yInyS2
0.2	5.35674(3)	13.2564(1)	329.424(5)	0.2831(3)	0.76(4)	2.8	1.29
0.4	5.34644(4)	13.3197(1)	329.727(6)	0.2832(3)	0.58(4)	2.9	1.26
0.5	5.33952(8)	13.3538(2)	329.72(1)	0.2816(3)	0.62(4)	3.0	1.26
0.6	5.33508(4)	13.3930(1)	330.133(6)	0.2821(3)	0.30(4)	3.1	1.42

Space group: R3̅m. Co/Fe on 9d (1/2,0,1/2), Sn(1) on 3a(0,0,0), Sn(2) on 3b (0,0,1/2), and S on 6c (0,0,z).

The compositional dependence of the lattice parameters of the two series of materials, Co2.5+Fe0.5–Sn2–InS2 (x = 0.0, 0.133) is similar (Figure ). In particular, the crystallographic c-parameter increases with increasing indium content, corresponding to an increase in the separation between kagome layers, while the in-plane a-parameter decreases slightly. An in-plane contraction on hole doping has been attributed to electronic factors, arising from the depopulation of antibonding states of predominantly d and d character in the vicinity of the Fermi level.[40]

Figure 3

Compositional variation of the lattice parameters of Co2.667Fe0.333Sn2-yInS2 (upper plot) and Co2.5Fe0.5Sn2–InS2 (lower plot), determined from Rietveld analysis of powder X-ray diffraction data at room temperature.

The introduction of holes through the substitution of tin by indium increases the electrical resistivity for both series (Figures and 5) as the upper conduction band is progressively depopulated. With increasing indium content, the weak temperature dependence of ρ(T) at y = 0.0, for which dρ/dT is positive, is progressively transformed to temperature-dependent, semiconducting ρ(T) behavior (dρ/dT negative). The resistivity at room temperature is increased by a factor of more than three across the series, with cobalt contents corresponding to x = 0.0, and by a similar factor for the series with x = 0.133.

Figure 4

Temperature dependence of electrical resistivity (upper plot) and Seebeck coefficient (lower plot) of Co2.5Fe0.5Sn2–InS2 phases (0.0 ≤ y ≤ 0.6).

Figure 5

Temperature dependence of electrical resistivity (upper plot) and Seebeck coefficient (lower plot) of Co2.667Fe0.333Sn2–InS2 phases (0.2 ≤ y ≤ 0.7).

The Seebeck coefficient (Figures and 5) is negative for all compositions investigated, consistent with the dominant charge carriers being electrons. These materials therefore provide a comparatively rare example of an n-type sulfide. The absolute value of the Seebeck coefficient, |S|, increases with increasing indium content in both series investigated, consistent with the gradual loss of metallic behavior on substitution of tin with indium. Moreover, the S(T) dependence becomes increasingly linear with increasing indium content, suggesting the more heavily substituted materials are degenerate semiconductors.

The power factors (S2σ) of the indium-containing phases (Figure ) exhibit a relatively weak temperature dependence, which contrasts with the behavior of indium-free (Co,Fe)3Sn2S2 phases.[45] For example, the power factor for Co2.5Fe0.5Sn1.8In0.2S2 shows a maximum variation of ca. 1.3 μW cm–1 K–2 over the whole of the temperature range investigated: the variation in the more cobalt-rich phase Co2.667Fe0.333Sn1.7In0.3S2, being similar. In both series, the power factor initially increases with indium substitution before decreasing at higher indium contents, suggesting there is an optimum carrier concentration. Efforts to measure the carrier concentration by Hall effect measurements were hampered by difficulties in obtaining suitable contacts.

Figure 6

Thermoelectric power factors (S2σ) for Co2.5Fe0.5Sn2–InS2 (0.0 ≤ y ≤ 0.6, upper plot) and Co2.667Fe0.333Sn2–InS2 phases (0.2 ≤ y ≤ 0.7, lower plot).

The thermal conductivity of materials of general formula Co2.5Fe0.5Sn2–InS2 (0.0 ≤ y ≤ 0.6) decreases with indium substitution (Figure ), although, at the highest temperatures, the thermal conductivity of all phases tends toward a common value of 3.5–3.6 W m–1 K–1. The lowest thermal conductivity is attained at a composition with 0.5 ≤ y ≤ 0.6. The series Co2.667Fe0.333Sn2–InS2 (0.0 < y ≤ 0.7) shows a similar decrease in thermal conductivity with indium substitution (Figure ), with the lowest values, of the order 3.0–3.1 W m–1 K–1, occurring at compositions in the region 0.6 ≤ y ≤ 0.7. Using the Wiedemann–Franz law (L0 = 2.44 × 10–8 W Ω K–2), the electronic contribution (κe) to the thermal conductivity was determined and the lattice contribution (κL) calculated as the difference (κ – κe). This demonstrates that the reduction in thermal conductivity that occurs across both series is principally due to the reduction in κe, with κL showing a much weaker compositional dependence (Figures S3 and S4). This is consistent with the expectation that little mass-fluctuation scattering will result from the replacement of tin with an element, indium, of similar atomic mass.

Figure 7

Temperature dependence of the total thermal conductivity (κ) of Co2.5Fe0.5Sn2–InS2 phases (0.0 ≤ y ≤ 0.6, upper plot) and Co2.667Fe0.333Sn2–InS2 phases (0.2 ≤ y ≤ 0.7, lower plot)

Combining the electrical-transport property data with the measured thermal conductivities enables calculation of the thermoelectric figure-of-merit, ZT (Figure ). Hole doping in the series Co2.5Fe0.5Sn2–InS2 leads to an increase in the figure-of-merit at temperatures below 500 K, with a maximum value of ZT = 0.23 being achieved for Co2.5Fe0.5Sn1.6In0.4S2 at 500 K. This can be associated principally with the improvement in power factor since the thermal conductivity of this substituted phase (3.35 W m–1 K–1) is comparable with that of the indium-free end-member (3.45 W m–1 K–1) at this temperature.

Figure 8

Temperature dependence of the thermoelectric figure-of-merit for Co2.5Fe0.5Sn2–InS2 (0.0 ≤ y ≤ 0.6, upper plot) and Co2.667Fe0.333Sn2–InS2 phases (0.2 ≤ y ≤ 0.7, lower plot).

Slightly greater enhancements in the figure-of-merit are observed in the series Co2.667Fe0.333Sn2–InS2, with the maximum ZT = 0.29, being obtained for the composition Co2.667Fe0.333Sn1.6In0.4S2 at 573 K. The compositional dependence of the figure-of-merit (Figure ) mirrors that of the power factor, increasing gradually to y = 0.6, before an abrupt decrease at y = 0.7, due principally to the increase in electrical resistivity. The increase in the figure-of-merit up to compositions with y = 0.6 can be associated with the marked increase in the absolute value of the Seebeck coefficient that occurs with increasing hole concentration, while the increased electrical resistivity has a marked impact on κe, the reduction of which combines with the increase in power factor to raise ZT.

The partial replacement of cobalt by iron in the end-member phases Co2.5Fe0.5Sn2S2 and Co2.667Fe0.333Sn2S2 leads to the creation of holes and depopulation of the conduction band. The subsequent substitution of tin by indium, introduces additional holes. Therefore, the total hole content in the series Co2.5+Fe0.5–Sn2–InS2 is given by (0.5 – x) + y. Comparison of the two nonstoichiometric series presented here reveals that the optimum figures-of-merit are exhibited by compositions corresponding to (0.5 – x) + y in the range 0.7–0.9 holes per formula unit. In the previously reported series Co3Sn2–InS2 the maximum figure-of-merit in the temperature range 400 ≤ T/K ≤ 500 occurs at x = 0.8. The parent phase, Co3Sn2S2, has 47 valence electrons. Band structure calculations[31,40] reveal that the Fermi level crosses the narrow half-occupied 24th (conduction) band. Hole doping, through substitution, at either the transition-metal or main-group metal site, removes electrons from this band moving EF toward the band edge, until at a level of 1 hole per formula unit, the 24th band is completely depopulated, EF moves into the band gap, and the material becomes a semiconductor. Further doping can shift EF into the lower energy 23rd valence band, leading to the re-emergence of a metal-like state.[44] A hole concentration of 0.7–0.9 positions EF near the lower energy edge of the conduction band, where the high degree of curvature may be the origin of the high Seebeck coefficient. Band structure calculations indicate that the conduction band is predominantly of d-character, with relatively little contribution from the p orbitals of the main-group metal.[40] The partial replacement of cobalt by iron may have an impact on the detailed form of this band and cause the critical region in which tuning of EF optimizes the Seebeck coefficient to move to lower energies. The maximum thermoelectric response may then require a higher hole content in doubly substituted materials, than in materials where substitution is carried out at the main-group site only.

As noted above the performance of n-type materials lags behind that of their p-type counterparts, representing a barrier to construction of an all-sulfide thermoelectric device. For example, while Bi2S3, doped with BiCl3, exhibits a maximum ZT ≈ 0.6 at 760 K,[22] it shows a lower performance at temperatures in the region (373 ≤ T/K ≤ 573), appropriate to energy harvesting from waste heat associated with industrial processes (ZT ≈ 0.25 at 473 K). Much of the focus on n-type sulfides has been directed toward phases related to chalcopyrite (CuFeS2)[14] and attempts to optimize the carrier concentration through chemical substitution.[48,49] Figures-of-merit in the range of 0.1 ≤ ZT ≤ 0.2 have been achieved at temperatures in the range 400 ≤ T/K ≤ 700. While ZT = 0.33 has been reported for Cu0.97Fe1.03S2,[24] this is at 700 K, significantly above the temperatures relevant to industrial waste heat. In the temperature range 373 ≤ T/K ≤ 573, a figure-of-merit that approaches ZT = 0.3 in the shandite-related materials reported here, exceeds that of the majority of candidate n-type sulfides that have been explored (Figure ). Materials derived from shandite may therefore offer an alternative n-type sulfide material for thermoelectric applications in the midrange of temperatures.

Figure 9

Comparison of the thermoelectric figure-of-merit of Co2.667Fe0.333Sn1.6In0.4S2 at 473 K, the midpoint of the range at which the majority of industrial waste heat is released, with that of other candidate thermoelectric materials, Bi2S3,[22] Cu4Sn7S16,[50] Cu0.02TiS2,[51] CuTi1.4Co0.6S4,[52] Cu2CoTi3S8,[53] CuFe2S3,[54] CuFeS1.8,[55] and MnBi4S7.[23]

Conclusions

We demonstrate that hole doping through simultaneous substitution at the transition-metal and main-group metal atom site in Co3Sn2S2 results in an increase in the thermoelectric figure-of-merit to a value that approaches ZT = 0.3 at temperatures as low as 473 K. Such materials are competitive with the more intensively investigated chalcopyrite-type and Bi2S3-type n-type phases. Materials such as Co2.667Fe0.333Sn1.4In0.6S2 are therefore attractive candidates for further optimization of thermoelectric properties through techniques such as nanostructuring and nanocompositing to reduce the comparatively high thermal conductivity, without impacting unduly on the promising electrical properties.