Enhancement of the thermoelectric performance via defect formation and device fabrication for Cu₂₆Ti₂(Sb,Ge)₆S₃₂ colusite

Abstract

A copper-based multicomponent sulphide, Cu₂₆Ti₂(Sb,Ge)₆S₃₂ colusite, is a promising thermoelectric material. We investigated the effects of sulphur deficiency on the crystal structure, electronic structure, and thermoelectric properties in the series Cu₂₆Ti₂Sb₄Ge₂S_32−x. By combining experiments and ab initio calculations, we found that sulphur deficiency induced the formation of interstitial Cu atoms in the sphalerite-like framework of Cu₂₆Ti₂Sb₄Ge₂S₃₂. This resulted in a decrease in the hole carrier concentration and a susbtantial enhancement of ZT up to unity at 673 K. We also fabricated a power generation device composed of the sulphur-deficient colusite, Ni–Sb-based compounds (interface material), and Ni. The maximum conversion efficiency of the device reached 3.2% with a temperature difference of 266 K.

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1 Introduction

There has been growing concern about ever-increasing energy consumption and the resulting serious environmental issues. Thermal-to-electrical energy conversion techniques are important for improving energy efficiency and decreasing carbon footprint emissions. As such a technique, thermoelectric (TE) power generation, which enables the direct conversion from heat into electricity, has gained growing attention.¹ TE energy conversion is based on the Seebeck effect, in which a temperature difference causes an electromotive force (voltage). The voltage, ΔV, is proportional to the temperature difference ΔT across the solid-state device as ΔV = −SΔT, where S is the Seebeck coefficient. To obtain a large output power, a high output voltage as well as low internal resistance are required for the device. Furthermore, low thermal conductance is a requisite characteristic for the device to decrease heat flow that does not contribute to power generation. Consequently, materials used in TE devices should have large S, low electrical resistivity, ρ, and low thermal conductivity, κ. By combining these parameters (S, ρ, and κ), the performance of TE materials can be expressed as ZT = S²ρ⁻¹κ⁻¹T, which is referred to the dimensionless figure of merit. Here, S²ρ⁻¹ is referred to the power factor, and κ is the sum of its electronic component κ_ele and lattice component κ_lat.

To achieve large-scale, cost-effective, and environmentally friendly TE applications, materials must not only be high-performing but also composed of constituent elements that are non-toxic, environmentally benign, and low-cost. Examples include Mg-based compounds (Mg₃(Bi,Sb)₂,^2–4 MgAgSb,^5–7 and Mg₂(Si,Sn)^8–10), Half-Heusler compounds (MNiSn and MCoSb, with M = Ti, Hf, Zr, and NbFeSb),^11–13 and sulphides (Cu-based,^14–16 Bi-based,^17,18 and Ti-based compounds^19–22). Cu-based sulphides have emerged as promising p-type TE materials, and their TE properties have been studied extensively since ∼2010. The worldwide research led to significant advances in TE Cu-based sulphides (e.g., chalcosite (Cu₂S),²³ digenite (Cu_1.8S),²⁴ tetrahedrite (Cu₁₂Sb₄S₁₃),^25,26 and colusite (Cu₂₆T₂M₆S₃₂ (T = Ti, V, Nb, Ta, Cr, Mo, W; M = Ge, Sn, Sb))^27–33 with ZT reaching ∼0.5–1 at 673 K. However, less effort has been devoted to the fabrication of TE devices/modules^34–36 unlike the Mg-based compounds^37–39 and Half-Heusler compounds.^11,13,40 To maximize the conversion efficiency of a TE module, it is crucial to minimize the electrical and thermal contact resistance between the TE material and the electrodes that connect the devices in series. It is often necessary to insert interface materials between the TE material and the electrode, and identification of the more suitable materials is critically important.

We have recently discovered a colusite, Cu₂₆Ti₂Sb₆S₃₂, which showed semiconducting properties and low κ_lat.³² The substitution of Ge⁴⁺ for Sb⁵⁺ increased the hole carrier concentration, n, leading to the enhancement of S²ρ⁻¹. The combination of large S²ρ⁻¹ and low κ_lat resulted in a ZT value of 0.9 at 673 K. From our subsequent investigations on Cu₂₆Ti₂Sb_6−xGe_xS₃₂, we found that the previously studied samples³² most probably present sulphur deficiency due to inadequate recovery of the sulphur residuals produced during the synthesis (reaction) process. In this study, we therefore investigated how the sulphur deficiency affects the crystal structure, electronic structure, and TE properties through experiments and ab initio calculations.

We then fabricated TE devices using the Cu₂₆Ti₂Sb_6−xGe_xS₃₂ colusites. In our previous study,³⁴ we explored diffusion barrier materials from pure metals and reported that a single-leg device of Cu₂₆Nb₂Ge₆S₃₂ with Au layers (diffusion barrier layers) showed low contact resistance at the Au/colusite interface and a TE conversion efficiency of 3.3% at a temperature difference of ΔT∼270 K. However, an issue arose from the macroscopic diffusion of Au into the colusite matrix. Specifically, the ΔV generated from the device was lower than the ΔV predicted based on the material's properties. Continued efforts are required to address this issue, while the exploration of diffusion barrier/interface materials holds comparable importance. In this study, we selected Ni as a diffusion barrier material. Ni is known to be reluctant to interdiffuse with Ag,⁴¹ which is often used as a paste/electrode material. However, direct hot-press bonding between Cu₂₆Ti₂Sb_6−xGe_xS₃₂ colusites and Ni was unsuccessful due to a reaction between the materials. Consequently, we explored interface materials to be placed between the colusite and Ni. As effective interface materials often share elements with TE materials (e.g., MgCuSb for MgAgSb, NiTe₂ for Bi_0.5Sb_1.5Te₃, and CoAl for CoSb₃),⁴² we selected Sb-based compounds, more specifically the Ni–Sb system (NiSb and NiSb₂) with metallic properties,⁴³ as potential candidates of interface materials for the colusite containing Sb.

2 Experimental procedures

2.1 Sample synthesis and device fabrication

We synthesized the samples with compositions of Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 0, 0.5, 1.0, 1.5). The elements (Cu, 99.99%, wire; Ti, 99.99%, powder; Sb, 99.9999%, grain; S, 99.99%, powder) were sealed in an evacuated quartz tube. The tube was heated to 1173 K, maintained at this temperature for 24 h, and subsequently cooled to room temperature (RT). Yellow solids (sulphur) remaining in the quartz tube were thoroughly collected. The reaction product and sulphur were manually crashed and mixed using an agate mortar and then molded into a pellet by cold pressing. The pellet was sealed in an evacuated quartz tube and subjected to heat treatment at 823 K for 50 h. The annealed sample was manually crushed and then pulverized by using a planetary ball mill (Pulverisette 7 premium line, Fritsch) at a disk rotation speed of 450 rpm for 1 h. The powder was ball-milled in a jar with an inner volume of 20 mL together with seven balls of 10 mm diameter in an Ar atmosphere. The jar and balls were made of tungsten carbide (WC). The obtained powder was loaded into a WC die with an inner diameter of 10 mm, which was placed in a sintering furnace (PLASMAN CSP-I-03121, S. S. Alloy). Hot-press sintering was performed at 773 K for 1 h in a flowing N₂ atmosphere under a uniaxial pressure of 200 MPa. The sintered sample was cut and polished into bars and disks for the measurement of TE properties. The relative density d of samples was evaluated as 100 × d_s/d_t in %, where d_s is the bulk density and d_t is the crystal density calculated as the ratio of the mass of a unit cell based on the starting composition (Cu₂₆Ti₂Sb₄Ge₂S_32−x) to the unit cell volume obtained from the X-ray diffraction analysis (Section 3.1).

Ni–Sb compounds (NiSb, NiSb₂, and Cu/Co-substituted NiSb: Ni_0.9Cu_0.1Sb and Ni_0.9Co_0.1Sb) were synthesized by directly reacting the elements (Ni, 99.9%, powder; Co, 99.9%, powder; Cu, 99.9%, powder; Sb, 99.9999%, powder). The elements were mixed and then molded into a pellet, which was sealed in an evacuated quartz tube. The pellet was heated to 1323 K, maintained at this temperature for 24 h, cooled to 873 K, maintained at this temperature for 100 h, and then cooled to RT.

The powders of Cu₂₆Ti₂Sb₄Ge₂S_31.5 (ball-milled), Ni–Sb based compounds, and Ni were placed in a WC die to form 5 layers in the order Ni/Ni–Sb/Cu₂₆Ti₂Sb₄Ge₂S_31.5/Ni–Sb/Ni and hot-pressed under the aforementioned conditions to fabricate the TE devices. The obtained pellet was cut and polished into bars for the measurement of power generation properties.

2.2 Characterization

The crystal phases in the sintered samples of Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 0, 0.5, 1.0, 1.5) and the samples of Ni–Sb-based compounds were identified by powder X-ray diffraction (PXRD). The PXRD data were collected in the range 10° ≤ 2θ ≤ 100° using a diffractometer (Miniflex600, RIGAKU) with a CuKα radiation source. The lattice parameters were obtained by the Rietveld analysis using a program (Rietan-FP).⁴⁴ High-temperature PXRD measurements were performed using a heating stage (BTS500, Anton Paar) equipped in the diffractometer under a flowing N₂ atmosphere up to 573 K to investigate lattice parameter evolution. More detailed phase identification was performed for the colusite samples. The data were collected in the range 5° ≤ 2θ ≤ 120° using a diffractometer (D8 Advance, Bruker) with a CuKα₁ (Ge(111) monochromator) radiation source. The data were analysed by Rietveld refinement using the FullProf and WinPlotr software packages.^45,46

The surface morphologies and chemical compositions of the sintered samples were investigated by scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDS). SEM and EDS were performed using a microscope (JCM-6000Plus NeoScope, JEOL).

2.3 Electrical and thermal property measurements and thermoelectric conversion efficiency evaluation

ρ and S were simultaneously measured by a four-probe DC method and a temperature differential method, respectively, at T = 300–673 K under a low-pressure He atmosphere using a measurement system (ZEM-3, ADVANCE RIKO). The Hall-effect measurement was performed using a four-probe (Hall-bar geometry) DC method using a laboratory-built system with a permanent magnet generating a magnetic field of 0.63 T at RT. We calculated the carrier concentration n as R_H⁻¹e⁻¹, based on the single-carrier model, where R_H is the Hall coefficient and e is the elementary charge, respectively. Thermal diffusivity (α) was measured at T = 300–673 K in a flowing Ar atmosphere using a light flash apparatus (LFA-467 HT HyperFlash, Netzsch). These data were used to calculate κ = αC_DPd_s, where C_DP is the Dulong–Petit value of specific heat. κ data for previously synthesized “Cu₂₆Ti₂Sb₄Ge₂S₃₂” shown in this paper were recalculated using C_DP.

The resistance scanning measurement was performed for the device composed of Cu₂₆Ti₂Sb₄Ge₂S_31.5, Ni–Sb-based compounds, and Ni by a four probe AC method using a laboratory-built system with a movable voltage probe. The TE conversion efficiency η of the device was evaluated in a vacuum using a measurement system (Mini-PEM, ADVANCE RIKO). η was calculated as P/(P + Q_out), where P is the output power and Q_out is the heat released into the low-temperature heat bath through the sample. In this measurement, the hot-side temperature of the device was set at T_H = 321–566 K, while keeping the cold-side temperature at T_C = 295–300 K.

2.4 Electronic structure calculations

Ab initio calculations were performed for Cu₂₆Ti₂Sb₆S₃₂ and two derivative compositions incorporating a S vacancy (Cu₂₆Ti₂Sb₆S₃₁□, □: vacancy) or an interstitial Cu (Cu₂₇Ti₂Sb₆S₃₂), as described below. The plane-wave-basis projector augmented wave (PAW) method⁴⁷ implemented in the Vienna Ab initio Simulation Package^48,49 was used. To model exchange–correlation effects, we employed the Perdew–Burke–Ernzerhof (PBE) functional⁵⁰ within the generalized gradient approximation (GGA). To treat the interactions among localized 3d electrons in Cu, the GGA + U scheme⁵¹ was used, with a U value of 4.2 eV.⁵² The valence configurations of the PAW potentials are as follows: [3d¹⁰ 4s¹] for Cu, [3s² 3p⁶ 3d³ 4s¹] for Ti, [5s² 5p³] for Sb, and [3s² 3p⁴] for S. The remaining electrons were treated as frozen core electrons. The criterion for total energy convergence in the self-consistent electronic loop was set to 1.0 × 10⁻⁶ eV cell⁻¹. For structure optimization, atomic positions and lattice parameters were relaxed until atomic residual forces were <5.0 × 10⁻³ eV Å⁻¹. The first Brillouin zone was sampled using Monkhorst–Pack k-point grids of 4 × 4 × 4,⁵³ and the plane-wave energy cutoff was set at 420 eV.

We performed the calculations for pristine Cu₂₆Ti₂Sb₆S₃₂, Cu₂₆Ti₂Sb₆S₃₁□, and Cu₂₇Ti₂Sb₆S₃₂. The cubic structure (space group P4̄3n, no. 218) of Cu₂₆Ti₂Sb₆S₃₂ includes non-equivalent crystallographic sites: three for Cu (6d, 8e, 12f), one for Ti (2a), one for Sb (6c), and two for S (8e, 24i).^32,54 One S atom at 8e or 24i was removed from the crystal structure to construct two Cu₂₆Ti₂Sb₆S₃₁□ models, whereas one additional Cu atom was placed at unoccupied “interstitial” sites (6b, 24i) to construct two Cu₂₇Ti₂Sb₆S₃₂ models. The electronic band structures and density of states (DOS) were calculated for the five optimized structural models. For the band structure calculations, the reciprocal path for Cu₂₆Ti₂Sb₆S₃₂, as suggested by SeeK-path,⁵⁵ was applied to all models. This approach enables direct comparison of the electronic structures of the pristine and defect-containing models, although the defects break the original symmetry of Cu₂₆Ti₂Sb₆S₃₂. For the DOS calculations, a Γ-centred k-point mesh of 9 × 9 × 9 was employed. Note that, in our calculations, two electrons per f.u. were intentionally removed to adjust the number of hole carriers in these non-Ge-substituted models to those for experimental Ge-substituted composition Cu₂₆Ti₂Sb₄Ge₂S_32−x. This procedure is useful to exclude the influence of interactions between Ge and other defects and to facilitate a concise discussion of sulphur deficiency.

The formation energies of a Cu interstitial and an S vacancy were calculated from the energy differences between the defect models and the pristine model, where two electrons were removed from both models, while including the chemical potentials of Cu or S to account for the exchange of these atoms with their reservoirs (i.e., the competing phases). The chemical potentials of Cu and S were determined from the equilibrium conditions in the computed phase diagram.

3 Results & discussion

3.1 Crystal structure and chemical composition

PXRD patterns of Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 0, 0.5, 1.0, 1.5) samples (after hot pressing) are shown in Fig. 1. For the x = 0 and x = 0.5 samples, all the diffraction peaks were indexed to the colusite structure (cubic, P4̄3n), suggesting single phase samples, but the peaks were accompanied by a small shoulder at the lower angle side (Fig. S1). This result suggests inhomogeneous composition distribution. The peak asymmetry could be reproduced by assuming the existence of two colusite phases with and without Ge. For the x = 0 sample, the chemical compositions/fractions obtained by the Rietveld analysis were Cu₂₆Ti₂Sb_3.4(1)Ge_2.6(1)S₃₂/∼94 wt% and Cu₂₆Ti₂Sb_6.0(1)Ge_0.0(1)S₃₂/∼6 wt%. The former phase has a smaller lattice parameter, a, (10.7157(1) Å) than the latter phase (10.7536(3) Å), which probably results from the smaller ionic radius of Ge⁴⁺ compared to Sb⁵⁺. Another possibility is that the composition distribution is linked to the formation of sulphur-deficient (Cu-rich) colusite (see Section 3.3). In any case, the amount of the secondary phase is likely to be small. A similar result was obtained for the x = 0.5 sample. Such a shoulder, if it exists, could not be detected in the PXRD patterns for the x = 1.0 and x = 1.5 samples. The Rietveld refinements indicated that the x = 1.0 sample was composed of a single colusite phase, whereas the x = 1.5 sample is composed of colusite and small amount of tetrahedrite (Cu₁₂Sb₄S₁₃, <2 wt%). The traces of secondary phases (Ge-poor or sulphur-deficient colusite for x = 0 and x = 0.5, and tetrahedrite for x = 1.5) in the samples should have minor effects on the TE properties.

Fig. 1 X-ray diffraction patterns for the samples of Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 0, 0.5, 1.0, 1.5). A simulated pattern for Cu₂₆Ti₂Sb₆S₃₂ and the peak position for CuKα radiation are shown at the bottom. An arrow indicates a peak from Cu₁₂Sb₄S₁₃. The left inset shows the expanded views of the 622 peaks. The right panel shows the lattice parameter, a, as a function of x. The closed circles are the data in this study and the open square indicates the data of “Cu₂₆Ti₂Sb₄Ge₂S₃₂” in our previous study (see text).

The most prominent variation with x was an increase in a from 10.714 Å (x = 0, primary colusite phase) to 10.757 Å (x = 1.5). It should be noted that the sulphur deficiency was hard to be confirmed by the Rietveld analysis due to the strong interaction between the site occupation factors and the thermal parameters. Instead, EDS showed that the content of sulphur decreased with x, while those of cations (Cu, Ti, Sb, and Ge) were close to their nominal values (Table S1). It is noteworthy that the value of a for the previously synthesized “Cu₂₆Ti₂Sb₄Ge₂S₃₂” sample³² was between those for the x = 1.0 and x = 1.5 samples of Cu₂₆Ti₂Sb₄Ge₂S_32−x (inset of Fig. 1). This fact suggests sulphur deficiency in the previously synthesized sample. The defect species that are preferentially generated (sulphur vacancies or interstitial cations), their crystallographic sites, and the mechanism of lattice expansion were investigated by ab initio calculations (see Section 3.3).

3.2 Characteristics of bulk ceramics and thermoelectric properties

The TE properties were measured for the sintered samples, whose dense characteristics were proved by SEM (Fig. 2). The values of d were ∼99% for x = 0 and x = 0.5, whereas ∼101% and ∼103% for x = 1.0 and x = 1.5, respectively. The samples were indeed dense, but the latter excessive densities raised questions about the validity of the assumed compositions (starting compositions). The causes of this result are discussed in Section 3.3. SEM images of the fractured surface for the x = 0 and x = 1 samples showed that the grain size was less than 1 µm (Fig. 2). The relatively small grain size is attributed to the ball-milling process before sintering.

Fig. 2 Secondary electron images for (a) polished surfaces of the Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 0, 0.5, 1.0, 1.5) samples and (b) fractured surfaces of the x = 0 and x = 1 samples.

Fig. 3 displays the TE properties for Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 0, 0.5, 1.0, 1.5) and previously synthesized “Cu₂₆Ti₂Sb₄Ge₂S₃₂”.³² The x = 0 sample exhibited metallic behaviour in S and ρ (Fig. 3a and b). The values of S and ρ increased with increasing x, indicating a decrease in n. Indeed, the value of n obtained from Hall effect measurements at RT decreased from 3.5 × 10²¹ cm⁻³ (x = 0) to 2.4 × 10²¹ cm⁻³ (x = 0.5), 1.8 × 10²¹ cm⁻³ (x = 1.0) and 0.9 × 10²¹ cm⁻³ (x = 1.5). A similar trend in the electronic properties associated with sulphur deficiency was observed for colusite Cu₂₆Cr₂Ge₆S_32−δ.³¹ The values of S²ρ⁻¹ for Cu₂₆Ti₂Sb₄Ge₂S_32−x were equal to 1.4 mWK⁻² m⁻¹ at 673 K for the x = 0–1.0 samples, whereas it decreased to 0.97 mWK⁻² m⁻¹ for the x = 1.5 sample (Fig. 3c). The decrease in n with x led to the reduction in the electronic thermal conductivity, κ_ele (Table S2). As a result, the value of κ at 673 K decreased from 1.3 WK⁻¹ m⁻¹ (x = 0) to 0.62 WK⁻¹ m⁻¹ (x = 1.5) (Fig. 3d). The lattice thermal conductivity κ_lat was estimated by subtracting κ_ele from κ. Here the values of κ_ele were estimated from the Wiedemann–Franz law, κ_ele = LTρ⁻¹, where the Lorentz number L was calculated using an equation, L = 1.5 + exp(−|S|/116), based on a single parabolic band model with acoustic phonon scattering.⁵⁶ In the lower temperature region, κ_lat values for the x ≥ 0.5 samples were equivalent and slightly lower than that for the x = 0 sample (Fig. 3e). Because the morphology of the sample (grain size) was similar between x = 0 and x = 1.0, as mentioned above (Fig. 2), the κ_lat reduction can be attributed to the structural modification due to sulphur deficiency (see Section 3.3). The combination of high S²ρ⁻¹ and low κ led to relatively high ZT, which increased from 0.7 (x = 0) to 0.9 (x = 0.5) and 1.0 (x = 1.0, 1.5) at 673 K (Fig. 3f). The values of ρ, S, κ as well as ZT for the previously synthesized “Cu₂₆Ti₂Sb₄Ge₂S₃₂”³² were between those for x = 1.0 and x = 1.5 (Fig. 3), consistent with the XRD results, as discussed above.

Fig. 3 (a) Seebeck coefficient, S, (b) electrical resistivity, ρ, (c) power factor, S²ρ⁻¹, (d) thermal conductivity, κ, (e) lattice thermal conductivity, κ_lat, and (f) dimensionless figure of merit, ZT, for the samples of Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 0, 0.5, 1.0, 1.5). The closed circles are the data in this study and the open squares indicate the data of “Cu₂₆Ti₂Sb₄Ge₂S₃₂” in our previous study (see text).

3.3 Possible defects

We performed ab initio calculations for the pristine model (Cu₂₆Ti₂Sb₆S₃₂), two sulphur vacancy models (Cu₂₆Ti₂Sb₆S₃₁□), and two Cu interstitial models (Cu₂₇Ti₂Sb₆S₃₂) (see Section 2.4). In these calculations, two electrons were intentionally removed from the models to simulate the hole concentration of the experimentally Ge-substituted samples. As a result, the pristine model exhibited a p-type degenerate semiconducting electronic structure (Fig. 4 and S2), consistent with the metallic properties observed in Cu₂₆Ti₂Sb₄Ge₂S₃₂ (Fig. 3).

Fig. 4 (a) Relaxed structures of Cu₂₆Ti₂Sb₆S₃₂ and Cu₂₇Ti₂Sb₆S₃₂. For the latter, a copper atom was placed at the 24i (interstitial) site. (b) Electronic band dispersion relations and element-projected density of states for Cu₂₆Ti₂Sb₆S₃₂ and Cu₂₇Ti₂Sb₆S₃₂.

First, we compared the stability of two sulphur vacancies at two different sites. The formation energy of a sulphur vacancy at the 8e site was found to be higher (+1.8 eV) than that at the 24i site, indicating that the 8e-site vacancy is energetically less favourable. Because the 8e site locates in a rigid [TiS₄]Cu₆ tetrahedral–octahedral complex,^30,54 vacancy formation at this site is not preferred. The electronic structure of Cu₂₆Ti₂Sb₆S₃₁□ with the 24i-site sulphur vacancy exhibits degenerate semiconducting characteristics similar to those of Cu₂₆Ti₂Sb₆S₃₂ (Fig. S2). This result was contrary to our initial anticipation that a neutral sulphur vacancy would lead to electron doping. The relaxed structure (Fig. S3) and the orbital projected DOS for Sb (Fig. S4) suggest that the neutral sulphur vacancy on 24i site induces the formation of a 5s² lone pair in Sb, thereby reducing the valence state of Sb from +5 to +3. Considering that Sb atoms are in tetrahedral coordination of S(24i) in colusite, it is reasonable to consider that the lone pair of the Sb³⁺ cation compensate the sulphur vacancy to form an SbS(24i)₃LP polyhedron. Furthermore, only a slight increase in the calculated lattice parameter a (∼0.002 Å) was observed after removing the sulphur atom from the 24i site, which disagrees with the increase of lattice parameter, determined from the XRD analyses (Fig. 1). In addition, the localization of two electrons from the sulphur vacancy prevents any decrease in hole concentration, as evidenced by the unchanged Fermi level relative to the valence band maximum (Fig. S2). This result is also inconsistent with the experimental values of n decreasing with x (Fig. 3), suggesting that sulphur vacancy formation is unlikely under our synthesis conditions.

According to our previous studies,⁵⁷ sulphur deficiency (volatilization) is compensated by the incorporation of cations into the unoccupied interstitial 24i site of the sphalerite-like framework of colusite. Indeed, an interstitial Cu atom at the 24i site (Fig. 4a) is energetically more favourable than one at the 6b site, with a calculated formation energy lower by 0.17 eV. The 24i-site interstitial caused an increase in the calculated a of 0.030 Å, which is significantly larger than that of the sulphur vacancy model and agrees with the experimental observations (Fig. 1). A Cu-excess composition/structure, if present, explains the geometrical densities exceeding 100% of the theoretical ones (i.e. without interstitial cations, Section 3.2). In addition, the number of hole carriers decreased as the Fermi level shifts toward the band edge to maintain charge balance (Fig. 4b), which is consistent with the measured TE properties (Fig. 3). Therefore, structural modifications due to Cu interstitials probably occurred in the Cu₂₆Ti₂Sb₄Ge₂S_32−x (x > 0) samples. Indeed, the formation energy of a Cu interstitial is lower than that of an S vacancy under all equilibrium conditions in the computed phase diagram. For example, under an S-poor condition in equilibrium with Cu₁₂Sb₄S₁₃, Cu₇S₄, and Cu₂S, the formation energies are 0.23 eV and 0.53 eV, respectively. This indicates that Cu interstitials are more readily formed than S vacancies in the colusite. It is noteworthy that the value of κ_lat near the room temperature was reduced at x > 0 (Fig. 3e). This result indicates that the interstitial Cu acts as a phonon scattering center, as reported previously.^57,58

3.4 Device characterization

TE devices composed of colusite (Cu₂₆Ti₂Sb₄Ge₂S_31.5, i.e., x = 0.5), Ni–Sb, and Ni layers were fabricated as described in Section 2.1. The device containing NiSb₂ was fractured while being removed from the die after sintering (Fig. 5a), whereas the device with NiSb was successfully fabricated (Fig. 5b). The coefficient of volumetric thermal expansion of NiSb (4.56 × 10⁻⁵ K⁻¹), calculated from the temperature dependence of lattice parameters between 300 K and 573 K (Fig. 5c and S5), was comparable to that of the colusite (4.82 × 10⁻⁵ K⁻¹). In contrast, the value of thermal expansion for NiSb₂ (3.43 × 10⁻⁵ K⁻¹) was significantly smaller. The well-matched thermal expansion coefficients are likely responsible for the observed crack-free NiSb/colusite interface (Fig. 5b). However, resistance scanning data for the device with NiSb exhibited a large step (contact resistivity, R_c) of ∼13 mΩ mm² at the NiSb/colusite interface as shown in Fig. 5d. The sum of R_c at both sides of the device equals to ∼33% of cumulative electrical resistivity of the device. Conversely, R_c between Ni and NiSb was negligibly small. It is noteworthy that the linear trend in the resistance scanning data within the colusite layer indicates its chemical composition homogeneity.

Fig. 5 Sintered samples composed of (a) Ni, NiSb₂, and Cu₂₆Ti₂Sb₄Ge₂S_31.5 (col.) layers and (b) Ni, NiSb, and col. layers. In (b), a secondary electron image of one end of the device is shown. (c) Temperature dependence of unit cell volumes normalized at 300 K for Cu₂₆Ti₂Sb₄Ge₂S_31.5, NiSb₂, and NiSb. (d) Cumulative electrical resistivity, R, for the devices composed of Ni, NiSb-based compounds, and Cu₂₆Ti₂Sb₄Ge₂S_31.5 (col.). (e) Temperature dependences of maximum conversion efficiency, η_max, for the device with Ni_0.9Co_0.1Sb. The calculated η_max based on the TE properties of Cu₂₆Ti₂Sb₄Ge₂S_32−x (x = 1.0) is also shown in (e).

We then investigated how chemical substitution in NiSb influences R_c. The devices containing Cu- and Co-substituted NiSb showed no crack near the interfaces between the NiSb-based compounds and the colusite (Fig. S6). The devices with Ni_0.9Cu_0.1Sb and Ni_0.9Co_0.1Sb exhibited, respectively, higher R_c (∼30, ∼50 mΩmm²) and lower R_c (∼9 mΩmm²) at the NiSb-based compounds/colusite interfaces compared to the device with NiSb (Fig. 5d). The interfaces were analysed by SEM (Fig. S7). For the devices containing NiSb and Ni_0.9Cu_0.1Sb, thin NiSbS, Sb₂S₃, and multiphase layers were formed. Conversely, for the device with Ni_0.9Co_0.1Sb, only small amounts of (Ni,Co)SbS and Sb₂S₃ were detected. The NiSbS layer likely forms through the sulphurization of NiSb. Given that NiSbS itself possesses metallic characteristics,⁵⁹ the formation of the Sb₂S₃ layer is primarily responsible for the increase in R_c (Fig. 5d). In devices containing Ni_0.9Co_0.1Sb, the presence of a small amount of Sb₂S₃ should be responsible for a non-negligible R_c.

The R_c value for the device with Ni_0.9Co_0.1Sb was ∼9 mΩ mm² (Fig. 5d). The R_c remained nearly constant after annealing at 573 K for 50 h, but increased significantly as the annealing temperature was elevated to 623 K and 673 K (Fig. S8). After annealing, a thin (Ni,Co)SbS layer formed and its thickness increased with elevating the annealing temperature (Fig. S9). Its metallic characteristics would have limited impact on R_c. For the sample annealed at 673 K, Sb₂S₃ was clearly visible in a SEM image (Fig. S9). Therefore, the formation of Sb₂S₃ is primarily responsible for the observed increase in R_c, which is consistent with the claim made above.

For the unannealed device containing Ni_0.9Co_0.1Sb, the ρ value, estimated from the slope of the resistance scanning data, was 9.7 Ω m at RT. This value was slightly higher than that for x = 0.5 of Cu₂₆Ti₂Sb₄Ge₂S_32−x (colusite used for the devise, Cu₂₆Ti₂Sb₄Ge₂S_31.5) but was comparable to that for x = 1.0 (Fig. 3b). The increase in ρ for the colusite phase was probably attributed to a decrease in sulphur content due to the reaction between the colusite and Ni_0.9Co_0.1Sb during the sintering. We therefore compared the experimental power generation properties for the device to simulate results based on the TE properties of x = 1.0 (Fig. S10 and Tables S3, S4).

The power generation properties of the device with Ni_0.9Co_0.1Sb were investigated with T_H reaching up to 573 K, while T_C was maintained at ∼300 K (Fig. 5e and S11). The maximum output power, P_max, obtained from the voltage–current plot increased with increasing temperature difference ΔT and reached 23 mW at ΔT = 266 K (Fig. S11a and b). It should be noted that the open circuit voltage V_oc and internal resistance R_in were reversible between the heating and cooling processes (Fig. S11c and d), indicating the device's stability under the current measurement conditions. η_max = P/(P + Q_out) increased with increasing ΔT and reached 3.2% at ΔT = 266 K (Fig. 5e and S11e, f). This value is equivalent to η_max measured for a Cu₂₆Nb₂Ge₆S₃₂-based device (3.3%),³⁴ while is lower than that for Cu₂ZnSnS₄-based single crystals (4%).⁶⁰ η_max for an ideal device with the TE properties of x = 1.0, calculated using COMSOL Multiphysics® and a web simulator,⁶¹ was 5.7% when T_L and T_H were set at 300 K and 573 K, respectively (Fig. 5e and Table S4). Because the V_oc values were comparable between the experiment and calculation, the reduced η_max for the fabricated device can be mainly attributed to the non-negligible contact resistance between the colusite and Ni_0.9Co_0.1Sb (resulting in an increase in device resistance) and the consequent reduction in P (Fig. S11). The calculated η_max for x = 1.0 reached 8.1% at ΔT = 373 K (T_L = 300 K, T_H = 673 K) (Fig. 5e), highlighting its high potential for TE applications. While this value is comparable to or still lower than other promising materials, e.g., Mg-based compounds and Half-Heusler compounds,^{11,13,37,38,40} Cu₂₆Ti₂Sb₄Ge₂S_32−x could be a strong candidate for practical application if the interfacial material is optimized, given that its primary constituent elements (Cu and S) are low-toxicity, abundant elements.

4 Conclusions

In summary, we synthesized a series of polycrystalline colusites Cu₂₆Ti₂Sb₄Ge₂S_32−x and addressed the role of sulphur deficiency in the crystal structure, electronic structure, and TE properties. From experimental data and ab initio calculations, we demonstrated that sulphur deficiency in the nominal composition induced the formation of “interstitial” Cu within the sphalerite-like framework, which resulted in lattice expansion and a decrease in the hole carrier concentration. Fine tuning of the carrier concentration led to a significant increase in ZT. We also explored interface materials derived from Ni–Sb-based compounds and fabricated a TE device composed of Ni, Ni_0.9Co_0.1Sb, and Cu₂₆Ti₂Sb₄Ge₂S_32−x, whose maximum conversion efficiency reached 3.2% at a temperature difference of 266 K. Further explorations of interface materials/diffusion barrier materials will open pathways for practical applications of Cu–S-based TE materials.

Author contributions

Koichiro Suekuni: conceptualization, data curation, funding acquisition, investigation, project administration, resources, supervision, visualization, writing – original draft, writing – review and editing. Mei Yamamoto: investigation, visualization, writing – review and editing. Susumu Fujii: investigation, methodology, resources, funding acquisition, visualization, writing – review and editing. Pierric Lemoine: investigation, visualization, validation, writing – review and editing. Philipp Sauerschnig: data curation, investigation, writing – review and editing. Michihiro Ohta: data curation, funding acquisition, investigation, resources, writing – review and editing. Emmanuel Guilmeau: validation, writing – review and editing. Michitaka Ohtaki: resources, writing – review and editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: powder X-ray diffraction patterns, chemical compositions, hole carrier concentration and total thermal conductivity at room temperature, electronic band dispersion relations and density of states, relaxed structures used for the calculations, temperature dependence of lattice parameters, secondary electron images of devices, resistivity scanning data, details of the finite-element method simulation, measured and calculated power generation properties. See DOI: https://doi.org/10.1039/d5ta08599c.

Acknowledgements

This work was financially supported by JSPS KAKENHI (grant no. JP24H00415 (K.S.), JP25K01503 (K.S.), and JP22H04914 (S.F.)), the Thermal and Electric Energy Technology Foundation (K.S.), the Research and Development Program for Promoting Innovative Clean Energy Technologies through International Collaboration funded by NEDO (grant no. JPNP20005 (M.Ohta and K.S.)), JST FOREST (grant no. JPMJFR235X (S.F.)), and JST CREST (grant no. JPMJCR25S3 (K.S.)).

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