Realizing the Ultralow Lattice Thermal Conductivity of Cu₃SbSe₄ Compound via Sulfur Alloying Effect

Abstract

Cu₃SbSe₄ is a potential p-type thermoelectric material, distinguished by its earth-abundant, inexpensive, innocuous, and environmentally friendly components. Nonetheless, the thermoelectric performance is poor and remains subpar. Herein, the electrical and thermal transport properties of Cu₃SbSe₄ were synergistically optimized by S alloying. Firstly, S alloying widened the band gap, effectively alleviating the bipolar effect. Additionally, the substitution of S in the lattice significantly increased the carrier effective mass, leading to a large Seebeck coefficient of ~730 μVK⁻¹. Moreover, S alloying yielded point defect and Umklapp scattering to significantly depress the lattice thermal conductivity, and thus brought about an ultralow κ_lat ~0.50 Wm⁻¹K⁻¹ at 673 K in the solid solution. Consequently, multiple effects induced by S alloying enhanced the thermoelectric performance of the Cu₃SbSe₄-Cu₃SbS₄ solid solution, resulting in a maximum ZT value of ~0.72 at 673 K for the Cu₃SbSe_2.8S_1.2 sample, which was ~44% higher than that of pristine Cu₃SbSe₄. This work offers direction on improving the comprehensive TE in solid solutions via elemental alloying.

1. Introduction

Thermoelectric (TE) technology has the capability to directly and reversibly convert heat into electricity, making it a promising source of clean energy. It plays a significant role in addressing the challenges posed by the energy and environmental crises [1,2,3]. Numerous TE materials are currently under exploration for power generation and solid-state cooling applications, leveraging the Seebeck and Peltier effects, respectively [4], such as skutterudites [5], half-Heusler compounds [6], Zintl phases [7], chalcogenides [8], oxides [9,10], and high-entropy alloys [11]. Commonly, the conversion efficiency of TE materials is assessed using the dimensionless figure of merit, ZT = S²σT/κ, where S, σ, T, and κ stand for the Seebeck coefficient, electrical conductivity, absolute temperature in Kelvin, and total thermal conductivity (comprising lattice part κ_lat and electronic part κ_ele), respectively [12,13]. Actually, achieving high conversion efficiency (η) necessitates a higher power factor (PF = S²σ) and/or lower κ [14,15,16,17,18,19,20]. Unfortunately, it is difficult to simultaneously optimize the S, σ, and κ_ele in the given TE material due to their strong coupling effects [12,21]. Nevertheless, κ_lat stands as the sole independently regulated TE parameter, leading to extensive research over the last two decades [16,17,19].

Copper-based chalcogenides have garnered significant attention because of their relatively favorable electrical transport and low thermal transport properties [22,23,24,25]. In addition, thermoelectric minerals like germanites, colusites, tetrahedrites, and other materials also have rather high ZT values [26,27,28]. Among them, the Cu₃SbSe₄ compound is a p-type semiconductor, featuring a narrow band gap of ~0.29 eV [29,30]. More importantly, its components are earth-abundant, inexpensive, non-toxic, and environmentally friendly [31,32]. However, its high κ and low σ, stemming from low carrier concentration and mobility, present challenges that hinder its practical use. Extensive efforts have been implemented to enhance the TE performance of Cu₃SbSe₄, including elemental doping [33,34,35,36,37], band engineering [38,39,40], and nanostructure modification [41,42]. These approaches have potential in improving the carrier concentration of (n), S, or κ_lat, and thus leading to an appealing figure of merit. Although high n can enhance σ, it has a negative impact on S and result in an increase in κ_ele. The TE performance of Cu₃SbSe₄ falls significantly short of that of Cu-based chalcogenides due to these two inherent issues. On one side, the narrow energy band gap of ~0.29 eV leads to bipolar diffusion, causing deterioration in electrical properties [29,30]. On the other side, the high thermal conductivity (κ_lat) inherently arises from its composition comprising lightweight elements and a diamond-like structure [25]. In other words, optimizing carrier concentration alone proves challenging in further enhancing the TE performance.

The formation of a solid solution via elemental alloying is an effective strategy for depressing the κ_lat and thereby enhancing the TE performance. For example, Skoug et al. demonstrated that the substitution of Ge on Sn sites can lead to the formation of Cu₂Sn_1−xGe_xSe₃ solid solutions, synergically optimizing the TE properties [43]. Jacob et al. reported that a high ZT_max value of ~0.42 was obtained in the Cu₂Ge(S_1−xSe_x)₃ system via Se alloying [44]. Wang et al. enhanced the TE properties of Cu₂Ge(Se_1−xTe_x)₃ by incorporating Te on the Se site, resulting in a ZT_max of ~0.55, which was 62% higher than that of the matrix [45]. The afore-mentioned research give us an idea that the Cu₃Sb(Se_1−xS_x)₄ solid solution is an effectively strategy for enhancing the thermoelectric performance of the Cu₃SbSe₄ compound via S alloying. Moreover, the development of TE materials with more cost-efficient constituent elements is of significant importance for large-scale practical applications.

Herein, we present the synthesis and thermoelectric characterization of the Cu₃Sb(Se_1−xS_x)₄ solid solutions with x covering the whole range from 0 to 1. The results demonstrate that the Cu₃SbSe₄-Cu₃SbS₄ solid solutions exhibit an extremely high Seebeck coefficient and ultralow thermal conductivity. Firstly, S alloying can widen the band gap, alleviating the bipolar effect. Additionally, S substitution in the lattice can significantly increase the carrier effective mass, leading to a remarkably high Seebeck coefficient of ~730 μVK⁻¹. Moreover, the κ_lat can be significantly depressed owing to point defect scattering and Umklapp scattering, thus obtaining a minimum κ_lat of ~0.50 Wm⁻¹K⁻¹. Consequently, the multiple effects of S alloying boost the TE performance of the Cu₃SbSe₄-Cu₃SbS₄ solid solution, and a maximum ZT value of ~0.72 at 673 K is obtained for the Cu₃SbSe_2.8S_1.2 sample.

2. Experimental Procedures

2.1. Synthesis

The Cu₃Sb(Se_1−xS_x)₄ solid solutions with varying S content (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, and 1) were synthesized by vacuum melting and plasma-activated sintering (Ed-PAS Ⅲ, Elenix Ltd., Zama, Japan). Concretely, the synthesis was divided into two steps. The first step was to synthesize the primary powders. Firstly, the starting materials, consisting of high-purity components (Cu: 99.99 wt.%; Sb: 99.99 wt.%; Se: 99.999 wt.%; S: 99.99 wt.%) corresponding to the nominal composition of Cu₃Sb(Se_1−xS_x)₄ (x = 0–1), were carefully sealed in the quartz tube under high vacuum conditions (<10⁻³ Pa). Afterwards, the sealed tubes were incrementally heated to 1173 K with a controlled rate of 20 K/h and maintained at 1173 K for a duration of 12 h. Following a holding period, the tubes were cooled down with a relatively low rate of 10 K/h until reaching 773 K, and finally the samples were quenched into water. Subsequently, the acquired quenched ingots underwent direct annealing at 573 K for a period of 48 h to facilitate the uniformity of chemical compositions. After this step, the obtained ingots were finely pulverized using an agate mortar to produce uniform powders. The second step was to synthesize the target samples. The resultant powders were then introduced into a graphite die of Ø12.7 mm in diameter and treated using the PAS technique at 673 K for a duration of 5 min while applying an axial pressure of 50 MPa. In detail, the sintering temperature reached to 523 K after an activation time of 10 s under the activation voltage of 20 V and the activation current of 300 A, and then the current was manually adjusted to increase by a rate of 1.5 K/s to reach the desired sintering temperature of 673 K after 225 s; the temperature was then held for 300 s. Ultimately, the samples were furnace-cooled to room temperature.

2.2. Characterization

The X-ray diffraction (XRD) patterns for the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) solid solutions were conducted using a Bruker D8 advance instrument, which was equipped with Cu Kα radiation (λ = 1.5418 Å). Lattice parameters were refined using the Rietveld method, employing the HighScore Plus computer program for analysis. The morphologies and compositions of the afore-mentioned solid solutions were performed by a Nova NanoSEM450 (FESEM) and a JEM-2010F (HRTEM), equipped with a detector of energy-dispersive X-ray spectroscopy (EDS).

2.3. Thermoelectric Property Measurements

The as-sintered cylinders were processed into bars of 10 mm × 2 mm × 2 mm and disks of Ø12.7 mm × 2 mm. The bars were used for concurrently measuring σ and S by the commercial measuring system (LINSEIS, LSR-3) under a helium atmosphere, spanning a temperature range from room temperature to 673 K. Thermal conductivity was calculated using the equation of κ = DC_pρ. Herein, the D, C_p, and ρ stand for the thermal diffusivity, specific heat, and density, respectively. The disks were used for simultaneously measuring D and C_p by utilizing a Laser Flash apparatus of Netzsch (LFA-457) under a static argon atmosphere. The ρ of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) solid solutions were conducted using Archimedes’ methods. The relative densities, in relation to the theoretical density of 5.86 g cm⁻³, have been provided in Table S1. The n (carrier concentration) and μ (carrier mobility) of the afore-mentioned solid solutions at 300 K were performed using the Hall effect system (LAKE SHORE, 7707 A) according to the van der Pauw method under a magnetic field strength of 0.68 T.

3. Results and discussion

3.1. Crystal Structure

The crystal structures and phase compositions for the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples were performed by XRD. Figure 1a shows the crystal structure of tetragonal Cu₃SbSe₄, with blue, gray, and green atoms representing Cu, Sb, and Se, respectively. As displayed in Figure 1b, the major diffraction peaks of the pristine sample (x = 0) are fully indexed to the zinc-blende-based tetragonal structure (I-42m space group) of Cu₃SbSe₄ (JCPDS No. 85-0003) without any detectable impurities [29]. With increasing S content (0 < x < 1), a continuous shift of the (112) diffraction peak towards higher angles can be seen (Figure 1c), demonstrating that S atoms replace Se at the Se site to form Cu₃Sb(Se_1−xS_x)₄ solid solutions. The shift in the diffraction peak can be ascribed to the smaller radius of S²⁻ (1.84 Å) in comparison to Se²⁻ (1.98 Å) [46]. For x = 1, the XRD peaks match the pattern of Cu₃SbS₄ (JCPDS No. 35-0581) [47].

The Rietveld refinement profiles of the Cu₃Sb(Se_1−xS_x)₄ (x = 0.3) samples based on the famatinite crystal structure are shown in Figure 1d. The data of the final agreement factors (R_p, R_wp, and R_exp) of Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples are listed in Table S2. The lattice parameter exhibits a linear decrease with increasing S concentration, and closely follows the expected Vegard’s law relationship [48] (Figure 1e), indicating the formation of Cu₃SbSe₄-Cu₃SbS₄ solid solutions.

3.2. Microstructure

The morphologies and chemical compositions of the Cu₃Sb(Se_1−xS_x)₄ (x = 0.3) sample were characterized by a SEM equipped with an EDS detector (Figure 2). As presented in Figure 2a,b, the SEM images of fracture surfaces (x = 0.3) indicated that they were isotropic materials. The nanopores (marked by the blue dotted circles) were observed on the fracture surface due to the Se/S volatilization of the synthesis process of the sample (Figure 2a), which can contribute to blocking the transport of mid-wavelength phonons [47]. To investigate the composition of the sample, we observed its polished surface (Figure 2c). According to the EDS elemental mapping (Figure 2d–h), the four constituent elements were uniformly distributed with no distinct micro-sized aggregations. This was combined with a back-scattered electron (BSE) image and elemental ratios (%), where Cu, Sb, Se, and S were present in proportions of 40.07:12.68:31.26:15.59 (as depicted in Figure S1), which demonstrated the formation of the Cu₃SbSe₄-Cu₃SbS₄ (x = 0.3) solid solution.

The morphologies and compositions of Cu₃Sb(Se_1−xS_x)₄ (x = 0.3) were further investigated at nanoscale using high-resolution TEM (HRTEM) (Figure 3). The TEM images demonstrated that many nanophases were distributed in the sample, and elemental mapping taking over the entire region revealed that the four constituent elements (Cu, Sb, Se, and S) were uniformly dispersed within the Cu₃SbSe₄-Cu₃SbS₄ solid solution (Figure 3a and Figure S2). As presented in Figure 3b, the grain boundary (indicated by blue dot lines) could be clearly observed in the sample. Meanwhile, as shown in Figure 3b,c, the crossed fringes, with interplanar spacing of 3.26 Å and 1.99 Å corresponded to the (112) and (204) planes of Cu₃SbSe₄, respectively [49]. Additionally, the SAED pattern taken from the Figure 3c along the [110] zone axis is displayed in Figure 3d. The ordered diffraction spots can be indexed to the (002), (1$\overline{1}$0), and (1$\overline{1}$2) planes of Cu₃SbSe₄, whose interplanar spacings are 5.64 Å, 4.06 Å, and 3.26 Å, respectively [50].

3.3. Charge Transport Properties

To explore the effects of S alloying on the TE properties of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) solid solutions, the charge transport properties were conducted. The temperature dependence of electrical conductivity (σ) of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) solid solutions is displayed in Figure 4a. The pristine Cu₃SbSe₄ exhibited a monotonous increase in σ with rising temperature, demonstrating characteristic behavior of a non-degenerate semiconductor. For the x > 0.2 samples, the samples showed a transition from non-degenerate semiconductors to a partially degenerate regime [51]. The σ exhibited an initial decrease followed by an increase, with the minimum value occurring at ~473 K, indicating its association with bipolar conduction [38,52]. The σ of S alloying samples increased with the S contents until x = 0.3, after which it started to decrease with a higher S content. Notably, the σ improved from ~4.6 S/cm of pristine Cu₃SbSe₄ to ~42 S/cm of x = 0.3 solid solution at room temperature, arising from the augmented carrier concentration (Table S1). It is worth noting that the solid solutions with high S content (x > 0.5) had lower σ compared to the pristine Cu₃SbSe₄, which was ascribed to the reduced n (carrier concentration) and diminished μ (carrier mobility). Furthermore, due to the intensified lattice vibration at elevated temperatures, the solid solutions exhibited lower σ than the pristine sample at high temperatures, indicating that the intensified lattice vibration in the solid solutions at elevated temperatures hindered the carrier migration [40,53].

Figure 4b illustrates the temperature-dependent S of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples. The p-type semiconductor behavior of solid solutions, characterized by dominant hole carriers, was evidenced by the positive S value observed across the entire temperature range.

Notably, the S value of the samples exhibited an initial ascent followed by a subsequent descent as the temperature rose, ultimately reaching its zenith at ~473 K. This behavior can be attributed to the influence of the bipolar effect [54]. The maximum S of ~730 μVK⁻¹ was obtained from the x = 0.6 solid solution. We calculated the E_g of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples with the formula: E_g = 2eS_maxT, where E_g, e, S_max, and T represent the band gap, elementary charge, maximal Seebeck coefficient, and the associated temperature, respectively [55]. The calculated E_g for the pristine Cu₃SbSe₄ of ~0.30 eV aligned well with the reported literature [36,56]; the results are displayed in Figure S3. Consequently, the introduction of alloyed S played a role in enlarging E_g from ~0.30 eV to ~0.69 eV, thus widening the band gap to alleviate the bipolar effect. For the semiconductors, we note that the increase in S (|S|) was directly proportional to the carrier effective mass and n^−2/3. We calculated the Pisarenko relation between |S| and n (indigo and red dashed lines with m* ~ 0.68 and 1.4 m_e, respectively) based on the single parabolic band model (SPB), as follows [57,58]:

$$S=\frac{8{\pi }^2{k}_B^2}{3e{\hslash }^2}m*T{\left(\frac{\pi }{3n}\right)}^{2/3}$$

(1)

where k_B, ℏ represent the Boltzmann constant, and Planck constant, respectively. The calculated m* was significantly enhanced from 0.68 for pristine Cu₃SbSe₄ to 5.03 m_e for the x = 0.6 sample (Table S1). As seen in Figure 4c, the calculated m* based on S (experimental values) of Cu₃Sb(Se_1−xS_x)₄ (x = 0.1–1) samples were above the Pisarenko line. Furthermore, the m* depended directly on the E_g ($\frac{{\hslash }^2{k}_B^2}{2m*}={\rm E}\left(1+\frac{{\rm E}}{{{\rm E}}_g}\right)$), where E the energy of electron states), which deviated from a single Kane band model [21,59,60], thus confirming the large S was related to E_g and m*. Consequently, the decreased carrier concentration (x > 0.5) and increased m*, resulted in the significant enhancement of S.

The temperature dependence of the power factors (S²σ) of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples are presented in Figure 4d. The S²σ of Cu₃SbSe₄-Cu₃SbS₄ solid solutions exhibited a similar temperature-dependent behavior as the electrical conductivity (σ). The temperature-dependent trend observed in the S²σ was mirrored in the behavior of the σ for the Cu₃SbSe₄-Cu₃SbS₄ solid solutions. Owing to their relatively elevated σ and S values, these samples demonstrated larger S²σ values compared to the pristine Cu₃SbSe₄, particularly within the lower temperature range. Notably, the x = 0.3 sample achieved a larger S²σ value than the other samples, and the peak S²σ value of Cu₃SbSe_2.8S_1.2 sample was ~670 μW m⁻¹ K⁻² at 673 K.

3.4. Thermal Transport Properties

The temperature dependence of the thermal transport properties of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) solid solutions are presented in Figure 5 and Figure S4. Obviously, the κ_tot decreased with increasing temperature, mainly attributed to the increased scattering by lattice vibrations at elevated temperatures [8,40,53] (Figure 5a). For instance, the κ_tot of pristine Cu₃SbSe₄ decreased from ~3.11 Wm⁻¹K⁻¹ at 300 K to ~1.03 Wm⁻¹K⁻¹ at 673 K. Similarly, the κ_tot of the x = 0.5 sample decreased from ~1.37 Wm⁻¹K⁻¹ at 300 K to ~0.52 Wm⁻¹K⁻¹ at 673 K. Generally, the κ_lat can be obtained by subtracting the electronic part (κ_ele) from the κ_tot using the Wiedeman–Franz relationship (the details are displayed in Supplementary Material) [61,62]:

$$\kappa { }_{\mathrm{ele}}=L\sigma \mathsf{{\rm T}}$$

(2)

where L is the Lorenz number and it can be expressed as Equation (3) [63,64]:

$$L=1.5+\exp \left[\frac{-\left|S\right|}{116}\right]$$

(3)

The calculated L values of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples ranged from 1.5 to 1.6 W Ω K⁻², and the results are listed in Figure S5. Owing to the enhanced carrier concentration (x < 0.6), the κ_ele showed a slight increase at low temperature after S alloying, as described in Figure 5b. The κ_lat of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples is plotted in Figure 5c, indicating a significant decrease within the measured temperature range after S alloying.

To explore the effects of S alloying on the phonon scattering and the significant reduction in κ_lat, the κ_lat of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) compounds was evaluated at room temperature by the Debye–Callaway model. The primary scattering mechanisms under consideration were point defect scattering and Umklapp scattering. Then, the κ_lat of the pristine (${\kappa }_{lat}^{pristine}$) and S-alloyed (κ_lat) Cu₃SbSe₄ compounds could be computed based on the Debye–Callaway model [48,65,66]:

$$\frac{{\kappa }_{\mathrm{lat}}^{}}{{\kappa }_{\mathrm{lat}}^{\mathrm{pristine}}}=\frac{\arctan \left(u\right)}{u}, u^2=\frac{{\pi }^2{\theta }_{\mathrm{D}}\mathsf{\Omega }}{h{v}^2}{\kappa }_{\mathrm{lat}}^{\mathrm{pristine}}\mathsf{\Gamma }$$

(4)

where u, θ_D, Ω, h, and ν represent the scaling parameter, Debye temperature, volume per atom, Planck constant, and average speed of sound, respectively (herein, θ_D = 131 K and ν= 1991.2 m/s [46]). Γ is the imperfection scale parameter, which is associated with the Γ_m (mass fluctuation) and Γ_s (strain field fluctuation) [67]:

$$\mathsf{\Gamma }={\mathsf{\Gamma }}_{\mathrm{m}}+{\mathsf{\Gamma }}_{\mathrm{s}}=x(1-x)\left[{\left(\frac{\Delta \mathrm{M}}{\mathrm{M}}\right)}^2+\epsilon {\left(\frac{\Delta \mathrm{r}}{r}\right)}^2\right]$$

(5)

where x, ∆M/M and ∆r/r are the S concentration in one molecular, the relative change of atomic mass, and atomic radius owing to the replacement of Se with S, respectively. The ε value can be computed using the following formula [68]:

$$\epsilon =\frac{2}{9}{\left(\frac{6.4\gamma \left(1+{\upsilon }_{\mathrm{p}}\right)}{1-{\upsilon }_{\mathrm{p}}}\right)}^2$$

(6)

where, γ and υ_p are the Grüneisen parameter and Poisson ratio, respectively (here, γ = 1.3 [46] and υ_p = 0.35 [69]).

The values of Γ_m and Γ_s for the Cu₃Sb(Se_1−xS_x)₄ compounds are presented in Table S3. Figure 5d shows how the scattering parameters Γ_m and Γ_s changed with varying Se-alloying levels. It was observed that Γ_m was smaller than Γ_s when the S content x ≤ 0.6, indicating that the Γ_s (strain field fluctuation) contributed greatly to the drop of κ_lat. As for the x > 0.6 samples, the Γ_m (mass fluctuation) was the dominant. It is commonly accepted that the atomic radius of S is different from that of the Se atom, inducing a localized lattice distortion and leading to local field fluctuations that hinder the propagation of heat-carrying phonons [70,71]. However, with increasing S content, the mass fluctuation gradually became the dominant factor. The experimental κ_lat closely aligned with the curve calculated by the Callaway model (Figure 5e), suggesting that point defects made a great contribution to suppress the κ_lat in the Cu₃Sb(Se_1−xS_x)₄ solid solutions [48]. For a more comprehensive evaluation of our results, a comparison of the our κ_lat data with the recently reported values of Cu₃SbSe₄ are illustrated in Figure 5f [33,34,36,38,39]. Remarkably, the Cu₃Sb(Se_1−xS_x)₄ (x = 0.5) sample achieved an outstandingly low κ_lat of ~0.50 W m⁻¹ K⁻¹ at 673 K.

3.5. Figure of Merit (ZT)

The temperature-dependent ZT of the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples are illustrated in Figure 6a. With the benefit of the collaborative enhancement of electrical and thermal transport properties, the x = 0.3 sample attained a maximum ZT value of ~0.72 at 673 K, which was 44% higher than that of pristine Cu₃SbSe₄. To further analyze our TE properties, the comparison of the ZT_max of the Cu₃SbSe₄-based materials is given in Figure 6b [33,34,35,36,37,38,39,40,72]. Obviously, our ZT_max of 0.72 was higher than that of other Cu₃SbSe₄-based materials, such as Cu₃Sb_0.97In_0.03Se₄ ~0.5, Cu₃Sb_0.985Ga_0.015Se₄ ~0.54, Cu₃SbSe_3.99Te_0.01 ~0.62, Cu₃Sb_0.92Sn_0.08S_3.75Se_0.25 ~0.67, Cu_2.95Sb_0.96Ge_0.04Se₄ ~0.70, and Cu_2.95Sb_0.98Sn_0.02Se₄ ~0.7 and is comparable to the ZT values for Cu₃Sb_0.98Bi_0.02Se_3.99Te_0.01 ~0.76 and Cu₃Sb_0.91Sn_0.03Hf_0.06Se₄ ~0.76. Although the Cu₃Sb(Se_1−xS_x)₄ (x = 0–1) samples had relative low ZT values in comparison with other high-performance TE materials, further enhancements of the ZT values can potentially be achieved by tuning the carrier concentration, dual-incorporation, and/or introducing band engineering.

4. Conclusions

In summary, a series of Cu₃SbSe₄-Cu₃SbS₄ solid solutions were synthesized by vacuum melting and plasma-activated sintering (PAS) techniques, and the effects of S alloying on TE performance were investigated. S alloying can widen the band gap, effectively alleviating the bipolar effect. Additionally, the S (Seebeck coefficient) was significantly improved because of the increased m*. Furthermore, the substitution of S for Se in Cu₃SbSe₄ lattice led to noticeable local distortions, yielding large strain and mass fluctuations to suppress the κ_lat, thus decreasing the κ_lat and κ_tot to ~0.50 Wm⁻¹K⁻¹ and ~0.52 Wm⁻¹K⁻¹ at 673 K, respectively. Consequently, a peak ZT value of ~0.72 was obtained at 673 K for the Cu₃Sb(Se_1−xS_x)₄ (x = 0.3) sample. Based on these results, it is speculated that further improvement in the figure of merit of Cu₃Sb(Se_1−xS_x)₄ solid solutions can be obtained by enhanced electrical transport properties. Our research offers a new strategy to develop high-performance TE materials in solid solutions via elemental alloying.