Skip to main content

Thermoelectric properties of the off-stoichiometric tetrahedrites Cu12+mSb4S13


Tetrahedrite Cu12Sb4S13 is attracting attention as a thermoelectric material owing to its inherently low thermal conductivity. Various studies have been conducted to improve the thermoelectric performance of tetrahedrite by doping transition elements at Cu sites or incorporating nanostructures and nano-inclusions. In this study, off-stoichiometric (Cu-poor and Cu-rich) tetrahedrites, Cu12+mSb4S13 (− 0.3 ≤ m ≤ 0.3) were synthesized and their thermoelectric properties were investigated. All the stoichiometric and off-stoichiometric specimens contained a single tetrahedrite phase, and as the Cu content increased, their lattice constant increased. The electrical conductivity exhibited a positive temperature dependence (non-degenerate semiconductor behavior), while it decreased with the Cu content. The Seebeck coefficient increased with the temperature as well as the Cu content. The thermal conductivity did not exhibit significant temperature dependence, but it decreased as the Cu content increased at a constant temperature. Therefore, Cu deficiency improved the electrical transport in the tetrahedrite but had a negative effect on enhancing the thermal transport. The Cu-poor composition increased the power factor, rather than the stoichiometric composition; Cu11.7Sb4S13 exhibited the highest power factor of 1.08 mWm−1 K−2 at 723 K. However, the Cu-rich composition reduced the thermal conductivity compared to the stoichiometric tetrahedrite; Cu12.3Sb4S13 exhibited the lowest thermal conductivity of 0.54 Wm−1 K−1 at 323 K and 0.65 Wm−1 K−1 at 723 K. A maximum dimensionless figure-of-merit of 0.91 was achieved at 723 K for Cu11.9Sb4S13.


Tetrahedrite is a low-cost and earth-abundant copper-antimony-sulfosalt (Cu12Sb4S13) that is a high-performance thermoelectric material at temperatures of approximately 723 K [1, 2]. Although there are excellent thermoelectric materials such as PbTe-based compounds in a similar temperature range, they are composed of toxic heavy metals and rare elements, which raise economic and environmental concerns. However, tetrahedrite consists of non-toxic (eco-friendly) and comparatively light elements. Tetrahedrite has a cubic unit cell (space group \(\mathrm{I}\overline{4}3m\)) with a complex crystal structure composed of three sublattices: Cu(I)S4 tetrahedra, SbS3 trigonal pyramids, and Cu(II)S3 triangles [3]. The low thermal conductivity of the tetrahedrite arises from the Cu atoms located in the plane S triangle, which vibrate irregularly owing to the unshared lone-pair electrons of the Sb atoms [4,5,6].

Generally, a dimensionless figure of merit (ZT = σα2κ−1T) is used to evaluate the thermoelectric performance of a material (where σ: electrical conductivity, α: Seebeck coefficient, κ: thermal conductivity, and T: temperature in Kelvin units). Therefore, a high power factor (PF = σα2) and low thermal conductivity are the criteria for excellent thermoelectric materials. Studies on tetrahedrite have been conducted to maximize the power factor and lower the thermal conductivity by controlling the carrier (hole) concentration by doping various transition elements at the Cu sites [7].

Few studies have been conducted on off-stoichiometric tetrahedrites that manipulate the Cu content. However, small variations in chemical composition in stoichiometry can affect the physical properties of semiconductors. Wei et al. [8] prepared Cu-poor permingeatites Cu3-xSbSe4 (x = 0–0.075) by mechanical alloying (MA) and spark plasma sintering (SPS), and reported that reducing the Cu content in the permingeatite could increase the electrical conductivity by increasing the carrier concentration via the addition of holes by Cu vacancies. Yan et al. [9] synthesized Cu-rich tetrahedrites Cu12+xSb4S13 (x = 0.5–1.5) by encapsulated melting (EM) and SPS, and suggested that the excess Cu in the tetrahedrite led to phase separation into Cu-rich and Cu-poor phases, which further reduced the lattice thermal conductivity. In this study, the off-stoichiometric tetrahedrites, Cu12+mSb4S13 (− 0.3 ≤ m ≤ 0.3), were prepared and the thermoelectric performance was investigated.

Experimental procedure

The stoichiometric and off-stoichiometric tetrahedrites, Cu12+mSb4S13 (m = − 0.3, − 0.2, − 0.1, 0, 0.1, 0.2, and 0.3), were synthesized via MA. After weighing elemental Cu (< 45 µm, purity 99.9%, Kojundo Chemical Lab.), Sb (< 150 µm, purity 99.999%, Kojundo Chemical Lab.), and S (< 75 µm, purity 99.99%, Kojundo Chemical Lab.) according to the corresponding compositions, the mixed powder and steel balls were loaded into a hardened steel jar. MA was conducted using a planetary ball milling system (Pulverisette5, Fritsch) at 350 rpm for 24 h in an Ar atmosphere. The synthesized powder was sintered using hot pressing (HP) at 723 K for 2 h under 70 MPa in vacuum. The detailed MA-HP processes for tetrahedrite have been described in our previous study [10].

The phase analysis was performed using X-ray diffraction (XRD; D8-Advance, Bruker) with Cu-Kα radiation. The lattice constant was estimated using Rietveld refinement program (TOPAS, Bruker). The microstructures of the hot-pressed samples were observed using scanning electron microscopy (SEM; Quanta400, FEI). The four-probe method (ZEM-3, Advance Riko) was used to measure the electrical conductivity and Seebeck coefficient. The laser flash equipment (TC-9000H, Advance Riko) was employed to estimate the thermal conductivity. Finally, the PF and ZT values were evaluated using the thermoelectric parameters obtained in the temperature range of 323–723 K.

Results and discussion

The XRD patterns of Cu12+mSb4S13 prepared via MA-HP are shown in Fig. 1. All the diffraction peaks matched the cubic tetrahedrite (ICDD PDF#024–1318). In addition, no secondary phases were identified in the stoichiometric and off-stoichiometric specimens. However, the diffraction peaks shifted to lower or higher angles according to the change in the Cu content (m), compared to the stoichiometric tetrahedrite, indicating lattice expansion or contraction. As shown in Fig. 2, the lattice constant increased from 1.0338 to 1.0384 nm as the Cu content increased from deficiency (m = − 0.3) to excess (m = 0.3). The lattice constant of the stoichiometric specimen (m = 0) was 1.0350 nm, which implies that the lattice contracted for the Cu-poor specimens and expanded for the Cu-rich specimens. Yan et al. [9] reported that the separation of Cu-rich and Cu-poor phases occurred in Cu12+xSb4S13 (x = 0.5–1.5), and the diffraction peaks for the Cu-rich phase appeared stronger as the Cu content increased. However, in this study, phase separation did not occur and a single phase was observed.

Fig. 1
figure 1

XRD patterns of off-stoichiometric tetrahedrites Cu12+mSb4S13 prepared using the MA-HP process

Fig. 2
figure 2

Variation of the lattice constant with Cu content for Cu12+mSb4S13

Figure 3 shows the fractured surfaces of hot-pressed Cu12+mSb4S13. The specimens yielded relative densities greater than 99.0% compared to the theoretical density of tetrahedrite (4.99 gcm−3) [11]. Consistent with the results of the XRD analysis, no secondary phases or residual elements were observed.

Fig. 3
figure 3

SEM images of fractured surfaces for Cu12+mSb4S13

Figure 4 shows the electrical conductivity of Cu12+mSb4S13. For the Cu-rich specimens, the electrical conductivity increased with the temperature in the range of 323–723 K, thereby exhibiting a non-degenerate semiconductor behavior. However, the Cu-poor specimens exhibited small temperature dependence, displaying a degenerate semiconductor behavior at temperatures above 623 K. In comparison with the stoichiometric specimen, the electrical conductivity of the Cu-rich specimens decreased at constant temperature, whereas it increased for the Cu-poor specimens. Thus, the electrical conductivity increased as the Cu content (m) decreased. Consequently, Cu11.7Sb4S13 exhibited the highest electrical conductivity of 4.5 × 104 Sm−1 at 623 K. Yan et al. [9] found a change in electrical conductivity in the Cu-excess tetrahedrites: the electrical conductivity of Cu12+xSb4S13 (x = 0.5 − 1.5) decreased as the Cu content increased, and thus Cu13.5Sb4S13 yielded the lowest value of 2.0 × 104 Sm−1 at 723 K. There are no reports on the effect of Cu deficiency on the electrical properties of the tetrahedrite. However, Wei et al. [8] reported that the electrical resistivity of permingeatite Cu3-xSbSe4 (x = 0 − 0.075) decreased significantly owing to the increased carrier (hole) concentration as the Cu content was deficient. Therefore, compared to stoichiometric Cu12Sb4S13, an excess of Cu was expected to contribute to lowering the carrier concentration, whereas a deficiency in the Cu content contributed to an increase in the carrier concentration.

Fig. 4
figure 4

Temperature dependence of the electrical conductivity for Cu12+mSb4S13

Figure 5 presents the Seebeck coefficient of Cu12+mSb4S13. The Seebeck coefficient is expressed as \(\alpha = \pm \left( {8/3} \right)(\pi /3n)^{2/3} \pi^{2} k_{B}^{2} m^{*} Te^{ - 1} h^{ - 2}\) (where n: the carrier concentration, kB: the Boltzmann constant, m*: the effective carrier mass, e: the electronic charge, and h: the Planck constant) [12]. Positive Seebeck coefficients confirm the p-type semiconductors. In general, as the Seebeck coefficient (the magnitude of absolute value, |α|) increases with the temperature, the rapid increase in the carrier concentration caused by the intrinsic transition above a certain temperature decreases the Seebeck coefficient. In this study, no intrinsic transition occurred in any of the specimens within the measured temperature range. As in our previous studies [13,14,15,16,17] in which the doping elements were substituted for the stoichiometric composition, the change in the carrier concentration was not significant. Thus, in this study, intrinsic transitions did not occur up to 723 K, and the intrinsic transition temperature of Cu12+mSb4S13 (− 0.3 ≤ m ≤ 0.3) was expected to be higher than 723 K. However, as the Cu content increased, the temperature dependence at high temperatures decreased, and the excess Cu seemed to contribute to lowering the intrinsic transition temperature. Conversely, Cu deficiency decreased the Seebeck coefficient owing to the increase in the carrier concentration, but contributed to increasing the intrinsic transition temperature. As the Cu content increased at a constant temperature, the Seebeck coefficient increased, and Cu12.3Sb4S13 exhibited the highest value of 208 μVK−1 at 723 K. This value is greater than the maximum Seebeck coefficient of 183 μVK−1 at 723 K for Cu12Sb4S13. Yan et al. [9] reported that the Seebeck coefficient increased as the Cu content increased for Cu-rich tetrahedrites Cu12+xSb4S13 (x = 0.5 − 1.5), and Cu13.5Sb4S13 achieved the highest Seebeck coefficient of 188 μVK−1 at 723 K. On the other hand, Wei et al. [8] found that the Seebeck coefficient decreased as the Cu content decreased for Cu-deficient permingeatites Cu3-xSbSe4 (x = 0−0.075) owing to the increase in the carrier concentration. This result is similar to the decrease in the Seebeck coefficient of Cu-poor tetrahedrites.

Fig. 5
figure 5

Temperature dependence of the Seebeck coefficient for Cu12+mSb4S13

Figure 6 shows the PF of Cu12+mSb4S13. As the Cu-poor specimens exhibited higher PF values than the Cu-rich specimens, the increased power factor of the tetrahedrite was more affected by the increase in the electrical conductivity than the increase in the Seebeck coefficient. The stoichiometric Cu12Sb4S13 exhibited a maximum PF of 0.95 mWm−1 K−2 at 723 K. The non-stoichiometric specimens, Cu11.7Sb4S13 and Cu11.9Sb4S13 exhibited the highest PF of 1.08 mWm−1 K−2 at 723 K, while Cu12.3Sb4S13 displayed a lower PF of 0.66 mWm−1 K−2 at 723 K. Therefore, when the tetrahedrite was Cu-poor, the carrier concentration could be increased to obtain power factors higher than that of the stoichiometric Cu12Sb4S13. Wei et al. [8] reported that since the Cu-deficient permingeatites Cu3-xSbSe4 (x = 0−0.075) exhibited the decreased Seebeck coefficient and electrical resistivity owing to the increased carrier concentration caused by Cu vacancies, Cu2.95SbSe4 exhibited a high PF of 0.90 mWm−1 K−2 at 523 K. On the other hand, Yan et al. [9] reported a lower PF of 0.72 mWm−1 K−2 at 723 K for the Cu-rich Cu13.5Sb4S13, because the carrier concentration was lowered by the excess Cu, which was not effective for enhancing electrical transport.

Fig. 6
figure 6

Temperature dependence of the power factor for Cu12+mSb4S13

Figure 7 presents the thermal conductivities of Cu12+mSb4S13. The thermal conductivity values showed little temperature dependence in the measurement temperature range. As the Cu content increased, the thermal conductivity decreased from 0.98 to 0.54 Wm−1 K−1 at 323 K, and from 0.97 Wm−1 K−1 to 0.65 Wm−1 K−1 at 723 K. Compared to the stoichiometric Cu12Sb4S13 (0.72–0.77 Wm−1 K−1 in the range 323–723 K), Cu-rich tetrahedrites exhibited lower thermal conductivity values. Assuming that the bipolar effect is excluded, the thermal conductivity consists of two components: the lattice thermal conductivity (κL: phonon contribution) and the electronic thermal conductivity (κE: charge-carrier contribution), which can be divided by the Wiedemann–Franz relation (κE = LσT) [18]. The temperature-dependent Lorenz number (L) ranges from (1.45–2.44) × 10–8 V2K−2 theoretically, and smaller values of L indicate non-degenerate semiconductor characteristics (larger values of L indicate a degenerate semiconductor or metallic behavior). Figure 8 shows the L values estimated using the relation \(\mathrm{L}= 1.5 +\mathrm{ exp}(-\left|\alpha \right|/116)\) [19]. As the Cu content decreased, the L increased from 1.70 × 10–8 to 1.89 × 10–8 V2K−2 at 323 K, and from 1.65 × 10–8 to 1.76 × 10–8 V2K−2 at 723 K. Therefore, as the Cu content decreased, a transition from the non-degenerate semiconductor to the degenerate semiconductor was possible, as shown in Fig. 4.

Fig. 7
figure 7

Temperature dependence of the thermal conductivity for Cu12+mSb4S13

Fig. 8
figure 8

Temperature dependence of the Lorenz number for Cu12+mSb4S13

Figure 9 presents the separated thermal conductivities of κE and κL. As the temperature increased, the κE increased owing to the increased heat transfer by carriers resulting from an increase in the carrier concentration. As the Cu content increased at a constant temperature, the carrier concentration decreased; thus, the Cu-rich specimens exhibited a lower κE than the Cu-poor specimens. Cu12.3Sb4S13 exhibited the lowest κE of 0.04 Wm−1 K−1 − 0.17 Wm−1 K−1 at 323–723 K. As shown in Fig. 9b, the κL of Cu-poor specimens decreased as the temperature increased (at least 0.40 Wm−1 K−1 at 723 K) owing to reduced heat transfer caused by phonon scattering. However, the Cu-rich specimens exhibited a low temperature dependence of 0.45 Wm−1 K−1 − 0.52 Wm−1 K−1 at 323–723 K. In comparison with the thermal conductivity data in Fig. 7, heat transfer by phonons dominated at low temperatures, while carriers had a greater contribution to heat transfer at high temperatures. Yan et al. [9] reported a very low κL of 0.25 Wm−1 K−1 at 723 K for Cu-rich Cu13.5Sb4S13, which was 59% lower than the stoichiometric Cu12Sb4S13. The tetrahedrite has been reported to possess an inherently low thermal conductivity owing to phonon scattering by excess Cu atoms, bringing the κL closer to the theoretical minimum value [20].

Fig. 9
figure 9

Temperature dependence of the a electronic thermal conductivity and b lattice thermal conductivity for Cu12+mSb4S13

Figure 10 shows the ZT of Cu12+mSb4S13. The ZT increased with increasing temperature, because the PF increased until the intrinsic transition temperature and thermal conductivity remained low. The ZT values were in the range 0.13–0.20 at 323 K and 0.71–0.91 at 723 K. Cu-poor Cu11.9Sb4S13 exhibited higher ZT values and exhibited a maximum ZT of 0.91 at 723 K. This was higher than the ZT of 0.86 at 723 K reported for the stoichiometric Cu12Sb4S13. Barbier et al. [21] reported a ZT of 0.60 at 723 K for Cu12Sb4S13 produced via EM-SPS. Yan et al. [9] obtained a ZT of 1.0 at 723 K for Cu-rich Cu13.5Sb4S13 prepared by the same process. However, in this study, excess Cu was not effective in improving the thermoelectric performance, because the PF decreased, although reduced the thermal conductivity effectively. Therefore, this study confirmed that the Cu deficiency in tetrahedrites contributed to the improvement of the thermoelectric performance, because the carrier concentration was optimized to maximize the power factor. Thus, a single off-stoichiometric tetrahedrite phase could be synthesized via MA-HP as a solid-state technique, and excellent thermoelectric performance was achieved when the Cu content was low.

Fig. 10
figure 10

Dimensionless figure of merit for Cu12+mSb4S13


Tetrahedrites Cu12+mSb4S13 (− 0.3 ≤ m ≤ 0.3) with stoichiometric and non-stoichiometric compositions were successfully synthesized by mechanical alloying and hot pressing without unreacted residual elements and secondary phases. Compared to the stoichiometric composition, the lattice constant increased as the Cu content increased, while it decreased as the Cu content decreased. As the Cu content (m) increased from -0.3 to 0.3, the electrical conductivity decreased, while the Seebeck coefficient increased, possibly due to the decreased carrier (hole) concentration arising from the additional supply of electrons. Cu11.7Sb4S13 exhibited the highest PF of 1.08 mWm−1 K−2 at 723 K because of the higher electrical conductivity of the Cu-poor specimens. The thermal conductivity decreased with the Cu content, and the decrease in the charge-carrier contribution was more prevalent than the decrease in the phonon contribution. Cu-poor specimens improved the electrical transport by donating additional holes, while Cu-rich specimens lowered the thermal conductivity by additional phonon scattering. Hence, the highest ZT of 0.91 was achieved for Cu11.9Sb4S13 at 723 K.


  1. G.J. Snyder, E.S. Toberer, Nat. Mater. 7, 105–114 (2008)

    ADS  Article  Google Scholar 

  2. X. Lu, D.T. Morelli, Phys. Chem. Chem. Phys. 15, 5762–5766 (2013)

    Article  Google Scholar 

  3. A. Pfitzner, M. Evain, V. Petricek, Acta Crystallogr. B 53, 337–345 (1997)

    Article  Google Scholar 

  4. Y. Bouyrie, C. Candolfi, S. Pailhès, M.M. Koza, B. Malaman, A. Dauscher, J. Tobola, O. Boisron, L. Saviot, B. Lenoir, Phys. Chem. Chem. Phys. 17, 19751–19758 (2015)

    Article  Google Scholar 

  5. W. Lai, Y. Wang, D.T. Morelli, X. Lu, Adv. Funct. Mater. 25, 3648–3657 (2015)

    Article  Google Scholar 

  6. E. Lara-Curzio, A.F. May, O. Delaire, M.A. McGuire, X. Lu, C.Y. Liu, E.D. Case, D.T. Morelli, J. Appl. Phys. 115, 193515 (2014)

    ADS  Article  Google Scholar 

  7. R. Chetty, A. Bali, R.C. Mallik, J. Mater. Chem. 3, 12364–12378 (2015)

    Google Scholar 

  8. T.R. Wei, F. Li, J.F. Li, J. Electron. Mater. 43, 2229–2238 (2014)

    ADS  Article  Google Scholar 

  9. Y. Yan, H. Wu, G. Wang, X. Lu, X. Zhou, Energy Storage Mater. 13, 127–133 (2018)

    Article  Google Scholar 

  10. S.Y. Kim, S.G. Kwak, J.H. Pi, G.E. Lee, I.H. Kim, J. Electron. Mater. 48, 1857–1863 (2019)

    ADS  Article  Google Scholar 

  11. J.W. Anthony, R.A. Bideaux, K.W. Bladh, M.C. Nichols, Handbook of Mineralogy, I. (Mineralogical Society of America, Virginia, 2003)

    Google Scholar 

  12. Y.C. Lan, A.J. Minnich, G. Chen, Z.F. Ren, Adv. Funct. Mater. 20, 357–376 (2010)

    Article  Google Scholar 

  13. S.G. Kwak, J.H. Pi, G.E. Lee, I.H. Kim, Korean J. Met. Mater. 58, 272–277 (2020)

    Article  Google Scholar 

  14. S.G. Kwak, G.E. Lee, I.H. Kim, Korean J. Met. Mater. 57, 328–333 (2019)

    Article  Google Scholar 

  15. S.Y. Kim, G.E. Lee, I.H. Kim, J. Electron. Mater. 49, 2775–2780 (2020)

    ADS  Article  Google Scholar 

  16. S.Y. Kim, G.E. Lee, I.H. Kim, J. Korean Phys. Soc. 74, 967–971 (2019)

    ADS  Article  Google Scholar 

  17. S.Y. Kim, J.H. Pi, G.E. Lee, I.H. Kim, Korean J. Met. Mater. 58, 340–347 (2020)

    Article  Google Scholar 

  18. X. Yan, B. Poudel, Y. Ma, W. Liu, G. Joshi, H. Wang, Y. Lan, D. Wang, G. Chen, Z. Ren, Nano Lett. 10, 3373–3378 (2010)

    ADS  Article  Google Scholar 

  19. T. Caillat, A. Borshchevsky, J.P. Fleurial, J. Appl. Phys. 80, 4442 (1996)

    ADS  Article  Google Scholar 

  20. R. Chetty, P. Kumar, G. Rogl, P. Rogl, E. Bauer, H. Michor, S. Suwas, S. Pucjegger, G. Giester, R.C. Mallik, Phys. Chem. Chem. Phys. 17, 1716–1727 (2015)

    Article  Google Scholar 

  21. T. Barbier, P. Lemoine, S. Gascoin, O.I. Lebedev, A. Kaltzoglou, P. Vaqueiro, A.V. Powell, R.I. Smith, E. Guilmeau, J. Alloys Compd. 634, 253–262 (2015)

    Article  Google Scholar 

Download references


This study was supported by the Basic Science Research Capacity Enhancement Project (National Research Facilities and Equipment Center) through the Korea Basic Science Institute funded by the Ministry of Education (Grant No. 2019R1A6C1010047).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Il-Ho Kim.

Ethics declarations

Conflict of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kwak, SG., Kim, IH. Thermoelectric properties of the off-stoichiometric tetrahedrites Cu12+mSb4S13. J. Korean Phys. Soc. 80, 1054–1059 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Hermoelectric
  • Tetrahedrite
  • Off-stoichiometry
  • Non-stoichiometry