1. Introduction

Thermoelectric materials have recently attracted a great deal of attention owing to their potential applications as alternative green energy sources. The thermoelectric effect involves the generation of the electrical energy from a heat source and the removal of the heat using the electric energy. Thermoelectricity offers numerous advantages, including the lack of moving parts and high stability. Its involvement concerns a wide power range, from the low power applications in wrist watches and in biomedical devices, up to the last scale heat recovery in the transportation vehicles.

Whether in cooling or in energy generation mode, the efficiency of a thermoelectric device increases with the increasing of the figure-of-merit of the used thermoelectric semiconductors. The latter is written as^[1]:

$$ZT=\frac{\sigma }{\kappa }{\alpha ^2}T,$$

(1)

where α is the Seebeck coefficient, and T is the temperature. σ and κ are the electrical and the thermal conductivities, respectively.

Currently, available thermoelectric materials have a ZT that is typically less than unity. Accordingly, the efficiency of thermoelectric devices is low, which presents an obstacle for their involvement. For instance, at an average temperature of 450 °C, the temperature difference between the hot and the cold sides must exceed 200 °C to obtain a conversion efficiency of 11%. Recently, several strategies have been tested to improve the figure-of-merit of some semiconductors. This is achieved by improving the electrical conductivity^{[2, 3]}, or decreasing the thermal conductivity in semiconductors with Glass Phonon behavior^[4] or in microstructures^{[5, 6]}.

Up to now, thermoelectric materials with high ZT values are essentially Bi₂Te₃, BiSbTe, PbTe, and Cu₂Se. These materials contain very toxic elements (Te, Pb, Sb, Se) and are very expensive, which limits their uses in thermoelectric devices.

Copper sulphide compounds have recently shown good thermoelectric performances^[7–9]. Similar to Cu₂Se, Cu_2-xS contain copper ions randomly distributed in the crystallographic lattice. These ions contribute to the electrical conductivity and, in addition, diffuse the phonons. These diffusions make the thermal conductivity low, which increases the figure-of-merit. Compared to Cu₂Se, Cu_2–xS may be the most favored because the sulfur is not very toxic and it is more earth-abundant than the selenium.

Depending on the value of x, Cu_2-xS may exist under the sulfur-rich phase or the copper-rich phase. The sulfur-rich phase (x = 1) is known as the covellite phase (CuS), and the copper-rich phase can exist in various formulas, including Chalcocite (Cu₂S), Djurlite (Cu_1.96S), Digenite (Cu_1.8S), and anilite (Cu_1.75S) phase. The decomposition from one composition to another can be performed by annealing^[10–12]. The temperature also causes temporary transitions during heating from the γ phase to the β phase and from the β phase to the α phase, and the inverse transitions during cooling^[13].

In this work, structural and thermoelectric properties of Cu_2–xS nanoparticles were studied. It is observed that the annealing temperature strongly affects the morphology and the thermoelectric properties of the treated compounds. Physical interpretations are given to explain the observed results.

2. Experimental detail

2.1 Samples synthesis

In a typical procedure, Cu_2–xS powders were prepared by the sol-gel method. The operating mode is similar to that followed by Riyaz et al. who synthesized only the covellite phase CuS^[14]. However, three different phases were obtained by annealing in this study. Fig. 1 displays the operating mode.

2.2 Characterization

X-ray diffraction measurements were performed in an XPERT-3 diffractometer with a copper anticathode (λ = 1.54 Å). This anticathode is bombarded by electrons accelerated using a voltage of 45 kV. All samples were compressed under a pressure of 7 tons and have a circular form with a diameter of 13 mm and a thickness of 1–3 mm. For a qualitative study, the crystallite sizes were approximately estimated using the Scherrer formula. This formula was applied on the most intense peaks in the XRD patterns and the mean value was taken. Thermogravimetric analysis (TGA) was performed on a TA Instrument Q500 apparatus in flowing air. Scanning electron microscopy was carried out on a VEGA3 TESCAN.

The electrical resistivity was measured by the four probe method. Parallelepiped samples with lengths of L = 10 mm, width of l = 3 mm, and thickness of e = 3 mm were traversed by a direct current without short-circuiting the ammeter and the voltmeter terminals. The Seebeck coefficient was measured by a lab-fabricated device. Each sample was put on two copper electrodes, brought to two different temperatures using a flexible heating resistor. The trace of the voltage, between the terminals of the sample, as a function of the temperature difference led to directly deduce the Seebeck coefficient. The used device is similar to that described by Mishra et al.^[15] and Berretta et al.^[16].

3. Results and discussion

3.1 Structural characterization

Fig. 2 shows the X-ray diffraction results for the samples prepared at various annealing temperatures. It is observed that the as-deposited compound exhibits a covellite phase (CuS) with a hexagonal lattice. With annealing at 300 °C, the phase Cu₂S was formed. Further increasing of the annealing temperature (to 350 °C) led to a mixed phase (Cu_1.8S + Cu₂S). Finally, the annealing at 400 °C gives a digenite phase (Cu_1.8S) with a hexagonal lattice. The obtained results match well with the standard references cited in Fig. 2 and with Refs. [17–19]. The transition from a sulfur-rich phase to a copper-rich phase is due to high volatilization of sulfur. It is worth noting that the annealing at 200 °C results in the mixed phase (CuS + Cu₂S) according to our previous study^[20].

To confirm the observed phase change, the DTA was performed. Fig. 3 shows the corresponding curves for the prepared sample without annealing. Three exothermic peaks were observed at 100, 190, and 240 °C. The first one is due to the vaporization of the water. The second and the third peaks are due to dehydration of CuS. An endothermic peak was observed at 340 °C, which corresponds to the transition to the digenite phase. For comparison, fractional decomposition of CuS to Cu₂S was also observed in Ref. [21]. The observed transition matches with the X-ray patterns (Fig. 2) and with the literature data^{[7, 22, 23]}. Another exothermic peak was also observed at about 800 °C. This peak corresponds to an expected transition from the digenite phase to the djurlite phase as shown in previous studies^{[7, 24]}.

Figs. 4 (a)–4(d) show the SEM images of the prepared nanoparticles. It is observed that the as-deposited compound is formed by grains, whose the size goes up to 4 μm, with large separation distances (Fig. 4(a)). With annealing at 300 °C, the compound becomes more uniform, but with much agglomeration and a lot of pores (Fig. 4(b)). Annealing at 350 °C results in the formation of grains with a high density as illustrated in Fig. 4(c). Finally, the annealing at 400 °C results in a dense compound as shown in Fig. 4(d).

It is well known that the phase transition in copper sulphide nanoparticles can be induced by thermal treatment during annealing or during the reaction^{[10–12, 19, 21, 25, 26]}. However, it is not reasonable to compare the obtained results with those from another study because the synthesis method is not the same (precursors, operating mode, duration, and atmosphere of annealing). Nevertheless, the phase transition by annealing is expected to be a sure event.

According to the SEM and XRD results, the mechanism of the growth and the phase transition from covellite to chalcocite and from chalcocite to digenite is proposed. This mechanism is roughly similar to that proposed by Quintana-Ramirez et al.^[26] for the copper sulphide thin films. At the first, grains of the covellite phase are formed following the reaction:

$${\rm C{u^{2 + }} + {S^{2 - }} \to CuS}.$$

(2)

With annealing, the sulfur ions leave the lattice since they are volatile and the covellite phase transforms into the chalcocite phase as following:

$${\rm 2CuS \to C{u_{\rm{2}}}S + S}.$$

(3)

According to our previous study^[20], the chalcocite phase presents, at the first, a lamellae shape for the annealing at 200 °C. With further increasing of the annealing temperature (to 300 °C), bonds get broken and a continuous shape is obtained. For the annealing at 350 °C, nucleation of the crystals of the digenite phase begins. In fact, the sulfur atoms in the chalcocite phase approximately maintain their positions, whereas the copper ions move through the available space, so that the distinction between interstitial and lattice ions is lost^[13]. This gives rise to an increased almost liquid-like ionic mobility. Consequently, the following reaction occurs:

$${\rm C{u_2}S \to C{u_{{\rm{1}}.8}}S + 0.2Cu}.$$

(4)

At 400 °C, chains of nanoparticles of the digenite phase are formed since the full phase transition from chalcocite to digenite is obtained.

3.2 Thermoelectric characterization

Fig. 5 displays the evolution of the crystallite size, along with the room temperature electrical resistivity as a function of the annealing temperature. It is noted that the crystallite size varies from 16 to 31 nm and that the resistivity increases by one order of magnitude when the annealing temperature varies from 350 to 400 °C.

Electrical resistivity of copper-based semiconductors depends on the shape of the compound and the chemical formula. In fact, it is defined by the ability for electrons to move into the upper energy levels leaving holes in the valence band. The crystallite size affects directly the energy band gap. In fact, when the crystallite size increases, the number of atoms (restricted in the crystallite) increases, which gives rise to more numerous overlaps between atoms orbits. The increase of the resistivity by increasing the crystallite size was also observed in TiO₂ nanomaterial^[27] and in CuO nanoparticles^[28]. This makes the energy band gap narrower and thus causes the electrical resistivity to decrease. However, porosity is also a pertinent parameter. The resistivity is expected to increase with increasing the pore size. On the other hand, in Cu_2–xS compounds, when x increases the copper ions on the top of the valence band decreases, which causes the energy band gap to increase^[29]. Therefore, the resistivity is expected to be greater for the chalcocite phase Cu₂S. In Fig. 5, crystallite size, chemical formula, and compression of the pellet compete. The resistivity increases by increasing the crystallite size, which is not expected. Thus, the electrical transport is mainly affected by the porosity although all pellets were prepared under the same pressure (7 tons).

Fig. 6 shows the evolution of the power factor as a function of the annealing temperature. It is noted that the sample Cu_1.8S is the most efficient with a power factor of 1.93 μWm⁻¹K⁻². This compound was considered as a good thermoelectric material^[7]. Moreover, all samples have a positive Seebeck coefficient indicating that the Cu_2–xS compounds are p-type semiconductors.

The evolution of the Seebeck coefficient of the compound Cu_1.8S with the measurement temperature was analyzed from room temperature to 116 °C. It is observed that this evolution exhibits a pronounced peak at 100 °C as illustrated in Fig. 7. This peak corresponds to the transition from the γ phase to the β phase. Ge et al.^[7] also observed this transition at the same temperature by studying the evolution of the electrical conductivity as a function of temperature. This shows that the measurement of the Seebeck coefficient can be a good method for observing the phase transition.

On the other hand, the Seebeck coefficient increases by 98% from the room temperature to the γ–β transition temperature. This result is similar to that observed in copper selenide Cu₂Se^[30]. The physical explanation given by Brown et al.^[30] was based on the consideration of the disorder in the vicinity of the transition. This explanation may be valid in copper sulphide. Indeed, the Seebeck coefficient is written^[31]:

$$\alpha = - \frac{1}{{{K_{\rm B}}T}}\frac{{{J_{{\rm qe}}}}}{{{J_{{\rm ee}}}}} - \frac{\mu }{{eT}}.$$

(5)

The first term represents the transport thermopower, including the heat transport per electron (J_qe) and the current transported by electron (J_ee). The second term is the presence thermopower, and it contains the chemical potential, μ. The physical origin of this term is the manner with which the carrier is transported and it is written as^{[32, 33]}:

$${\alpha _{{\text{presence}}}} = - {\text{ }}\frac{1}{e}{\left( {\frac{{\partial S}}{{\partial N}}} \right)_U},$$

(6)

where S is the entropy, N is the number of carriers, and U is the internal energy.

According to Eq. (6), the presence thermopower can be enhanced by enhancing the effect of the number of carriers on the entropy of the atoms-carriers ensemble. This may be reached in a system with numerous states.

When atoms vibrate, the number of the accessible states increases. In the vicinity of the continuous transition, the atomic vibrations become more and more numerous and intense. Thus, the entropy increases quickly with increasing the number of carriers, which results in a dramatic increase in the presence thermopower. This observation is useful for (i) observing the phase transition, and (ii) using a given semiconductor in the thermoelectric devices in the vicinity of its transition temperature.

4. Conclusion

Copper sulphide powders were successfully synthesized by the sol–gel method. The different phases were obtained by annealing. The electrical resistivity and the crystallite size were observed to be affected by the phase transition. The thermoelectric analyses show that the digenite phase (Cu_1.8S) has the highest power factor at room temperature.

The Seebeck coefficient of the compound Cu_1.8S exhibits a maximum at the γ–β transition temperature, indicating a dramatic change in the presence thermopower. This is due to the fast increase in the disorder in the atoms-holes ensemble.

The success of further refinement will open new doors for developing new functional abundant and non-toxic materials in thermoelectric devices at low cost.