1 Introduction

Utilizing waste heat is critical for reducing fossil fuel consumption and decreasing CO2 concentrations in the atmosphere. Thermoelectric (TE) technology can directly convert heat into useful electricity, showing a great potential in the applications of harvesting waste heat from industrial processes or automobiles [1,2,3,4]. The energy conversion efficiency of a TE material is evaluated by the dimensionless TE figure of merit, zT = S2σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κ is the thermal conductivity. The quantity S2σ is called power factor (PF), which is associated with the electrical transport properties. To make the TE technology practically in large-scale use, the materials with high zT are required to enable high energy conversion efficiency.

Cu2S is a p-type semiconducting compound that has attracted great attention in TE community in the past several years [5, 6]. The stoichiometric Cu2S compound possesses two phase transitions. One is at about 370 K, and the other is at about 700 K. Below 370 K, Cu2S is called as low-chalcocite γ phase (L-chalcocite), which is a normal solid. Between 370 and 700 K, Cu2S crystalizes in the hexagonal β phase (H-chalcocite) [7]. Above 700 K, it further transforms to the α phase with a fcc cubic structure. The details of phase structures including lattice parameters are shown in Table 1 [8].

Table 1 Crystal structures and lattice parameters of different phase structures in Cu2S [8]
Full size table

Both β-Cu2S and α-Cu2S belong to the superionic conductors, in which the sulfur atoms maintain a rigid sublattice, while the “liquid-like” Cu ions are distributed throughout many possible positions inside the rigid sublattice with high diffusivities. On the one hand, the highly disordered diffusing copper ions strongly scatter the heat-carrying phonons, resulting in very short phonon mean free path. On the other hand, the liquid-like nature of Cu ions also effectively eliminates part transverse phonons, leading to much reduced heat capacities (Cp) which are below the limit value of 3 NkB (where N is the number of atoms composed of lattice and kB is Boltzmann constant) in a normal solid. Hence, very low lattice thermal conductivity (κL), about 0.3 W·m−1·K−1, was obtained in Cu2S [9]. As a result of such low κL, a maximum zT of 0.6 was achieved in Cu2S at 1000 K in spite of the relatively low carrier concentration (p) (~ 1×1018 cm−3) and small σ (~ 1×103 S·m−1) [9]. Considering that the elements are low cost, nontoxic, and earth-abundant, Cu2S becomes a potential candidate which can be used in the waste heat recovery industry.

Optimizing the electrical transport properties and reducing the κ are two common strategies to improve the zT of established TE materials [10,11,12]. Considering the intrinsic ultralow κL, improving the zT of Cu2S should focus on the optimization of electrical transport properties, especially enhancing its p. The binary phase diagram of Cu–S shows that the Cu composition in cubic Cu2−δS phase can be down to δ = 0.27 at 780 K [7]. Thus, introducing Cu-deficiency is an effective way to generate additional holes to enhance the p. When the Cu-deficiency content δ = 0.03, the p at 300 K is increased to 7.3 × 1020 cm−3, about two orders of magnitude higher than the that of stoichiometric Cu2S. Meanwhile, the intrinsic ultralow κL can be well maintained in the Cu-deficient Cu2−δS compounds. Consequently, a record-high zT of 1.7 at 1000 K has been achieved in Cu1.97S [9]. Further increasing Cu-deficiency can continuously enhance the p. When the Cu-deficiency content δ = 0.2, the p is as high as 5.4 × 1021 cm−3 at 300 K [13]. However, such high p significantly deviates the optimal p range, thus the zTs are poor for these Cu2−δS samples with large content of Cu-deficiency [13]. Beyond introducing Cu-deficiency, doping the foreigner elements is also a very familiar way to tune the electrical transport properties of established TE materials [14,15,16]. However, very little work has been performed on doping the foreigner elements in Cu2S to optimize the electrical transport properties. Actually, so far, Li is the only electropositive element which was reported to be doped into Cu2S successfully. In 2004, Balapanov et al. [17] fabricated several Cu2−xLi x S (0 < x < 0.25) compounds and measured their ionic conductivities. It is found that Li dopants can decrease the ionic conductivity by increasing the ionic activation energy. Nevertheless, the TE properties of these Li-doped Cu2S compounds have not been characterized. Most recently, Kang et al. [18] investigated the TE properties of Li-doped Cu2Se compounds. They found that doping Li at Cu-sites can increase the σ and then improve the zT. Similar phenomenon might also happen in Cu2S system.

In this study, a series of Cu2−xLi x S samples with different Li-doping contents (x = 0, 0.005, 0.010, 0.050, and 0.100) were synthesized. Their electrical and thermal transport properties were measured in the temperature range from 300 to 900 K. A systematic evaluation about the effect of Li doping at Cu-sites on crystal structure and TE properties was performed. As a result of the optimized electrical transport properties, a maximal zT of 0.84 at 900 K was obtained in Cu1.99Li0.01S, about 133% improvement as compared with that in Cu2S matrix.

2 Experimental

Polycrystalline Cu2−xLi x S (x = 0, 0.005, 0.010, 0.050, and 0.100) samples were prepared by melting-quenching-annealing method. High-purity raw elements Cu (shots, 99.999%, Alfa Aesar), S (pieces, 99.999%, Alfa Aesar), and Li (ingot, 99.999%, Sigma-Aldrich) were weighted out in stoichiometric proportions and then sealed in carbon-coated silica tubes under a vacuum level of − 100 kPa. The sealed tubes were slowly raised to 923 K and dwelled for 4 h, and then continually raised to 1383 K and dwelled for 12 h. After that, these tubes were slowly cooled down to 923 K. After annealing for 3 days at 923 K, these tubes were naturally cooled to room temperature. Finally, the ingots were pulverized into powders in agate mortars and sintered by spark plasma sintering (SPS, Sumitomo SPS-2040) at 723 K under a pressure of 65 MPa for 5 min. Electrically insulating and thermally conducting boron nitride layers were sprayed onto the surface of carbon foils before the SPS process in order to prohibit direct current (DC) pulsed currents going through powders.

The phase compositions in the prepared samples were identified by room-temperature powder X-ray diffraction measurements (RT-PXRD, Rigaku D/max 2550 V) with Cu Kα source. The sample morphologies and elemental distribution were measured by energy dispersive spectroscopy (EDS, Oxford Horiba 250). X-ray photoelectron spectroscopy (XPS, ESCALAB 250, Thermo Scientific) was used to identify the binding energies of each component elements. The σ and S of bar-shaped samples were measured simultaneously using a commercial system (ZEM-3, ULVAC). The κ was calculated according to the formula κ = D × Cp × d, where D is the thermal diffusivity, Cp is the heat capacity, and d is the density. Thermal diffusivity (D) was measured using the laser flash method (LFA-457, Netzsch) on a round specimen with the size of 10 mm in diameter and around 1.5 mm in thickness. The specific heat (Cp) was derived from the Dulong–Petit law, while the densities (d) were obtained by measuring the weights and volumes of the samples. The Hall coefficient (RH) was measured by a physical properties measurement system (PPMS, quantum design). The hole p was calculated via p = 1/eRH, where e is the elementary charge.

3 Results and discussion

The phase purity and crystal structure of the synthesized Cu2−xLi x S (x = 0, 0.005, 0.010, 0.050, and 0.100) samples were examined by XRD with Cu Kα radiation at 300 K. As shown in Fig. 1, XRD patterns of Cu2−xLi x S (x ≤ 0.05) can be well indexed to the low-chalcocite phase (space group P21/c, PDF No. 83-1462). No other phases are detected. This suggests that doping Li at Cu-sites in Cu2S does not change the structure symmetry of Cu2S when x ≤ 0.050. For Cu1.9Li0.1S with a high Li-doping content, some new diffraction peaks are observed, which are indexed to Cu1.96S phase (space group P43212, PDF No. 29-0578). In contrast with the good stability of those samples with Li-doping content x ≤ 0.05, it is found that Cu1.9Li0.1S is unstable in air. After polishing, the surface of the Cu1.9Li0.1S bulk sample gradually changes from shiny to gray, which might be caused by the oxidation of Li elements. Thus, in the following part, only the electrical and thermal transport properties of those stable Cu2−xLi x S (x ≤ 0.05) samples are discussed.

Fig. 1
figure 1

Room-temperature powder XRD patterns for Cu2−xLi x S (x = 0, 0.005, 0.010, 0.050, and 0.100) samples

Full size image

For the Cu-deficient Cu2−δS compounds, the single low-chalcocite phase only exists in a very narrow composition range with 1.991 ≤ δ ≤ 2.000 at 300 K [7]. According to the Cu–S phase diagram, when δ is smaller than the limit value of 1.991, the Djurleite phase (space group P43212, PDF No. 29-0578) appears and the Cu2−δS (1.965 ≤ δ ≤ 1.991) becomes a mixture of the low-chalcocite phase and Djurleite phase [19]. Thus, the absence of Djurleite phase in our synthesized Cu2−xLi x S (x ≤ 0.050) samples proves that almost all Li dopants enter into the Cu-sites and the actual content of Cu-vacancy inside the crystal structure should be very small. However, due to the similar ionic radii between Li+ (76 pm) and Cu+ (77 pm) under the six-coordination [20], these Li dopants scarcely induce any peak shift in the XRD patterns of the Li-doped samples. Figure 2 presents EDS mappings of Cu1.995Li0.005S and Cu1.99Li0.01S samples. Owing to the light atomic mass, the signal of Li cannot be detected by EDS analysis. However, it is clear that Cu and S are homogeneously distributed inside the matrix without any elemental agglomeration or deficiency. This suggests that there are no Li-included secondary phases formed during the synthesis process. Combining the absence of Djurleite phase in XRD patterns (Fig. 1), it is reasonable to speculate that the real chemical compositions in the present Cu2−xLi x S (x ≤ 0.05) samples are close to the nominal chemical composition.

Fig. 2
figure 2

Elemental EDS mappings of a Cu1.995Li0.005S and b Cu1.99Li0.01S

Full size image

Figure 3 shows Cu 2p, S 2p, and Li 1s XPS spectra for Cu1.95Li0.05S. The Cu 2p XPS spectra consist of two peaks corresponding to the spin–orbit-split 2p3/2 and 2p1/2. For Cu1.95Li0.05S, the 2p3/2 and 2p1/2 peaks locate at 932.9 and 952.7 eV, respectively, which are almost the same with those of the pristine Cu2S [13]. The S 2p binding energy in Cu1.95Li0.05S is also the same with that in the pristine Cu2S, suggesting that introducing Li in Cu2S scarcely changes the valence states of Cu and S [13]. Likewise, the Li 1s signal is detected at 55.2 eV, slightly higher than those observed in the metallic Li [21]. Combining the above XRD and EDS analyses, it can be concluded that Li is doped in the samples prepared in this study.

Fig. 3
figure 3

XPS spectra for a Cu 2p, b S 2p, c Li 1s in Cu1.95Li0.05S

Full size image

Figure 4 shows the measured TE properties for the synthesized Cu2−xLi x S (x = 0, 0.005, 0.010, and 0.050) samples, in which the overall measurement errors in the σ, S, and κ were estimated to be about ± 5%, ± 3%, and ± 7% [22]. All samples possess positive S throughout the entire measured temperature range, indicating that holes are the dominate carriers. The σ of Cu2S is quite low with a value of about 0.1 × 104 S·m−1 at 300 K. This low σ is mainly contributed by the wide band gap (~ 1.2 eV) of Cu2S [23]. As shown in Fig. 4a, b, with the increase in Li-doping content, S gradually decreases, while σ increases in the whole measured temperature range. For Cu1.95Li0.05S, the σ increases to about 0.87 S·m−1 at 300 K, about one order of magnitude higher than that of Cu2S matrix. In contrast, the S value of Cu1.95Li0.05S at 300 K is reduced to 80 μV·K−1, only a half as large as that of Cu2S matrix. These lead to the significant enhancement of PF (PF = S2σ) in the Li-doped samples, especially at temperatures above 600 K (Fig. 4c). The maximal PF value is about 6.4 μW·cm−1·K−2 at 800 K in Cu1.95Li0.05S, which is comparable with that observed in the Cu-deficient Cu2S compounds [9]. Figure 4d shows that the κ values of all Cu2−xLi x S (x = 0, 0.005, 0.010, and 0.050) samples have a weak temperature dependence. This is a common feature observed in almost all superionic TE materials reported so far, which might be related with the strong anharmonicity in these compounds [24,25,26]. The κ values of Cu1.995Li0.005S and Cu1.99Li0.01S are slightly higher than that of Cu2S matrix. However, when the Li-doping content is raised to x = 0.050, κ is obviously increased. At 300 K, the κ value of Cu1.95Li0.05S is about 0.84 W·m−1·K−1, around twice that of Cu2S matrix.

Fig. 4
figure 4

Electrical and thermal transport properties of Cu2−xLi x S (x = 0.005, 0.010, and 0.050) samples: a electrical conductivity (σ), b Seebeck coefficient (S), c power factor (PF), and d thermal conductivity (κ)

Full size image

The significantly improved electrical transport properties in Cu2−xLi x S samples are very interesting. As mentioned above, XRD and EDS analyses confirm that almost all the Li dopants enter into the lattice of the Cu2−xLi x S (x ≤ 0.05) samples. Thus, the presence of secondary phases is ruled out as the reason for the improved electrical transport properties in the Li-doped samples. In Cu2S, it is generally regarded that the valence states of Cu and S are + 1 and − 2, respectively [13]. Considering that Li only has one s electron in the outermost shell, it is expected that doping Li at Cu-sites should scarcely change the p. However, the Hall measurements shown in Fig. 5a suggest that the p increases with the increase in the Li-doping content. At 300 K, the p value of Cu1.95Li0.05S is 1.5 × 1020 cm−3, which is about one order of magnitude higher than that of the Cu2S matrix. In Cu-based compounds, the p-type electrical transport behavior is mainly contributed by the presence of intrinsic Cu vacancies formed during the fabrication process [27, 28]. Doping Li at Cu-sites might change the Cu-vacancy formation energy and modify the content of Cu-vacancy inside the lattice, leading to the enhanced p in the Li-doped samples. However, the modification is very tiny, and thus, it cannot be detected by above XRD and EDS analyses. Similar phenomenon has also been observed in S-alloyed Cu2Se system [29]. As a result of such significantly enhanced p, the σ of Li-doped Cu2S is greatly increased although the carrier mobility (μ) is reduced somewhat (Fig. 5a). Lukashev et al. [30] calculated the band structure of Cu2S, and they found that the valence band maximum (VBM) is dominated by the Cu-d state and s state. Similar results have also been reported by Sun et al. [31] recently. However, due to the nature of the close shell d10 configurations of monovalent Cu, these d electrons have a very small contribution to the group velocity and the band shape in the valence band maximum [31]. Thus, the band shape of Cu2S in VBM would be scarcely modified by the Li dopants. This can be confirmed by the Pisarenko plot (S vs. p) shown in Fig. 5b, which suggests that the Li-doped Cu2S samples well follow the theoretical Pisarenko relation with the effective mass, m* = 1.3m0, where m0 is the free electron mass. This result further proves the “electron crystal” feature of Cu2S that the sulfur sublattice dominates the electrical transports, while the Cu atoms only provide electrons to determine the location of Fermi level.

Fig. 5
figure 5

a Hall carrier concentration (p) and Hall mobility (μ) as a function of Li-doping content for Cu2−xLi x S (x = 0, 0.005, 0.010, and 0.050) samples; b experimental and calculated Pisarenko plots (S vs. p) at 300 K (line being calculated curve based on single-parabolic band model)

Full size image

Another abnormal phenomenon observed in Li-doped Cu2S samples is the raised κ shown in Fig. 4d. The total κ of a solid is a sum of two contributions: the lattice thermal conductivity (κL) and the carrier thermal conductivity (κc). According to the Wiedemann–Franz law, the κc can be estimated by κc = LTσ, where L is the Lorenz number. Here, the L values are obtained by the following equation [32, 33],

$$L = \left( {\frac{{k_{\text{B}} }}{e}} \right)^{2} \times \left\{ {\frac{{\left( {\lambda + 3} \right)F_{\lambda + 2} \left( \eta \right)}}{{\left( {\lambda + 1} \right)F_{\lambda } \left( \eta \right)}} - \left[ {\frac{{\left( {\lambda + 2} \right)F_{\lambda + 1} \left( \eta \right)}}{{\left( {\lambda + 1} \right)F_{\lambda } \left( \eta \right)}}} \right]^{2} } \right\}$$
(1)

where kB is the Boltzmann constant, e is the electron charge, λ is the scattering factor, and η is the reduced Fermi energy. The η can be calculated from the S by the equation,

$$S = - \frac{{k_{\text{B}} }}{e}\left[ {\eta - \frac{{\left( {\lambda + 2} \right)F_{\lambda + 1} \left( \eta \right)}}{{\left( {\lambda + 1} \right)F_{\lambda } \left( \eta \right)}}} \right]$$
(2)

where λ = 0 by assuming that the charge carriers are scattered by acoustic phonons in the present study. The Fermi integrals are given by \(F_{m} \left( \eta \right) = \mathop \smallint \limits_{0}^{\infty } \frac{{x^{m} {\text{d}}x}}{1 + \exp (x - \eta )}\), where x is the reduced carrier energy. The calculated L values are shown in Fig. 6a.

Fig. 6
figure 6

Temperature dependences of a Lorenz number (L) and b lattice thermal conductivity (κL) for Cu2−xLi x S (x = 0, 0.005, 0.010, and 0.050) samples

Full size image

Based on these L values, the lattice thermal conductivities of the Cu2−xLi x S samples from 300 to 900 K are shown in Fig. 6b. Clearly, the raised κ values presented in Fig. 4d are mainly contributed to the increased κL. This is quite abnormal because doping foreigner elements usually strengthens the point scattering to phonons and reduces the κL [34]. Although the atomic radii between Cu+ and Li+ under the six-coordination are similar [19], the different atomic masses should induce strong mass fluctuation and affect the normal transport of heat-carrying phonons. One possible reason for this abnormal phenomenon is the increased Cu ionic activation energy in Li-doped Cu2S samples. In Cu2S, the intrinsic ultralow κL mainly comes from the highly disordered migrating Cu ions inside the sulfur framework. Owing to the weak chemical bonding between Cu and S, these Cu ions possess very low ionic activation energies, about 0.19 eV in the hexagonal β-Cu2S phase and 0.09 eV in the cubic α-phase, respectively [17]. Thus, these Cu ions can easily migrate among the sulfur sublattice with high diffusivities (~ 1×10−5 cm2·s), which can strongly scatter the phonons and disrupt the normal heat propagation [17]. Doping Li significantly increases the ionic activation energy due to the “mixed mobile ions effect,” i.e., the ionic conductivity of a compound with more than one mobile ions will be drastically reduced compared to the single-ion conducting phase [17]. In 2004, Balapanov et al. [17] systematically investigated the effect of Li-doping on the Cu-ion migration behavior in Cu2S. They found that the ionic conductivity of Cu1.95Li0.05S is about one fourth that of Cu2S matrix under the same temperature range. Correspondingly, the ionic activation energy of Cu1.95Li0.05S is raised to 0.5 eV at 628 K, increasing by about 160% as compared with that of Cu2S matrix. Thus, the Cu-ion short-range migration would be significantly suppressed in the present Li-doped samples, which will definitely lessen the phonon scattering and result in the high κL as shown in Fig. 5b.

Figure 7 shows the dimensionless zT calculated based on the measured σ, S, and κ, where the measurement errors in the zT were estimated to be about ± 12% [22]. Owing to the significantly optimized electrical transport properties, Li-doped Cu2S samples demonstrate much improved zT as compared with the Cu2S matrix despite the raised κ in these Li-doped samples. For Cu1.99Li0.01S, the maximum zT at 900 K is 0.84, about three times that of the Cu2S matrix.

Fig. 7
figure 7

Temperature dependence of TE figure of merit (zT) for Cu2−xLi x S (x = 0, 0.005, 0.010, and 0.050) samples

Full size image

4 Conclusion

In this work, a series of Cu2−xLi x S samples with different Li-doping contents (x = 0, 0.005, 0.010, 0.050, and 0.100) were successfully synthesized. The effects of Li-doping on the phase composition, electrical, and thermal transport properties were investigated. It is found that the room-temperature crystal structure of Cu2S can be well maintained until the Li-doping content reaches x = 0.050. Doping Li at Cu-sites significantly improves the p while scarcely modifies the initial band structure. Thus, the electrical transport properties in Cu2−xLi x S have been significantly improved. For Cu1.95Li0.05S, the maximal PF is about 6.4 μW·cm−1·K−2 at 800 K, which is comparable with that observed in Cu-deficient Cu2S compounds. Doping Li into Cu2S suppresses the Cu-ion migration by increasing the ionic activation energy; thus, the κ values of Cu2−xLi x S increase. As a result of the optimized electrical transport properties, a maximal zT of 0.84 at 900 K is obtained in Cu1.99Li0.01S, increasing by about 133% relative to that in the Cu2S matrix.