Thermoelectric performance of ternary Cu-based chalcogenide Cu₂TiTe₃

Thermoelectric (TE) technology builds a direct bridge between electrical energy and thermal energy, offering a promising solution to solve the growing environmental pollution and energy crisis.^1,2 The energy conversion efficiency of TE technology is mainly dependent on the material's dimensionless figure of merit (zT  $= S 2σT/κ$⁠, where S, σ, κ, and T are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively). To achieve high zT, a TE material should possess high S, large σ, and low κ.³ 

The past two decades have witnessed the great progress in the development of high performance TE materials. Many effective strategies, such as band engineering,^4,5 all-scale hierarchical architecture,^6,7 resonant scattering,^8,9 phonon-liquid,^10,11 meta-phase,¹² entropy engineering,^13–16 and attuned electronic structure and mismatched phonon structure,¹⁷ have been proposed to decouple the highly correlated TE parameters and improve the zT. Meanwhile, many novel TE materials have been discovered, showing high zT values that are comparable or even superior to those of the state-of-the-art TE materials (e.g., Bi₂Te₃, PbTe, and SiGe). Among them, Cu-based chalcogenides have attracted great attention in TE community due to the nontoxic and earth-abundant feature of Cu and the novel and abnormal physical mechanisms observed in some of them.¹⁸ Cu-based diamond-like compounds, whose crystal structure originates from zinc blende, are one important branch of Cu-based TE chalcogenides.^19,20 Their TE performance well obeys the “unity-η” rule, i.e., both the peak power factor (PF =  $S 2σ$⁠) and the maximum zT can be achieved when the distortion parameter η is close to 1.⁵ Cu-based liquid-like compounds, whose crystal structure consists of a rigid sublattice formed by anions and a liquid-like Cu-sublattice, are another important branch of Cu-based TE chalcogenides.^21–23 The highly diffusive Cu ions greatly disturb the propagation of transverse waves, leading to the abnormal heat capacity and ultralow lattice thermal conductivity. Combining the decent electrical transport performance provided by the rigid sublattice, high zTs with the maximum exceeding 2.0 have been achieved in Cu-based liquid-like compounds.¹¹ 

Beyond Cu-based diamond-like compounds and Cu-based liquid-like compounds, there are many other kinds of Cu-based chalcogenides, which also show good TE performance. Typical examples are Cu₁₂Sb₄S₁₃,²⁴ Cu₂₆Nb₂Ge₆S₃₂,²⁵ BaCu₂Se₂,²⁶ and BiCuSeO.^27,28 Actually, in the inorganic crystal structure database (ICSD), there are more than 4000 entries of Cu-based chalcogenides. Many of them have not been investigated by TE community.²⁹ In this study, we report the TE properties of a ternary Cu-based chalcogenide Cu₂TiTe₃, which has relatively large average atomic weight and is composed of environmental-friendly elements. Due to the high valence band degeneracy (N_v = 5) and moderate bandgap (E_g = 0.34 eV), Cu₂TiTe₃ has decent electrical transport performance comparing with other reported Cu-based TE chalcogenides, with a high PF of 7.5 μW cm⁻¹ K⁻² at 300 K. Combining the low lattice thermal conductivity, a maximum zT of 0.38 is achieved for Cu₂TiTe₃ at 600 K.

We prepared polycrystalline Cu₂TiTe₃ by using a melting-annealing method. Highly pure elements, Cu (99.999%, shot), Ti (rod, 99.99%), and Te (99.999%, shot) were weighed out according to the chemical stoichiometry of Cu₂TiTe₃ and sealed into a silicon tube under high vacuum condition. The tube was heated to 1273 K and held at this temperature for 24 h. Then, the temperature was cooled to 700 K and held at this temperature for 100 h, followed by natural cooling to room temperature. The ingot was ground into fine powders and then sintered into a disk with a diameter of 10 mm by spark plasma sintering (Sumitomo SPS-2040). The sintering temperature and pressure are 623 K and 46 MPa, respectively. The phase composition, electrical, and thermal transport properties of the prepared Cu₂TiTe₃ were measured. The measurement details can be found elsewhere.¹⁰ The relative density of the sintered Cu₂TiTe₃ is 96%.

Cu₂TiTe₃ crystalizes in a monoclinic structure (No. 12 space group, C2/m) at room temperature.³⁰ Its cell volume is 295.89 ų. As shown in Fig. 1(a), its crystal structure is constructed by two kinds of twisted [CuTe₄]^7– tetrahedra and one kind of [TiTe₆]^8– octahedra. Inside the twisted [CuTe₄]^7– tetrahedra, four Cu–Te bonds have three different bond lengths. The case is similar in the twisted [TiTe₆]^8– octahedra. The twisted [CuTe₄]^7– tetrahedra and [TiTe₆]^8– octahedra are connected in a variety of ways, such as co-vertex, co-edges, and co-plane, forming a complex monoclinic structure [Fig. 1(a)], which facilitates for achieving low lattice thermal conductivity. Distorted polyhedra cause a change in the length of Te–Te bonding, which might lead to strong anti-bonding interaction.

Figure 1(b) shows the powder x-ray diffraction (PXRD) of the prepared Cu₂TiTe₃. Rietveld refinement indicates that all diffraction peaks can be indexed belonging to the monoclinic structure of Cu₂TiTe₃ (PDF #86-1850). The refined lattice parameters are a = 19.798, b = 3.970, and c = 7.077 Å, which are comparable with those in ICSD database (a = 19.798, b = 3.982, and c = 7.100 Å). EDS mapping further proves that all elements are uniformly distributed inside the matrix as is shown in Fig. 1(c). No obvious elemental enrichment is observed. These results indicate that the prepared Cu₂TiTe₃ is phase pure. The selected area electron diffraction (SAED) pattern shown in Fig. 1(d) indicates that the prepared Cu₂TiTe₃ crystallizes in the monoclinic structure, being consistent with the PXRD pattern. The spacing of the [200] plane (d) is calculated with a value of d = 9.96 Å, which is close to the value obtained from the PDF #86-1850 (d = 9.88 Å).

Figure 2(a) shows the measured σ, S, and PF of Cu₂TiTe₃. The σ is about 7 × 10⁴ S m⁻¹ at 300 K. It decreases with increasing temperature, showing heavily doped semiconducting behavior. Similar with most Cu-based TE chalcogenides, Cu₂TiTe₃ also demonstrates positive S, indicating that the dominating carriers are holes. In Cu-based compounds, the Cu vacancies are easily to be formed during the fabrication process. These Cu vacancies act as electron-acceptors, yielding the heavily doped semiconducting behavior shown in Fig. 2(a). The PF for Cu₂TiTe₃ is about 7.5 μW cm⁻¹ K⁻² at 300 K, which is higher than most Cu-based TE chalcogenides at the same temperature, such as 2.6 μW cm⁻¹ K⁻² for Cu₂Te,²¹ 3.8 μW cm⁻¹ K⁻² for CuGaTe₂,³¹ and 2.3 μW cm⁻¹ K⁻² for Cu₂SnSe₃.¹⁹ To further assess the quality of Cu₂TiTe₃, its electronic quality factor (B_E), which is doping-independent,³² is calculated, with a value of 2.2 μW cm⁻¹ K⁻² at 300 K. As shown in Fig. 2(b), this value is among the highest numbers in Cu-based TE chalcogenides.^{19–23,26,28,31,33–35}

In order to understand the decent electrical transport performance of Cu₂TiTe₃, its electronic structure is calculated by using the Vienna ab initio simulation package (VASP).^36,37 The Perdew–Burke–Ernzerhof-type generalized gradient approximation is adopted,³⁸ and the cut-off energy is set as 520 eV in a gamma-centered 3 × 3 × 5 k-mesh grid. As shown in Fig. 3, Cu₂TiTe₃ is an indirect-gap semiconductor with a narrow bandgap of 0.34 eV. The projected density of states of electronic structure indicates that the valence band maximum (VBM) is mainly dominated by Te, Ti, and Cu, while the conduction band minimum (CBM) is mainly dominated by Ti. Interestingly, except the peak at the Γ point, there are two additional peaks locating along the Γ_X route and Γ_N route. The wave function results reveal that the peak along the Γ_X route is composed of Ti d-Te p bonding and Cu d-Te p interaction, while the other two bands are composed of Ti d-Te p bonding, as shown in Fig. 3. The band degeneracy of the peaks locating along the Γ_X route and Γ_N route is 2, while that at the Γ point is 1. Since these three peaks have nearly the same energy, the valence band degeneracy of Cu₂TiTe₃ near VBM is up to 5, which is higher than most Cu-based chalcogenides reported before, such as N_v = 3 for Cu₂X (X = S, Se, and Te), N_v = 3 for Cu(In,Ga)Te₂, and N_v = 1 for Cu₂SnSe₃.³⁹ The higher N_v is beneficial for achieving larger density-of-state effective mass under the same Fermi level, which is responsible for the decent electrical transport performance mentioned above.

The thermal transport properties of Cu₂TiTe₃ are shown in Fig. 4(a). The κ of Cu₂TiTe₃ is about 1.8 W m⁻¹ K⁻¹ at 300 K. It decreases with increasing temperature, reaching about 1.4 W m⁻¹ K⁻¹ at 600 K. Such reduction is mainly caused by the lowered lattice thermal conductivity κ_L with increasing temperature. By using the Wiedemann–Franz law (κ_e = LσT, where L is the Lorentz constant calculated by $L=1.5+ e − | S | 116$⁠), the κ_L of Cu₂TiTe₃ is determined to be around 1.4 W m⁻¹ K⁻¹ at room temperature. As shown in Fig. 4(b), this value is higher than those of Cu-based liquid-like compounds, such as 0.59 W m⁻¹ K⁻¹ for Cu₂Se and 0.39 W m⁻¹ K⁻¹ for Cu₂S,^21–23 but much lower than those of Cu-based diamond-like compounds, such as 6.7 W m⁻¹ K⁻¹ for CuGaTe₂,³¹ 4.8 W m⁻¹ K⁻¹ for Cu₂ZnSnS₄,³³ and 2.7 W m⁻¹ K⁻¹ for Cu₂SnSe₃.¹⁹ 

The κ_L is determined by the equation κ_L = 1/3C_vv_ml, where C_v is the specific heat, v_m is the speed of sound, and l is the phonon mean free path. The low v_m is one reason for the low κ_L of Cu₂TiTe₃. The measured transverse, longitudinal, and average speed of sound of Cu₂TiTe₃ are 1752, 3037, and 1945 m s⁻¹, respectively. The v_m estimated from the phonon dispersion spectrum is 2081 m s⁻¹, which is comparable with the experimental result (1945 m s⁻¹). The average speed of sound v_m of Cu₂TiTe₃ is lower than many Cu-based TE chalcogenides, such as 2938 m s⁻¹ for CuFeS₂⁴⁰ and 2312 W m⁻¹ K⁻¹ for CuGaTe₂.³¹ It is already comparable with those of PbTe and GeTe.^41,42

In addition, Fig. 4(c) shows the phonon dispersion spectrum of Cu₂TiTe₃, which is obtained by constructing 2 × 2 × 2 supercells under the phonopy package⁴³ based on the frozen phonon method, where the k-space grid is taken to be 3 × 3 × 3. The partial density of states suggest that the low-lying optical modes are mainly contributed by the Te and Cu elements. Through the analysis of phonon vibration modes, it is found that the low-frequency optical modes (around 1 THz) are mainly contributed to the global motion of clusters composed of Ti–Te–Cu, which is depicted in Fig. 4(d). This atomic cluster corresponds to Ti–Te bonding and Ti–Cu bonding in the Cu₂TiTe₃ structure. On the one hand, these clusters form chemical bonding at VBM and are beneficial to electrical transport. On the other hand, the low-lying optical modes produced by these clusters can introduce additional resonant scattering to impede the normal transport of acoustic phonons with similar frequencies and reduce the κ_L.

Based on the measured σ, S, and κ, the TE figure-of-merit (zT) of Cu₂TiTe₃ is calculated. As shown in Fig. 5, Cu₂TiTe₃ exhibits a zT of 0.12 at 300 K. It increases with increasing temperature, reaching 0.38 at 600 K. Under the same temperature, this value is much higher than many Cu-based compounds reported before,^{19–23,31,34,40} such as 0.21 for Cu₂SnSe₃,¹⁹ 0.30 for CuGaTe₂,³¹ and 0.20 for Cu₂S.²³ 

In summary, this work prepares pure phase Cu₂TiTe₃ and systematically investigates its TE performance. Due to the moderate bandgap and high valence band degeneracy, Cu₂TiTe₃ shows good electrical transport performance. Combining the low lattice thermal conductivity related to the global motion of clusters, Cu₂TiTe₃ exhibits a decent zT of 0.38 at 600 K. Via tuning the carrier concentration to improve the electrical transport performance or strengthening the phonon scattering to reduce the κ_L, higher zT can be expected for this ternary Cu-based TE chalcogenide.

This work was supported by the National Natural Science Foundation of China (No. 52122213), the Shanghai Pilot Program for Basic Research-Chinese Academy of Science, Shanghai Branch (No. JCYJ-SHFY-2022-002), and Shanghai Government (No. 20JC1415100). T. D. thanks the support from the National Natural Science Foundation of China (No. 52203294) and the China Postdoctoral Science Foundation (No. 2022M723271).