Improved thermoelectric performance of solid solution Cu4Sn7.5S16 through isoelectronic substitution of Se for S

Cu-Sn-S family of compounds have been considered as very competitive thermoelectric candidates in recent years due to their abundance and eco-friendliness. The first-principles calculation reveals that the density of states (DOS) increases in the vicinity of the Fermi level (Ef) upon an incorporation of Se in the Cu4Sn7.5S16−xSex (x = 0–2.0) system, which indicates the occurrence of resonant states. Besides, the formation of Cu(Sn)-Se network upon the occupation of Se in S site reduces the Debye temperature from 395 K for Cu4Sn7S16 (x = 0) to 180.8 K for Cu4Sn7.5S16−xSex (x = 1.0). Although the point defects mainly impact the phonon scattering, an electron-phonon interaction also bears significance in the increase in phonon scattering and the further reducion of lattice thermal conductivity at high temperatures. As a consequence, the resultant TE figure of merit (ZT) reaches 0.5 at 873 K, which is 25% higher compared to 0.4 for Cu4Sn7.5S16.


Measurements.
Hall coefficients (R H ) were measured by using a four−probe configuration in a system (PPMS, Model−9) with a magnetic field up to ± 5 T. The Hall mobility (μ) and carrier concentration (n H ) were subsequently determined according to the relations μ = |R H |σ and n H = −1/(e R H ) respectively, where e is the electron charge. The Seebeck coefficients (α) and electrical conductivities (σ) were measured simultaneously by using a ULVAC ZEM−3 instrument system under a helium atmosphere from RT to ~900 K, with uncertainty of <6.0% for each.
The thermal conductivities were calculated based on the equation κ = dλC p , where the thermal diffusivities λ were measured by the TC−1200RH instrument under vacuum, with an uncertainty of <10%, whereas the heat capacities (C p ) were estimated based on Dulong-Petit rule above RT. The three physical parameters (α, σ, κ) were finalized by taking the average values of several samples tested by the same method. The total uncertainty for ZT value was ∼18%. In addition, the heat capacities (C p ) for the Se-incorporated sample Cu 4 Sn 7.5 S 16−x Se x (x = 1.0) were measured with the measurement system (PPMS, Quantum Design) in the temperature range of 2.0-153 K, and the Debye temperature (Θ D ) was then determined using the equation 19 : Here, β was obtained from a simple Debye model 13,20 in the low temperatures below 10 K, and n is the number of atoms per chemical formula. The lattice contributions (κ L ) were obtained by subtracting the electronic contribution (κ e ) from the total κ, i.e., κ L = κ − κ e . Here κ e is expressed by the Wiedemann-Franz law, κ e = L 0 σT, where L 0 is the Lorenz number, estimated at 1.5 × 10 −8 WΩK −2 for not fully degenerate environment of semiconductors 21 . Characterization. The chemical compositions of the sample (x = 1.0) were checked using an electron probe micro-analyzer (EPMA) (S-4800, Hitachi, Japan) with an accuracy >97%. The microstructures of the samples (x = 0, 1.0) have been examined using high-resolution transmission electron microscopy (HRTEM). HRTEM images were obtained at 220 kV using JEM-2010F (Field emission TEM). The XRD patterns were collected by powder X-ray diffractometer (D8 Advance) operating at 50 kV and 40 mA with Cu Kα radiation (λ = 0.15406 nm) and a scan rate of 4° min −1 in the range from 10° to 120°. The lattice constants a and c were obtained from the refinement of the X-ray patterns using Jade software.
Raman spectra of three Cu 4 Sn 7.5 S 16−x Se x powders (x = 0, 1.0 and 2.0) were recorded at 300 K from 50 to 4000 cm −1 at a resolution of 0.6 cm −1 using an Invia-Reflex Raman spectrometer with Nd:YAG laser source (l = 532.0 nm). The spectrum of the sample Cu 4 Sn 7.5 S 16 was presented for comparison. A 50× objective lens was employed via a confocal geometry to transmit the incident laser beam and collect the scattered radiation. Laser intensity was mandatorily attenuated to prevent the samples from decomposing.
First-Principles Calculations. First-principles calculations were carried out using spin-polarized DFT with generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) implemented in VASP code 22,23 . The DFT + U methodology with a value of U = 5.0 eV was used in this work 24 . The valence electronic states were expanded in the basis of plane waves, and the core-valence interaction is represented using the scalar relativistic projector augmented wave (PAW) 25

Results and Discussions
Compositions and structures. Scanning electron microscopy (S-4800, Hitachi, Japan) was employed to check the homogeneity of the microstructure of the sample (x = 1.0). The mapping pictures of four elements (Cu, Sn, S and Se) and EDAX spectrum are shown in Fig. S1. We observed slight segregations for Cu and Se. The average chemical compositions taken from different mappings for each element are presented in Table S1, where the number of moles of S is normalized to 15. Generally, the relative molars of Cu, Sn, S and Se identified are close to those of nominal compositions, only a little deficiency in Se and excess in Sn. These results suggest that the compositions are almost as intended as in the nominal materials.
The X-ray diffraction patterns of the powders Cu 4 Sn 7.5 S 16−x Se x (x = 0, 0.5, 1.0, 2.0) at RT are shown in Fig. 1, where all peak positions are observed the same as those of stoichiometric Cu 4 Sn 7 S 16 (PDF: 51-0932) with no visible impurity phase identified. The result thus indicates that the synthesized samples are crystallized in a single phase, as shown in Fig. 1a,b is a close-up view of the XRD patterns between 26° to 38°. We observed that the peak positions corresponding to the crystal planes (202) and (208) shift towards low angle, except for the sample at x = 0.5, whose peak positions do not follow the trend. The reason is unknown. The possible explanation is that this material contains a serious segregation, which influences its peak positions. Anyhow, the movement in peak positions indicates that the crystal lattice dilates when Se substitutes for S. This dilation is also indicated by linearly increased lattice parameters, a and c, displayed in Fig. 1c, and can be explained by the larger atomic size of Se (1.18 Ǻ) than that of S (1.04 Ǻ) 26 . As such, the tensile stress might occur.
The microstructure upon an incorporation of Se was observed using high-resolution TEM (HRTEM) for the sample (x = 2.0), and that of the Sb-free sample (x = 0) are presented for comparison. The results are shown in  Figure 2c is the SAED pattern for x = 2.0 and Fig. 2d its corresponding HRTEM image. An inset in Fig. 2d indicates that the d spacing between (202) crystal planes is about 0.314 nm. These observations suggest that the Se atoms are almost incorporated into the crystal lattice of Cu 4 Sn 7.5 S 16 at x ≤ 2.0. Besides, both samples exhibit a typical polycrystalline structure, but the grain size in the sample at x = 2.0 seems to be smaller than that at x = 0.
Upon the incorporation of Se, we believe that Se atoms are most likely settled in the S site rather than in Cu and Sn sites, because Se has the same valence electrons as S. This assumption can be substantiated by the low formation energies (d H ) calculated when Se resides in S sites. Since the d H value, which gradually increases from 0.78 (eV) (x = 0) to 2.73 (eV) (x = 2.0), is much lower than those in the case of Se residing in Cu (8.16 eV) and Sn (5.59 eV) sites when x = 0.5. Therefore, we mainly focus on the band structure calculation in the event Se occupies S site. Figure 3 shows the density of states (DOS) of the compounds Cu 4 Sn 7.5 S 16−x Se x (x = 0.5, 1.0, 1.5 and 2.0) pursuant to the first-principles, where the DOS at x = 0 is presented for comparison 5 . When Se is incorporated into the S site (Fig. 3), the DOS is more localized in both the valence and conduction bands, and it significantly increases in the vicinity of the Fermi level (E f ) for the samples at x = 0.5 and 1.0, exhibiting a behavior of resonant states. At x ≥ 1.5, the DOS near the Fermi level decreases. Further, there is a band splitting in the conduction band (CB) between 1.0-1.7 eV, without a tendency of degeneracy. The E f seems to be pinned in the middle of CB, with no visible tendency of movement either. Transport and TE properties. In order to understand the effects of the band structure modification on the transport and physical properties, we have measured the Hall coefficients of the compounds, and then calculated the Hall carrier concentration (n H ) and mobility (μ). The results are indicated in Fig. 4, where we observed visible changes in both n H and μ. The n H value enhances from 4.48 × 10 16 cm −3 (x = 0) to 7.18 × 10 16 cm −3 (x = 2.0), while the mobility μ decreases from 5.66 cm 2 v −1 s −1 to 1.53 cm 2 v −1 s −1 . Since the isoelectronic substitution could neither create extra electrons in the compound, nor alter the chemical environment in accordance to the estimation using the valence counting rule 27,28 , therefore, the changes in n H and μ are mainly attributed to the formation of the conductive network of Cu-Se when Se replaces S. Figure 5 represents the Seebeck coefficient (α) and electrical conductivity (σ) measured in the temperature range from RT to ~900 K, where those for x = 0 and Cu 4 Sn 7 S 16 are presented for comparison. The α value shows no visible decreasing tendency at x ≤ 1.0, probably due to the generation of the resonant states near the Fermi level 29 , which increases the relatively effective mass m * /m. Due to such, the α values at x = 0.5 and 1.0 are seemingly larger than those at the corresponding carrier concentrations determined by the Pisarenko relation 30 at RT (indicated by a solid line in Fig. 5b). At ~890 K the α values at x = 0.5 (1.0) are 306.3 (294.19 μVK −1 ), only 8.3% (11.9%) less than 334.1 (μVK −1 ) at x = 0 (Fig. 5a); while the α value at x = 2.0 is 221.5 μVK −1 , about 33.7% less. The electrical conductivity (σ) (shown in Fig. 5c) increases from 1.57 × 10 3 Ω −1 m −1 (x = 0) to 2.67 × 10 3 Ω −1 m −1 (x = 2.0) at ~890 K as a result of an increased carrier concentration. The power factors PF, PF = α 2 σ, are shown in Fig. 5d. At x = 1.0 the PF reaches the highest (2.24 μW/cm-K 2 ) at ~890 K, about 10% higher than that at x = 0.
In light of the above measurements, we conclude that the created resonant states near the E f and the formation of Cu(Sn)-Se network have a profound impact on the electrical property. They thus play a big role in improving the TE performance.
It is well known that the electronic thermal conductivity κ e is determined by the electrical conductivity σ, whereas the lattice part κ L is substantially independent of the charge carrier system except for, perhaps the scattering of lattice vibrations (phonons) by charge carriers at high carrier densities 21 . At a temperature far above the Debye temperature, all phonon modes are activated, and increased umklapp and lattice disorder and/or phonon-electron scattering would mainly cause the lattice thermal conductivity reduction. Upon Se incorporation, the scattering from introduced lattice disorder along with the umklapp process should play a big role in reducing the lattice contribution. To verify this assumption, we have measured the thermal diffusivities of different samples and obtained thermal conductivities (κ), which are presented in Fig. 6a. At a temperature above ~720 K, the κ value generally decreases as Se content increases, and at ~890 K it reduces to 0.39 WK −1 m −1 for x = 1.0. The composition dependence of lattice parts (κ L ) shares some similarities to total κ at x ≤ 1.0, and at ~890 K it reduces to 0.34 WK −1 m −1 for x = 1.0 (Fig. 6b). Although the lattice part κ L decreases as Se content increases, the values of m * /m e and quality factor B (B = μ H (m * /m e ) 3/2 T 5/2 /κ L ) 21 increase simultaneously as x value increases, until they start to decrease at x = ~0.75, as shown in Fig. 6c. This further confirms the importance of the created resonant states near the Fermi level. Combined with the three physical properties (α, σ and κ), we attain the TE figure of merit (ZT), shown in Fig. 6d. At x = 1.0 the ZT value reaches the highest (ZT = 0.5) at 873 K, 25% higher compared to ZT = 0.4 at x = 0. Although this value is lower that those in other Cu-Sn-S compounds, such as Cu 3 Sn 1.2 S 4 (ZT = 0.75 at 790 K) 7 and Co-Cu 2 SnS 3 (ZT = 0.85 at 723 K) 6 , it still stands out among the highest in the family of Cu 4 Sn 7 S 16 compounds.
To further verify the increase in phonon scattering upon Se incorporation, we have analyzed the Raman spectra, shown in Fig. 7, where the Raman spectra of Cu 4 Sn 7 S 16 and Cu 4 Sn 7.5 S 16 5 are used for comparison. The features of the presented spectra upon Se incorporation bear an overall resemblance to those of Cu 4 Sn 7 S 16 and Cu 4 Sn 7.5 S 16 , which suggests that the molecular structures are rather similar upon Se incorporation. However, the main modes at 94.1 cm −1 , 311 cm −1 and 350 cm −1 become less pronounced as Se content increases. Meanwhile, the peak position shifts to the low frequency side (red shift) as well. This indicates that the increased structural disorder is a    Owing to the presence of the tensile stress, the lattice structure expands (Fig. 1c). In addition, the presence of the tensile stress along with the lattice structure dilation is closely related to the creation of the extra conductive paths in the framework and favor the large DOS in both the valence and conduction bands 10,32 . Therefore, the carrier concentration increases. On the other hand, the substitution of Se for S can reduce the Debye temperature 13 or sound velocity 33 . To confirm this issue, we have measured the heat capacities of the sample Cu 4 Sn 7.5 S 16−x Se x (x = 1.0) in the temperature range of 2.0-153 K (Fig. 8), and then determined the β value using the relation of C p /T ~ T 2 in the low temperatures, according to Eq. (2). As shown in Fig. 8 and its inset, there is an almost linear relation between C p /T and T 2 . Therefore, the Debye temperatures (Θ D ) was determined to be 180.8 K. This temperature is much lower than 395 K for the sample Cu 4 Sn 7 S 16 1 , which indicates the possibility of the extra reduction in lattice part κ L at high temperatures [13][14][15][16] .
With  where u and Г are the disorder scaling parameter and the disorder scattering parameter respectively. Here we use the factor Г below to predict the κ L values for the Cu-Sn-S based chalcogenides 34 , where χ i , ΔM i /M and Δδ i /δ are the molar fraction of extra Se, the relative change of atomic mass due to the replacement of S by Se, and the local change in lattice parameter. The other related parameters are presented in ref. 5 . The fitting result using above model is drafted in Fig. 6 as a blue solid curve. Basically, the model enables a good prediction of the temperature dependent lattice thermal conductivity below ~770 K, confirming the dominant effect of the structural disorder upon Se substitution for S. While above ~770 K the estimated κ L data is higher than the experimental one, indicating the presence of other phonon scattering mechanism, which is most likely the increased phonon-electron scattering at high temperatures.

Conclusions
Cu 4 Sn 7.5 S 16 family of compounds with Se isoelectronic substitution for S have been prepared and their transport and thermoelectric properties have been investigated. The first-principles calculation reveals that upon the incorporation of Se, the Fermi level still pins within the conduction band without any movement tendency. However, the DOS is more localized in both the valence and conduction bands, and increases in the vicinity of the Fermi level (E f ), which indicates the occurrence of resonant states. As such, the effective mass (m * /m e ) and quality factor (B) increase and thereby profoundly impact the TE performance. Further, there exists another phonon scattering mechanism in the Se-incorporated Cu 4 Sn 7.5 S 16 system, in addition to the dominant point defect scattering of phonons. This extra mechanism is likely due to the scatterings from the phonon-electron interaction at high temperatures. As a consequence, the TE figure of merit (ZT) enhances by ~25%, if compared to 0.4 for Cu 4 Sn 7.5 S 16 .