Improved Thermoelectric Performance in Nonstoichiometric Cu2+

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Improved Thermoelectric Performance in Non-stoichiometric Cu2+#Mn1-#SnSe4 Quaternary Diamond-like Compounds Qingfeng Song, Pengfei Qiu, Hongyi Chen, Kunpeng Zhao, Dudi Ren, Xun Shi, and Lidong Chen ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b19791 • Publication Date (Web): 02 Mar 2018 Downloaded from http://pubs.acs.org on March 4, 2018

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ACS Applied Materials & Interfaces

Improved Thermoelectric Performance in Non-stoichiometric Cu2+δMn1-δSnSe4 Quaternary Diamond-like Compounds Qingfeng Song,†, § Pengfei Qiu,*, † Hongyi Chen,†, §, ‡ Kunpeng Zhao,†, § Dudi Ren,† Xun Shi,*, † and Lidong Chen† †

State Key Laboratory of High Performance Ceramics and Superfine Microstructure,

Shanghai Institute of Ceramics, Chinese Academy of Science, Shanghai 200050, China §

University of Chinese Academy of Sciences, Beijing 100049, China

‡

School of Physical Science and Technology, ShanghaiTech University, Shanghai

201210, China Keywords: thermoelectric, diamond-like, non-stoichiometric, doping, refinement

Abstract Novel quaternary Cu2MnSnSe4 diamond-like thermoelectric material was discovered recently based on the pseudocubic structure engineering. In this study, we show that introducing off-stoichiometry in Cu2MnSnSe4 effectively enhances its thermoelectric performance by simultaneously optimizing the carrier concentrations and suppressing the lattice thermal conductivity. A series of non-stoichiometric Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1) samples has been prepared by the melting-annealing method. The X-ray analysis and the scanning electron microscopy measurement show that all nonstoichiometric samples are phase pure. The Rietvield refinement demonstrates that substituting part of Mn by Cu well maintains the structure distortion parameter η close to 1, but it induces obvious local distortions inside the anion-centered tetrahedrons. Significantly improved carrier concentrations are observed in these non-stoichiometric Cu2+δMn1-δSnSe4 samples, pushing the power factors to the theoretical maximal value predicted by the single parabolic model. Substituting part of Mn by Cu also reduces the lattice thermal conductivity, which is well interpreted by the Callaway model. Finally, a maximal thermoelectric dimensionless figure-of-merit zT around 0.60 at 800 K has been obtained in Cu2.1Mn0.9SnSe4, which is about 33% higher than that in the Cu2MnSnSe4 matrix compound.

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1. Introduction Driven by the need for safe, clean, and sustainable energy source, thermoelectric (TE) technology has attracted growing interesting in recent years. The TE technology can convert heat into electricity by the Seebeck effect or pump heat for cooling by the Peltier effect.1 Due to the advantages of solid-state operation, compact design, vast scalability, zero-emissions, and long operating lifetime with no maintenance, the TE technology shows a great potential to be used in energy harvesting applications.2, 3 The conversion efficiency of a TE device is highly dependent on the dimensionless 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 total thermal conductivity (including the lattice thermal conductivity κL and carrier thermal conductivity κe).4 The quantity S2σ is called power factor (PF), which is associated with the electrical transport properties. The normal ways to improve the zT of a TE material are to increase the power factors PF by optimizing electronic properties, and/or to reduce the lattice thermal conductivity κL by engineering lattice vibrations or phonons.5-7 The past decade has witnessed remarkable progress in thermoelectrics. Despite the development of the classical TE materials, many new high-performance TE materials have been successfully discovered.8 Among them, diamond-like compounds are a new class of TE materials with relatively low thermal conductivities and decent electrical transports. There are about 1000 types of ternary and quaternary diamond-like compounds.9 These compounds are derived from II-VI cubic zinc-blende structure with the two or three kinds of cations orderly cross-substituted the Zn-sites. At the same time, the crystal structure is also changed from high-symmetry cubic to low-symmetry noncubic because of the lattice distortion induced by the atomic size mismatch among the substituted elements. The structure distortion parameter η (= c/2a, where c and a are the lattice parameters along z-axis and x-axis, respectively) is usually used to reflect the compression or tension in the crystal lattice along the z-axis of these non-cubic diamondlike compounds.10 In 2009, the TE properties of the diamond-like compound Cu2ZnSnSe4 were reported.11, Cu2CdSnSe4,13

12

Since then, a series of diamond-like compounds, such as

Cu2ZnGeSe4,14

Cu2CdGeSe4,15

Cu2MgSnSe4,16

CuInTe2,17

and

CuGaTe218, was successively investigated. Some of them were reported with high TE 2 - 25 ACS Paragon Plus Environment

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performances with zT around unit, comparable with those of the classical TE materials. In 2014, the pseudocubic structure approach has been proposed to screen and select high TE performance compounds.

19

diamond-like

compounds

from

these

low-symmetry

non-cubic

The diamond-like compounds with η closer to 1 usually possess the

energy-splitting parameter ∆CF closer to 0 and higher-degree cubic-like degenerate bandedge electronic states, and consequently better TE performance. Using this pseudocubic structure approach, one can easily discover new diamond-like materials with the η close to 1, or establish proper molar ratios for two or more diamond-like materials to form a solid solution to push the η close to 1. All these two directions assure good TE performance.19 The quaternary diamond-like compound Cu2MnSnSe4 is a typical example discovered most recently based on the pseudocubic structure approach.20 Its crystal structure is shown in Figure 1a. The structure can be regarded as a double-periodic cubic zinc-blende supercell in the z-direction, in which Zn is orderly substituted by Cu, Mn, and Sn, showing a pseudocubic framework. The structure distortion parameter η of Cu2MnSnSe4 is 0.986. Likewise, the anion sublattice shows a locally distorted non-cubic framework consisting of irregular Se anion-centered tetrahedrons (see Figure 1a), in which the Se anions deviate off the ideal tetrahedral sites due to the different bonding lengths and bonding angles between the cations (Cu, Mn, and Sn) and the Se anions.19 Such locally distorted framework results in low lattice thermal conductivity as compared with those for binary ZnSe21 and ternary diamond-like compound17, 18. A maximal zT of 0.45 at 850 K has been achieved in the chemical stoichiometric Cu2MnSnSe4.20 Particularly, the carrier concentration corresponding to this zT is only 3 × 1019 cm-3, which is much lower than the optimal value in the order of 1020 cm-3 observed in other quaternary diamond-like compounds reported before.14, 22 This indicates that the zT of Cu2MnSnSe4 can be further enhanced. In this study, we tried to improve the TE performance of Cu2MnSnSe4 by introducing the off-stoichiometry to enhance carrier concentrations and optimize power factors. A series of Cu2+δMn1-δSnSe4 samples has been prepared and their crystal structure, electrical and thermal transport properties have been systematically investigated. Enhanced zT with a maximum around 0.60 at 800 K has been obtained in 3 - 25 ACS Paragon Plus Environment


Cu2.1Mn0.9SnSe4, which is about 33% higher than that in Cu2MnSnSe4. Especially, the zT enhancement occurs in the entire temperature range, which is meaningful for enhancing energy conversion efficiency in real applications.

2. Experimental and calculation details High purity elements, Cu (shots, 99.999%), Mn (pieces, 99.95%), Sn (shots, 99.999%), and Se (shots, 99.999%) were weighed out in the atomic ratio of Cu2+δMn1δSnSe4

(δ = 0, 0.025, 0.05, 0.075, and 0.1), and then sealed in evacuated quartz ampoules.

The sealed ampoules were heated up to 873 K at a speed of 50 K/h and then kept at 873 K for 14 h. Subsequently, they were further raised to 1423 K at a rate of 100 K/h and remained at this temperature for 72 hours. Then the sealed ampoules were naturally cooled to room temperature. The obtained ingots were manually ground into fine powders and then cold pressed into disks. These disks were sealed in evacuated quartz ampoules again and annealed at 873 K for 7 days. The final products were manually ground into fine powders and then sintered by spark plasma sintering (SPS) at 773 K for 10 min under an axis pressure of 60 MPa. High densities (> 97% of the theoretical density) were obtained for all samples. X-ray diffraction analysis (D8 ADVANCE, Bruker Co. Ltd) was used to examine phase purity and chemical compositions of the synthesized samples. The samples were scanned in the 2θ range of 10°–90° with a step of 0.02° and counting time of 2 s per step. Rietveld refinements were performed using the Fullprof software (Version 2016). The chemical compositions and the microstructure analysis were examined by scanning electron microscopy (SEM, ZEISS Supra 55). Electrical conductivity and Seebeck coefficient at 300-800 K were measured by using the ZEM-3 (ULVAC Co. Ltd.) apparatus under Helium atmosphere. Thermal conductivity at 300-800 K was calculated by multiplying the measured values of thermal diffusivity D, heat capacity Cp, and density ρ (κ = ρDCp). The thermal diffusivity was measured in argon atmosphere by using the laser flash method (LFA 427, Netzsch Co. Ltd). The heat capacity was estimated by the Neumann-Kopp law by using the heat capacity of each component elements. The density was measured by using the Archimedes method. The measurement errors for the electrical resistivity, Seebeck coefficient, and thermal conductivity are 5%, 7%, and 5%, 4 - 25 ACS Paragon Plus Environment

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respectively. Electrical conductivity, thermal conductivity, and Hall coefficient (RH) below 300 K were measured in a Physical Property Measurement System (Quantum Design). Hall coefficients (RH) were measured by sweeping the magnetic field up to 3 T in both positive and negative directions. Hall carrier concentration (pH) and Hall mobility (µH) below room temperature were estimated by pH = 1/eRH and µH = σRH, respectively. Density-functional theory (DFT) calculations were performed with the projectoraugmented wave (PAW) method as implemented in the highly efficient Vienna Ab Initio Simulation Package (VASP). For the geometry relaxation of the primitive unit cell with the stannite structure, a k-point mesh of 9 × 9 × 9 was applied without including the spin– orbit coupling. The cutoff energy of the plane-wave was set at 400 eV. The energy convergence criterion was chosen of 10 × 10-5 eV per unit cell. We used the modified Becke-Johnson potential (MBJ) + U method to calculate the electronic structure. The effective Coulomb repulsion parameter U was set 4 eV based on the published literature of Cu based semiconductors.23 3. Results and discussion For thermoelectrics, the electrical and thermal transport properties are usually very sensitive to the secondary phases. Therefore, phase purity has to be checked firstly. The powder X-ray diffraction (PXRD) patterns of the Cu2+δMn1-δSnSe4 samples (δ = 0, 0.025, 0.05, 0.075, and 0.1) are shown in Figure 1b. All samples are well indexed to the tetragonal stannite structure ( I 42m , PDF#26-0542). No extra diffraction peaks are observed. This suggests that all the excess Cu atoms may enter into the Mn-sites. Taking Cu2.1Mn0.9SnSe4 as an example, Figure 2 shows the backscattered electron imaging mapping performed by scanning electron microscopy. All elements, Cu, Mn, Sn, and Se, are homogeneously distributed inside the matrix. No elemental agglomeration is observed. These results further suggest that all samples prepared in the present study are phase pure. Figure 3a shows the lattice parameters (c and a) of all Cu2+δMn1-δSnSe4 samples refined by using the FullProf Program Suite based on the room-temperature PXRD data. Since the radius of Mn (rMn2+ = 66 pm) is larger that of Cu (rCu+ = 60 pm), replacing part of Mn by Cu should reduce the lattice parameter. Surprisingly, the lattice parameters 5 - 25 ACS Paragon Plus Environment


along both z-axis and x-axis (c and a) are almost the same for all samples. Wolfgang et al. prepared the non-stoichiometric Cu2+xZn1-xGeSe4 and they found that the lattice parameters were also independent on the off-stoichiometry.14, 24 Similar results were also found in Cu2+xMg1-xSnSe4 compounds.16 Due to the unchanged c and a, the structure distortion parameters η (= c/2a) of the present Cu2+δMn1-δSnSe4 samples (see Table I) are similar to the matrix compound. The unchanged lattice parameters in the non-stoichiometric Cu2+δMn1-δSnSe4 samples are very interesting. In order to further clarify this, more detailed X-ray refinement has been performed. In the binary blende ZnSe, the Se is located at the ideal tetrahedral sites (0.25, 0.25, 0.25).25 However, in the quaternary Cu2MnSnSe4, the initial Zn cations are substituted by three different cations (Cu, Mn, and Sn) with different electronegativities and radii. These three different cations form distinct chemical bonds with the Se anions with different bonding lengths, such as 2.41 Å for Cu-Se, 2.52 Å for Mn-Se, and 2.58 Å for Sn-Se, pushing the Se anions moving away from the ideal tetrahedral sites (0.25, 0.25, 0.25) to the sites (0.248, 0.248, 0.133) in the quaternary Cu2MnSnSe4. As shown in Figure 3b, substituting part of Mn by Cu shrinks the distance between the Mn sites and the Se sites due to the shorter Cu-Se bonding length than the Mn-Se bonding length. Correspondingly, with increasing the off-stoichiometry content δ, a monotonously decrease of the x (or y) and z coordinates is observed (see Figure 3c). The internal distortion parameter (φ), which is defined as φ = [(1/4 − x)2 + (1/4 − y)2 + (1/8 − z)2]1/2, is explored to evaluate the degree of local crystal structure distortion in Cu2+δMn1-δSnSe4.26 As shown in Figure 3d, the φ increases with increasing δ, suggesting that the substitution Mn by Cu strengthens the local distortion of the crystal structure in Cu2+δMn1-δSnSe4. On one hand, such strengthened local structure distortion caused by the shortened distance between the Mn sites and the Se sites releases the distortion caused by the radii gap between Mn and Cu, leading to the almost unchanged a and c values with increasing the off-stoichiometric content δ from 0 to 0.1 (see Figure 3a). On the other hand, such local structure distortion also introduces additional strain field fluctuations to affect the normal transport of heat-carrying phonons.19 Thus, reduced lattice thermal conductivities are expected in these Cu2+δMn1-δSnSe4 samples, which is shown below. The measured TE properties of Cu2+δMn1-δSnSe4 are shown in Figure 4. All samples 6 - 25 ACS Paragon Plus Environment

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possess positive Seebeck coefficient (S) throughout the entire measured temperature range, indicating that holes are the dominate carriers. Such p-type electrical transport behavior is attributed by the presence of intrinsic Cu vacancies inside the crystal structure, which is also a common phenomenon observed in most Cu-based materials.1, 27 at around 400 K, both S and σ show non-monotonic variations, which might be related with the phase transitions.20, 28 For the stoichiometric Cu2MnSnSe4, the σ is very low. With increasing the δ, the σ is gradually increased throughout the entire measured temperature range. For instance, the σ for Cu2.1Mn0.9SnSe4 is 2.5 × 104 S m-1 at 300 K, about one order of magnitude higher than that for the stoichiometric Cu2MnSnSe4. In contrast, the Seebeck coefficient S is gradually decreased with increasing the δ. The S for Cu2.1Mn0.9SnSe4 is 67.8 µV K-1 at 300 K, about 32% of that for the stoichiometric Cu2MnSnSe4. As a result of the significantly enhanced σ, the PFs of the nonstoichiometric samples are greatly enhanced. At 800 K, the PF for Cu2.1Mn0.9SnSe4 is 7.0 µW cm-1 K-2, approximate two times of that for the stoichiometric Cu2MnSnSe4. Figure 4d shows the total thermal conductivity (κ) for all Cu2+δMn1-δSnSe4 samples. The maximal κ in the stoichiometric Cu2MnSnSe4 is only about 2.9 W m-1 K-1 at 300 K, which is quite low as compared with the binary ZnSe (~ 19 W m−1 K−1 at 300 K)21 or ternary diamond-like compounds (e.g. CuInTe2 ~ 6.0 W m−1 K−1 and CuGaTe2 ~ 7.5 W m−1 K−1 at 300 K)17,

18

. At 800 K, the κ is even below 1 W m-1 K-1. Changing the

stoichiometry has a weak influence on the total κ. All Cu2+δMn1-δSnSe4 samples still maintain the low κ. The variations of σ and S shown in Figure 4a and 4b are mainly caused by the modified carrier concentrations. In stoichiometric Cu2MnSnSe4, the valence states of Cu and Mn are +1 and +2, respectively.20 The substitution of Mn by Cu scarcely changes the valence state of Cu and Mn, as confirmed by the X-ray photoelectron spectroscopy (XPS) characterization shown in Figure S1, thus additional holes will be created to take part in the electrical transports. Figure 5a shows the measured Hall carrier concentration pH for all Cu2+δMn1-δSnSe4 samples. As we expected, the pH monotonously increases with increasing δ at room temperature. The pH for Cu2.1Mn0.9SnSe4 is 2.9 × 1020 cm-3 at 300 K, about one order of magnitude higher than that for the stoichiometric Cu2MnSnSe4. This significantly enhanced pH also suggests that the valence state of Cu in these non7 - 25 ACS Paragon Plus Environment


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stoichiometric samples should be +1. Beyond the carrier concentration, the carrier mobility µH is also one important parameter for the TE materials. Based on the measured Hall carrier concentrations, the Hall carrier mobilities µH of all Cu2+δMn1-δSnSe4 samples are calculated and listed in Table I. At 300 K, the µH is 5.1 cm2 V-1 s-1 for Cu2.1Mn0.9SnSe4, only one third of that for the stoichiometric Cu2Mn0.9SnSe4. In Figure 5b, we also plot the relationship between the carrier mobility and the carrier concentration. Our experimental data well satisfy the µH ~ pH-1/3 relationship predicted by the single parabolic band model, suggesting that the charge carrier scattering by acoustic phonons is still the dominant mechanism for these non-stoichiometric Cu2+δMn1-δSnSe4 samples at room temperature.29 According to the single parabolic band model together with the relaxation time approximation, the Seebeck coefficient S and carrier concentration pH are described as14, 30 =

−

(1),

∗ 4π

(2),

and =

where =

/"# $

is the reduced Fermi energy, kB is the Boltzmann constant, m* is the

density-of-state effective mass, h is the Planck constant, and λ is the scattering factor. The ,

Fermi integrals are given by % = &-

' ( )'

'*'+

, where x is the reduced carrier

energy. Assuming acoustic phonon scattering is the predominant carrier scattering mechanism near room temperature (λ = 0) and m* = 1.2 me (me is the free-electron mass), the calculated Pisarenko plot (S vs. pH) is plotted in Figure 5c. Clearly, the experimental data well fall on this plot, suggesting that all Cu2+δMn1-δSnSe4 samples possess similar effective mass. Interestingly, some other Cu/Se-based quaternary diamond-like compounds, e.g. Cu2ZnSnSe422 and Cu2ZnGeSe414, also possess similar effective mass with the present Cu2+δMn1-δSnSe4 samples. The weak influence of non-stoichiometry on both µH and m* is quite interesting because it is expected that the presence of Cu at Mn-sites might introduce additional impurity scattering to the charge carriers, leading to the deterioration on the µH or the increase of m*. In order to understand this phenomenon, the band structure of the 8 - 25 ACS Paragon Plus Environment

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stoichiometric Cu2MnSnSe4 is calculated. As shown in Figure 6, the valence band maximum is found at the G point, with the contribution mainly from Se-3p states and Cu3d states.10,

31, 32

Similar band structure characters have been also observed in other

Cu/Se-based quaternary diamond-like compounds, such as Cu2CdGeSe4, or even in binary Cu2Se.32,

33

Hence, the similar m* observed in these quaternary diamond-like

compounds is reasonable because the valence band maximum is weakly dependent on the transitional elements (e.g. Zn/Cd) and the group IV elements (e.g. Sn/Ge). Meanwhile, considering the too localized d orbitals, Cu atoms contribute very little to the group velocities and band shapes.33 Thus, the electrical transport properties should be mainly determined by the Se atoms. In this case, the substitution of Mn by Cu would only shift downward the Fermi level while scarcely affect the µH and m*. Meanwhile, Figure 6 also shows that the initial triply degenerate valence band Γ15v in cubic zinc blende splits into a non-degenerate band Γ4v and a doubly-degenerate band Γ5v by crystal field effect in quaternary Cu2MnSnSe4. The crystal field splitting energy, ∆CF = E(Γ5v) - E(Γ4v), is only 0.02 eV. Such small ∆CF, i.e. high band convergence, is consistent with the lattice distortion parameter η highly close to 1 in Cu2MnSnSe4.19 Because the substitution of Mn by Cu scarcely changes the η, the non-stoichiometric Cu2+δMn1-δSnSe4 samples would have the similar ∆CF at the valence band maximum with the stoichiometric sample, which is another reason for the similar m* observed in Figure 5c. Based on the single parabolic band model, we have calculated the relationship between PF (= S2σ) and pH at 800 K. As shown in Figure 5d, the optimal carrier concentration for Cu2MnSnSe4 is around 3.0 × 1020 cm-3 at 800 K. Using Cu to replace part Mn atoms pushes the pH to the optimal range, and thereby results in the greatly optimized PFs. For Cu2.1Mn0.9SnSe4, because its carrier concentration pH is very close to the optimum value, the PF reaches around 7.0 µW cm-1 K-2 at 800 K, almost two times of that for the stoichiometric Cu2MnSnSe4. As mentioned above, the substitution of Mn by Cu leads to some local distortions inside the crystal structure, which might strengthen the scattering to the heat-carrying lattice phonons. In order to confirm this, the lattice thermal conductivities (κL) of the Cu2+δMn1-δSnSe4 samples are calculated by subtracting the electronic part from the total κ. The electronic thermal conductivity κe is calculated according to the Wiedeman-Franz 9 - 25 ACS Paragon Plus Environment


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law (κe = LσT, where L is the Lorenz number). In this study, the L values are calculated according to34

0

. = /

−1

2 3

(3),

The calculated temperature-dependent Lorenz number L and κL values for all samples are shown in Figure 7a and b. The κL values basically satisfy the κL~T -1 law, suggesting that the phonon-phonon scattering is the dominated scattering mechanism for these samples. With increasing the δ, the κL is slightly decreased, which is more clearly depicted in Figure 7c. For Cu2.1Mn0.9SnSe4, the κL is about 2.5 W m-1 K-1 at 300 K, which has about 14% reduction as compared with that for the stoichiometric Cu2MnSnSe4 sample. Generally, the Callaway model well interprets the lattice thermal conductivity in solids. According to the Callaway model, the κL is given by34, 35

κ4 = "# ⁄54678 9:$⁄
= "# ?@ ⁄A26 78 ℏ:$D

(5),

where ΘD is the Debye temperature. The coefficient for the Rayleigh-type point defect 0 scattering rate A is given by 9 = E- F⁄G467HIJ K, where Ω0 is the unit cell volume and Γ

is the scattering parameter. The scattering parameter Γ can be calculated by the model of Slack and Abeles, taking Γ = ΓM + ΓS, where ΓM and ΓS are scattering parameters related to mass fluctuation and strain field fluctuation, respectively. They can be expressed as36, 37

∆L

∆>

F = FL + FN = O1 − O Q + S T L >

(6),

where χ, ∆M/M, and ∆r/r are the molar fraction of the substitution, the relative change of atomic mass and radius due to the replacement of Mn by Cu. The parameter ε is usually obtained by fitting the experimental results. In this study, ε is 86, which is comparable with those in other diamond-like compounds such as Cu2ZnGeSnSe4-xSx.38 The short dashed line in Figure 7c shows the predicated κL at 300 K based on the Callaway model. The experimental κL data well fall on this calculated line, suggesting that the Callaway 10 - 25 ACS Paragon Plus Environment

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model can also well interpret the κL in Cu2MnSnSe4. Figure 7d plots the scattering parameters ΓM and ΓS as a function of the off-stoichiometric content δ. With increasing δ, both the strain field fluctuation and mass fluctuation are strengthened. Meanwhile, for each composition, ΓS is larger than ΓM, which implies that the strain field fluctuation contributes more to the reduction of κL than the mass fluctuation. This is consistent with the severe local distortions inside the crystal structure shown in Figure 3d. The substitution of Mn by Cu shrinks the distances between Mn sites and Se sites and increases the local distortion in the non-cubic anion sublattice, which is the main reason for the larger ΓS observed in Figure 7d. The temperature dependence of thermoelectric figure of merit zT (= S2σT/( κL + κe)) for all Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1) samples is presented in Figure 8a. Due to the enhanced power factor and the well maintained low thermal conductivity, significantly enhanced zTs are observed in the non-stoichiometric samples. A maximal zT of 0.60 at 800 K is achieved in Cu2.1Mn0.9SnSe4 sample, proving that introducing the off-stoichiometry is an effective strategy to improve zT for the quaternary diamond-like compounds.14, 15, 39 Based on the single parabolic band model, it is possible to predict the zT in Cu2+δMn1-δSnSe4. Utilizing the experimental lattice thermal conductivity κL = 0.65 W m-1 K-1, the calculated zT versus carrier concentration at 800 K is shown in Figure 8b. Our experimental data well fall on this theoretical curve. Especially, when the off-stoichiometric content δ reaches 0.1, the carrier concentration is tuned to the optimal range, thus the experimental zT is comparable with the calculated maximal zT. Further zT improvement can be expected by reducing κL via alloying other elements to strengthen the scattering to the high-frequencies phonons or introducing the nanocomposites to strengthen the scattering to the low-frequencies phonons.34, 38, 40, 41

4.Conclusion In this study, a series of Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1) samples has been prepared by the melting-annealing method. The phase composition, crystal structure, electrical and thermal transport properties were systemically investigated. All the excess Cu atoms enter into the Mn-sites without forming the secondary phases. These Cu atoms at the Mn-sites scarcely change the structure distortion 11 - 25 ACS Paragon Plus Environment


parameter, and thus the high band degeneracy is well maintained in the nonstoichiometric Cu2+δMn1-δSnSe4 samples. Combining the increased carrier concentrations, the power factors for the non-stoichiometric Cu2+δMn1-δSnSe4 are significantly improved to reach the maximal value. Meanwhile, the Cu atoms at the Mn-sites induce obviously local distortions inside the anion-centered tetrahedron, which yields large strain fluctuation to suppress the lattice thermal conductivity. A maximal zT of 0.60 at 800 K is achieved in Cu2.1Mn0.9SnSe4, among the highest zT reported in quaternary diamond-like compounds.


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Figure 1. a) Crystal structure of quaternary Cu2MnSnSe4 (stannite, space group I 42m ) and local distorted anion-centered tetrahedron. b) The room-temperature powder X-ray diffraction (PXRD) patterns for Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1).

Figure 2. Scanning electron microscopy (SEM) and elemental Backscattered electron mapping images of the Cu2.1Mn0.9SnSe4 sample.



Figure 3. The refined a) lattice parameters, b) distances between Mn sites and Se sites, c) atomic coordinates of the Se sites, d) internal distortion parameters φ as a function of the off-stoichiometry content δ for Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1). The dashed curves are guides to the eyes. The inset in c) shows a projection of the unit cell of Cu2MnSnSe4 in the c-direction; the arrows indicate the movement of Se atoms toward the Mn sites when increasing δ.


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Figure 4. Temperature dependences of a) the electrical conductivity σ, b) the Seebeck coefficient S, c) the power factor PF, and d) the total thermal conductivity κ for the Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1) samples.



Figure 5. a) Measured Hall carrier concentration pH at 300 K for the Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1) samples. The dashed line is a guide to the eyes. Hall carrier concentration dependences of b) the Hall carrier mobility µH and c) the Seebeck coefficient S at 300 K. d) The power factor at 800 K as a function of the Hall carrier concentration. The dashed lines in b-d) are calculated by the single parabolic band model with m* = 1.2 me.


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Figure 6. (a) Calculated band structure and (b) density of states (DOS) for Cu2MnSnSe4 compound. The inset in a) shows the magnification of the band structure at the valence band maximum.



Figure 7. a) Calculated temperature-dependent Lorenz number L by using the single parabolic model. b) Temperature dependence of the lattice thermal conductivity κL for the Cu2+δMn1-δSnSe4 (δ = 0, 0.025, 0.05, 0.075, and 0.1) samples. c) Room-temperature lattice thermal conductivity κL, d) the mass fluctuation parameter (ΓM), and strain field fluctuation parameter (ΓS) as a function of the off-stoichiometric content δ. The short dashed line represents the κL ~ T

−1

law in b). The dashed lines are guides to the eyes in

d).


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Figure 8. a) Temperature dependence of the TE figure of merit (zT) for the Cu2+δMn1δSnSe4

(δ = 0, 0.025, 0.05, 0.075, and 0.1) samples. b) zT as a function of the Hall carrier

concentration pH at 800 K. The short dashed line represents the curve calculated by the single parabolic band model.

Table 1. Room-temperature structure parameters and transport properties for Cu2+δMn1δSnSe4

(δ = 0, 0.025, 0.05, 0.075, and 0.1). Composition

δ=0

δ = 0.025

δ = 0.05

δ = 0.075

δ = 0.1

a (Å)

5.764(8)

5.761(5)

5.761(2)

5.760(8)

5.760(9)

c (Å)

11.366(2)

11.366(1)

11.367(1)

11.366(5)

11.370(5)

0.9858

0.9864

0.9865

0.9865

0.9869

σ (10 S m )

0.36

0.76

1.19

1.62

2.49

S (µV K-1)

212

167

117

88

67

0.21

0.46

1.09

2.42

2.89

µH (cm V s )

15.2

10.5

6.6

3.6

4.9

m* (me)

1.13

1.30

1.40

1.71

1.44

η (c/2a) -1

4

-3

20

pH (10 cm ) 2

-1 -1



Associated Content Supporting Information X-ray photoelectron spectra for the Cu and Mn in Cu2+δMn1-δSnSe4 (δ = 0, 0.05, and 0.1) samples. This material is available free of charge via the Internet at http://pubs.acs.org/. Author Information Corresponding Authors *E-mail: [email protected]. *E-mail: [email protected]. ORCID Xun Shi: 0000-0001-6011-1210 Notes The authors declare no competing financial interest.

Acknowledgements This work was financially supported by the National Natural Science Foundation of China (NSFC) under the No. 51625205, the Key Research Program of Chinese Academy of Sciences (Grant No. KFZD-SW-421), International S&T Cooperation Program of China (2015DFA51050), and the Shanghai Government (Grant No.15JC1400301 and 16XD1403900).

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Improved Thermoelectric Performance in Nonstoichiometric Cu2+

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