Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
pubs.acs.org/IC
Lattice Dynamics and Thermal Conductivity in Cu2Zn1−xCoxSnSe4
Yingcai Zhu,†,‡,% Yong Liu,§,% Guangkun Ren,∥ Xing Tan,∥ Meijuan Yu,† Yuan-Hua Lin,∥ Ce-Wen Nan,∥ Augusto Marcelli,⊥,# Tiandou Hu,*,† and Wei Xu*,†,# †
Beijing Synchrotron Radiation Facility, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China University of Chinese Academy of Sciences, Beijing 100049, China § AECC Beijing Institute of Aeronautical Materials, Beijing 100095, China ∥ State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and Engineering, Tsinghua University, Beijing 100084, P. R. China ⊥ INFN - Laboratori Nazionali di Frascati, Via E. Fermi 40, Frascati 00044, Italy # RICMASS, Rome International Center for Materials Science Superstripes, Via dei Sabelli 119A, 00185 Rome, Italy ‡
S Supporting Information *
ABSTRACT: The quaternary compound Cu 2 ZnSnSe 4 (CZTSe), as a typical candidate for both solar cells and thermoelectrics, is of great interest for energy harvesting applications. Materials with a high thermoelectric efficiency have a relatively low thermal conductivity, which is closely related to their chemical bonding and lattice dynamics. Therefore, it is essential to investigate the lattice dynamics of materials to further improve their thermoelectric efficiency. Here we report a lattice dynamic study in a cobalt-substituted CZTSe system using temperature-dependent X-ray absorption fine structure spectroscopy (TXAFS). The lattice contribution to the thermal conductivity is dominant, and its reduction is mainly ascribed to the increment of point defects after cobalt substitution. Furthermore, a lattice dynamic study shows that the Einstein temperature of atomic pairs is reduced after cobalt substitution, revealing that increasing local structure disorder and weakened bonding for each of the atomic pairs are achieved, which gives us a new perspective for understanding the behavior of lattice thermal conductivity.
1. INTRODUCTION Energy harvesting stimulates scientific and technological interests not only because of the increasing energy demand but also due to the recent energy crisis. Moreover, all renewable energy resources are promising for providing alternative energy for human beings. Thermoelectric materials, which can convert waste heat to electricity, could play a key role in the future for more efficient energy production and utilization.1 The conversion efficiency of thermoelectric materials depends on the figure of merit, zT = S2σT/κ. Here, S is the Seebeck coefficient, σ the electrical conductivity, T the absolute temperature, and κ the thermal conductivity. Thus, good thermoelectric materials should have a large power factor (S2σ) with relatively low thermal conductivity. Several classical thermoelectric materials, such as PbTe,2,3 PbSe,4 Bi2Te3,5 skutterudites,6 and SiGe,7 have been developed and improved. However, these kinds of materials either contain expensive elements or are environmentally harmful, limiting their wide application. Therefore, it is necessary to develop new good thermoelectric materials with low cost and environmentally friendly properties. Recently, the quaternary Cu2ZnSnSe4 (CZTSe)-based compounds consisting of earth© XXXX American Chemical Society
abundant elements have been considered as new prospective thermoelectric materials.8−11 Controlling heat flow is critical for improving thermoelectric efficiency, and various ways can suppress the lattice thermal conductivity, including alloying,12 nanostructuring,13−16 strong lattice anharmonicity,17 point defects,18 and structural heterogeneity.19 The lattice thermal conductivity is closely bound up with the structure and lattice dynamics of a material. Hence, it is mandatory to develop a comprehensive understanding of lattice dynamics on the atomic scale. However, there have been few studies of the lattice dynamics of quaternary CZTSe compounds. In this work, we investigated the lattice dynamics of the pristine and Co-substituted CZTSe to decipher the behavior of the thermal conductivity. The increment of point defects after Co substitution, which can cause the decrease of phonon relaxation time, is the main reason for the suppression of lattice thermal conductivity. Moreover, a lattice dynamic study through TXAFS shows that the total disorder of local structure Received: March 5, 2018
A
DOI: 10.1021/acs.inorgchem.8b00569 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
Figure 1. LeBail refinement of XRD patterns for (a) Cu2ZnSnSe4, (b) Cu2Zn0.99Co0.01SnSe4, (c) Cu2Zn0.98Co0.02SnSe4, and (d) Cu2Zn0.96Co0.04SnSe4. was introduced, we recorded XAFS spectra at Cu, Zn, Sn, and Se Kedges in transmission mode. XAFS spectra at the Co K-edge were collected in fluorescence mode using a Lytle-type gas-filled detector. The TXAFS analyses were performed at the Cu, Zn, and Se K-edges forx = 0 and x = 0.04 samples from 10 to 300 K, by hosting the sample in a continuous flow He cryostat, of which the temperature control accuracy is within ±1 K. All TXAFS was performed in transmission mode.
is increased and the bond strength between atoms is weakened after Co substitution, providing atomic insight into the manipulation of lattice thermal conductivity.
2. EXPERIMENTAL SECTION 2.1. Synthesis. All compounds were prepared by direct reaction of the highly pristine elements. Powders of Cu (99.99%, Alfa), Zn (99.99%, Alfa), Sn (99.99%, Alfa), Se (99.99%, Alfa), and Co (99.99%, Alfa) w ere mixed uniformly in stoichiometric ratios Cu2Zn1−xCoxSnSe4 (x = 0, 0.01, 0.02, and 0.04). After that, the mixtures were sealed in quartz tubes under high vacuum, put into a muffle furnace, heated slowly to 1170 K, and kept for 6 h. Then, each mixture was cooled to 773 K followed by an annealing at this temperature for 2 days. The obtained ingots were ground into a fine powder and sintered by spark plasma sintering (SPS) at 823 K for 5 min under a pressure of 50 MPa. The disk-shaped samples we obtained were cut along their radial direction in 3 × 3 × 12 mm3 rectangles for the following characterizations. 2.2. Characterization. Powder X-ray diffraction (XRD) patterns were collected with a Bruker D8 Focus diffractometer using Cu Kα radiation (λ = 1.54 Å). The Seebeck coefficient and the electrical conductivity were measured using a ZEM-2 (ULVACU-RIKO, Japan) at the temperature range from room temperature to 673 K. The thermal conductivity (κ) was calculated by the equation κ = DCpd, where D is the diffusivity, Cp is the specific heat, and d is the density. The thermal diffusivity (D) was measured using the laser flash method (NETZSCH, LFA427, Germany). The heat capacity (Cp) was estimated using the method of DuLong−Petit. The density (d) was measured by the Archimedes method. The uncertainty in the thermal conductivity measurements is estimated to be within 10%. The uncertainties of the Seebeck coefficient and the electrical conductivity are ∼3% and ∼5%, respectively. As a result, the combined uncertainty for determination of zT is ∼20%. X-ray absorption fine structure spectroscopy (XAFS) at Cu, Zn, Co, and Se K-edges was performed at the 1W1B and 1W2B end stations of the Beijing Synchrotron Radiation Facility (BSRF) using a doublecrystal Si (111) monochromator, while XAFS at the Sn K-edge was recorded at the BL14W1 end station of the Shanghai Synchrotron Radiation Facility (SSRF) using a double-crystal Si (311) monochromator. XAFS data were collected for all Cu2Zn1−xCoxSnSe4 (x = 0, 0.01, 0.02, and 0.04) samples at room temperature. Using ion chambers filled with argon/nitrogen gas before and after the sample
3. RESULTS AND DISCUSSION 3.1. Crystal Structure of Bulk Cu2Zn1−xCoxSnSe4. CZTSe has been reported to crystallize in two major phases, the stannite and kesterite structures, which cannot be distinguished by XRD.20,21 In addition, it is reported that CZTSe with the kesterite structure is more stable compared to its stannite counterpart.22 Thus, we use the kesterite structure (I4̅) to refine the XRD patterns (Figure 1 and Table S1). The refined ratio c/2a (Figure S1) remains almost constant for Cu2Zn1−xCoxSnSe4 due to the similar atomic radii of Cu, Zn, and Co. The bond distances (Cu−Se, Zn−Se, and Sn−Se), extracted from extended X-ray absorption fine spectroscopy (EXAFS) of Cu, Zn, and Sn K-edge of Cu2Zn1−xCoxSnSe4, almost remain the same with increasing Co content, as shown in Figure S2. There is no impurity observed from the XRD patterns. The XRD patterns of the sample before and after SPS are compared in Figure S3, showing no significant texture in these materials. Therefore, we can conclude that the samples are highly pristine and that the cobalt atoms are incorporated inside the lattice of the CZTSe system. It is well-known that X-ray or neutron diffraction can be employed to resolve the long-range ordered crystallographic structures. To extract finer structural information, one should resort to techniques that are sensitive to the local structures and complementary to the diffraction techniques. XAFS is an element-selective local structural probe, ideal for studying ordered or disordered systems. The element selectivity of the XAFS enables the probing of the local structure around specific elements. Hence, we use this technique to identify the substituted sites of Co. In Figure 2, the EXAFS oscillations B
DOI: 10.1021/acs.inorgchem.8b00569 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
0.04 sample at 673 K. Further, the magnitude of the Seebeck coefficient (α) increases as temperature increases, revealing that minority carrier transport is negligible at this temperature range.25 The total thermal conductivity is the sum of the lattice and electrical contributions. The electrical thermal conductivity and the electrical conductivity are correlated by the Wiedemann− Franz law, κe = LσT, where L is the Lorentz number. The Lorenz numbers (Figure S4) were calculated based on the single parabolic band (SPB) model assuming that the acoustic phonon scattering is the dominant scattering mechanism for the electron (λ = 0).26 As shown in Figure 3(c), the total thermal conductivity of the x = 0.04 sample decreases by 15% at 323 K compared with that of the pristine sample, which mainly arises from the reduction of the lattice thermal conductivity (Figure 4). However, the behavior of the lattice
Figure 2. Comparison of the Cu, Zn, and Co K-edge EXAFS data of Cu2Zn1−xCoxSnSe4 at room temperature.
χ(k) of the Co K-edge are compared with those of the Cu and Zn K-edges. We can see that the phase and shape of the oscillations for the Co and Cu K-edges arepractically the same, pointing out identical local structural configurations around cobalt and copper atoms. By contrast, the oscillations of the Co K-edge have a significant difference compared to that of the Zn K-edge, especially at the lowk part. In other words, EXAFS spectra provide robust evidence that, instead of the Zn site as suggested by stoichiometry, Co occupies the Cu site in Cu2Zn1−xCoxSnSe4. A quantitative structural fit will be discussed in the next section together with structural dynamics. 3.2. Transport Properties and Thermoelectric Performances. The electrical conductivity shown in Figure 3(a)
Figure 4. Temperature-dependent lattice thermal conductivity of Cu2Zn1−xCoxSnSe4.
thermal conductivity cannot be simply described by a 1/T dependence across the whole temperature range, which means that there exist other phonon scattering mechanisms, except for Umklapp scattering. Generally, Umklapp scattering plays a leading role at high temperatures, while grain boundary scattering dominates at low temperatures. Besides, the grain size has no significant change after Co substitution. Figure S5 shows the scanning electron microscopy (SEM) images of cross sections for x = 0 and x = 0.04 samples. We can see that the grains are relatively compact and that the grain sizes for both the pristine sample and the x = 0.04 sample are around 1.5 μm. Therefore, point defect scattering may mainly account for the decrease in lattice thermal conductivity. This is in agreement with our structure study which indicated that Co occupied the Cu sites rather than the Zn sites, which may cause considerable lattice imperfections, such as VZn2− and CuZn+ antisites. The lattice thermal conductivity is given by27 1 1 κL = CV vl = CV v 2τ 3 3
Figure 3. Temperature dependence of (a) the electrical conductivity, (b) the Seebeck coefficient, (c) the total thermal conductivity, and (d) the figure of merit zT for the Cu2Zn1−xCoxSnSe4 samples.
(τ = l / v )
decreases with increasing temperature, indicative of a metal transport behavior. In addition, there is a kink in the electrical conductivity at around 423 K, indicating the occurrence of a phase transition. The phase transitions were commonly reported in similar quaternary systems such as Cu2+xZn1−xGeSe4 and Cu2ZnGeSe4−xSx systems.23,24 Figure 3(b) shows the Seebeck coefficient of Cu2Zn1−xCoxSnSe4. The positive Seebeck coefficients mean that the hole is the main species of charge carrier. A maximum Seebeck coefficient of 166 μV/K can be obtained for the x =
(1)
where CV is the specific heat at constant volume, v the phonon velocity, l the phonon mean free path, and τ the phonon relaxation time. In eq 1, v can be approximated to the average of the longitudinal (vl) and transverse (vt) velocities at the low frequency limit.27 We performed ultrasonic measurements to obtain the velocities, which are listed in Table 1. The uncertainty of speed is 2%. We can see that both vl and vt decreased after Co substitution. As a result, the square averaged sound velocity (v2) of the x = 0.04 sample, calculated by eq S1, C
DOI: 10.1021/acs.inorgchem.8b00569 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry Table 1. Sound Velocities and Debye Temperatures for x = 0 and x = 0.04 Samples sample
vl (m/s)
vt (m/s)
v (m/s)
ΘD (K)
x=0 x = 0.04
3947.6 3780.4
1971.3 1922.1
2211.6 2154.1
231.8 225.8
decreased by 5% compared with that of the pristine sample. However, the lattice thermal conductivity of the x = 0.04 sample decreased by 13% at 323 K compared with that of the pristine sample. Because CV is the same for these two samples, the decrease in phonon relaxation time is responsible for the reduction of lattice thermal conductivity, which is mainly caused by the increment of point defects after Co substitution. To verify this, we estimated the lattice thermal conductivity with a different phonon scattering mechanism. The calculation details are shown in eqs S2−S9 and Figure S6. As shown in Figure S6(a), with a different Umklapp phonon scattering, the change of lattice thermal conductivity is identical in the entire temperature range. Figure S6(b) shows that grain boundary scattering has little effect on the lattice thermal conductivity at this temperature range. With a different point defect scattering, the change of lattice thermal conductivity shown in Figure S6(c) is remarkable at room temperature, while the change decreases with increasing temperature. This changing behavior of lattice thermal conductivity is consistent with our experimental results. Therefore, the increment of point defects plays an important role in controlling the lattice thermal conductivity. The Debye temperature of the pristine sample, determined by eq S9, is 231.8 K, which is in agreement with the result of 232 K from a first-principles calculation.28 By contrast, the Debye temperature of the x = 0.04 sample is decreased to 225.8 K due to the reduction of average sound velocity. As shown in Figure 3(d), the maximum zT is 0.31 at 673 K for the x = 0.04 sample, comparable to values from previous investigations. There is no significant improvement in zT via Co substitution due to the unexpected reduction of electrical conductivity. 3.3. Local Structure and Temperature Dependence of Mean Square Relative Displacement (MSRD). The lattice thermal conductivity originates from lattice phonons, which transport the heat by diffusions or collisions. Previously, the lattice dynamics were studied using the density functional theory and the density functional perturbation theory.29,30 Here, we show how it is possible to probe the lattice dynamics via TXAFS, which has been applied to understand the local structural dynamics of superconductors.31 By exploring the bond distance and temperature dependence of the MSRD, we are able to extract the structural disorder (a static contribution) and temperature-induced disorder. It is important to perform TXAFS measurements at low temperature down to tens of kelvins. The advantages of low temperature TXAFS are (1) an improved S/N ratio since the thermally induced vibrations cause a large amount of noise in the EXAFS oscillations at high k values and (2) an easy extraction of the intrinsic properties of the system when phase transitions are not present at the measured temperature range. We investigated the lattice dynamics of CZTSe through TXAFS at the Cu K-edge (8979 eV), Se K-edge (12658 eV), and Zn K-edge (9659 eV). InFigure 5, we compare the Fourier transforms (FTs) of the weighted temperature-dependent EXAFS oscillations. Apparently, the intensity of the first peak at 2.4 Å increases as the temperature decreases, and new peaks
Figure 5. Fourier transforms of the temperature-dependent Cu K-edge EXAFS oscillations of the pristine Cu2ZnSnSe4 sample.
at 3.5 and 4.3 Å appear at temperatures lower than 150 K. At the Cu K-edge, the first peak corresponds to the scattering of photoelectrons by the four Se atoms in the first shell, while the second peak at 3.5 Å can be assigned to Zn, Sn, and Cu atoms in the second shell. The fitting and calculations were performed using the ARTEMIS software and FEFF6.0 code as embedded in the IFFEFIT package.32 The many body reduction factor S02 and the energy differences were also fitted to compensate for the experimental uncertainty. Then, by fixing the coordination number to nominal values, we fitted the bond distance and mean square relative displacement for each pair, e.g., Cu−Se, Zn−Se, and Se−Sn. After trying to fit with two shells, we found that the uncertainty increases unreasonably. In order to extract physical insights, we then performed a systematic fit of the first shell for all absorption edges. The selected k and R ranges are 3.7−12.6 Å−1 and 1.25−2.95 Å for the Cu K-edge, 4.1−14.4 Å−1 and 1.3−2.8 Å for the Zn K-edge, and 3.7−13.8 Å−1 and 1.2−3.0 Å for the Se K-edge, respectively. Based on the Nyquist criterion, the number of independent data points, Nind ∼ (2ΔkΔR)/π, is about 9.5, 9.4, and 11 for Cu, Zn, and Se Kedges, respectively, while the number of fitted variables is only 3, 3, and 4, respectively. The result of the fit is quite good for the first shell. In Figure S7, we present the comparison of the fitted and experimental Fourier transform amplitudes of the Cu, Zn, and Se K-edge EXAFS oscillations at 10 K. The MSRD (σ2 = σ02 + σvib2(T)) of EXAFS measures the deviation of a pair of absorber and backscatter atoms from the interatomic equilibrium distance,33,34 where σ02 is the static disorder and σvib2(T) is the dynamic disorder.,35 The static disorder σ02 probes the structural disorder due to the topological disorder of the atoms, whereas the dynamic disorder contribution σvib2(T) is related to the temperatureinduced atomic vibrations. As the Debye model is more suitable for monatomic Bravais lattices,33 the vibrational term σvib2(T) in our system was described by the correlated Einstein model. The bond vibrational modes are considered as independent Einstein oscillators with the frequency ωE.36 Under harmonic approximation, σvib2(T) can be expressed as37 σvib 2(T ) = D
ℏ2 coth(TE/2T ) 2μkBTE
(2) DOI: 10.1021/acs.inorgchem.8b00569 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry where ℏ is the reduced Plank constant, kB the Boltzmann constant, μ the reduced mass of the atom pair (μ ∼ 35.2, 35.7, and 47.4 amu for Cu−Se, Zn−Se, and Se−Sn pairs, respectively), and TE the Einstein temperature (TE = ℏωE/ kB). We can calculate the local force constants ( f = μωE2) with the value of Einstein frequency (ωE), which can characterize the strength of different bonds.33 In Figures 6, S8, and S9, experimental MSRD curves of Cu2Zn1−xCoxSnSe4 (x = 0, 0.04) are presented at the Cu, Zn,
the converted local force constants of atomic bonds (Cu−Se, Zn−Se, and Se−Sn) of the x = 0.04 sample were found to drop by 6%, 2%, and 11%, respectively, compared with those of the pristine sample. This indicates that the bond strength between atoms is weakened after Co substitution. Further, we can conclude that the Sn−Se bond is the strongest bond, while the Cu−Se bond is the weakest one in this CZTSe system.
4. CONCLUSION We investigated the lattice dynamics and thermal conductivity of the Co-substituted quaternary compound CZTSe. EXAFS shows that a Co atom replaced a Cu site rather than a Zn site as suggested by stoichiometry, leading to an increment of point defects, which is the main reason for the decrease in lattice thermal conductivity. A lattice dynamic study via TXAFS shows that the total disorder increased and the Einstein temperatures of each bond (Cu−Se, Zn−Se, and Se−Sn) decreased after Co substitution, which is the origin of the reduction of lattice thermal conductivity. Our findings provide a new perspective on the manipulation of lattice thermal conductivity in thermoelectric materials.
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b00569. LeBail fitting parameters of the XRD pattern of Cu2Zn1−xCoxSnSe4 (Table S1); refined ratio c/2a of Cu2Zn1−xCoxSnSe4 (Figure S1); bond distance of Cu2Zn1−xCoxSnSe4 (Figure S2); XRD patterns of pristine CZTSe before and after the SPS procedure (Figure S3); temperature-dependent Lorenz number of Cu2Zn1−xCoxSnSe4 (Figure S4); SEM images of the pristine sample and x = 0.04 sample (Figure S5); calculation of lattice thermal conductivity with the different scattering mechanism (Figure S6); FT of Cu, Zn, and Se K-edge EXAFS of CZTSe at 10 K (Figure S7); comparison of experimental MSRD factors of the Zn−Se and Se−Sn pairs for Cu 2 ZnSnSe 4 and Cu2Zn0.96Co0.04SnSe4 samples (Figures S8 and S9) (PDF)
Figure 6. Comparison of experimental MSRD (mean square relative displacement) factors (symbols) of the Cu−Se pair for the (a) Cu2ZnSnSe4 and (b) Cu2Zn0.96Co0.04SnSe4 samples by fitting with the Einstein model. The inset in (a) shows the first coordination of a Cu (blue) atom with four Se (red) atoms.
and Se K-edges, respectively. The fitted results, including atomic disorder, Einstein temperature, vibrational frequency, and local force constants, are listed in Table 2. The static Table 2. Comparison of Atomic Disorder (σ2), Einstein Temperature (TE), Vibrational Frequency (ωE), and Local Force Constant (f) of the Corresponding Cu−Se, Zn−Se, and Se−Sn Bonds As Extracted from TemperatureDependent EXAFS at the Cu, Zn, and Se K-Edge for the Cu2Zn1−xCoxSnSe4 (x = 0 and x = 0.04) Samples edge Cu Kedge Zn Kedge Se Kedge
sample x x x x x x
= = = = = =
0 0.04 0 0.04 0 0.04
σ2 (Å2) (300 K) 0.0080 0.0084 0.0066 0.0068 0.0041 0.0043
TE (K) 250.3 242.4 280.0 276.8 320.9 302.3
± ± ± ± ± ±
2.5 2 2.7 1.9 7.2 9.3
ωE (THz)
f (eV Å−2)
± ± ± ± ± ±
3.92 3.68 4.97 4.86 8.67 7.7
32.7 31.7 36.6 36.2 42.0 39.5
0.3 0.2 0.3 0.2 0.9 1.2
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. *E-mail:
[email protected]. ORCID
Wei Xu: 0000-0001-8006-2399 Author Contributions %
These authors contributed equally.
Notes
The authors declare no competing financial interest.
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disorder is almost constant for Cu, Zn, and Se K-edges. The values of total disorder forCu−Se, Zn−Se, and Se−Sn bonds. By contrast, the total disorder for each bonds increase upon Co substitution, as shown in Table 2, which is mainly due to the increasing dynamic disorder. This is consistent with the result of increasing point defects after Co substitution. The fitting results show that the Einstein temperature (TE) and the vibrational frequency (ωE) of each bond of Co-substituted CZTSe are smaller than those of pristine CZTSe. As a result,
ACKNOWLEDGMENTS This work was supported by the National Science Foundation of China (U1532128). Y.Z. acknowledges the financial support of the China Scholarship Council (CSC) and thanks Prof. G. Jeffrey Snyder for insightful comments and discussion. We acknowledge Lei Hu for the refinement of XRD patterns. We are grateful to the Beijing Synchrotron Radiation Facility and E
DOI: 10.1021/acs.inorgchem.8b00569 Inorg. Chem. XXXX, XXX, XXX−XXX
Article
Inorganic Chemistry
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Shanghai Synchrotron Radiation Facility for professional support from all staff during runs at the 1W1B, 1W2B, and BL14W1 beamlines. We acknowledge, in particular, Pengfei An and Lirong Zheng for their help in XAFS measurements.
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DOI: 10.1021/acs.inorgchem.8b00569 Inorg. Chem. XXXX, XXX, XXX−XXX
