Ultra-low lattice thermal conductivity and significantly enhanced near

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Ultra-low lattice thermal conductivity and significantly enhanced nearroom-temperature thermoelectric figure of merit in #-Cu2Se through suppressed Cu vacancy formation by over-stoichiometric Cu addition Jang-Yeul Tak, Woo Hyun Nam, Changhoon Lee, Sujee Kim, Young Soo Lim, Kyungmoon Ko, Soonil Lee, Won-Seon Seo, Hyung Koun Cho, Ji-Hoon Shim, and Cheol-Hee Park Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b00254 • Publication Date (Web): 26 Apr 2018 Downloaded from http://pubs.acs.org on April 26, 2018

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Chemistry of Materials

Ultra-low lattice thermal conductivity and significantly enhanced nearroom-temperature thermoelectric figure of merit in α-Cu2Se through suppressed Cu vacancy formation by over-stoichiometric Cu addition

Jang-Yeul Tak,†,‡,# Woo Hyun Nam,†,# Changhoon Lee,§,ǁ,# Sujee Kim,ǁ Young Soo Lim,*,£ Kyungmoon Ko,¥ Soonil Lee,† Won-Seon Seo,† Hyung Koun Cho,‡ Ji-Hoon Shim,*,§,ǁ and Cheol-Hee Park*,¥

†

Energy and Environmental Division, Korea Institute of Ceramic Engineering and

Technology, Jinju 52851, Korea. ‡

School of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon

16419, Korea. §

Department of Chemistry, Pohang University of Science and Technology, Pohang 37673,

Korea. ǁ

Division of Advanced Nuclear Engineering, Pohang University of Science and Technology,

Pohang 37673, Korea. £

Department of Materials System Engineering, Pukyong National University, Busan 48547,

Korea. ¥

LG Chem/Research Park, Daejeon 34122, Korea.

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ABSTRACT Finding alternatives for Bi2Te3, the only thermoelectric material for near-roomtemperature (RT) applications, is of great importance in thermoelectrics. Here, we report a very promising near-RT thermoelectric figure of merit (ZTmax = 0.9 at 390 K, ZTave = 0.68 between RT and 390 K) for Cu-excess α-Cu2+xSe, comprising low-cost, abundant, and nontoxic elements. Although α-Cu2+xSe has a propensity to form a large number of Cu vacancies to stabilize its structure by diminishing Cu-Cu interactions, excess Cu leads to a decrease in hole concentration by suppressing the formation of Cu vacancies, resulting in a power factor optimization in Cu-excess compounds. These effects of Cu addition were also elucidated by density functional theory calculations and the Boltzmann transport equation. Furthermore, we directly measured the Lorentz number (2.12 × 10-8 V2 K-2 at RT) of α-Cu2Se for the first time, and determined the origin of its very low lattice thermal conductivity (0.27 W m-1 K-1 at RT). Based on phonon calculations, it is suggested that this ultra-low lattice thermal conductivity is associated with the structural instability of α-Cu2Se, as evidenced by the existence of negative phonon frequency in its phonon dispersion. Based on our findings, we propose a new way to control the thermoelectric transport properties of α-Cu2+xSe through overstoichiometric Cu addition, and we also suggest that Cu-excess α-Cu2Se is a very promising thermoelectric material to replace Bi2Te3 for near-RT applications.


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INTRODUCTION Thermoelectric technology enables direct energy conversion between heat and electricity in a solid-state material without moving parts. Since the first modern thermoelectric device was realized by Goldsmid,1 there has been growing broad interest in its various applications, from efficient utilization of limited fossil energy to smart heat dissipation.2-4 Since energy conversion efficiency is governed by the thermoelectric figure of merit, ZT (= S2σT κ-1, where S is the Seebeck coefficient, σ is the electrical conductivity, T is the absolute temperature, and κ is the thermal conductivity), much attention has been focused on enhancing the performance of thermoelectric materials. In particular, substantial efforts have been devoted to the exploration of near-room-temperature (RT) thermoelectric materials for its various applications (e.g., thermoelectric refrigeration and climate control, and low-temperature thermoelectric generation including human body heat harvesting);5-8 however, most research has been focused on Bi2Te3-based compounds.9-15 Although there has been significant progress in increasing the ZT of Bi2Te3 over the last few decades, its relatively high cost and the scarcity of Te have urged the development of alternatives to Bi2Te3 to expand present applications and to promote upcoming thermoelectric technologies. Meanwhile, β-Cu2Se, comprised of low-cost, abundant, and non-toxic elements, has gained much attention recently due to its high ZT at high temperatures.16-20 Cu2Se undergoes a phase transition from its low-temperature phase of monoclinic α-Cu2Se (C2/c) to the hightemperature phase of cubic β-Cu2Se (Fm-3m) when the temperature is increased above ~410 K.21-24 β-Cu2Se is a superionic conductor with kinetically disordered Cu ions within a facecentered cubic sublattice of Se. It was originally investigated for radioisotope thermal generators in the 1960s.25 Liu et al. rediscovered the excellent thermoelectric performance (ZT of 1.5 at 1000 K) of β-Cu2Se and reported its liquid-like phonon behavior which can lead to extreme suppression of lattice thermal conductivity.16 Since this report, its ZT value has 3 ACS Paragon Plus Environment


been improved through various approaches and the highest ZT of 2.4 at 1000 K was realized in Cu2Se/carbon nanotube hybrid composites very recently by thermal conductivity reduction through additional phonon scattering by the carbon nanotubes.26 However, despite its excellent ZTs, both the fast migration of Cu ions and the preferential evaporation of Se at elevated temperatures cause severe changes in its composition, invoking solid-state precipitation of Cu on the surface and eventual deterioration from the initial performance of β-Cu2Se.25,27,28 Therefore, the enhancement of its chemical stability is regarded as the biggest challenge for practical usage of β-Cu2Se. On the other hand, the low-temperature phase of α-Cu2Se is a non-superionic conductor in which Cu atoms are localized in the lattice, such that the instability issue can be disregarded in this phase.16,29 The ZT of α-Cu2Se is less than 0.3 at RT and its low ZT originates mostly from its high hole concentration (~1021 cm-3) due to the easily produced Cu vacancies in this phase.27-31 The formation of large amounts of Cu vacancies in Cu2Se has been demonstrated by near-infrared spectroscopy and high-resolution transmission electron microscopy in literature.32-34 Attempts have been made to optimize the carrier concentration by doping with foreign elements; however, most successful ZT enhancements in α-Cu2Se have been realized by thermal conductivity reduction rather than by optimizing the power factor, even with doped compounds.27-31 Olvera et al. achieved a ZT of ~0.6 at RT in Cu2Se/CuInSe2 nanocomposites through exceptional softening of lattice vibrations, which might be attributable to the coexistence of Cu-Se and (Cu/In)-Se types of bonding.28 Yang et al. reported a ZT of ~0.4 at RT through a reduction in lattice thermal conductivity by alloy scattering.30 It is also noteworthy that undoped α-Cu2Se can exhibit a very high ZT of ~2.3 near the transition temperature due to critical scattering of electrons and phonons influenced by a transition to β-Cu2Se phase even though it is possible only within narrow a temperature range during the transition (Figure 1).31 Nonetheless, α-Cu2Se has received less attention than 4 ACS Paragon Plus Environment

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β-Cu2Se, and detailed investigation of its thermoelectric transport properties has not yet been carried out. Herein, we propose a new strategy for enhancing ZT through optimization of the carrier concentration in Cu-excess α-Cu2+xSe and report significantly improved near-RT thermoelectric performances (ZTave = 0.68) (Figure 1). The origin of spontaneous formation of Cu vacancies even in a Cu-excess condition is discussed in terms of orbital interaction and is elucidated by density functional theory (DFT) calculations. The significant suppression of Cu vacancy formation by excess Cu is verified by detailed studies on charge transport properties. Furthermore, the Lorentz number of α-Cu2Se (L = 2.12 × 10-8 V2 K-2) has been measured directly for the first time and its very low lattice thermal conductivity (~0.27 W m-1 K-1) was also unveiled. Simulation of phonon behaviors of α-Cu2Se revealed that the observed ultra-low lattice thermal conductivity is induced by the structural instability arising form interacion between Cu+ ions. With these results, we suggest that α-Cu2Se is a promising thermoelectric material to replace Bi2Te3 for near-RT applications. Furthermore, since ZT enhancement in this study is achieved only by power factor optimization rather than by thermal conductivity reduction, we believe that there is room for further enhancement of its ZT by thermal conductivity reduction.

EXPERIMENTAL SECTION Fabrication of Cu2+xSe compounds. In this experiment, Cu2+xSe (x = 0, 0.025, 0.05, 0.075, and 0.1) compounds were synthesized by a solid-state reaction. Cu (99.999%, Alfa Aesar) and Se (99.999%, 5N Plus) were used as starting materials. Mixtures of starting materials in evacuated silica tubes were reacted at 823 K for 24 h. The ingots were pulverized by a mortar and pestle, and then consolidated by hot pressing under a uniaxial pressure of 60 MPa at 823 K for 1 h. The relative densities of all the compounds were above 99%. 5 ACS Paragon Plus Environment


Characterization techniques. Crystal structures of Cu2+xSe were characterized using an X-ray diffractometer (New D8 Advance, Bruker) with Cu Kα radiation, and microstructures were investigated using a transmission electron microscope (TEM, JEM-4010, JEOL) operating at an acceleration voltage of 400 kV and an optical microscope (OM, DXM1200F, Nikon). Compositional analysis was carried out by an electron probe micro-analyzer (EPMA, JXA-8100, JEOL) with attached wavelength-dispersive spectroscopy (WDS). Temperaturedependent electrical conductivity and Seebeck coefficient were measured up to 473 K by using a four-point probe method (ZEM-3, ULVAC-RIKO). Furthermore, thermal conductivity was measured by using a laser flash method (DLF-1300, TA Instruments). Due to the phase transition mentioned above, anomalous behaviors were observed around 410 K in all the temperature-dependent thermoelectric transport properties of Cu2+xSe. Roomtemperature charge transport properties were investigated by a Hall measurement system (ResiTest 8300, Toyo Corporation) under a magnetic field of 0.57 T.

Calculation methods. In order to elucidate the origin of Cu vacancy formation in this system, we optimized the atomic positions of pure α-Cu2Se, and Cu vacancies were introduced into α-Cu2Se on the basis of a first principles electronic band calculation while keeping the cell parameters at the values found in the experimental structure.22 In our first principles electronic band calculation, we employed the frozen-core projector augmented wave method encoded in the Vienna ab initio simulation package.35-37 Unless otherwise specified, the generalized-gradient approximation of Perdew, Burke and Ernzerhof was used for the exchange-correlation functional with a plane-wave-cut-off energy of 500 eV,38 a set of 80 k-points for the irreducible Brillouin zone, and the self-consistent field convergence thresholds of 10-5 eV and 0.001 eV Å-1 for total electronic energy and force, respectively. The 6 ACS Paragon Plus Environment

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optimized atomic positions of α-Cu2Se are presented in the Supporting Information, Table S1. We also investigated transport properties using BoltzTraP code which is based on Boltzmann transport theory under the rigid band approximation and constant relaxation time approximation.39-44 To ensure convergence of the calculation, we used dense 2000 k-points in the full Brillouin zone. Phonon properties were investigated by using the frozen phonon method implemented in PHONOPY.45 All the phonon dispersion calculations were performed after relaxation of atomic positions. To obtain precise phonon dispersions, we used a 2×2×1 supercell with 3×2×2 k-points, and the kinetic energy cutoff was 500 eV.

RESULTS AND DISCUSSION Structural characterization. Figure 2a represents X-ray diffraction (XRD) patterns of the Cu-excess Cu2+xSe compounds prepared by solid state reaction followed by hot pressing. The Cu2Se without excess Cu is mainly composed of monoclinic α-Cu2Se (JCPDS card no. 27-1131), and a small amount of cubic phase (JCPDS card no. 65-2981) is also detected in Cu2Se. However, cubic α-Cu2Se peaks cannot be observed at all in Cu-excess compounds. Therefore, it was found that Cu2Se prefers the monoclinic phase at RT especially in this Cuexcess condition. An additional peak of metallic Cu (JCPDS card no. 04-0836) is observed at 2θ = 43.3° in all the compounds, and its intensity increases with the amount of excess Cu. Therefore, this result shows that Cu-excess compounds possess a certain amount of metallic Cu excluded from the formation of the α-Cu2Se phase. To understand the distribution of metallic Cu in the compounds, we tried to investigate the microstructure of Cu2.1Se by using TEM (Figure S1) and OM (Figure S2). However, the metallic Cu phase could not be observed, and only submicron-sized Cu2O particles located at the grain boundaries of Cu2Se could be detected in Figure S1. This result suggests that original metallic Cu inclusions in the compounds were oxidized to Cu2O particles due to the inevitable exposure to oxygen gas 7 ACS Paragon Plus Environment


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during the TEM sample preparation. Based on X-ray photoelectron spectroscopy studies, other groups have reported similar oxidation behavior of Cu in the Cu2Se phase during their fabrication processes.28,29 Considering the volume expansion by oxidation of Cu (~67%), the original size of the Cu inclusion can be estimated to be a few hundred nm.22,46 We observed indirectly the distribution of metallic Cu inclusions along the grain boundaries using OM after chemical etching process (Figure S2). Compositional analysis was performed to analyze the actual Cu mole ratio in the compounds by using WDS attached to EPMA (Figure 2b). We repeated the WDS characterizations five times for each compound to confirm the accurate mole ratio in the sintered compound. The actual Cu mole ratio was linearly proportional to the excess Cu content; however, the measured ratio was slightly higher than the original ratio in all compounds. This suggests that there was preferential evaporation of Se during the consolidation process using a hot press, and it also suggests that the preferential evaporation can lead to the formation of metallic Cu even in the stoichiometric Cu2Se compound, as detected in its oxide form of Cu2O in the literature.28,29

Charge transport properties in Cu-excess Cu2+xSe.

Figure 3a shows temperature-

dependent electrical conductivities of the Cu2+xSe compounds. All samples exhibited negative temperature-dependence in their electrical conductivities, indicating that the charge transport is dominantly governed by acoustic phonon scattering (Figure S3).27,29,31,47 The electrical conductivity of the stoichiometric Cu2Se is ~2336 S cm-1 at RT; however, it decreases monotonously with increasing Cu content and reachs its lowest value of ~93 S cm-1 in Cu2.1Se at RT in this experiment. To understand the effects of the excess Cu on the charge transport properties, we carried out Hall measurements of the compounds at RT (Table 1). The hole concentration in the stoichiometric Cu2Se is ~9.7 × 1020 cm-3, and it is quite 8 ACS Paragon Plus Environment

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consistent with values reported in the literature.48 This high intrinsic hole concentration in Cu2Se arises from its strong tendency to generate a large quantity of intrinsic defects of Cu vacancies which act as good acceptors. There have been studies to compensate the high hole concentration by introducing dopants (Br, I, In, and Sn),27-29,31 and Day et al. expected an optimum hole concentration of 3 × 1019 cm-3 for α-Cu2Se based on the single parabolic band model.29 Although there have been many thermoelectric studies on Cu-deficient Cu2Se, the incorporation of excess Cu has not yet been tried to minimize its well-known chemical instability since most studies have focused on its high-temperature thermoelectric properties. However, a Cu-deficiency facilitates the formation of Cu vacancies, leading to a high hole concentration, far beyond its optimized carrier concentration for α-Cu2Se.16,29 On the other hand, when we concentrate on its near-RT properties, the consideration of instability is no longer needed because the α-phase is not a superionic conductor.16 In this experiment, the hole concentration could be reduced successfully by the incorporation of excess Cu for the first time (Figure 3b), and the hole concentration could be brought down to 3.3 × 1019 cm-3 in Cu-excess Cu2.1Se compound. Meanwhile, the decrease in the carrier concentration by excess Cu led to an increase in the mobility, which is desirable for power factor optimization, since both the reduction of its high intrinsic hole concentration and the enhancement of mobility were achieved simultaneously. It suggests that the charge transport is also affected by ionized impurity scattering, which increases in mobility with decreasing carrier concentration.49,50 Therefore, our results show that the charge transport in α-Cu2Se is dominantly governed by the acoustic phonon scattering and also partially influencened by the ionized impurity scattering. To clarify the role of excess Cu on charge transport, we plotted the RT mobilities as a function of carrier concentration in Figure 3c and compared our results to the reported mobilities in stoichiometric and Cu-deficient compounds without doping of foreign elements.16,29,31,51 9 ACS Paragon Plus Environment


Regardless of their Cu/Se ratios, a general trend in the mobility can be observed clearly that the mobility decreases with increasing carrier concentration. Therefore, it was elucidated that the effects of metallic Cu inclusions on charge transport can be neglected. On the other hand, mobilities in doped compounds deviate considerably from the general trend as shown in Figure 3d.29,30 Doped compounds exhibit much lower mobility than those in the general trend in Figure 3c, and this can be attributed to the effects of alloy scattering by foreign elements.29 These results confirm that the incorporation of excess Cu is much more beneficial for the control of intrinsic hole concentration and also for the enhancement of mobility than conventional doping, from the view-point of carrier optimization.

The origin of Cu vacancies in α-Cu2Se. It is intriguing that there is still a substantial amount of Cu vacancies even though metallic Cu inclusions coexist in the matrix. It is of interest and of importance to examine the origin of Cu vacancy formation and the role of Cu vacancies in this system. Basically, there are three possible interactions: Cu-Se, Cu-Cu, and Se-Se. Among them, Se-Se interactions should be negligible due to the long distance between Se atoms, and Cu-Se metal-ligand interactions should contribute to the stabilization of αCu2Se. The problem is Cu-Cu interaction. In α-Cu2Se, the Cu+ ion has 10 d-electrons and the d-level is fully occupied. In an orbital interaction between Cu+ ions with a fully occupied dlevel, the bonding and antibonding levels are fully filled as shown in Figure 4a, hence leading to instability of α-Cu2Se. In general, the antibonding level is higher in energy than the bonding level, which means that the fully occupied antibonding level gives rise to serious destabilization of the system. For this reason, Cu vacancies are developed to avoid instability arising from interactions between Cu+ ions in α-Cu2Se. The α-Cu2Se is composed of 12 nonequivalent Cu sites and 6 nonequivalent Se sites. We estimated Cu vacancy formation energy for 12 nonequivalent Cu sites on the basis of a first 10 ACS Paragon Plus Environment

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principles electronic band calculation and the results are shown in Figure 4b. It shows that all calculated formation energies are negative values. This means that the development of Cu vacancies contributes to the stabilization of α-Cu2Se by means of diminishing interaction between Cu+ ions. Thus, we anticipate that, as the interaction between Cu+ ions becomes stronger, the destabilization of α-Cu2Se is increased. The average distances between adjacent Cu+ ions from Cu(1) to Cu(12) sites are listed in Table S2. The long distance between Cu+ ions means that their interaction would be weak. Indeed, the calculated Cu vacancy formation energy for Cu(1), (2), and (3) sites shows the longer average distances between adjacent Cu+ ions are relatively small, which means that the stabilization of α-Cu2Se arising from Cu vacancy formation is weak. This would be caused by the long distance between Cu+ ions. On the other hand, the calculated Cu vacancy formation energy for Cu(3)-Cu(12) sites, with a shorter average distance, is relatively large, indicating it would be energetically favorable, and associated with a strong Cu-Cu interaction. Namely, the destabilization of α-Cu2Se originating in Cu-Cu interactions is relieved from Cu vacancy formation. We note that the trend of calculated Cu vacancy formation energies is not exactly consistent with the sequence of average Cu-Cu distances. There are Cu-Se, Cu-Cu, and Se-Se interactions. When a Cu vacancy is introduced, structural distortion is induced and then Cu-Cu interactions as well as Cu-Se and Se-Se interactions are affected by structural distortion.

Power factor optimization by the incorporation of excess Cu. Figure 5a represents temperature-dependent Seebeck coefficients of Cu2+xSe. The Seebeck coefficient in a degenerate semiconductor with a single parabolic band can be described by the Pisarenko relation in eq 1.4 S=

8π 2 k 2T 3qh

2

m*d (

π 2/3 ) , 3p

(1)



where q is the charge of carrier, k is the Boltzmann constant, h is the Planck constant, md* is the density of state (DOS) effective mass, and p is the hole concentration. The Seebeck coefficient increases monotonously when the excess Cu content increases in the temperature region of the α-phase, due to a decrease in carrier concentration by suppressed Cu vacancy formation as previously discussed. Based on a Pisarenko plot (Figure 5b) at RT, the effects of excess Cu on the Seebeck coefficient were investigated. Regardless of the existence of metallic Cu inclusions in the Cu-excess Cu2+xSe compounds, the Seebeck coefficients seem to follow a certain general trend with the reported values in undoped Cu2Se compounds as indicated by the dashed line.16,29,31,52 The DOS effective mass estimated by using equation 1 decreases with increasing Cu content and the values (2.49, 2.29, 2.19, 1.70, and 1.21 mh for x = 0, 0.025, 0.05, 0.075, and 0.1, respectively) were quite consistent with reported values (Figure S4).16,29,31,52 Therefore, the incorporation of excess Cu changes the chemical potential in Cu2+xSe by control of vacancy formation, while the metallic Cu in Cu-excess compounds influences neither the Seebeck coefficient nor the charge transport properties of α-Cu2Se. As a result, we can improve the near-RT power factor of α-Cu2Se significantly by the incorporation of excess Cu (Figure 5c). In this experiment, the maximum power factor of 9.6 × 10-4 W m-1 K-2 was obtained at 373 K in Cu2.05Se and it is the highest power factor ever achieved in α-phase. Furthermore, the optimum hole concentration in α-Cu2Se for the power factor S2σ τ-1 at RT was estimated by the Boltzmann transport equation (BTE) assuming that the relaxation time τ is energy-independent (Figure 5d). The calculated power factor (S2σ τ-1) was optimized around a carrier concentration of ~3 × 1020 cm-3, and this result is quite consistent with our experimental result in the inset. These results show that that Cu-excess is an effective way to improve the near-RT power factor of α-Cu2Se without significant deterioration in its charge transport behavior.


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Ultra-low lattice thermal conductivity and near-RT thermoelectric performances in Cu-excess Cu2Se. As well as enhancing the power factor, the incorporation of excess Cu leads to a dramatic decrease in thermal conductivity (Figure 6a). The thermal conductivity decreases monotonously with an increasing amount of excess Cu. The thermal conductivity of Cu2.1Se (0.4 W m-1 K-1) is much lower than that of stoichiometric Cu2Se (1.8 W m-1 K-1) at RT. One might attribute this reduction to the existence of metallic Cu inclusions in the matrix; however, it was mostly caused by a reduction in electrical conductivity. To elucidate the effects of Cu-excess on thermal transport, we plotted the thermal conductivity of the αphase at RT as a function of electrical conductivity in Figure 6b.16,29-31 Surprisingly, all the data points exhibit an obvious linear relationship between thermal and electrical conductivities in both phases regardless of large differences in their preparation methods, doping type, range of electrical conductivity, the existence of metallic Cu phase, and etc. This linear relationship between electrical and thermal conductivities was also observed in the βphase at 425 K (Figure S5). This linear relation is the Wiedemann-Franz law itself (κ = κL + LσT, where κL is the lattice thermal conductivity and L is the Lorentz number), and it demonstrates that metallic Cu in α-Cu2Se is almost inert to any kind of thermoelectric transport properties, such as mobility, DOS effective mass, Seebeck coefficient, or lattice thermal conductivity. The reason for this extraordinary inertness of metallic Cu is still unclear; however, it is worth investigating further since the formation of metallic Cu inclusions is an obvious feature of Cu-excess compounds and even in stoichiometric Cu2Se due to the formation of a large amount of Cu vacancies in this phase and inevitable preferential evaporation of Se during the sintering process, as observed in Figure 2b. Using the slope in Figure 6b and Figure S5, we can measure directly the Lorentz number of each phase for the first time. The Lorentz numbers in α- and β-phases were measured to be 2.12 × 10-8 V2 K-2 at RT and 1.98 × 10-8 V2 K-2 at 425 K, respectively. Our results are in 13 ACS Paragon Plus Environment


reasonably good agreement with the estimated Lorentz numbers (L = ~2.0 × 10-8 V2 K-2 at RT and ~1.85 × 10-8 V2 K-2 at 425 K) of Cu2Se using the single parabolic band model from the literature.53 Also, we can measure directly the lattice thermal conductivity of both phases by simple extrapolation to σ = 0. The lattice thermal conductivity of the α-phase at RT (0.27 W m-1 K-1) is much lower than that of the β-phase (0.55 W m-1 K-1) even though the latter is characterized at a higher temperature of 425 K. Therefore, the ultra-low intrinsic lattice thermal conductivity of α-Cu2Se is clearly another promising point for its use as a near-RT thermoelectric material.

Negative phonon frequency in α-Cu2Se. As we discussed in the section on the origin of Cu vacancies in α-Cu2Se, this phase is quite unstable, caused by interaction between Cu+ ions and this instability in α-Cu2Se is mitigated by Cu vacancy formation. Since phonon transport properties are associated with structural instability of materials,54,55 this structural instability can be presumed to be closely related to the observed ultra-low lattice thermal conductivity of α-Cu2Se. Phonon properties for α-Cu2Se were investigated via phonon dispersion based on ab initio density functional theory by using the frozen phonon method to investigate the relationship between phonon transport and structural instability.45 Figure 6c represents the phonon dispersion calculated for pure α-Cu2Se. The phonon dispersion shows negative phonon frequency indicating structural instability, which should lead to phonon softening and enhancing phonon scattering. Consequently, phonon softening and enhanced phonon scatting caused by structural instability should be associated with the ultra-low lattice thermal conductivity of α-Cu2Se.

Near-RT thermoelectric performances in Cu-excess Cu2Se. The collective effects of excess Cu on the thermoelectric transport properties can be expressed in ZT (Figure 6d). A 14 ACS Paragon Plus Environment

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very high ZT of 0.90 at 400 K could be achieved in α-Cu2.075Se through suppressed vacancy formation by excess Cu, and it is the highest ZT reported for α-Cu2Se except for the peak ZT which was achievable only in the vicinity of the transition temperature.31 Furthermore, the average ZT increases with increasing Cu content up to x = 0.75, and a maximum ZTave of 0.68 was achieved in Cu2.075Se within the temperature range from RT to the transition temperature (Figure S6). With these results, it is shown clearly that α-Cu2Se is a very promising near-RT thermoelectric material for replacing Bi2Te3-based compounds, and that over-stoichiometric Cu addition is an effective way to enhance its thermoelectric performance.

CONCLUSIONS In summary, significantly enhanced near-RT thermoelectric properties for Cu-excess αCu2+xSe (x = 0, 0.25, 0.5, 0.075, and 0.1) were demonstrated. These compounds were synthesized by solid state reactions and consolidated by hot pressing. The stoichiometric compound consists of mixed phases; however, the existence of excess Cu drive the compounds to have a monoclinic phase. Although metallic Cu inclusions are produced in the Cu-excess compounds, they were found to be almost inert to any kind of thermoelectric transport properties. Hole concentration could be reduced significantly by excess Cu addition, and consequent power factor optimization could be achieved in the Cu-excess compounds. One of the most interesting findings in this study is the direct measurement of Lorentz number for α-Cu2Se. Based on the κ versus σ plot, using our results and reported values in literature, we found that α-Cu2Se has a constant Lorentz number of 2.12 × 10-8 V2 K-2 at RT regardless of its stoichiometry and also that α-Cu2Se has a very low lattice thermal conductivity of 0.27 W m-1 K-1. This ultra-low lattice thermal conductivity, arising from the structural instability of α-Cu2Se and an optimized power factor in Cu-excess α-Cu2+xSe gave a significantly improved near-RT ZT of 0.9 at 390 K. Furthermore, it exhibited a very 15 ACS Paragon Plus Environment


promising ZTave of 0.68 within the temperature range of RT to 390 K. We believe that our results are an important stepping stone to finding an alternative for the only near-RT thermoelectric material, Bi2Te3, in α-Cu2Se-based compounds.


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ASSOCIATED CONTENT Supporting Information Additional figures and table. This material is available free of charge on the ACS Publications website.

AUTHOR INFORMATION Corresponding Author *(Y.S.L.) E-mail: [email protected] *(J.-H.S) E-mail: [email protected] *(C.-H.P.) E-mail: [email protected] Author Contributions #

J.-Y.T., W.H.N, and C.L. contributed equally to this work. Y.S.L. and C.-H.P. initiated the

concepts and designed the experiments. J.-Y.T. and K.K. performed the experiments and the measurements. J.-Y.T., W.H.N., C.L., Y.S.L, J.-H.S, and C.-H.P. carried out detail data analysis. C.L., S.K., J.-H.S. performed the calculations. W.H.N., C.L., and Y.S.L. wrote and edited the manuscript. S.L., W.-S.S., H.K.C. contributed with discussion and commented on the manuscript. All the authors shared ideas, contributed to the interpretation of the results.

ACKNOWLEDGMENT This work was supported by the Technology Innovation Program (10083640) through the Korea Evaluation Institute of Industrial Technology funded by the Ministry of Trade, Industry and Energy, Republic of Korea. It also was supported by the Nano·Material Technology Development Program (2011-0030147), the Midcareer Researcher Program (2015R1A2A2A01005929),

and

National

Nuclear


R&D

Program

(NRF-


2017M2B2A9072831) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology, Republic of Korea.


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Figure 1. Significantly enhanced average ZT at near-RT in Cu2.075Se.



Figure 2. Structural characterization of α-Cu2+xSe. (a) XRD patterns and (b) actual Cu mole ratio of the Cu2+xSe compounds after sintering.


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Figure 3. Charge transport properties in Cu-excess Cu2+xSe. (a) Temperature-dependent electrical conductivities of Cu2+xSe compounds. (b) Carrier concentrations and mobilities of the compounds at RT as a function of excess Cu content. (c-d) RT mobilities of compounds as a function of carrier concentration. For comparison, RT mobilities of undoped and doped Cu2Se compounds are also shown in (c) and (d), respectively.16,29-31,51 The green dashed line in (d) indicates general mobility trend in the undoped compounds.



Figure 4. Cu vacancies in α-Cu2Se. (a) Orbital interaction diagram for interaction between Cu+ ions and (b) formation energy of Cu vacancies as a function of average Cu-Cu distance.


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Figure 5. Power factor optimization through over-stoichiometric Cu addition. (a) Temperature-dependent Seebeck coefficients of Cu2+xSe compounds. (b) Pisarenko plot at RT showing the dependence of Seebeck coefficients on carrier concentration for the compounds. The black dashed lines indicate the contour lines of the md* (1.0 - 3.0 mh). For comparison, reported Seebeck coefficients in undoped Cu2+xSe compounds are also shown.16,29,31,52 The red dashed line (b) is a visual guide. (c) Temperature-dependent power factors of the compounds. (d) Calculated power factor (S2σ τ-1) of Cu2Se as a function of carrier concentration. Experimental power factor at RT is shown in the inset.



Figure 6. Promising near-RT thermoelectric performance. (a) Temperature-dependent thermal conductivities of Cu2+xSe compounds. (b) Thermal conductivities of compounds at RT as a function of electrical conductivity. For comparison, RT thermal conductivities of undoped and doped compounds are also shown.16,29-31 The solid line in (b) is based on the Wiedemann-Franz law, and its slope and y-intercept are directly related to the Lorentz number (2.12 × 10-8 V2 K-2) and lattice thermal conductivity (0.27 W m-1 K-1) in α-Cu2Se, respectively. (c) Calculated phonon dispersion for α-Cu2Se. (d) Temperature-dependent ZT values in the compounds.


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Table 1. Hall measurement results in Cu2+xSe compounds at RT. Cu2+xSe

x=0

x = 0.025

x = 0.05

x = 0.075

x = 0.1

p [cm-3]

9.7 × 1020

5.7 × 1020

3.5 × 1020

1.0 × 1020

3.3 × 1019

µ [cm2 V-1 s-1]

12.9

16.2

18.9

20.7

22.0



TABLE OF CONTENTS


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Ultra-low lattice thermal conductivity and significantly enhanced near

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