⇦Chinese Physics Letters, 2021, Vol. 38, No. 11, Article code 117201 Enhanced Thermoelectric Properties of Cu$_{x}$Se ($1.75 \le x \le 2.10$) during Phase Transitions Zhongmou Yue (岳仲谋)1,2, Kunpeng Zhao (赵琨鹏)3*, Hongyi Chen (陈弘毅)4, Pengfei Qiu (仇鹏飞)1,2, Lidong Chen (陈立东)1,2, and Xun Shi (史迅)1,2* Affiliations 1State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China 2Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China 3State Key Laboratory of Metal Matrix Composites, School of Materials Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China 4College of Chemistry and Chemical Engineering, Central South University, Changsha 410083, China Received 26 August 2021; accepted 17 September 2021; published online 27 October 2021 Supported by the National Key Research and Development Program of China (Grant No. 2018YFB0703600), the National Natural Science Foundation of China (Grant Nos. 91963208, 51625205, 51961135106, and 51902199), Shanghai Government (Grant No. 20JC1415100), the CAS-DOE Program of Chinese Academy of Sciences (Grant No. 121631KYSB20180060), and the Shanghai Sailing Program (Grant No. 19YF1422800).
*Corresponding authors. Email: zkp.1989@sjtu.edu.cn; xshi@mail.sic.ac.cn. Citation Text: Yue Z M, Zhao K P, Chen H Y, Qiu P F, and Chen L D et al. 2021 Chin. Phys. Lett. 38 117201    Abstract Coupling of a phase transition to electron and phonon transports provides extra degree of freedom to improve the thermoelectric performance, while the pertinent experimental and theoretical studies are still rare. Particularly, the impaction of chemical compositions and phase transition characters on the abnormal thermoelectric properties across phase transitions are largely unclear. Herein, by varying the Cu content $x$ from 1.75 to 2.10, we systemically investigate the crystal structural evolution, phase transition features, and especially the thermoelectric properties during the phase transition for Cu$_{x}$Se. It is found that the addition of over-stoichiometry Cu in Cu$_{x}$Se could alter the phase transition characters and suppress the formation of Cu vacancies. The critical scatterings of phonons and electrons during phase transitions strongly enhance the Seebeck coefficient and diminish the thermal conductivity, leading to an ultrahigh dimensionless thermoelectric figure of merit of $\sim $1.38 at 397 K in Cu$_{2.10}$Se. With the decreasing Cu content, the critical electron and phonon scattering behaviors are mitigated, and the corresponding thermoelectric performances are reduced. This work offers inspirations for understanding and tuning the thermoelectric transport properties during phase transitions. DOI:10.1088/0256-307X/38/11/117201 © 2021 Chinese Physics Society Article Text Thermoelectric (TE) technology enables direct energy conversion between heat and electricity based on the Seebeck effect and Peltier effect.[1–3] Near-room-temperature solid-state heat pumps made from TE materials have attracted considerable interest by the electronic industry due to its ability in quickly cooling micro-processors, chips, and sensors.[4–7] The cooling capability of a TE device largely relies on the material's performance, which is mainly gauged by the dimensionless TE figure of merit, $zT = S^{2}T/\rho \kappa$, where $S$ is the Seebeck coefficient, $\rho$ is the electrical resistivity, $\kappa$ is the thermal conductivity, and $T$ is the absolute temperature. Over the past several decades, substantial efforts have been devoted to exploration and development of near-room-temperature TE materials. A series of promising TE materials with high performance have been discovered, such as MgAgSb,[8] Mg$_{3}$Bi$_{2}$,[9,10] Ag$_{2}$(Se/S/Te),[11–17] and nanostructured Bi$_{2}$Te$_{3}$[18–20] materials. However, most of these materials contain elements with high cost, high reactivity, or causticity. Bi$_{2}$Te$_{3}$-based materials are still the only TE material system that be widely used in commercial applications.[21] Developing novel high-performance and low-cost TE materials near room temperature is of momentous significance for the widespread use of TE cooling technology. The traditional research paradigm of TEs usually focuses on the exploration of materials with ordered and static crystal structures, which limits the regulation of electron and phonon transports. With the change of external temperature or pressure, some materials undergo phase transformations, during which large atomic migration, dynamic fluctuations or reconstructions are involved.[22–25] This may cause strong critical scattering of phonons and electrons and thus induce phonon softening and band broadening.[26,27] These new phenomena and effects are distinct from the conventional TE transport behavior, providing a new tuning knob to decouple the thermal and electrical transports toward higher performance.[28,29] Copper selenide (Cu$_{2}$Se) semiconductor, a well-known liquid-like TE material,[30–39] is featured by an order-disorder phase transition at around 400 K.[22,24,26–28,30,40–46] At room temperature, Cu$_{2}$Se has a layered crystal structure ($\alpha$-Cu$_{2}$Se) with Cu atoms alternately distributed at interlayers of the slightly distorted face-centered-cubic (fcc) Se sublattice [see Fig. 1(a)]. With increasing the temperature, a portion of Cu migrates from the copper rich to the copper deficient layer, transforming into a disordered antifluorite cubic structure ($\beta$-Cu$_{2}$Se) above 400 K [see Fig. 1(c)].[42] Such a structural transformation process has been reported as both the second- and the first-order phase transition.[22,24,28,43,47] Liu et al. firstly reported the abnormal TE properties of Cu$_{2}$Se during phase transitions.[22] They found that the measured thermal diffusivity and electrical conductivity can be greatly decreased, while the Seebeck coefficient can be sharply improved as the temperature approaches the phase transition point of Cu$_{2}$Se. The similar phenomenon was subsequently observed by several other groups.[26,43,45,46,48] A peak $zT$ of 2.3 was attained when the Dulong–Petit heat capacity was used to calculate the thermal conductivity $\kappa$.[28] Chen et al. pointed out that the extraction of the true $\kappa$ should exclude the heat exchange term from phase transition.[41] As such, the maximum $zT$ value during phase transition was corrected to be 0.86, which is still three times higher than the normal phases.[41] Apart from the anomalous $\kappa$, the underlying mechanism behind the enhancement of $S$ during phase transition remains an open issue. Liu et al. suggested that the extra enhancement of $S$ in Cu$_{2}$Se could be induced by the critical scattering of electrons, which strongly alters the carrier mobility and its energy dependency.[28] Brown et al. surmised that the improvement of $S$ may be caused by the entropy increment stemming from the rearrangement of Cu ions during phase transition.[48] Mahan et al. believed the cation disorder broadened the band energy and thus gave rise to the anomalous $S$.[26] Most recently, Sun et al. investigated the temperature dependent electronic structure of Cu$_{2}$Se using high-resolution angle-resolved photoemission spectroscopy.[27] They found that the electronic states were gradually changed when heating across the phase transition, which played a key role in the drastic temperature evolution of $S$. As stated widely in literature, no unified understanding or conclusion has yet been reached. More efforts, including both theoretical and experimental studies, are needed to provide a more complete picture for these unusual properties. However, most previous works mainly focused on the theoretical investigation, while the experimental studies on the transport properties during phase transition are very rare. Particularly, the TE properties of Cu deficient or Cu excess Cu$_{x}$Se ($1.75 \le x \le 2$.10) during phase transition have not yet been reported up to date. As the Cu content has a large impact on both the phase transition characters and the thermoelectric properties, Cu$_{x}$Se thus offers a good example to systematically investigate the role of chemical composition on the electron and phonon transports during phase transitions. In this work, via a routine melting-annealing recipe, we successfully synthesized a series of Cu$_{x}$Se samples with $x$ ranging from 1.75 to 2.10. The influence of Cu content on the crystal structures, phase transition characters, and TE properties during phase transitions are systematically investigated. In particular, the relevant mechanisms of phonon and electron transports during the structural transformation processes are deeply discussed and analyzed. We believe this work provides new insights for understanding and engineering the TE properties during phase transitions. Experiment. Polycrystalline Cu$_{x}$Se ($x = 1.75,\, 1.80,\, 1.85,\, 1.90,\, 1.95,\, 2.00,\, 2.03$ and 2.10) samples were prepared from high purity elements: Cu (shots, 99.999%, Alfa Aesar) and Se (shots, 99.999%, Alfa Aesar). The mixture of elements with different Cu/Se atomic ratios were weighted out according to the nominal chemical compositions. Then the mixture was loaded in a pyrolytic boron nitride crucible and sealed in silica tubes under vacuum. Subsequently, the tubes were heated up to 1423 K in 12 h and held at this temperature for 12 h, then cooled to 923 K over 48 h and followed by an annealing process over six days. A few Cu metal whiskers were observed on the surface of Cu$_{x}$Se ($x \ge 2.0$) ingots, which were removed before sintering. The ingots were handed ground to fine powders in an agate mortar and sintered by a spark plasma sintering facility (SPS, Sumitomo SPS-2040) at 673 K for 8 min under a pressure of 65 MPa. To reduce the impact of electrical current, the inner surface of the carbon dies was coated with electrically insulating BN layers to prevent the Cu migration during the sintering process. The relative densities of all samples were above 98%. The crystal structures of synthesised Cu$_{x}$Se samples were examined by powder x-ray diffraction (PXRD, Rint 2000, Rigaku, Japan) using Cu $K_\alpha$ source ($\lambda = 1.5405$ Å) at room temperature and at 450 K. The scan speed is 2$^{\circ}$/min and the scan step is 0.02$^{\circ}$. The actual chemical composition of the sintered pellets was analyzed using field emission scanning electron microscopy (SEM, ZEISS SUPRA 55) equipped with energy dispersive microscopy (EDS, OXFORD Aztec XMax80). The differential scanning calorimetry (DSC) measurements were performed on Netzsch 200F3 with aluminium pans. To calculate the speed of phase transition, all samples were subjected to heating rates of 1.0, 2.0, 5.0, 10.0 K/min. The thermal diffusivity was measured ($\lambda_{\rm m}$) by the laser flash method (Netzsch LFA457) under continuous argon flow. The temperature interval was set to be as small as 1 K during the phase transition region. The sample density $d$ was measured by the Archimedes method. As mentioned previously, the thermal conductivity during the phase transition should be calculated by $\kappa =C_{\rm p 0} \times d \times \lambda_{0}$, where $C_{\rm p 0}$, $\lambda_{0}$ are the heat capacity and thermal diffusivity without phase transition contribution, respectively. The measured heat capacity $C_{\rm p}$ could be divided into two parts: one is the normal heat capacity ($C_{\rm p 0}$) from phonons and electrons without the contribution from phase transition, and the other is the extra energy ($C_{\rm pt}$) required to transform the low-temperature trigonal phase to high-temperature cubic phase. Therefore, by subtracting $C_{\rm pt}$ from the measured $C_{\rm p}$, we can obtain the value of $C_{\rm p 0}$, which is also close to the theoretical Dulong–Petit value. The Seebeck coefficient $S$ and electrical resistivity $\rho$ during phase transitions were measured using a home-made measurement system based on the thermal expansion system (Netzsch DIL 402C) with a heating rate of 0.1 K/min. The electrical properties before and after the phase transitions were re-measured using a commercial apparatus ZEM-3 (ULVAC) to authenticate the data. Uncertainties in the electrical resistivity, Seebeck coefficient, and thermal diffusivity were $\pm 4$–9, $\pm 4$, and $\pm 5$–10%, respectively.[49] Hall coefficient ($R_{\scriptscriptstyle {\rm H}}$) measurements were performed on a physical property measurement system (PPMS, Quantum Design) with magnetic field sweeping from $-3$ T to 3 T. The Hall carrier concentration $p$ and carrier mobility $\mu$ were calculated by $p=1/(e R_{\scriptscriptstyle {\rm H}}$) and $\mu =\sigma R_{\scriptscriptstyle {\rm H}}$, respectively. Results and Discussion. Figure 1(d) shows the room-temperature powder x-ray diffraction patterns for Cu$_{x}$Se ($x = 1.75,\, 1.80,\, 1.85,\, 1.90,\, 1.95,\, 2.00,\, 2.03$ and 2.10) samples. Clearly, the phase structures of Cu$_{x}$Se are very sensitive to their chemical compositions. All the diffraction peaks can be indexed to the trigonal structure of $\alpha$-Cu$_{2}$Se (ICSD-4321181) when the nominal Cu content $x \ge 2.0$. With the decreasing Cu content, the diffraction peaks belonging to cubic $\beta$-Cu$_{2}$Se phase ($Fm \bar{3}m$, ICSD-150758) gradually increase, indicating a mixture of $\alpha$-and $\beta$-Cu$_{2- x}$Se phases in the region of $1.90 \le x \le 1.95$. However, with further decreasing the Cu content, the diffraction peaks of $\alpha$-Cu$_{2}$Se phase disappear, while the remaining peaks well match with the $\beta$-Cu$_{2}$Se phase. An impurity phase of Cu$_{3}$Se$_{2}$ (ICSD-16949) is observed for Cu$_{1.75}$Se. These results agree well with the data from previous studies[50] and the Cu–Se binary diagram proposed by Heyding.[51] Note that a small amount of Cu metal whiskers was observed on the surface of the ingots of Cu$_{x}$Se with $x \ge 2.0$, which were removed before spark plasma sintering. Thus, the measured chemical composition of $x \ge 2.0$ pellets may deviate from their nominal ones, while the other samples have compositions closing to the nominal contents, as corroborated by our energy dispersive spectroscopy (EDS) results (see Fig. S1 in the Supplementary Material).
cpl-38-11-117201-fig1.png
Fig. 1. Crystal structures and x-ray diffraction (XRD) patterns for Cu$_{x}$Se. Crystal structures for (a) the low temperature trigonal phase, (b) intermediate phase, and (c) high temperature cubic phase. (d) Room-temperature powder x-ray diffraction (XRD) patterns and (e) enlarged XRD patterns at $2\theta = 42^{\circ}$–$46^{\circ}$.
Apart from the crystal structure, the Cu content of Cu$_{x}$Se also exerts a significant impact on their phase transition temperature and characters. As shown in Fig. 2(a), a sharp endothermic peak is clearly observed at around 412.7 K in the heat capacity ($C_{\rm p}$) curves for the Cu$_{2.10}$Se sample, corresponding to the phase transition from ordered $\alpha$-phase to disordered $\beta$-phase. The $\lambda$-like peak in heat capacity is a signature of second-order phase transition.[28] With decreasing the content of Cu, the critical temperature of phase transition ($T_{\rm p}$) is gradually reduced [see Fig. 2(b)]. For Cu$_{1.80}$Se, the $T_{\rm p}$ is only 281.6 K, which is below the ambient temperature and 131 K lower than that of Cu$_{2.10}$Se. Meanwhile, the intensity of the $C_{\rm p}$ peak is also gradually weakened with decreasing the amount of Cu content. As shown in Fig. 2(c), the enthalpy change of phase transition ($\Delta H$) for Cu$_{1.80}$Se is about 3.6 J/g, which is only one ninth of that for Cu$_{2.10}$Se (33.3 J/g). The reduced $\Delta H$ is mainly ascribed to the less content of $\alpha$-phase in Cu deficient Cu$_{x}$Se. The structural transformation is further confirmed by the high temperature XRD measurements. All the diffraction peaks of Cu$_{x}$Se at 450 K can be well indexed to the cubic structure of $\beta$-phase [see Fig. 2(d)]. In addition, the diffraction peaks gradually shift to higher 2$\theta$ angles, suggesting a shrinkage of unit cells when introducing more Cu vacancies into Cu$_{x}$Se. The variation of phase transition characters should have a direct impact on the thermal and electrical transport properties during phase transitions.
cpl-38-11-117201-fig2.png
Fig. 2. Phase transition characters for Cu$_{x}$Se. (a) Heat capacity measured by the differential scanning calorimetric (DSC) method. (b) Critical temperature $T_{\rm p}$ as a function of Cu/Se atomic ratio. (c) Phase transition enthalpy $\Delta H$ as a function of Cu/Se atomic ratio. The data points of hollow symbols are taken from Refs. [31,43,44,52]. (d) High temperature powder XRD patterns measured at 450 K.
Figure 3 shows the thermal transport properties for Cu$_{x}$Se ($x = 2.10,\, 2.03,\, 2.00,\, 1.95,\, 1.90,\, 1.85,\, 1.80$ and 1.75) near room temperature and during phase transitions. Owing to the heat exchange from phase transition, the true thermal diffusivity $\lambda_{0}$ during phase transitions could largely deviate from the measured thermal diffusivity $\lambda_{\rm m}$. According to Chen et al., the correlation between $\lambda_{\rm m}$ and $\lambda_{0}$ could be written as[41] $$\begin{align} \frac{\lambda_{\rm m} }{\lambda_{0} }\approx\,& \frac{1}{1+{C_{\rm pt} } / {C_{\rm p0} }}+\frac{{C_{\rm pt} } / {C_{\rm p0} }}{1+{C_{\rm pt} } / {C_{\rm p0} }}\\ &\cdot \exp\Big[-\frac{1.81 L^{2} B}{\lambda_{0} \pi^{2}}\cdot \frac{1+{C_{\rm pt} } / {C_{\rm p0} }}{1}\Big], \end{align} $$ where $B$ is the speed of phase transition, $L$ is the thickness of the material, $C_{\rm p 0}$ is the normal heat capacity from the phonons and electrons, $C_{\rm pt} =\Delta H \times \frac{\partial a_{\rm eq}}{\partial T}$ is the equivalent heat capacity arising from phase transitions. As can be seen, $\lambda_{\rm m}/\lambda_{0}$ is mainly related to $C_{\rm pt}/C_{\rm p 0}$ and $B$. The term $C_{\rm pt}/C_{\rm p 0}$ could be easily derived from the measured heat capacity curves (Fig. S5), while the speed of phase transition $B$ could be obtained by fitting the heat flow curves with different heating rates. The fitting curves and fitting parameters are given in Fig. S6 and Table S2, respectively. Figure 3(a) shows the relationship between phase transition speed $B$ and $T/T_{\rm p}$ for Cu$_{x}$Se ($x =2.10$–1.95). The obtained $B$ value for Cu$_{2.00}$Se is around 0.19 s$^{-1}$ during phase transitions, which is decreased to 0.086 s$^{-1}$ and 0.047 s$^{-1}$ for Cu$_{2.10}$Se and Cu$_{1.95}$Se, respectively. Interestingly, the Cu$_{1.95}$Se sample shows the lowest speed of phase transition while the activation energy is the lowest ($E \sim 171$ kJ/mol). According to our previous work,[41] the speed of phase transition can be expressed as $$ B=A\cdot n\cdot \exp \Big(-\frac{E}{RT}\Big)\cdot \frac{(1-a_{\rm eq})^{n-1}}{a_{\rm eq}}. $$ Here, $A$ is the pre-exponential factor related to the mole fraction of high temperature phase, $n$ is the reaction order, $E$ is the activation energy, $R$ is the gas constant, and $a_{\rm eq}$ is the mole fraction of high temperature phase in the equilibrium state. The speed of phase transition, $B$, is not only related with the activation energy $E$, but also related with the reaction order and the mole fraction of the high-temperature phase. The Cu$_{2.00}$Se and Cu$_{2.10}$Se samples are pure trigonal phases while Cu$_{1.95}$Se is a mixture of trigonal phase and high-temperature cubic phase. As a result, the obtained $A$ for Cu$_{1.95}$Se is smaller than that of Cu$_{2.00}$Se and Cu$_{2.10}$Se, leading to a lower $B$ in Cu$_{1.95}$Se though its activation energy $E$ is also low. Nevertheless, these $B$ values are still quite large compared to those in Ag$_{2}$S and Ag$_{2}$Se.[41] The large $B$ and $C_{\rm pt}/C_{\rm p 0}$ imply that $\lambda_{\rm m}/\lambda_{0}$ can be significantly lower than 1 and thus the true $\lambda_{0}$ is much higher than the measured $\lambda_{\rm m}$. As shown in Fig. 3(b), the measured minimal thermal diffusivity for Cu$_{2.00}$Se is 0.072 mm$^{2}$/s, while the true minimal thermal diffusivity for Cu$_{2.00}$Se is 0.21 mm$^{2}$/s. Nevertheless, the thermal diffusivity curves for the $x = 2.10,\, 2.03,\, 2.00$, and 1.95 samples still exhibit an obvious dip during phase transitions even though the contribution of heat exchange is removed. Based on the determined true $\lambda_{0}$, we calculated the thermal conductivity during phase transitions using the equation $\kappa=C_{\rm p 0} d \lambda_{0}$, where $d$ is the sample density. As shown in Fig. 3(c), the $\kappa$ shows a temperature dependence similar to $\lambda_{0}$. When approaching the critical temperature $T_{\rm p}$, the $\kappa$ values of Cu$_{2.00}$Se, Cu$_{2.03}$Se and Cu$_{2.10}$Se are dramatically decreased due to the strong critical scatterings of electron and phonon during second-order phase transitions. A minimal $\kappa$ of 0.24 W$\cdot$m$^{-1}$ K$^{-1}$ is obtained in Cu$_{2.10}$Se, which is 2.4 times lower than those of normal $\alpha$-phase and $\beta$-phase. With decreasing the Cu/Se atomic ratio, the $\lambda_{0}$ and $\kappa$ gradually increase during the whole temperature range, which are mainly attributed to the weakened critical scattering and lowered electrical resistivity. The temperature-dependent $\kappa$ for Cu$_{1.90}$Se and Cu$_{1.85}$Se changes smoothly from the mixed phase to single $\beta$-phase, which agrees with the character of first-order phase transition.[53] In addition, there is no abrupt change in $\kappa$ for Cu$_{1.80}$Se and Cu$_{1.75}$Se because these samples are single $\beta$-phases at room temperature.
cpl-38-11-117201-fig3.png
Fig. 3. Thermal transport properties for Cu$_{x}$Se near room temperature and during phase transitions. (a) $B$ as a function of $T/T_{\rm p}$ for the $x = 2.10,\, 2.03,\, 2.00$ and 1.95 samples. Here, $B$ refers to the speed of phase transitions. (b) Temperature dependence of measured thermal diffusivity $\lambda_{\rm m}$ and corrected thermal diffusivity $\lambda_{0}$. (c) Temperature dependence of thermal conductivity $\kappa$ calculated from $\lambda_{0}$ and heat capacity $C_{\rm p0}$. The color regions represent the temperature range of phase transitions.
Figure 4 presents the electrical transport properties for Cu$_{x}$Se ($x = 1.75,\, 1.80,\, 1.85,\, 1.90,\, 1.95,\, 2.00,\, 2.03$ and 2.10) near room temperature and during phase transitions. The nominally stoichiometric Cu$_{2}$Se is an intrinsic p-type conductor due to the easily formation of Cu vacancies inside the crystal lattices.[35] Each Cu vacancy provides one hole according to the simple electron-counting rule. Experimentally, very high hole concentration with the value around $6 \times 10^{20}$ cm$^{-3}$ is usually detected in Cu$_{2}$Se[50,54] [see Fig. 4(a)]. Via introducing excess Cu into Cu$_{x}$Se ($x > 2.0$), the formation of Cu vacancies can be largely suppressed, leading to a much lower hole concentration in Cu$_{2.10}$Se ($1.7 \times 10^{20}$ cm$^{-3}$). In contrast, the hole concentration $p$ is immensely improved when decreasing the Cu/Se atomic ratio in Cu$_{x}$Se. A maximum $p$ of $7 \times 10^{21}$ cm$^{-3}$ is obtained in Cu$_{1.75}$Se, which is 40 times higher than that of Cu$_{2.10}$Se. The general increase trend with decreasing Cu content is in accordance with the results from previous studies. Because of the variation of crystal structure and the enhanced scattering by Cu vacancies, the carrier mobility $\mu$ is gradually decreased with the decreasing Cu/Se atomic ratio [see Fig. 4(b)]. The electrical transport properties during phase transitions were delicately measured by a home-made system based on the thermal expansion equipment. To authenticate the data, the electrical properties before and after the phase transitions were re-measured using a commercial apparatus ZEM-3. The results are shown in Figs. 4(c)–4(d) and Fig. S2. With decreasing the Cu/Se atomic ratio, the overall $\rho$ and $S$ are greatly enhanced at normal phase regions and during phase transitions owing to the improved hole concentrations. More remarkably, the Cu$_{x}$Se samples with different compositions exhibit distinct temperature-dependent transport properties. Both electrical resistivity $\rho$ and Seebeck coefficient $S$ for Cu$_{2.00}$Se, Cu$_{2.03}$Se and Cu$_{2.10}$Se are sharply increased when the temperature approaches the critical temperature $T_{\rm p}$, while the $\rho$ and $S$ for Cu$_{1.95}$Se are only slight improved before they drop to the normal value of $\beta$-phase. The temperature-dependent $\rho$ and $S$ for Cu$_{1.90}$Se and Cu$_{1.85}$Se change continuously and slowly from the mixed phases to single $\beta$-phase. No knee points are observed in the curves of $\rho$ and $S$ for Cu$_{1.80}$Se and Cu$_{1.75}$Se because their phase transitions are below room temperature. Figures 4(e) and 4(f) show the net increment of Seebeck coefficient $\Delta S$ and electrical resistivity $\Delta \rho$ during phase transitions as a function of Cu/Se atomic ratio. Obviously, both $\Delta S$ and $\Delta \rho$ are gradually lowered with decreasing $x$. The $\Delta \rho$ for Cu$_{2.10}$Se is around 7.1 $\Omega\cdot$m, which is decreased to 1.6 $\Omega\cdot$m for Cu$_{2.00}$Se and further decreased to 0.13 $\Omega\cdot$m for Cu$_{1.95}$Se. Similarly, the $\Delta S$ for Cu$_{2.10}$Se is around 31.2 µV/K, which is decreased to 9.2 µV/K for Cu$_{1.95}$Se and further decreased to nearly zero for Cu$_{1.90}$Se and other Cu-deficient samples. In addition, it is found that the critical temperature of phase transition is much lowered when decreasing the Cu content, which is coincident with our DSC results.
cpl-38-11-117201-fig4.png
Fig. 4. Electrical transport properties for Cu$_{x}$Se near room temperature and during phase transitions. (a) Hall carrier concentration $p$ and (b) carrier mobility $\mu_{\scriptscriptstyle {\rm H}}$ as a function of Cu/Se atomic ratio at 300 K. The data from Refs. [31,50,54–56] are included for comparison. The dashed lines are guide to the eyes. Temperature dependence of (c) electrical resistivity $\rho$ and (d) Seebeck coefficient $S$. The color regions represent the temperature range of phase transitions. The net increment of (e) electrical resistivity $\Delta \rho$ and (f) Seebeck coefficient $\Delta S$ during phase transitions as a function of Cu/Se atomic ratio.
The above results suggest that the variation in chemical compositions changes the characteristic of phase transitions and thus alters the transport behavior during phase transitions. In terms of microscopic mechanism, Seebeck coefficient is the ratio of entropy to charge in the process of carrier transport.[48] Generally, the entropy of charge transport can be divided into two components: one is the net entropy change with the addition of a carrier to the system; the other is the ratio of transported energy to the absolute temperature.[48] Thus, the total Seebeck coefficient is the sum of contributions from these two components, i.e., $$ S=S_{\rm presence} +S_{\rm transport}. $$ Typically, $S_{\rm presence}$ is dominated by the distribution of the carriers in different degenerate energy levels, which is correlated with the electronic structures and electron density of states near Fermi level. $S_{\rm transport}$, which is associated with the scattering mechanism of charge carriers, is induced by the manner in which charge is transported.[57] During the structural transformation process of Cu$_{2}$Se, the structural entropy will dramatically change over a wide temperature range, accompanied by the reconstruction and broadening of energy band. These changes lead to a substantial enhancement in $S_{\rm presence}$. On the other hand, the fluctuations in sample density, structure, and atomic positions result in strong critical scattering of carriers, which increases the transport entropy of carriers and thereby enhance $S_{\rm transport}$. As a total result, the Seebeck coefficient $S$ during phase transitions is greatly improved for Cu$_{2}$Se. Meanwhile, the critical scattering of carriers reduces the carrier mobility and thus increases the electrical resistivity $\rho$ when the temperature is raised to the critical phase transition point. With decreasing the Cu content, the phase transition character is modified, and the phase transition enthalpy is lowered, as reflected by our heat capacity analysis. Both the structural entropy and transport entropy are gradually reduced, leading to a smaller $\Delta S$ during phase transitions. Concurrently, the scattering intensity of carriers is also mitigated as the Cu content decreases from 2.10 to 1.75, giving rise to a higher carrier mobility during phase transitions. Therefore, the net increment of electrical resistivity ($\Delta \rho$) is also lowered with decreasing the Cu content. Benefitting from the extremely low $\kappa$ and high Seebeck coefficient, the $zT$ values of Cu$_{x}$Se samples are substantially improved during phase transitions (see Fig. 5). A maximum $zT$ of 1.38 is achieved at 397 K for Cu$_{2.10}$Se, which represents a 280%–320% improvement over those of normal $\alpha$-phase and $\beta$-phase. Note such a remarkable $zT$ is also one of the highest values recorded below 400 K. With the decreasing Cu/Se atomic ratio, the peak $zT$ is gradually lowered due to the weak critical behaviors and over-high carrier concentrations.
cpl-38-11-117201-fig5.png
Fig. 5. Figure of merit for Cu$_{x}$Se near room temperature and during phase transitions. (a) Dimensionless figure of merit ($zT$) as a function of temperature for Cu$_{x}$Se ($x =1.75,\, 1.80,\, 1.85,\, 1.90,\, 1.95,\, 2.00,\, 2.03$ and 2.10). The color regions represent the temperature range of phase transitions. (b) The maximum $zT$ during phase transitions as a function of Cu/Se atomic ratio.
In summary, we have successfully synthesized a series of Cu$_{x}$Se samples and systematically investigated their crystal structures, chemical compositions, phase transition features, and particularly the electron and phonon transports during phase transitions. The crystal structures and phase transitions of Cu$_{x}$Se are very sensitive to the chemical compositions. Cu$_{x}$Se ($2.00 \le x \le 2.10$) is single $\alpha$-phase with trigonal structure; Cu$_{x}$Se ($1.90 \le x \le 1.95$) is a mixture of $\alpha$-and $\beta$-phases, while Cu$_{x}$Se ($1.75 \le x \le 1.85$) is single $\beta$-phase with cubic structure at 300 K. Thanks to the strong critical behaviors of electrons and phonons during phase transitions, a record high $zT$ of 1.38 is obtained at 397 K for Cu$_{2.10}$Se, which is at least 2.8 times larger than that of normal $\alpha$-phase and $\beta$-phase. With the decreasing Cu/Se atomic ratio, the phase transition temperature is gradually reduced, and the phase transition character is altered. Accordingly, the critical behaviors of electrons and phonons during phase transitions are mitigated, resulting in a smaller reduction of $\kappa$ and a lower increment of $\rho$ and $S$, as well as a lower $zT$ when decreasing the Cu contents. This work demonstrates that the addition of overs-stoichiometry Cu in Cu$_{x}$Se is an effective way to enhance the TE properties during phase transitions. Data availability. The raw/processed data required to reproduce these findings are available from the corresponding author on reasonable request. References Recent advances in high-performance bulk thermoelectric materialsComplex thermoelectric materialsAdvanced Thermoelectric Design: From Materials and Structures to DevicesOn-chip cooling by superlattice-based thin-film thermoelectricsSmall-scale energy harvesting through thermoelectric, vibration, and radiofrequency power conversionOverview of Solid-State Thermoelectric Refrigerators and Possible Applications to On-Chip Thermal ManagementThermoelectric microdevice fabricated by a MEMS-like electrochemical processHigh thermoelectric performance of MgAgSb-based materialsDiscovery of high-performance low-cost n-type Mg3Sb2-based thermoelectric materials with multi-valley conduction bandsManipulation of ionized impurity scattering for achieving high thermoelectric performance in n-type Mg 3 Sb 2 -based materialsCrystalline Structure-Dependent Mechanical and Thermoelectric Performance in A g 2 S e 1 ‐ x S x SystemRoom-temperature ductile inorganic semiconductorRoom‐temperature plastic inorganic semiconductors for flexible and deformable electronicsThermoelectrics: p‐Type Plastic Inorganic Thermoelectric Materials (Adv. Energy Mater. 23/2021)Flexible thermoelectrics: from silver chalcogenides to full-inorganic devicesDuctile Ag 20 S 7 Te 3 with Excellent Shape‐Conformability and High Thermoelectric PerformanceSemiconductor glass with superior flexibility and high room temperature thermoelectric performanceHigh-Thermoelectric Performance of Nanostructured Bismuth Antimony Telluride Bulk AlloysThermoelectric performance of p-type zone-melted Se-doped Bi0.5Sb1.5Te3 alloysThe Thermoelectric Properties of Bismuth TellurideThermoelectric cooling materialsStructure-transformation-induced abnormal thermoelectric properties in semiconductor copper selenideEntropy optimized phase transitions and improved thermoelectric performance in n-type liquid-like Ag9GaSe6 materialsThe order–disorder transition in Cu 2 Se and medium-range ordering in the high-temperature phaseEnhancement of thermoelectric performance across the topological phase transition in dense lead selenideThe Seebeck coefficient of superionic conductorsDevelopment and evaluation of a new merged sea surface height product from multi-satellite altimetersUltrahigh Thermoelectric Performance by Electron and Phonon Critical Scattering in Cu 2 Se 1-x I xThermoelectric materials with crystal-amorphicity duality induced by large atomic size mismatchHigh-performance thermoelectric Cu2Se nanoplates through nanostructure engineeringCopper ion liquid-like thermoelectricsMeasuring Ionic Conductivity in Mixed Electron-ionic Conductors Based on the Ion-blocking MethodCu-based thermoelectric materialsCu 2 Se-Based liquid-like thermoelectric materials: looking back and stepping forwardEnhanced Thermoelectric Performance through Tuning Bonding Energy in Cu 2 Se 1– x S x Liquid-like MaterialsRecent Advances in Liquid‐Like Thermoelectric MaterialsUltrahigh thermoelectric performance in Cu 2−y Se 0.5 S 0.5 liquid-like materialsBlocking Ion Migration Stabilizes the High Thermoelectric Performance in Cu 2 Se CompositesNumber mismatch between cations and anions as an indicator for low lattice thermal conductivity in chalcogenidesAn Instant Change of Elastic Lattice Strain during Cu 2 Se Phase Transition: Origin of Abnormal Thermoelectric PropertiesThermal Conductivity during Phase TransitionsCrystal structure across the β to α phase transition in thermoelectric Cu 2− x SeApparent critical phenomena in the superionic phase transition of Cu 2- x SePhase transition and high temperature thermoelectric properties of copper selenide Cu 2− x Se (0 ≤ x ≤ 0.25)Discovery of colossal Seebeck effect in metallic Cu2SeRelating phase transition heat capacity to thermal conductivity and effusivity in Cu 2 SePromising and Eco‐Friendly Cu 2 X‐Based Thermoelectric Materials: Progress and ApplicationsPhase transition enhanced thermoelectric figure-of-merit in copper chalcogenidesThermoelectric properties of copper-deficient Cu2-Se (0.05 ≤ x ≤ 0.25) binary compoundsTHE COPPER/SELENIUM SYSTEMStudying Cu2–xSe phase transformation through DSC examinationMultiple phase transitions and structural oscillations in thermoelectric Cu2S at elevating temperaturesImpacts of Cu deficiency on the thermoelectric properties of Cu2−XSe nanoplatesSelf-propagating high-temperature synthesis for compound thermoelectrics and new criterion for combustion processingUltralow Lattice Thermal Conductivity and Significantly Enhanced Near-Room-Temperature Thermoelectric Figure of Merit in α-Cu 2 Se through Suppressed Cu Vacancy Formation by Overstoichiometric Cu AdditionEnhanced Seebeck coefficient from carrier-induced vibrational softening
[1] Shi X, Chen L, and Uher C 2016 Int. Mater. Rev. 61 379
[2] Snyder G J and Toberer E S 2008 Nat. Mater. 7 105
[3] Shi X L, Zou J, and Chen Z G 2020 Chem. Rev. 120 7399
[4] Chowdhury I, Prasher R, Lofgreen K, Chrysler G, Narasimhan S, Mahajan R, Koester D, Alley R, and Venkatasubramanian R 2009 Nat. Nanotechnol. 4 235
[5] Hudak N S and Amatucci G G 2008 J. Appl. Phys. 103 101301
[6] Sharp J, Bierschenk J, and Lyon H B 2006 Proc. IEEE 94 1602
[7] Snyder G J, Lim J R, Huang C K, and Fleurial J P 2003 Nat. Mater. 2 528
[8] Zhao H Z, Sui J E, Tang Z J, Lan Y C, Jie Q G, Kraemer D, McEnaney K N, Guloy A, Chen G, and Ren Z F 2014 Nano Energy 7 97
[9] Zhang J, Song L, Pedersen S H, Yin H, Hung L T, and Iversen B B 2017 Nat. Commun. 8 13901
[10] Mao J, Shuai J, Song S W, Wu Y X, Dally R, Zhou J W, Liu Z H, Sun J F, Zhang Q Y, dela C C, Wilson S, Pei Y Z, Singh D J, Chen G, Chu C W, and Ren Z F 2017 Proc. Natl. Acad. Sci. USA 114 10548
[11] Liang J, Qiu P, Zhu Y, Huang H, Gao Z, Zhang Z, Shi X, and Chen L 2020 Research 2020 6591981
[12] Shi X, Chen H Y, Hao F, Liu R H, Wang T, Qiu P F, Burkhardt U, Grin Y, and Chen L D 2018 Nat. Mater. 17 421
[13] Chen H Y, Wei T R, Zhao K P, Qiu P F, Chen L D, He J, and Shi X 2021 InfoMat 3 22
[14] Gao Z Q, Yang Q Y, Qiu P F, Wei T R, Yang S Q, Xiao J, Chen L D, and Shi X 2021 Adv. Energy Mater. 11 2170086
[15] Liang J S, Wang T, Qiu P F, Yang S Q, Ming C, Chen H Y, Song Q F, Zhao K P, Wei T R, Ren D D, Sun Y Y, Shi X, He J, and Chen L D 2019 Energy & Environ. Sci. 12 2983
[16] Yang S Q, Gao Z Q, Qiu P F, Liang J S, Wei T R, Deng T T, Xiao J, Shi X, and Chen L D 2021 Adv. Mater. 33 2007681
[17] He S Y, Li Y B, Liu L, Jiang Y, Feng J J, Zhu W, Zhang J Y, Dong Z R, Deng Y, Luo J, Zhang W Q, and Chen G 2020 Sci. Adv. 6 eaaz8423
[18] Poudel B, Hao Q, Ma Y, Lan Y C, Minnich A, Yu B, Yan X A, Wang D Z, Muto A, Vashaee D, Chen X Y, Liu J M, Dresselhaus M S, Chen G, and Ren Z F 2008 Science 320 634
[19] Zhai R S, Wu Y H, Zhu T J, and Zhao X B 2018 Rare Met. 37 308
[20] Witting I T, Chasapis T C, Ricci F, Peters M, Heinz N A, Hautier G, and Snyder G J 2019 Adv. Electron. Mater. 5 1800904
[21] Mao J, Chen G, and Ren Z F 2021 Nat. Mater. 20 454
[22] Liu H L, Shi X, Kirkham M, Wang H, Li Q, Uher C, Zhang W Q, and Chen L D 2013 Mater. Lett. 93 121
[23] Jiang B, Qiu P, Chen H, Huang J, Mao T, Wang Y, Song Q, Ren D, Shi X, Chen L 2018 Mater. Today Phys. 5 20
[24] Lu P, Qiu W J, Wei Y Y, Zhu C X, Shi X, Chen L D, and Xu F F 2020 Acta Crystallogr. Sect. B-Struct. Sci. Cryst. Eng. Mat. 76 201
[25] Chen L C, Chen P Q, Li W J, Zhang Q, Struzhkin V V, Goncharov A F, Ren Z F, and Chen X J 2019 Nat. Mater. 18 1321
[26] Mahan G D 2015 J. Appl. Phys. 117 045101
[27] Sun S, Li Y, Chen Y, Xu X, Kang L, Zhou J, Xia W, Liu S, Wang M, Jiang J, Liang A, Pei D, Zhao K, Qiu P, Shi X, Chen L, Guo Y, Wang Z, Zhang Y, Liu Z, Yang L, and Chen Y 2020 Chin. Sci. Bull. 65 1888
[28] Liu H L, Yuan X, Lu P, Shi X, Xu F F, He Y, Tang Y S, Bai S Q, Zhang W Q, Chen L D, Lin Y, Shi L, Lin H, Gao X Y, Zhang X M, Chi H, Uher C 2013 Adv. Mater. 25 6607
[29] Zhao K, Eikeland E, He D et al. 2021 Joule 5 1183
[30] Yang L, Chen Z G, Han G, Hong M, Zou Y C, Zou J 2015 Nano Energy 16 367
[31] Liu H, Shi X, Xu F, Zhang L, Zhang W, Chen L, Li Q, Uher C, Day T, and Snyder G J 2012 Nat. Mater. 11 422
[32] Liu Y Y, Qiu P F, Chen H Y, Chen R, Shi X, and Chen L D 2017 J. Inorg. Mater. 32 1337
[33] Qiu P, Shi X, and Chen L 2016 Energy Storage Mater. 3 85
[34] Zhang Z, Zhao K, Wei T R, Qiu P, Chen L, and Shi X 2020 Energy & Environ. Sci. 13 3307
[35] Zhao K, Blichfeld A B, Chen H, Song Q, Zhang T, Zhu C, Ren D, Hanus R, Qiu P, Iversen B B, Xu F, Snyder G J, Shi X, and Chen L 2017 Chem. Mater. 29 6367
[36] Zhao K, Qiu P, Shi X, and Chen L 2020 Adv. Funct. Mater. 30 1903867
[37] Zhao K P, Qiu P F, Song Q F, Blichfeld A B, Eikeland E, Ren D D, Ge B H, Iversen B B, Shi X, and Chen L D 2017 Mater. Today Phys. 1 14
[38] Yang D W, Su X L, Li J, Bai H, Wang S Y, Li Z, Tang H, Tang K C, Luo T T, Yan Y G, Wu J S, Yang J H, Zhang Q J, Uher C, Kanatzidis M G, and Tang X F 2020 Adv. Mater. 32 2003730
[39] Deng T T, Wei T R, Huang H, Song Q F, Zhao K P, Qiu P F, Yang J, Chen L D, and Shi X 2020 npj Comput. Mater. 6 81
[40] Bai H, Su X L, Yang D W, Zhang Q J, Tan G J, Uher C, Tang X F, and Wu J S 2021 Adv. Funct. Mater. 31 2100431
[41] Chen H, Yue Z, Ren D, Zeng H, Wei T, Zhao K, Yang R, Qiu P, Chen L, and Shi X 2018 Adv. Mater. 31 1806518
[42] Eikeland E, Blichfeld A B, Borup K A, Zhao K, Overgaard J, Shi X, Chen L, and Iversen B B 2017 IUCrJ 4 476
[43] Kang S D, Danilkin S A, Aydemir U, Avdeev M, Studer A, and Snyder G J 2016 New J. Phys. 18 013024
[44] Xiao X X, Xie W J, Tang X F, and Zhang Q J 2011 Chin. Phys. B 20 087201
[45] Byeon D, Sobota R, Delime-Codrin K, Choi S, Hirata K, Adachi M, Kiyama M, Matsuura T, Yamamoto Y, Matsunami M, and Takeuchi T 2019 Nat. Commun. 10 72
[46] Brown D R, Heijl R, Borup K A, Iversen B B, Palmqvist A, Snyder G J 2016 Phys. Status Solidi RRL 10 618
[47] Liu W D, Yang L, Chen Z G, and Zou J 2020 Adv. Mater. 32 1905703
[48] Brown D R, Day T, Borup K A, Christensen S, Iversen B B, and Snyder G J 2013 APL Mater. 1 052107
[49]Wang H, Porter W, Bottner H, Konig J, Chen L, Bai S, Tritt T, Mayolett A, Senawiratne J, Smith C, Harris F, Sharp J, Lo J, Kleinke H, and Kiss L 2011 Annex VIII—Thermoelectric Materials for Waste Heat Recovery: An International Collaboration for Transportation Applications (Oak Ridge: ORNL Press) chap 4 p 14
[50] Yu J, Zhao K, Qiu P, Shi X, and Chen L 2017 Ceram. Int. 43 11142
[51] Heyding R D 1966 Can. J. Chem. 44 1233
[52] Chrissafis K, Paraskevopoulos K M, Manolikas C 2006 J. Therm. Anal. 84 195
[53] Duan J L, Zhu C X, Guan M J, Lu P, He Y, Fu Z Q, Zhang L L, Xu F F, Shi X, and Chen L D 2018 Ceram. Int. 44 13076
[54] Yang L, Chen Z G, Han G, Hong M, and Zou J 2016 Acta Mater. 113 140
[55] Su X L, Fu F, Yan Y G, Zheng G, Liang T, Zhang Q, Cheng X, Yang D W, Chi H, Tang X F, Zhang Q J, and Uher C 2014 Nat. Commun. 5 4908
[56] Tak J Y, Nam W H, Lee C, Kim S, Lim Y S, Ko K, Lee S, Seo W S, Cho H K, Shim J H, Park C H 2018 Chem. Mater. 30 3276
[57] Emin D 1999 Phys. Rev. B 59 6205