Thermoelectric materials with crystal-amorphicity duality induced by large atomic size mismatch

Abstract

•Discovering a material series with crystal structure not previously reported•Large S/Te size mismatch in (Cu,Ag)2(Te,S) inducing crystal-amorphicity duality•Ultralow thermal conductivity and high thermoelectric figure of merit zT Exploration and discovering of novel high-performance materials are the “fountain of youth” for science, engineering, and technology. Here, we report a high-performance thermoelectric material series, (Cu1−xAgx)2(Te1−ySy), structurally featured by the S/Te size mismatch-induced crystal-amorphicity duality. The entanglement of a highly disordered yet crystalline anionic sublattice and an amorphous cationic sublattice gives rise to extremely low thermal conductivities and a state-of-the-art figure of merit zT of 2.0 in the x = y = 0.22 sample. These results attest to the crystal-amorphicity duality as a paradigm-shifting approach beyond the classic “phonon-glass electron-crystal” and “phonon-liquid electron-crystal” paradigm in the development of high-performance thermoelectrics. Discovering novel materials and attaining higher performance are the eternal pursuit of thermoelectric materials research. Here, we report a material series, (Cu1−xAgx)2(Te1−ySy) (0.16 ≤ x ≤ 0.24, 0.16 ≤ y ≤ 0.24), which adopts a complex orthorhombic structure differing from any known crystal structure of (Cu/Ag)2(S/Te). This material series is featured by the crystal-amorphicity duality induced by the large anionic size mismatch: a crystalline sublattice of highly size-mismatched anions Te/S coexists with an amorphous-like sublattice of cations Cu/Ag. In the context of structure-property correlation, the crystal-amorphicity duality gave rise to not only interesting electrical properties but also exceptionally low lattice thermal conductivities from 300 to 1,000 K. A state-of-the-art figure of merit zT of 2.0 is obtained in the x = y = 0.22 sample at 1,000 K. These results give insights into crystal-amorphicity duality as a paradigm-shifting materials design approach to develop high-performance thermoelectric materials. Discovering novel materials and attaining higher performance are the eternal pursuit of thermoelectric materials research. Here, we report a material series, (Cu1−xAgx)2(Te1−ySy) (0.16 ≤ x ≤ 0.24, 0.16 ≤ y ≤ 0.24), which adopts a complex orthorhombic structure differing from any known crystal structure of (Cu/Ag)2(S/Te). This material series is featured by the crystal-amorphicity duality induced by the large anionic size mismatch: a crystalline sublattice of highly size-mismatched anions Te/S coexists with an amorphous-like sublattice of cations Cu/Ag. In the context of structure-property correlation, the crystal-amorphicity duality gave rise to not only interesting electrical properties but also exceptionally low lattice thermal conductivities from 300 to 1,000 K. A state-of-the-art figure of merit zT of 2.0 is obtained in the x = y = 0.22 sample at 1,000 K. These results give insights into crystal-amorphicity duality as a paradigm-shifting materials design approach to develop high-performance thermoelectric materials. Nowadays, the concerns about the environmental issues of fossil fuel usage have made the development of sustainable energy technologies an urgent front-burner task. 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Sci. 2019; 12: 216-229Crossref Google Scholar In the following, we report a TE material series, (Cu1−xAgx)2(Te1−ySy), which display high TE performance and crystal-amorphicity duality stemming from large anionic size mismatch. The average crystal structure is solved from the single-crystal X-ray diffraction (XRD) data, revealing both the ordered and disordered components of the material. In particular, the anions Te/S form a periodic framework whereas the cations Cu/Ag are short-range ordered, leading to extremely low lattice thermal conductivity, good electronic transport properties, and a high zT value of ∼2.0 at 1,000 K in the (Cu0.78Ag0.22)2(Te0.78S0.22) sample. Doping and/or alloying semiconductors and semimetals is the main approach to develop the state-of-the-art TE materials. In this route, the major restriction is the solubility limit of the doping element, which is governed by the atomic size mismatch between the dopant and the host atom to be substituted. The Hume-Rothery rules state that large atomic size mismatch (> 15%) tends to facilitate phase separation.23Hume-Rothery W. Powell H.M. On the theory of super-lattice structures in alloys.Zeitschrift für Kristallographie - Crystalline Materials. 1935; 91: 23-47Crossref Google Scholar Cu2S, Cu2Te, Ag2S, and Ag2Te are the semiconductors and semimetals known for their potentials in TEs. Given the atomic size of Cu (1.35 Å), Ag (1.60 Å), S (1.00 Å), and Te (1.40 Å),25Slater J.C. Atomic radii in crystals.J. Chem. Phys. 1964; 41: 3199-3204Crossref Scopus (1563) Google Scholar especially the large atomic mismatch between S and Te, what would happen, solid solutions or phase separation, if we melt and cool the admixture of Cu, Ag, S, and Te? In the efforts to answer this question, we observed intriguing phenomena in the phase formation of the materials series with nominal compositions (Cu1−xAgx)2(Te1−ySy), 0.13 ≤ x = y ≤ 0.26; x = 0.16, y = 0.24; and x = 0.24, y = 0.16. To characterize the phase purity, crystal structure, microstructures, and compositions of (Cu1−xAgx)2(Te1−ySy), we conducted scanning electron microscopy (SEM), energy dispersive X-ray (EDS) analysis, and powder XRD measurements. As shown in Figures 1A and S1, elemental segregations and impurity phases are observed in the samples with x = y = 0.13 and 0.26, which is consistent with our previous observation that Ag is nearly immiscible in Cu2X (X = S, Te).26Zhao K. Liu K. Yue Z. Wang Y. Song Q. Li J. Guan M. Xu Q. Qiu P. Zhu H. et al.Are Cu2Te-based compounds excellent thermoelectric materials?.Adv. Mater. 2019; 31e1903480Crossref PubMed Scopus (42) Google Scholar,27Guan M. Zhao K. Qiu P. Ren D. Shi X. Chen L. Enhanced thermoelectric performance of quaternary Cu2-2xAg2xSe1-xSx liquid-like chalcogenides.ACS Appl. Mater. Interfaces. 2019; 11: 13433-13440Crossref PubMed Scopus (21) Google Scholar Notably, homogeneous element distributions are observed in the samples with x and y ranging from 0.16 to 0.24, and the quantitative elemental analysis is in accordance with the nominal compositions. The powder XRD patterns for (Cu1−xAgx)2(Te1−ySy) samples are depicted in Figures 1B and S2. When the Ag content x and S content y are between 0.16 and 0.24, all the diffraction peaks can be well indexed to an orthorhombic structure, suggesting a single-phased material formed over such a wide composition range. Note that neither of Cu2X, Ag2X, or CuAgX (X= S or Te) compunds28Evans H.T. The crystal structures of low chalcocite and djurleite.Zeitschrift für Kristallographie. 1979; 150: 299-320Crossref Scopus (157) Google Scholar, 29Asadov Y.G. Rustamova L.V. Gasimov G.B. Jafarov K.M. Babajev A.G. Structural phase transitions in Cu 2– x Te crystals ( x = 0.00, 0.10, 0.15, 0.20, 0.25).Phase Transit. 1992; 38: 247-259Crossref Scopus (37) Google Scholar, 30Sadanaga R. Sueno S. X-ray study on the α-β transition of Ag2S.Mineral. J. 1967; 5: 124-143Crossref Google Scholar, 31Jiang J. Zhu H. Niu Y. Zhu Q. Song S. Zhou T. Wang C. Ren Z. Achieving high room-temperature thermoelectric performance in cubic AgCuTe.J. Mater. Chem. A. 2020; 8: 4790-4799Crossref Google Scholar adopt an orthorhombic crystal structure at any temperature. Thus, the observed orthorhombic structure is beyond the convention of solid solutions. Beyond the 0.16–0.24 range, impurity peaks are observed, agreeing well with our SEM-EDS results and the Hume-Rothery rules.23Hume-Rothery W. Powell H.M. On the theory of super-lattice structures in alloys.Zeitschrift für Kristallographie - Crystalline Materials. 1935; 91: 23-47Crossref Google Scholar In the following discussions, we will focus on the samples with the same Ag content x and S content y, aka (Cu1−xAgx)2(Te1−xSx), if not otherwise noted. Single-crystal XRD data measured on the (Cu0.82Ag0.18)2(Te0.82S0.18) sample at 100, 295, and 400 K point toward an orthorhombic structure (Imma) with a large unit cell (a = 16.3803(8) Å, b = 7.3157(4) Å, c = 11.1689(6) Å at 295 K). The detailed crystallographic data are summarized in Table 1 and the atomic positions are listed in Table 2. As depicted in Figure 1D, the solved crystal structure is complicated, consisting of thirteen cationic sites and four anionic sites. In particular, one of the anionic sites is preferably occupied by S atoms, whereas the other three anionic sites are preferably occupied by Te atoms. For simplicity, we assume three anionic sites are solely occupied by Te and one anionic site is solely occupied by S in the structural model for the follow-up discussion and the electronic band structure calculations. At this stage, we are unable to differentiate the preferred occupation of the thirteen cationic sites by Cu and Ag because of the high disorder. The cationic sites are partially occupied by Cu and Ag ions. Each anion Te/S is surrounded by multiple Cu/Ag ions in the form of different polyhedrons, as shown in Figure S3. The S-Cu/Ag bond distance is 2.2697–2.4996 Å, which is shorter than the Te-Cu/Ag bond distance of 2.3956–2.7944 Å as expected. That being said, the Cu ions take the appropriate sites to relax the large strain of Te/S sublattice. The Te/S sites are fully occupied, forming a largely ordered periodic framework (cf. Figure 1E), whereas all the Cu/Ag sites are partially occupied with site occupancy factors (SOFs) ranging from 0.138 to 0.561. In total, there are 48 Cu/Ag ions spread over 140 positions in each unit cell, resulting in a highly disordered cationic sublattice (cf. Figure 1F). We infer that the highly size-mismatched yet crystalline Te/S sublattice drives the Cu/Ag sublattice to an amorphous state; the latter helps release the large strain of the former to escape phase separation.Table 1Crystallographic information for (Cu0.82Ag0.18)2(Te0.82S0.18) at 295 KSample(Cu2Te)0.82(Ag2S)0.18a / Å16.3803(8)b / Å7.3157(4)c / Å11.1689(6)Volume / Å31,338.4(1)Space groupImmaCrystal systemorthorhombicρcalc / g cm−36.965 Open table in a new tab Table 2Refined atomic coordinates, site occupancies, and isotropic atomic displacement parameters for (Cu0.82Ag0.18)2(Te0.82S0.18) at 295 KSitesWyckoffXyZOccupancyU (Å2)Te18i0.7194(1)0.250.4153(2)10.0293(9)Te28i0.3756(2)0.250.8011(2)10.046(1)Te34e0.50.750.8523(4)10.0652(14)S4a0.500.510.027(3)Cu/Ag116j0.7295(4)0.3885(11)0.6347(5)0.522(16)0.048(3)Cu/Ag216j0.6488(5)0.5983(12)0.7938(9)0.561(18)0.083(4)Cu/Ag38i0.5873(9)0.250.5775(12)0.52(2)0.077(5)Cu/Ag48i0.5541(10)0.750.6303(11)0.45(3)0.077(8)Cu/Ag516j0.5870(8)0.581(2)0.6687(18)0.374(19)0.102(8)Cu/Ag68h0.50.410(3)0.945(2)0.31(3)0.098(15)Cu/Ag78h0.50.427(3)0.817(3)0.21(2)0.064(14)Cu/Ag88g0.750.479(4)0.750.25(2)0.080(12)Cu/Ag916j0.6303(12)0.415(3)0.5858(15)0.264(18)0.087(10)Cu/Ag1016j0.6295(14)0.575(5)0.968(4)0.19(3)0.064(14)Cu/Ag118f0.580(7)0.510.26(7)0.12(4)Cu/Ag124e0.50.250.628(5)0.18(2)0.077(7)Cu/Ag138h0.50.445(7)0.700(5)0.138(16)0.077(7) Open table in a new tab We observed super-structure peaks along the a axis corresponding to a super cell with a triple a axis length. Similar to the cases of Cu2Se and Cu2Se1−xTex,32Eikeland E. Blichfeld A.B. Borup K.A. Zhao K. Overgaard J. Shi X. Chen L. Iversen B.B. Crystal structure across the beta to alpha phase transition in thermoelectric Cu2-xSe.IUCrJ. 2017; 4: 476-485Crossref PubMed Scopus (48) Google Scholar the solved crystal structure should be regarded as an average structure. The details of correlated disorder require the analyses of the diffuse scattering.33Roth N. Iversen B.B. Solving the disordered structure of beta-Cu2-xSe using the three-dimensional difference pair distribution function.Acta Crystallogr. A Found. Adv. 2019; 75: 465-473Crossref PubMed Scopus (16) Google Scholar Note that Ag plays a crucial role in stabilizing this orthorhombic structure because the crystal structure of Ag-free Cu12Te5S is actually distinct from the structure of Cu10Ag2Te5S (i.e., (Cu5/6Ag1/6)2(Te5/6S1/6)) shown in Figure S4. We have performed extended X-ray absorption fine structure (EXAFS) analyses. Although the whole EXAFS spectra are too complex to extract detailed structural information, the Ag K-edge absorption spectrum of the (Cu0.82Ag0.18)2(Te0.82S0.18) sample is found to be close to that of the Ag2S standard sample (Figure S5), suggesting similar local structures around the Ag sites. The crystal structure of (Cu1−xAgx)2(Te1−xSx) obtained from the analyses of single-crystal diffraction data points toward the crystal-amorphicity duality, which is corroborated by the powder XRD data. In addition to sharp diffraction peaks, broad humps are clearly observed in the powder XRD patterns, a signature of the amorphous components in the (Cu1−xAgx)2(Te1−xSx) samples (cf. Figure 1B). The lattice parameters, obtained through the Rietveld refinement analyses, as a function of Ag/S content are shown in Figure 1C and Table S1. It is interesting to note that a and b gradually increase whereas c inversely decreases with increasing Ag and S contents. Nevertheless, the rough linear trend of lattice parameters implies that Ag and S substitutionally dope on the Cu and Te sites. Other than a broad hump of heat capacity anomaly observed near room temperature (Figure S6) and a small change in the SOF of Cu/Ag (cf. Tables S2–S4), the crystal structure is nearly unchanged from 100 to 400 K. The obtained orthorhombic phase is stable up to 800 K, at which it undergoes an orthorhombic-to-cubic phase transition, as demonstrated by the results of our heat capacity and high-temperature XRD measurements (Figure S6). Note that the hump feature in the XRD pattern of high-temperature cubic phase is less salient but still discernible compared with the counterpart of low-temperature orthorhombic phase. To cross-check and supplement the structural details derived from XRD data, we characterized the (Cu0.82Ag0.18)2(Te0.82S0.18) sample by means of the aberration-corrected scanning transmission electron microscopy (STEM) using a high-angle annular dark-field (HAADF) detector and electron energy loss spectroscopy (EELS). Figures 2A and 2B are the atomically resolved HAADF-STEM images along the [111] zone axis. The Cu/Ag atoms are too disordered to discern. Nonetheless, the periodic anionic framework composed of S and Te is clearly captured in Figure 2B, which is in good agreement with our structural model (Figure 2C). The dimmer spots, marked by the pink arrows in Figure 2B, indicate more S and less Te on these sites. Concomitantly, the brighter spots, marked by the red squares, indicate more Te and less S on these sites (Figure 2C). To better characterize the structural features, we turn to the [010] zone axis, along which the S, Te, and Cu/Ag atom columns are well separated. As shown in Figures 2D and 2E, the Te atoms form a ring-like arrangement with a S atom in the center whereas the Cu/Ag atoms locate in between S and Te. This is also consistent with the aforementioned structural model (Figure 2F). The brighter spots, marked by the green arrows in Figure 2D, indicate Te substitutions on the S sites. The atomic-scale point defects would effectively scatter short-wavelength phonons at elevated temperature. Besides, the sign of Cu/Ag atoms (red circles) can be found along this direction, although it is not as clear as Te/S atoms. The EELS data in Figure S7 further confirm the distribution of all elements, especially the distribution of Ag atoms that are not determined in our structural model. All the above-mentioned evidences corroborate that the as-formed phase is a crystal-amorphicity dual material with multiple point defects. How does the coexistence of an amorphous sublattice and a crystalline sublattice in a single-phased material impact the thermal transport behavior? The temperature dependence of the total thermal conductivity κ is plotted in Figure 3A. The small discontinuous jumps at approximately 800 K for (Cu1−xAgx)2(Te1−xSx) are attributed to the orthorhombic-to-cubic structural phase transition (cf. Figure S6). All (Cu1−xAgx)2(Te1−xSx) samples exhibit very low κ values in the whole temperature range, which is significantly lower than that of Cu2Te. The reduction in κ is mainly caused by the decreased electronic thermal conductivity (κe) (cf. Figure S8). The lattice thermal conductivity (κL), calculated by subtracting the electronic thermal conductivity (κe) from the total thermal conductivity, is shown in Figure 3B. All samples show extraordinarily low κL with the values of 0.2–0.3 W m−1 K−1 from 300 to 1,000 K. These values are not only significantly lower than those of the well-known crystalline TE materials, such as Bi2Te3 and PbTe,34Hao F. Qiu P. Tang Y. Bai S. Xing T. Chu H.-S. Zhang Q. Lu P. Zhang T. Ren D. et al.High efficiency Bi2Te3-based materials and devices for thermoelectric power generation between 100 and 300°C.Energy Environ. Sci. 2016; 9: 3120-3127Crossref Google Scholar,35Pei Y. Shi X. LaLonde A. Wang H. Chen L. Snyder G.J. Convergence of electronic bands for high performance bulk thermoelectrics.Nature. 2011; 473: 66-69Crossref PubMed Scopus (2628) Google Scholar but also smaller than some amorphous materials, such as α-SiO2,36Cahill D.G. Pohl R.O. Heat flow and lattice vibrations in glasses.Solid State Commun. 1989; 70: 927-930Crossref Scopus (270) Google Scholar α-Si,37Pompe G. Hegenbarth E. Thermal conductivity of amorphous Si at low temperatures.phys. stat. sol. 1988; 147: 103-108Crossref Scopus (27) Google Scholar and α-Se38White G.K. Woods S.B. Elford M.T. Thermal conductivity of selenium at low temperatures.Phys. Rev. 1958; 112: 111-113Crossref Scopus (15) Google Scholar (cf. Figure 3B and Table 3). Moreover, the κL is nearly independent of temperature, which is in contrast to the strong temperature dependence (e.g., κL ∼ T−1 because of the Umklapp process) of conventional normal crystalline compounds. The low temperature κL of (Cu1−xAgx)2(Te1−xSx) is shown in Figure 3C and compared with those of crystalline and amorphous SiO2. The (Cu1−xAgx)2(Te1−xSx) samples display glass-like thermal conduction behavior with a plateau between 10 and 30 K. Such behavior is often observed in amorphous materials (e.g., α-SiO2) but rarely observed in crystalline compounds (e.g., crystalline SiO2), which usually exhibit a well-defined peak (aka a dielectric peak) indicating the onset of the Umklapp process. Notably, a thermal conductivity plateau has been also observed in crystalline, but highly disordered, TE clathrates.39Bentien A. Christensen M. 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Phys. 2016; 119: 185102Crossref Scopus (22) Google ScholarTable 3Comparison of some physical properties between crystal-amorphicity dual (Cu1−xAgx)2(Te1−xSx); crystalline Cu2Te; crystalline Ag2S; and amorphous α-SiO2 α-Si, and α-Se at room temperatureCrystal-amorphicity dualityCrystallineAmorphousMaterials(Cu1−xAgx)2(Te1−xSx)Cu2TeAg2Sα-SiO2α-Siα-SeκL (W/mK)0.2–0.30.40.541.4210.15lphonon (Å)2.4–3.03.54.69.33.52.4μ (cm2/Vs)12–14134050.1–30.14The κL, lphonon, and μ refer to the lattice thermal conductivity, phonon mean free path, and carrier mobility, respectively. Open table in a new tab The κL, lphonon, and μ refer to the lattice thermal conductivity, phonon mean free path, and carrier mobility, respectively. The phonon mean free path lphonon is estimated from the equation κL = 1/3Cv v lphonon,43Toberer E.S. Zevalkink A. Snyder G.J. Phonon engineering through crystal chemistry.J. Mater. Chem. 2011; 21: 15843-15852Crossref Scopus (552) Google Scholar where Cv and ν are the isochoric heat capacity and sound velocity, respectively. As shown in Figure 3D, the derived lphonon for (Cu1−xAgx)2(Te1−xSx) first drastically declines below 30 K and then scarcely changes above 30 K, which also resemble the behavior of amorphous SiO2. The lphonon at room temperature is only approximately 2.4–3.0 Å, which is very close to the average interatomic distance (2.67 Å). Hence, the glass-like exceptionally low κL and lphonon for (Cu1−xAgx)2(Te1−xSx) is a consequence of the large unit cell, the multiple point defects, and especially the crystal-amorphicity duality character, which jointly cover a wide wavelength range of heat-carrying phon