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High-temperature thermoelectric properties of Cu1.97Ag0.03Se1+y

High-temperature thermoelectric properties of Cu1.97Ag0.03Se1+y Mater Renew Sustain Energy (2014) 3:26 DOI 10.1007/s40243-014-0026-5 OR IGINAL PAPER High-temperature thermoelectric properties of Cu Ag Se 1.97 0.03 1+y • • • Tristan W. Day Kasper A. Borup Tiansong Zhang • • • Fivos Drymiotis David R. Brown Xun Shi • • Lidong Chen Bo B. Iversen G. Jeffrey Snyder Received: 17 January 2014 / Accepted: 24 February 2014 / Published online: 14 March 2014 The Author(s) 2014. This article is published with open access at Springerlink.com Abstract Copper selenide is of recent interest as a high- Thermoelectric generators and coolers have the advantages performance p-type thermoelectric material. Adding Ag to of being silent, having no moving parts, and being free copper selenide increases the dimensionless figure-of-merit from greenhouse and ozone-depleting gases. The maxi- zT up to 780 K, with Cu Ag Se reaching a zT of 1.0 at mum efficiency of a thermoelectric material is governed by 1.97 0.03 2 -1 -1 870 K. The increase compared with Cu Se can be the figure-of-merit, zT, which is equal to S Tq j , where explained by analyzing the Hall carrier concentration and S is the Seebeck coefficient, T is the absolute temperature, effective mass. Addition of Ag reduces the carrier con- q is the electrical resistivity, and j is the thermal con- centration to a nearly optimum value at high temperature. ductivity. Thermoelectric materials in general must have If the Hall carrier concentration were to be further reduced low electrical resistivity, low thermal conductivity, and a 20 -3 to 6.6 9 10 cm at 750 K, the average zT would be controllable carrier concentration. substantially improved for waste heat recovery A new class of high-performance thermoelectric mate- applications. rials is the superionic coinage-metal chalcogenides. Some examples are Cu Se [3], AgCrSe [4], Ag Se [5–8], 2-x 2 2?x Keywords Thermoelectrics  Copper selenide  Carrier and Ag Te [8]. These materials all undergo a structural concentration optimization  Cu Ag Se phase transition above which the metal ions become 1.97 0.03 1?y mobile, which leads to enhanced phonon scattering and consequently low thermal conductivity. This combined Introduction with excellent electrical conductivity makes this class of materials promising for use as thermoelectrics. Materials that convert heat directly into electricity, called Cu Se was found to have a zT of 1.5 at 1,000 K [3]. A 2-x thermoelectrics, have been used to construct reliable gen- related compound is Cu Ag Se [9], which was 1.97 0.03 1?y studied from the late 1960s through the late 1970s as a erators of electrical power for spacecraft [1] and, under an applied current, as solid-state cooling devices [2]. candidate for use in radioisotope thermal generators (RTGs) [10]. The y = 0 compound (Cu Ag Se), syn- 1.97 0.03 thesized by 3 M, reached a zT of 1.1 at 870 K [10], which T. W. Day  F. Drymiotis  D. R. Brown  G. J. Snyder (&) is comparable to the zT of 1.0 at 870 K achieved in Department of Materials Science, California Institute of Technology, Pasadena, CA 91106, USA Cu Ag Se in this work. Recently, the ‘‘overstoichio- 1.97 0.03 e-mail: jsnyder@caltech.edu metric’’ composition Cu Ag Se was studied and found 1.98 0.2 to reach a maximum zT of 0.52 at 650 K before the onset of K. A. Borup  B. B. Iversen bipolar conduction [11]. While Cu Ag Se was 1.97 0.03 1?y Department of Chemistry and iNANO, Center for Materials Crystallography, Aarhus University, Aarhus 8000, Denmark tested under RTG conditions in order to evaluate its per- formance as an energy converter, no attempt was made to T. Zhang  X. Shi  L. Chen analyze its thermoelectric properties in order to optimize its CAS Key Laboratory of Energy-conversion Materials, zT. Furthermore, no such analysis has been done for Cu 2- Shanghai Institute of Ceramics, Chinese Academy of Sciences, Se. Therefore, we seek to analyze these materials together Shanghai 200050, China 123 Page 2 of 7 Mater Renew Sustain Energy (2014) 3:26 to determine the suitability of a single model for describing the sample was heated at 1 K/min, while fast diffracto- them and whether they can achieve greater zT values. grams were recorded from 24.5 to 54.5 2H and a scan The data will be analyzed using an effective mass speed of 12/min. approach. The premise of this approach is that at a par- ticular temperature, the intricacies of the band structure are Results and discussion reflected by two parameters, the effective mass and the mobility parameter, with the carrier concentration and Powder X-ray diffraction shows that Cu Ag Se is chemical potential determined from the Hall effect and the 1.97 0.03 1?y not single phase (Fig. 1); rather it is composed of Cu Seebeck effect, respectively. 2- Ag Se, CuAgSe [16], and at least one more unidentified x x impurity phase, i.e., some of the Ag enters the Cu Se matrix and some forms CuAgSe (which has also been Experimental evaluated as a thermoelectric material and found to have low zT values) [17]. In Cu Ag Se, the CuAgSe phase Ingots of Cu Se, Cu Se, Cu Ag Se, and 2 1.98 1.97 0.03 1.97 0.03 is observed to dissolve at about 380 K, slightly before the Cu Ag Se were formed by melting Cu (shot, 1.97 0.03 1.009 superionic phase transition just above 400 K. At 420 K, all 99.9999 % pure, Alfa Aesar, Puratronic), Ag (shot, peaks can be indexed and refined in the high-temperature 99.9999 % pure, Alfa Aesar, Puratronic), and Se (shot, Cu Se structure (antifluorite, space group Fm3m) except 99.999 % pure, Alfa Aesar, Puratronic) in quartz ampoules -5 evacuated to less than 6 9 10 torr. The ampoules were for a few, low-intensity peaks from one or more unidenti- ramped to 1,373 K at 100 K/h, held at that temperature for fied impurities. The main phase peaks are satisfactorily 12 h, and then quenched. The ingots were ball-milled to described by the antifluorite structure when Cu interstitials form powders, then re-sealed in quartz ampoules, heated at are incorporated on the octahedral sites and at trigonal 1,273 K for 5 days, cooled to 973 K, held at that temper- planar sites. The atomic positions were stable when refined. ature for 3 days and then quenched. The ingots thus The room-temperature Cu Se structure is not known but obtained were ball-milled again and then hot-pressed at comparison with phase pure Cu Se PXRD patterns [18] 973 K and 40 MPa for 6 h [12]. The geometric densities of reveals another set of peaks not belonging to the impurity the hot-pressed pellets were greater than 95 % of their at high temperatures, CuAgSe, or pure Cu Se. These peaks theoretical values. disappear at the phase transition and can hence either be an impurity, which dissolves, or belong to the main phase if The thermoelectric properties of the samples were measured with custom-built and commercial apparatus. this has a slightly different structure than pure Cu Se. In this study, the compositions Cu Se, Cu Se, The thermal diffusivity a was measured with a Netzsch 2 1.98 LFA 457 laser flash analysis unit. The total thermal con- Cu Ag Se, and Cu Ag Se were synthesized, 1.97 0.03 1.97 0.03 1.009 ductivity was calculated from j = adC , where d is the and data on Cu Ag Se from a recent publication by p 1.98 0.2 geometric density, and C is the heat capacity. The Seebeck Ballikaya et al. [11] are included for a more complete coefficient S was measured with a custom-built device [13] analysis. and with an ULVAC ZEM-3. The resistivity q and Hall The thermoelectric properties of a material depend resistance were measured with a custom-built system [14] strongly on the Hall carrier concentration, n , whose magnitude can vary with temperature and via chemical using van der Pauw geometry and a 2-T magnetic field to determine the Hall carrier concentration n = 1/eR and doping. In the aforementioned materials, n can be H H H decreased by substituting Ag for Cu, or increased by add- the Hall mobility l = R /q. C was measured on a Net- H H p ? 2- zsch 200F3 differential scanning calorimeter from 317 to ing Se to create Cu vacancies. Each additional Se ion is ? ? 913 K. equivalent to 2 Cu vacancies; each Cu vacancy donates Powder X-ray diffraction (PXRD) patterns were col- one hole to the valence band. Furthermore, previous work lected using a Rigaku SmartLab diffractometer equipped on the band gap of Cu Se [19] shows that the valence and with a Cu K source, parallel beam optics, and a Rigaku conduction bands are separated by a band gap much greater D/tex detector. A hot-pressed pellet of Cu Ag Se was than k T, so that only one type of carrier is present. The 1.97 0.03 B placed under dynamic vacuum on an Anton-Paar DHS- Hall carrier concentration for all samples is shown in 1100 hot stage with an X-ray transparent graphite dome. Fig. 2a. Above the phase transition, the Hall carrier con- PXRD patterns were collected at 300 and 420 K and used centration of Cu Ag Se is greater than that of 1.97 0.03 1.009 for phase identification and refinement of the high-tem- Cu Ag Se due to the greater deficiency of metal ions. 1.97 0.03 Likewise, the Hall carrier concentration of Cu Se is perature phase using the FullProf suite [15]. Diffracto- 1.98 grams were recorded every 20 K from 300 to 500 K in the greater than that of Cu Se. This could be because substi- 2H range from 10 to 100. Between these measurements, tution of Ag for Cu alters the native vacancy concentration 123 Mater Renew Sustain Energy (2014) 3:26 Page 3 of 7 Fig. 1 Temperature resolved PXRD of Cu Ag Se from 1.97 0.03 300 to 500 K. On the bottom, arrows mark CuAgSe peaks, while hat symbol marks impurities that dissolve at the phase transition. Asterisk marks the stable impurity peaks. Unmarked peaks on the bottom have corresponding peaks in the low-temperature structure of Cu Se Fig. 2 Transport properties as (a) (b) functions of temperature of 4x10 Cu Se, Cu Ag Se and 2-x 1.97 0.03 1?y literature data on Cu Ag Se 1.98 0.2 from Ballikaya et al. [11]. Hall carrier concentration n , Seebeck coefficient S, resistivity q, Hall mobility l , total thermal conductivity, and figure-of-merit zT are shown in 0 500 700 900 500 700 900 a, b, c, d, e, and f, respectively. The resistivity of Cu Ag Se 1.98 0.2 is not shown because it is (d) (c) several times greater than that of 10 20 Cu Ag Se Cu Se 1.97 0.03 the other compositions. Above Cu Ag Se the phase transition and up to Cu Se 1.97 0.03 1.009 2-x 780 K, Cu Ag Se achieves 1.97 0.03 Cu Ag Se 1.98 0.2 higher zT values (f) than do Cu Se and Cu Se because its 2 1.98 Hall carrier concentration is closer to the optimum value 2 (Fig. 3). Cu Ag Se is under- 1.98 0.2 0 0 doped compared with both 500 700 900 500 700 900 compositions of Cu Ag Se , as indicated 1.97 0.03 1?y (e) (f) by its greater Seebeck 1.5 1.2 coefficient (a) and lower zT values at all temperatures 1.0 1.0 0.8 0.6 0.5 0.4 0.2 0.0 0.0 500 700 900 500 700 900 [K] [K] -1 -1 -3 [W m K ] [mΩ cm] [cm ] -1 2 -1 -1 [μV K ] [-] [cm V s ] Page 4 of 7 Mater Renew Sustain Energy (2014) 3:26 of Cu Se. The Hall carrier concentration of Cu Ag Se greater zT.Cu Ag Se reaches a peak zT of 0.52 at 2 1.98 0.2 1.98 0.2 19 -3 is at least an order of magnitude less (*10 cm )than 650 K and then decreases due to bipolar conduction. 20 21 -3 the other compositions (*10 –10 cm )due to the To understand why Cu Ag Se achieves a greater zT 1.97 0.03 excess of metal ions [11]. Between 750 and 800 K, the up to 780 K than do the other samples, we analyze n and Hall carrier concentrations of Cu Se and Cu Ag the effective mass m*. The carrier mobility in this model is 2-x 1.97 0.03- Se dramatically increase. The exponential character of limited by acoustic phonon scattering, and the effective 1?y this increase seems to indicate bipolar conduction. mass is treated as a constant at each temperature. The However, the concomitant decreases in Seebeck and results of our analysis are shown in Fig. 3 and Table 1. resistivity are not observed. While Hall carrier concen- We estimated the effective mass m* at 575 K (the tration data for Cu Ag Se were not available above highest temperature for which R data were available for 1.98 0.2 H 575 K in Ballikaya et al. [11], the influence of a con- Cu Ag Se) and 750 K (the lowest temperature at which 1.98 0.2 duction band separated from the valence band by a band none of the samples exhibit a sharp increase in Hall carrier gap of order k T is corroborated by the decrease in the concentration) by using m* as a fitting parameter to fit a Seebeck coefficient of that composition at 725 K, as theoretical curve to S versus n data (Fig. 3a). The theo- showninFig. 2b. retical dependence of S on the dimensionless Fermi level g Cu Se and Cu Ag Se exhibit the steady is given by Eq. (1). The following equations are valid if the 2-x 1.97 0.03 1?y increase with temperature of the Seebeck coefficient electron mobility is limited by acoustic phonon scattering, (Fig. 2b) and of the resistivity q (Fig. 2c) expected of a as per the discussion of our Hall mobility data above. k is single-carrier semiconductor. Cu Ag Se has greater Boltzmann’s constant, e is the elementary charge, and F (g) 1.98 0.2 j values of S and q than do the other samples in the entire is the Fermi integral of order j, given by Eq. (2). e is the temperature range due to its much lower Hall carrier con- electronic energy level normalized by k T. centration, and it shows a peak in S at about 725 K. k 2F ðÞ g B 1 The Hall mobilities, l ,ofCu Se, Cu Ag Se , S ¼  g ð1Þ H 2-x 1.97 0.03 1?y e F ðÞ g and Cu Ag Se above the phase transition are low 1.98 0.2 compared with those of other high-performance p-type e de 2 -1 -1 thermoelectric materials, such as 40–6 cm V s in Na- FðÞ g ¼ ð2Þ 1 þ expðÞ e  g doped PbTe between 600 and 750 K, depending on carrier -p concentration [20]. The Hall mobility scales with T [21]. g is set by the Hall carrier concentration and the effective The average value of p taken from the data shown in mass m*. The relationship between these variables is given Fig. 2d and above the phase transition is about 3.1. Values by Eq. (3). of p between 1 and 1.5 usually indicate that acoustic 3=2 phonons limit electron mobility in the material [21], while 2m k T n ¼ 4p F ðÞ g ð3Þ values greater than 1.5 indicate a temperature-dependent H 1=2 effective mass [22]. The thermal conductivity data are shown in Fig. 2e. The At a fixed temperature, we compute g from S for each sudden increase in j around the phase transition tempera- sample and then use m* to compute a theoretical n that we ture is due to the sharp peak in C [18]. Cu Ag Se has fit to the n data. The effective mass increases with p 1.98 0.2 H temperature (Table 1), which we predicted based on the the lowest thermal conductivity values because it has the lowest lattice thermal conductivity, presumably due to Hall mobility data. The same trends of effective mass, Hall carrier concentration, resistivity, and Seebeck coefficient disorder caused by the greater amount of Ag, and because it has the lowest carrier concentration of the compositions with temperature were observed by Voskanyan et al. [23], studied and therefore the lowest electronic thermal though they estimated different values of the effective conductivity. mass, e.g., 2.2 m at 750 K as opposed to 6.2 m at 750 K e e The zT data are shown in Fig. 2f. The zT values of because they used assumed values of n instead of Cu Se and Cu Ag Se all increase continuously calculating them from R . Voskanyan et al. proposed a 2-x 1.97 0.03 1?y H from the phase transition temperature to the maximum second valence band as a possible cause of the increasing temperature at which they were measured. The effective mass. While this may explain of the trend of m* Cu Ag Se sample reaches a zT of 1.0 at 870 K. Cu Se with T, a two-band model is much more complex than a 1.97 0.03 2 single-band model, requires more assumptions, and does reaches a zT of 1.16 at 870 K, but between 450 and 780 K has an average zT of 0.59, whereas Cu Ag Se has an not guarantee a unique solution. Here, we use a single band 1.97 0.03 in this analysis in order to estimate the maximum average zT of 0.66 in the same temperature range. Above 780 K, the increasing values of q in Cu Ag Se and the achievable zT and optimum Hall carrier concentration in 1.97 0.03 decreasing values of j in Cu Se mean that Cu Se has a this material. We must emphasize that because the 2 2 123 Mater Renew Sustain Energy (2014) 3:26 Page 5 of 7 Fig. 3 Analysis of the effective (a) 400 (b) 8 mass and Hall carrier concentration explains and predicts the optimization of 300 6 Cu Ag Se for 1.97 0.03 thermoelectric use. a The Seebeck coefficient as a function of Hall carrier 200 4 concentration with the effective 750 K 575 K mass as a fitting parameter. b The Hall mobility as a 100 2 function of Hall carrier 575 K 750 K concentration with l as a fitting parameter. The lattice thermal conductivity (c) was computed 0 0 21 21 0. 0 1. 0 2.0x10 0.0 1.0 2.0x10 from the resistivity and the -3 -3 Lorenz number L. The optimum [cm ] [cm ] Hall carrier concentration (d) increases with temperature. 0.7 1.0 (c) (d) The Hall carrier concentration of Cu Ag Se also increases 1.97 0.03 750 K 0.6 750 K with temperature, so it has a 0.8 0.5 Hall carrier concentration close 575 K to the optimum value up to 0.6 575 K 750K 0.4 750 K. The lines in c are Effective Mass Model average values of j at the Cu Ag Se 0.3 1.97 0.03 0.4 indicated temperature Cu Ag Se 1.97 0.03 1.009 0.2 Cu Ag Se 1.98 0.2 575 K Cu Se 0.2 0.1 Cu Se 1.98 0.0 0.0 21 2 4 6 2 4 6 2 4 6 0.0 1.0 2.0x10 19 20 21 22 10 10 10 10 -3 [cm ] -3 [cm ] Cu Ag Se has a greater Hall mobility than does Table 1 Thermoelectric material properties estimated from the 1.97 0.03 1.009 effective mass model Cu Ag Se, despite having a greater carrier 1.97 0.03 concentration and more defects. 575 K 750 K The thermal conductivity is made up of a lattice con- m (m ) 3.1 6.2 tribution j and an electronic contribution j . j is equal L E E 2 -1 -1 l (cm V s ) 5.9 1.9 to LT/q, where L is the Lorenz number, given by Eq. (5). -1 -1 j (W m K ) 0.53 0.54 We estimated the Lorenz number of each sample at each B (–) 0.28 0.48 temperature studied using the previously determined Fermi level g. The Lorenz numbers of the samples were between -8 -8 2 -2 1.5 9 10 and 1.9 9 10 V K at 575 and 750 K, respectively. effective mass is not constant with temperature, our k 3F ðÞ g F ðÞ g  4F ðÞ g 0 2 1 predictions are valid only at fixed temperatures as a L ¼ ð5Þ function of Hall carrier concentration. F ðÞ g The estimated values of l (Table 1) fit to the data j of each composition is shown in Fig. 3c, along with shown in Fig. 3b, decrease with temperature, as expected the average j at each temperature, the values of which are from the raw Hall mobility measurements. The Hall shown in Table 1. j does not change significantly from mobility is given by Eq. (4). l is the mobility of a single 575 to 750 K; therefore, the optimization of zT in this electron in the material. The Fermi integral term accounts materials system will hinge only on the electrical transport for energy level degeneracy and scattering. The effective properties. The slight increase in j with temperature in mass m* and the n data are used to compute g, which is Table 1 is due to uncertainty in the calculated j . Taking then used with the l data to fit l . H 0 the estimates for m*, l , and j , we can calculate a zT 0 L F ðÞ g 1=2 versus Hall carrier concentration curve to determine the l ¼ l ð4Þ H 0 2F ðÞ g 0 maximum zT at a given temperature and the optimum Hall -1 -1 -1 [μV K ] [W m K ] [-] 2 -1 -1 [cm V s ] Page 6 of 7 Mater Renew Sustain Energy (2014) 3:26 Acknowledgments T.W.D. and G.J.S. thank the U.S. Air Force carrier concentration (Fig. 3d). Looking at the zT versus Office of Scientific Research for support. T.W.D. thanks Heng Wang Hall carrier concentration curve for 575 K, it is clear that for help with the dimensionless quality factor. T.Z., X.S., and L.C. Cu Ag Se is under-doped, leading to a decrease in zT 1.98 0.2 thank for financial support the National Basic Research Program of above 650 K due to bipolar conduction. Cu Ag Se has China (973-program) under Project No. 2013CB632501 and National 1.97 0.03 Natural Science of Foundation of China (NSFC) under Project No. the Hall carrier concentration closest to the optimum value 51222209. K.A.B. and B.B.I. thank the Danish National Research at every temperature at which we calculated an effective Foundation (DNRF93). mass, which explains why that composition has the greatest zT of all the compositions included in the analysis. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, dis- According to our model, a maximum zT of 1.0 at 750 K tribution, and reproduction in any medium, provided the original is possible in this material system. The dimensionless author(s) and the source are credited. quality factor B [24–26] (Eq. 6) is a measure of the max- imum zT at a given temperature and depends only on material properties and temperature. References 7=2 3=2 5=2 k lðÞ m T B 0 B ¼ ð6Þ 1. LaLonde, A.D., et al.: Lead telluride alloy thermoelectrics. Mater. 1=2 3=2 2 p  h e Today 14(11), 526–532 (2011) 2. Bell, L.E.: Cooling, heating, generating power, and recovering The quality factors calculated for this material system waste heat with thermoelectric systems. Science 321, 1457–1461 increase with temperature (Table 1), meaning the (2008) theoretical maximum zT also increases with temperature. 3. Liu, H., et al.: Copper ion liquid-like thermoelectrics. Nat. Mater. According to Fig. 3d, the optimum Hall carrier 11(5), 422–425 (2012) 4. Gascoin, F., Maignan, A.: Order-disorder transition in AgCrSe :a concentration n increases with temperature as well, 2 H,opt new route to efficient thermoelectrics. Chem. Mater. 23(10), which combined with the increasing trend with temperature 2510–2513 (2011) of n in Cu Ag Se means that that composition has a H 1.97 0.03 5. 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Abstract

Mater Renew Sustain Energy (2014) 3:26 DOI 10.1007/s40243-014-0026-5 OR IGINAL PAPER High-temperature thermoelectric properties of Cu Ag Se 1.97 0.03 1+y • • • Tristan W. Day Kasper A. Borup Tiansong Zhang • • • Fivos Drymiotis David R. Brown Xun Shi • • Lidong Chen Bo B. Iversen G. Jeffrey Snyder Received: 17 January 2014 / Accepted: 24 February 2014 / Published online: 14 March 2014 The Author(s) 2014. This article is published with open access at Springerlink.com Abstract Copper selenide is of recent interest as a high- Thermoelectric generators and coolers have the advantages performance p-type thermoelectric material. Adding Ag to of being silent, having no moving parts, and being free copper selenide increases the dimensionless figure-of-merit from greenhouse and ozone-depleting gases. The maxi- zT up to 780 K, with Cu Ag Se reaching a zT of 1.0 at mum efficiency of a thermoelectric material is governed by 1.97 0.03 2 -1 -1 870 K. The increase compared with Cu Se can be the figure-of-merit, zT, which is equal to S Tq j , where explained by analyzing the Hall carrier concentration and S is the Seebeck coefficient, T is the absolute temperature, effective mass. Addition of Ag reduces the carrier con- q is the electrical resistivity, and j is the thermal con- centration to a nearly optimum value at high temperature. ductivity. Thermoelectric materials in general must have If the Hall carrier concentration were to be further reduced low electrical resistivity, low thermal conductivity, and a 20 -3 to 6.6 9 10 cm at 750 K, the average zT would be controllable carrier concentration. substantially improved for waste heat recovery A new class of high-performance thermoelectric mate- applications. rials is the superionic coinage-metal chalcogenides. Some examples are Cu Se [3], AgCrSe [4], Ag Se [5–8], 2-x 2 2?x Keywords Thermoelectrics  Copper selenide  Carrier and Ag Te [8]. These materials all undergo a structural concentration optimization  Cu Ag Se phase transition above which the metal ions become 1.97 0.03 1?y mobile, which leads to enhanced phonon scattering and consequently low thermal conductivity. This combined Introduction with excellent electrical conductivity makes this class of materials promising for use as thermoelectrics. Materials that convert heat directly into electricity, called Cu Se was found to have a zT of 1.5 at 1,000 K [3]. A 2-x thermoelectrics, have been used to construct reliable gen- related compound is Cu Ag Se [9], which was 1.97 0.03 1?y studied from the late 1960s through the late 1970s as a erators of electrical power for spacecraft [1] and, under an applied current, as solid-state cooling devices [2]. candidate for use in radioisotope thermal generators (RTGs) [10]. The y = 0 compound (Cu Ag Se), syn- 1.97 0.03 thesized by 3 M, reached a zT of 1.1 at 870 K [10], which T. W. Day  F. Drymiotis  D. R. Brown  G. J. Snyder (&) is comparable to the zT of 1.0 at 870 K achieved in Department of Materials Science, California Institute of Technology, Pasadena, CA 91106, USA Cu Ag Se in this work. Recently, the ‘‘overstoichio- 1.97 0.03 e-mail: jsnyder@caltech.edu metric’’ composition Cu Ag Se was studied and found 1.98 0.2 to reach a maximum zT of 0.52 at 650 K before the onset of K. A. Borup  B. B. Iversen bipolar conduction [11]. While Cu Ag Se was 1.97 0.03 1?y Department of Chemistry and iNANO, Center for Materials Crystallography, Aarhus University, Aarhus 8000, Denmark tested under RTG conditions in order to evaluate its per- formance as an energy converter, no attempt was made to T. Zhang  X. Shi  L. Chen analyze its thermoelectric properties in order to optimize its CAS Key Laboratory of Energy-conversion Materials, zT. Furthermore, no such analysis has been done for Cu 2- Shanghai Institute of Ceramics, Chinese Academy of Sciences, Se. Therefore, we seek to analyze these materials together Shanghai 200050, China 123 Page 2 of 7 Mater Renew Sustain Energy (2014) 3:26 to determine the suitability of a single model for describing the sample was heated at 1 K/min, while fast diffracto- them and whether they can achieve greater zT values. grams were recorded from 24.5 to 54.5 2H and a scan The data will be analyzed using an effective mass speed of 12/min. approach. The premise of this approach is that at a par- ticular temperature, the intricacies of the band structure are Results and discussion reflected by two parameters, the effective mass and the mobility parameter, with the carrier concentration and Powder X-ray diffraction shows that Cu Ag Se is chemical potential determined from the Hall effect and the 1.97 0.03 1?y not single phase (Fig. 1); rather it is composed of Cu Seebeck effect, respectively. 2- Ag Se, CuAgSe [16], and at least one more unidentified x x impurity phase, i.e., some of the Ag enters the Cu Se matrix and some forms CuAgSe (which has also been Experimental evaluated as a thermoelectric material and found to have low zT values) [17]. In Cu Ag Se, the CuAgSe phase Ingots of Cu Se, Cu Se, Cu Ag Se, and 2 1.98 1.97 0.03 1.97 0.03 is observed to dissolve at about 380 K, slightly before the Cu Ag Se were formed by melting Cu (shot, 1.97 0.03 1.009 superionic phase transition just above 400 K. At 420 K, all 99.9999 % pure, Alfa Aesar, Puratronic), Ag (shot, peaks can be indexed and refined in the high-temperature 99.9999 % pure, Alfa Aesar, Puratronic), and Se (shot, Cu Se structure (antifluorite, space group Fm3m) except 99.999 % pure, Alfa Aesar, Puratronic) in quartz ampoules -5 evacuated to less than 6 9 10 torr. The ampoules were for a few, low-intensity peaks from one or more unidenti- ramped to 1,373 K at 100 K/h, held at that temperature for fied impurities. The main phase peaks are satisfactorily 12 h, and then quenched. The ingots were ball-milled to described by the antifluorite structure when Cu interstitials form powders, then re-sealed in quartz ampoules, heated at are incorporated on the octahedral sites and at trigonal 1,273 K for 5 days, cooled to 973 K, held at that temper- planar sites. The atomic positions were stable when refined. ature for 3 days and then quenched. The ingots thus The room-temperature Cu Se structure is not known but obtained were ball-milled again and then hot-pressed at comparison with phase pure Cu Se PXRD patterns [18] 973 K and 40 MPa for 6 h [12]. The geometric densities of reveals another set of peaks not belonging to the impurity the hot-pressed pellets were greater than 95 % of their at high temperatures, CuAgSe, or pure Cu Se. These peaks theoretical values. disappear at the phase transition and can hence either be an impurity, which dissolves, or belong to the main phase if The thermoelectric properties of the samples were measured with custom-built and commercial apparatus. this has a slightly different structure than pure Cu Se. In this study, the compositions Cu Se, Cu Se, The thermal diffusivity a was measured with a Netzsch 2 1.98 LFA 457 laser flash analysis unit. The total thermal con- Cu Ag Se, and Cu Ag Se were synthesized, 1.97 0.03 1.97 0.03 1.009 ductivity was calculated from j = adC , where d is the and data on Cu Ag Se from a recent publication by p 1.98 0.2 geometric density, and C is the heat capacity. The Seebeck Ballikaya et al. [11] are included for a more complete coefficient S was measured with a custom-built device [13] analysis. and with an ULVAC ZEM-3. The resistivity q and Hall The thermoelectric properties of a material depend resistance were measured with a custom-built system [14] strongly on the Hall carrier concentration, n , whose magnitude can vary with temperature and via chemical using van der Pauw geometry and a 2-T magnetic field to determine the Hall carrier concentration n = 1/eR and doping. In the aforementioned materials, n can be H H H decreased by substituting Ag for Cu, or increased by add- the Hall mobility l = R /q. C was measured on a Net- H H p ? 2- zsch 200F3 differential scanning calorimeter from 317 to ing Se to create Cu vacancies. Each additional Se ion is ? ? 913 K. equivalent to 2 Cu vacancies; each Cu vacancy donates Powder X-ray diffraction (PXRD) patterns were col- one hole to the valence band. Furthermore, previous work lected using a Rigaku SmartLab diffractometer equipped on the band gap of Cu Se [19] shows that the valence and with a Cu K source, parallel beam optics, and a Rigaku conduction bands are separated by a band gap much greater D/tex detector. A hot-pressed pellet of Cu Ag Se was than k T, so that only one type of carrier is present. The 1.97 0.03 B placed under dynamic vacuum on an Anton-Paar DHS- Hall carrier concentration for all samples is shown in 1100 hot stage with an X-ray transparent graphite dome. Fig. 2a. Above the phase transition, the Hall carrier con- PXRD patterns were collected at 300 and 420 K and used centration of Cu Ag Se is greater than that of 1.97 0.03 1.009 for phase identification and refinement of the high-tem- Cu Ag Se due to the greater deficiency of metal ions. 1.97 0.03 Likewise, the Hall carrier concentration of Cu Se is perature phase using the FullProf suite [15]. Diffracto- 1.98 grams were recorded every 20 K from 300 to 500 K in the greater than that of Cu Se. This could be because substi- 2H range from 10 to 100. Between these measurements, tution of Ag for Cu alters the native vacancy concentration 123 Mater Renew Sustain Energy (2014) 3:26 Page 3 of 7 Fig. 1 Temperature resolved PXRD of Cu Ag Se from 1.97 0.03 300 to 500 K. On the bottom, arrows mark CuAgSe peaks, while hat symbol marks impurities that dissolve at the phase transition. Asterisk marks the stable impurity peaks. Unmarked peaks on the bottom have corresponding peaks in the low-temperature structure of Cu Se Fig. 2 Transport properties as (a) (b) functions of temperature of 4x10 Cu Se, Cu Ag Se and 2-x 1.97 0.03 1?y literature data on Cu Ag Se 1.98 0.2 from Ballikaya et al. [11]. Hall carrier concentration n , Seebeck coefficient S, resistivity q, Hall mobility l , total thermal conductivity, and figure-of-merit zT are shown in 0 500 700 900 500 700 900 a, b, c, d, e, and f, respectively. The resistivity of Cu Ag Se 1.98 0.2 is not shown because it is (d) (c) several times greater than that of 10 20 Cu Ag Se Cu Se 1.97 0.03 the other compositions. Above Cu Ag Se the phase transition and up to Cu Se 1.97 0.03 1.009 2-x 780 K, Cu Ag Se achieves 1.97 0.03 Cu Ag Se 1.98 0.2 higher zT values (f) than do Cu Se and Cu Se because its 2 1.98 Hall carrier concentration is closer to the optimum value 2 (Fig. 3). Cu Ag Se is under- 1.98 0.2 0 0 doped compared with both 500 700 900 500 700 900 compositions of Cu Ag Se , as indicated 1.97 0.03 1?y (e) (f) by its greater Seebeck 1.5 1.2 coefficient (a) and lower zT values at all temperatures 1.0 1.0 0.8 0.6 0.5 0.4 0.2 0.0 0.0 500 700 900 500 700 900 [K] [K] -1 -1 -3 [W m K ] [mΩ cm] [cm ] -1 2 -1 -1 [μV K ] [-] [cm V s ] Page 4 of 7 Mater Renew Sustain Energy (2014) 3:26 of Cu Se. The Hall carrier concentration of Cu Ag Se greater zT.Cu Ag Se reaches a peak zT of 0.52 at 2 1.98 0.2 1.98 0.2 19 -3 is at least an order of magnitude less (*10 cm )than 650 K and then decreases due to bipolar conduction. 20 21 -3 the other compositions (*10 –10 cm )due to the To understand why Cu Ag Se achieves a greater zT 1.97 0.03 excess of metal ions [11]. Between 750 and 800 K, the up to 780 K than do the other samples, we analyze n and Hall carrier concentrations of Cu Se and Cu Ag the effective mass m*. The carrier mobility in this model is 2-x 1.97 0.03- Se dramatically increase. The exponential character of limited by acoustic phonon scattering, and the effective 1?y this increase seems to indicate bipolar conduction. mass is treated as a constant at each temperature. The However, the concomitant decreases in Seebeck and results of our analysis are shown in Fig. 3 and Table 1. resistivity are not observed. While Hall carrier concen- We estimated the effective mass m* at 575 K (the tration data for Cu Ag Se were not available above highest temperature for which R data were available for 1.98 0.2 H 575 K in Ballikaya et al. [11], the influence of a con- Cu Ag Se) and 750 K (the lowest temperature at which 1.98 0.2 duction band separated from the valence band by a band none of the samples exhibit a sharp increase in Hall carrier gap of order k T is corroborated by the decrease in the concentration) by using m* as a fitting parameter to fit a Seebeck coefficient of that composition at 725 K, as theoretical curve to S versus n data (Fig. 3a). The theo- showninFig. 2b. retical dependence of S on the dimensionless Fermi level g Cu Se and Cu Ag Se exhibit the steady is given by Eq. (1). The following equations are valid if the 2-x 1.97 0.03 1?y increase with temperature of the Seebeck coefficient electron mobility is limited by acoustic phonon scattering, (Fig. 2b) and of the resistivity q (Fig. 2c) expected of a as per the discussion of our Hall mobility data above. k is single-carrier semiconductor. Cu Ag Se has greater Boltzmann’s constant, e is the elementary charge, and F (g) 1.98 0.2 j values of S and q than do the other samples in the entire is the Fermi integral of order j, given by Eq. (2). e is the temperature range due to its much lower Hall carrier con- electronic energy level normalized by k T. centration, and it shows a peak in S at about 725 K. k 2F ðÞ g B 1 The Hall mobilities, l ,ofCu Se, Cu Ag Se , S ¼  g ð1Þ H 2-x 1.97 0.03 1?y e F ðÞ g and Cu Ag Se above the phase transition are low 1.98 0.2 compared with those of other high-performance p-type e de 2 -1 -1 thermoelectric materials, such as 40–6 cm V s in Na- FðÞ g ¼ ð2Þ 1 þ expðÞ e  g doped PbTe between 600 and 750 K, depending on carrier -p concentration [20]. The Hall mobility scales with T [21]. g is set by the Hall carrier concentration and the effective The average value of p taken from the data shown in mass m*. The relationship between these variables is given Fig. 2d and above the phase transition is about 3.1. Values by Eq. (3). of p between 1 and 1.5 usually indicate that acoustic 3=2 phonons limit electron mobility in the material [21], while 2m k T n ¼ 4p F ðÞ g ð3Þ values greater than 1.5 indicate a temperature-dependent H 1=2 effective mass [22]. The thermal conductivity data are shown in Fig. 2e. The At a fixed temperature, we compute g from S for each sudden increase in j around the phase transition tempera- sample and then use m* to compute a theoretical n that we ture is due to the sharp peak in C [18]. Cu Ag Se has fit to the n data. The effective mass increases with p 1.98 0.2 H temperature (Table 1), which we predicted based on the the lowest thermal conductivity values because it has the lowest lattice thermal conductivity, presumably due to Hall mobility data. The same trends of effective mass, Hall carrier concentration, resistivity, and Seebeck coefficient disorder caused by the greater amount of Ag, and because it has the lowest carrier concentration of the compositions with temperature were observed by Voskanyan et al. [23], studied and therefore the lowest electronic thermal though they estimated different values of the effective conductivity. mass, e.g., 2.2 m at 750 K as opposed to 6.2 m at 750 K e e The zT data are shown in Fig. 2f. The zT values of because they used assumed values of n instead of Cu Se and Cu Ag Se all increase continuously calculating them from R . Voskanyan et al. proposed a 2-x 1.97 0.03 1?y H from the phase transition temperature to the maximum second valence band as a possible cause of the increasing temperature at which they were measured. The effective mass. While this may explain of the trend of m* Cu Ag Se sample reaches a zT of 1.0 at 870 K. Cu Se with T, a two-band model is much more complex than a 1.97 0.03 2 single-band model, requires more assumptions, and does reaches a zT of 1.16 at 870 K, but between 450 and 780 K has an average zT of 0.59, whereas Cu Ag Se has an not guarantee a unique solution. Here, we use a single band 1.97 0.03 in this analysis in order to estimate the maximum average zT of 0.66 in the same temperature range. Above 780 K, the increasing values of q in Cu Ag Se and the achievable zT and optimum Hall carrier concentration in 1.97 0.03 decreasing values of j in Cu Se mean that Cu Se has a this material. We must emphasize that because the 2 2 123 Mater Renew Sustain Energy (2014) 3:26 Page 5 of 7 Fig. 3 Analysis of the effective (a) 400 (b) 8 mass and Hall carrier concentration explains and predicts the optimization of 300 6 Cu Ag Se for 1.97 0.03 thermoelectric use. a The Seebeck coefficient as a function of Hall carrier 200 4 concentration with the effective 750 K 575 K mass as a fitting parameter. b The Hall mobility as a 100 2 function of Hall carrier 575 K 750 K concentration with l as a fitting parameter. The lattice thermal conductivity (c) was computed 0 0 21 21 0. 0 1. 0 2.0x10 0.0 1.0 2.0x10 from the resistivity and the -3 -3 Lorenz number L. The optimum [cm ] [cm ] Hall carrier concentration (d) increases with temperature. 0.7 1.0 (c) (d) The Hall carrier concentration of Cu Ag Se also increases 1.97 0.03 750 K 0.6 750 K with temperature, so it has a 0.8 0.5 Hall carrier concentration close 575 K to the optimum value up to 0.6 575 K 750K 0.4 750 K. The lines in c are Effective Mass Model average values of j at the Cu Ag Se 0.3 1.97 0.03 0.4 indicated temperature Cu Ag Se 1.97 0.03 1.009 0.2 Cu Ag Se 1.98 0.2 575 K Cu Se 0.2 0.1 Cu Se 1.98 0.0 0.0 21 2 4 6 2 4 6 2 4 6 0.0 1.0 2.0x10 19 20 21 22 10 10 10 10 -3 [cm ] -3 [cm ] Cu Ag Se has a greater Hall mobility than does Table 1 Thermoelectric material properties estimated from the 1.97 0.03 1.009 effective mass model Cu Ag Se, despite having a greater carrier 1.97 0.03 concentration and more defects. 575 K 750 K The thermal conductivity is made up of a lattice con- m (m ) 3.1 6.2 tribution j and an electronic contribution j . j is equal L E E 2 -1 -1 l (cm V s ) 5.9 1.9 to LT/q, where L is the Lorenz number, given by Eq. (5). -1 -1 j (W m K ) 0.53 0.54 We estimated the Lorenz number of each sample at each B (–) 0.28 0.48 temperature studied using the previously determined Fermi level g. The Lorenz numbers of the samples were between -8 -8 2 -2 1.5 9 10 and 1.9 9 10 V K at 575 and 750 K, respectively. effective mass is not constant with temperature, our k 3F ðÞ g F ðÞ g  4F ðÞ g 0 2 1 predictions are valid only at fixed temperatures as a L ¼ ð5Þ function of Hall carrier concentration. F ðÞ g The estimated values of l (Table 1) fit to the data j of each composition is shown in Fig. 3c, along with shown in Fig. 3b, decrease with temperature, as expected the average j at each temperature, the values of which are from the raw Hall mobility measurements. The Hall shown in Table 1. j does not change significantly from mobility is given by Eq. (4). l is the mobility of a single 575 to 750 K; therefore, the optimization of zT in this electron in the material. The Fermi integral term accounts materials system will hinge only on the electrical transport for energy level degeneracy and scattering. The effective properties. The slight increase in j with temperature in mass m* and the n data are used to compute g, which is Table 1 is due to uncertainty in the calculated j . Taking then used with the l data to fit l . H 0 the estimates for m*, l , and j , we can calculate a zT 0 L F ðÞ g 1=2 versus Hall carrier concentration curve to determine the l ¼ l ð4Þ H 0 2F ðÞ g 0 maximum zT at a given temperature and the optimum Hall -1 -1 -1 [μV K ] [W m K ] [-] 2 -1 -1 [cm V s ] Page 6 of 7 Mater Renew Sustain Energy (2014) 3:26 Acknowledgments T.W.D. and G.J.S. thank the U.S. Air Force carrier concentration (Fig. 3d). Looking at the zT versus Office of Scientific Research for support. T.W.D. thanks Heng Wang Hall carrier concentration curve for 575 K, it is clear that for help with the dimensionless quality factor. T.Z., X.S., and L.C. Cu Ag Se is under-doped, leading to a decrease in zT 1.98 0.2 thank for financial support the National Basic Research Program of above 650 K due to bipolar conduction. Cu Ag Se has China (973-program) under Project No. 2013CB632501 and National 1.97 0.03 Natural Science of Foundation of China (NSFC) under Project No. the Hall carrier concentration closest to the optimum value 51222209. K.A.B. and B.B.I. thank the Danish National Research at every temperature at which we calculated an effective Foundation (DNRF93). mass, which explains why that composition has the greatest zT of all the compositions included in the analysis. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, dis- According to our model, a maximum zT of 1.0 at 750 K tribution, and reproduction in any medium, provided the original is possible in this material system. The dimensionless author(s) and the source are credited. quality factor B [24–26] (Eq. 6) is a measure of the max- imum zT at a given temperature and depends only on material properties and temperature. References 7=2 3=2 5=2 k lðÞ m T B 0 B ¼ ð6Þ 1. 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Materials for Renewable and Sustainable EnergySpringer Journals

Published: Mar 14, 2014

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