High-temperature thermoelectric properties of Cu1.97Ag0.03Se1+y
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Copper selenide is of recent interest as a high-performance p-type thermoelectric material. Adding Ag to copper selenide increases the dimensionless figure-of-merit zT up to 780 K, with Cu1.97Ag0.03Se reaching a zT of 1.0 at 870 K. The increase compared with Cu2Se can be explained by analyzing the Hall carrier concentration and effective mass. Addition of Ag reduces the carrier concentration to a nearly optimum value at high temperature. If the Hall carrier concentration were to be further reduced to 6.6 × 1020 cm−3 at 750 K, the average zT would be substantially improved for waste heat recovery applications.
KeywordsThermoelectrics Copper selenide Carrier concentration optimization Cu1.97Ag0.03Se1+y
Materials that convert heat directly into electricity, called thermoelectrics, have been used to construct reliable generators of electrical power for spacecraft  and, under an applied current, as solid-state cooling devices . Thermoelectric generators and coolers have the advantages of being silent, having no moving parts, and being free from greenhouse and ozone-depleting gases. The maximum efficiency of a thermoelectric material is governed by the figure-of-merit, zT, which is equal to S2Tρ−1κ−1, where S is the Seebeck coefficient, T is the absolute temperature, ρ is the electrical resistivity, and κ is the thermal conductivity. Thermoelectric materials in general must have low electrical resistivity, low thermal conductivity, and a controllable carrier concentration.
A new class of high-performance thermoelectric materials is the superionic coinage-metal chalcogenides. Some examples are Cu2−xSe , AgCrSe2 , Ag2+xSe [5, 6, 7, 8], and Ag2Te . These materials all undergo a structural phase transition above which the metal ions become mobile, which leads to enhanced phonon scattering and consequently low thermal conductivity. This combined with excellent electrical conductivity makes this class of materials promising for use as thermoelectrics.
Cu2-xSe was found to have a zT of 1.5 at 1,000 K . A related compound is Cu1.97Ag0.03Se1+y , which was studied from the late 1960s through the late 1970s as a candidate for use in radioisotope thermal generators (RTGs) . The y = 0 compound (Cu1.97Ag0.03Se), synthesized by 3 M, reached a zT of 1.1 at 870 K , which is comparable to the zT of 1.0 at 870 K achieved in Cu1.97Ag0.03Se in this work. Recently, the “overstoichiometric” composition Cu1.98Ag0.2Se was studied and found to reach a maximum zT of 0.52 at 650 K before the onset of bipolar conduction . While Cu1.97Ag0.03Se1+y was tested under RTG conditions in order to evaluate its performance as an energy converter, no attempt was made to analyze its thermoelectric properties in order to optimize its zT. Furthermore, no such analysis has been done for Cu2−xSe. Therefore, we seek to analyze these materials together to determine the suitability of a single model for describing them and whether they can achieve greater zT values.
The data will be analyzed using an effective mass approach. The premise of this approach is that at a particular temperature, the intricacies of the band structure are reflected by two parameters, the effective mass and the mobility parameter, with the carrier concentration and chemical potential determined from the Hall effect and the Seebeck effect, respectively.
Ingots of Cu2Se, Cu1.98Se, Cu1.97Ag0.03Se, and Cu1.97Ag0.03Se1.009 were formed by melting Cu (shot, 99.9999 % pure, Alfa Aesar, Puratronic), Ag (shot, 99.9999 % pure, Alfa Aesar, Puratronic), and Se (shot, 99.999 % pure, Alfa Aesar, Puratronic) in quartz ampoules evacuated to less than 6 × 10−5 torr. The ampoules were ramped to 1,373 K at 100 K/h, held at that temperature for 12 h, and then quenched. The ingots were ball-milled to form powders, then re-sealed in quartz ampoules, heated at 1,273 K for 5 days, cooled to 973 K, held at that temperature for 3 days and then quenched. The ingots thus obtained were ball-milled again and then hot-pressed at 973 K and 40 MPa for 6 h . The geometric densities of the hot-pressed pellets were greater than 95 % of their theoretical values.
The thermoelectric properties of the samples were measured with custom-built and commercial apparatus. The thermal diffusivity α was measured with a Netzsch LFA 457 laser flash analysis unit. The total thermal conductivity was calculated from κ = αdCp, where d is the geometric density, and Cp is the heat capacity. The Seebeck coefficient S was measured with a custom-built device  and with an ULVAC ZEM-3. The resistivity ρ and Hall resistance were measured with a custom-built system  using van der Pauw geometry and a 2-T magnetic field to determine the Hall carrier concentration nH = 1/eRH and the Hall mobility μH = RH/ρ. Cp was measured on a Netzsch 200F3 differential scanning calorimeter from 317 to 913 K.
Powder X-ray diffraction (PXRD) patterns were collected using a Rigaku SmartLab diffractometer equipped with a Cu Kα source, parallel beam optics, and a Rigaku D/tex detector. A hot-pressed pellet of Cu1.97Ag0.03Se was placed under dynamic vacuum on an Anton-Paar DHS-1100 hot stage with an X-ray transparent graphite dome. PXRD patterns were collected at 300 and 420 K and used for phase identification and refinement of the high-temperature phase using the FullProf suite . Diffractograms were recorded every 20 K from 300 to 500 K in the 2Θ range from 10° to 100°. Between these measurements, the sample was heated at 1 K/min, while fast diffractograms were recorded from 24.5° to 54.5° 2Θ and a scan speed of 12°/min.
Results and discussion
In this study, the compositions Cu2Se, Cu1.98Se, Cu1.97Ag0.03Se, and Cu1.97Ag0.03Se1.009 were synthesized, and data on Cu1.98Ag0.2Se from a recent publication by Ballikaya et al.  are included for a more complete analysis.
Cu2-xSe and Cu1.97Ag0.03Se1+y exhibit the steady increase with temperature of the Seebeck coefficient (Fig. 2b) and of the resistivity ρ (Fig. 2c) expected of a single-carrier semiconductor. Cu1.98Ag0.2Se has greater values of S and ρ than do the other samples in the entire temperature range due to its much lower Hall carrier concentration, and it shows a peak in S at about 725 K.
The Hall mobilities, μH, of Cu2−xSe, Cu1.97Ag0.03Se1+y, and Cu1.98Ag0.2Se above the phase transition are low compared with those of other high-performance p-type thermoelectric materials, such as 40–6 cm2 V−1 s−1 in Na-doped PbTe between 600 and 750 K, depending on carrier concentration . The Hall mobility scales with T−p . The average value of p taken from the data shown in Fig. 2d and above the phase transition is about 3.1. Values of p between 1 and 1.5 usually indicate that acoustic phonons limit electron mobility in the material , while values greater than 1.5 indicate a temperature-dependent effective mass .
The thermal conductivity data are shown in Fig. 2e. The sudden increase in κ around the phase transition temperature is due to the sharp peak in Cp . Cu1.98Ag0.2Se has the lowest thermal conductivity values because it has the lowest lattice thermal conductivity, presumably due to disorder caused by the greater amount of Ag, and because it has the lowest carrier concentration of the compositions studied and therefore the lowest electronic thermal conductivity.
The zT data are shown in Fig. 2f. The zT values of Cu2−xSe and Cu1.97Ag0.03Se1+y all increase continuously from the phase transition temperature to the maximum temperature at which they were measured. The Cu1.97Ag0.03Se sample reaches a zT of 1.0 at 870 K. Cu2Se reaches a zT of 1.16 at 870 K, but between 450 and 780 K has an average zT of 0.59, whereas Cu1.97Ag0.03Se has an average zT of 0.66 in the same temperature range. Above 780 K, the increasing values of ρ in Cu1.97Ag0.03Se and the decreasing values of κ in Cu2Se mean that Cu2Se has a greater zT. Cu1.98Ag0.2Se reaches a peak zT of 0.52 at 650 K and then decreases due to bipolar conduction.
Thermoelectric material properties estimated from the effective mass model
μ0 (cm2 V−1 s−1)
κL (W m−1 K−1)
At a fixed temperature, we compute η from S for each sample and then use m* to compute a theoretical nH that we fit to the nH data. The effective mass increases with temperature (Table 1), which we predicted based on the Hall mobility data. The same trends of effective mass, Hall carrier concentration, resistivity, and Seebeck coefficient with temperature were observed by Voskanyan et al. , though they estimated different values of the effective mass, e.g., 2.2 me at 750 K as opposed to 6.2 me at 750 K because they used assumed values of nH instead of calculating them from RH. Voskanyan et al. proposed a second valence band as a possible cause of the increasing effective mass. While this may explain of the trend of m* with T, a two-band model is much more complex than a single-band model, requires more assumptions, and does not guarantee a unique solution. Here, we use a single band in this analysis in order to estimate the maximum achievable zT and optimum Hall carrier concentration in this material. We must emphasize that because the effective mass is not constant with temperature, our predictions are valid only at fixed temperatures as a function of Hall carrier concentration.
Cu1.97Ag0.03Se1.009 has a greater Hall mobility than does Cu1.97Ag0.03Se, despite having a greater carrier concentration and more defects.
κL of each composition is shown in Fig. 3c, along with the average κL at each temperature, the values of which are shown in Table 1. κL does not change significantly from 575 to 750 K; therefore, the optimization of zT in this materials system will hinge only on the electrical transport properties. The slight increase in κL with temperature in Table 1 is due to uncertainty in the calculated κE. Taking the estimates for m*, μ0, and κL, we can calculate a zT versus Hall carrier concentration curve to determine the maximum zT at a given temperature and the optimum Hall carrier concentration (Fig. 3d). Looking at the zT versus Hall carrier concentration curve for 575 K, it is clear that Cu1.98Ag0.2Se is under-doped, leading to a decrease in zT above 650 K due to bipolar conduction. Cu1.97Ag0.03Se has the Hall carrier concentration closest to the optimum value at every temperature at which we calculated an effective mass, which explains why that composition has the greatest zT of all the compositions included in the analysis.
The quality factors calculated for this material system increase with temperature (Table 1), meaning the theoretical maximum zT also increases with temperature. According to Fig. 3d, the optimum Hall carrier concentration nH,opt increases with temperature as well, which combined with the increasing trend with temperature of nH in Cu1.97Ag0.03Se means that that composition has a Hall carrier concentration close to nH,opt at and below 750 K.
Our transport property measurements show that below 780 K Cu1.97Ag0.03Se1+y has superior zT values compared with Cu2−xSe because it has a Hall carrier concentration closer to the optimum value. We have analyzed the Hall carrier concentration and effective mass in these materials and in recently published data on Cu1.98Ag0.2Se for a more complete analysis, and found that these materials together follow the trends expected despite the complexity of the atomic structure and presumed complexity of the electronic structure. This model predicts that a maximum zT of 1.0 at 750 K is possible in this material system.
Each zT versus Hall carrier concentration curve in Fig. 3 indicates that zT of Cu2Se can be increased simply by reducing the Hall carrier concentration. This means that if Cu2Se is to be a commercially viable thermoelectric material, the addition of expensive Ag may be unnecessary. Any means of removing charge carriers from the material could improve its thermoelectric properties above the phase transition. Such means could include anion substitution [27, 28] or doping with divalent cations . Furthermore, our analysis is based only on electronic parameters, so separate optimization of the lattice thermal conductivity may improve the zT of this material even further.
T.W.D. and G.J.S. thank the U.S. Air Force Office of Scientific Research for support. T.W.D. thanks Heng Wang for help with the dimensionless quality factor. T.Z., X.S., and L.C. thank for financial support the National Basic Research Program of China (973-program) under Project No. 2013CB632501 and National Natural Science of Foundation of China (NSFC) under Project No. 51222209. K.A.B. and B.B.I. thank the Danish National Research Foundation (DNRF93).
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