# Na-Doping Effects on Thermoelectric Properties of Cu\({}_{2-x}\)Se Nanoplates
## 3 Results and Discussion  
The XRD patterns of the as-synthesized samples of undoped Cu\({}_{2-x}\)Se nanowire and nanoplate and Na-doped Cu\({}_{2-x}\)Se nanoplate are shown in Figure 1. All of the reflection peaks can be indexed to the face-centered-cubic Cu\({}_{1.8}\)Se (JCPDS 71-0044), and no impurities were detected within the detection limit of the X-ray. The peaks for Cu\({}_{2-x}\)Se nanowire sample are quite broad mainly due to the finite size of our products. The lattice constants can be refined as \(a=5.674\) (1), 5.737 (1) and 5.738 (1) A for nanowire, nanoplate and Na-doped nanoplate Cu\({}_{2-x}\)Se samples, respectively, which match the literature value listed on JCPDS Card No. 71-0044 well. It can be concluded that the lattice constant of the as-synthesized nanopowders is unchanged upon Na doping. This implies that Cu\({}^{+}\) (0.077 nm) ions are not substituted by much larger Na\({}^{+}\) (0.133 nm) ions in this experimental condition. A similar result was observed when Na was doped in a system of Cu\({}_{3}\)S [29]. On the other hand, Na-doped Cu\({}_{2-x}\)Se shows a peak shift in comparison with the pattern of as-synthesized Na-doped Cu\({}_{2-x}\)Se nanoplates after the SPS process (refer to the inset 002 peaks). The lattice constants for Na-doped nanoplate Cu\({}_{2-x}\)Se samples after SPS is 5.766 (9) A. This small lattice expansion (\(\sim\)5%) may be the result of Na incorporation into the structure of Cu\({}_{2-x}\)Se by electrochemical reactions at the interfaces during the SPS process. Rather than the shift peak position, the SPS process did not significantly modify the crystal structure of nanoplate and Na-doped nanoplate sample. However, the structural changes occur for nanowire samples from cubic to orthorhombic Cu\({}_{2-x}\)Se after SPS treatment, although they were sintered under the same conditions (i.e., 450 \({}^{\circ}\)C, 50 MPa, and 5 min) by the SPS technique. Figure 1: Powder X-ray diffraction (XRD) patterns of as-synthesized samples of nanowire, nanoplate and Na-doped nanoplate Cu\({}_{2-x}\)Se compared with those of the standard cards (JCPDS 71-0044). The inset shows the comparison of peak position for as-synthesized (dashed line) and after SPSed (solid line) samples of Na-doped Cu\({}_{2-x}\)Se nanoplate. (SPS: spark plasma sintering)  
According to the Hall coefficient measurements, the carrier concentrations of nanoplate and Na-doped nanoplate are estimated to be \(5.71\times 10^{22}/\mathrm{cm^{3}}\) and \(2.80\times 10^{22}/\mathrm{cm^{3}}\), respectively. Na doping reduce the carrier concentration of Cu\({}_{2-x}\)Se. This means that Na acts as an electron donor to the nanoplate. The generated electrons by Na recombine with holes, resulting in a decrease of the hole concentration by the electron-hole pairs [30]. This is consistent with the observed decreased electrical conductivity in Na-doped Cu\({}_{2-x}\)Se nanoplates shown in the next section. As expected, Na-doped nanoplate showed a lower carrier mobility than an undoped nanoplate due to the higher carrier concentration. The carrier mobility of nanoplate and Na-doped nanoplate were estimated to be 0.96 and 1.32 cm\({}^{2}\)/Vs, respectively. In our synthetic process, Cu\({}_{2-x}\)Se with different shapes were achieved under different conditions (see Experimental Section for details). Figure 2 shows the morphologies of the as-obtained Cu\({}_{2-x}\)Se observed by SEM. It was found that the morphology of products depends on the concentration of reactants and the reducing reagent. It is not very clearly known at present why reaction concentration can change the morphologies significantly. One possible reason may be that the concentration affects the growth rate of crystals [31]. Figure 2a,b display the SEM images of the Cu\({}_{2-x}\)Se nanoplate with a hexagonal morphology. In general, the lateral dimensions of the nanoplates are 1-3 \(\upmu\)m. The thickness of the nanoplate was about \(\sim\)50 nm, shown in a vertical SEM image of a single Cu\({}_{2-x}\)Se nanoplate (Figure 2b).