## 3 Results and Discussion
Figure 1: Scanning Electron Microscopy (SEM) images of Hf\({}_{0.35}\)Zr\({}_{0.35}\)7 Ti\({}_{0.3}\)NiSn\({}_{0.99}\)Sb\({}_{0.01}\). (**a**) Contact surface of melt spun ribbon. (**b**) Free surface of melt spun ribbon. (**c**) Fractured surface of SPSed bulk. Sb was doped at the Sn-site of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn to generate electron carriers. Figure 3a shows the temperature dependence of \(\sigma\) for SPSed bulks of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{1-x}\)Sb\({}_{x}\) (\(x\) = 0.01, 0.02, 0.03). The \(\sigma\) values of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{0.99}\)Sb\({}_{0.01}\), Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{0.98}\)Sb\({}_{0.02}\), and Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{0.99}\)Sb\({}_{0.03}\) were about 5002, 5943, and 7521 S cm\({}^{-1}\) at 300 K, respectively, and they decreased with increasing temperature in all samples, suggesting a degenerate semiconducting behavior. As clearly shown in Figure 3a, higher Sb-doping content resulted in higher \(\sigma\), which indicated that Sb is an efficient doping element. Detailed study on the contribution of grain boundary to temperature-dependent \(\sigma\) and mobility will be reported elsewhere after the estimation of energy-dependent carrier relaxation time as well as the measurement of temperature-dependent transport parameters, such as concentration and mobility. On the other hand, measured absolute value of \(S\) (inset of Figure 3b) was in a trade-off relationship with \(\sigma\). Band engineering effect such as band convergence [17; 18; 19] enlarged \(S\) while maintaining \(\sigma\) was not observed in Sb-doped Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn. The \(S\) values for all \(n\)-type semiconductors were  
Figure 3: Temperature dependence of (**a**) electrical conductivity and (**b**) power factor for SPSed bulks of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{1-x}\)Sb\({}_{x}\) (\(x\) = 0, 0.01, 0.02, 0.03). Inset of (b) is the temperature-dependent Seebeck coefficient. Figure 2: X-Ray Diffraction (XRD) patterns for SPSed bulks of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{1-x}\)Sb\({}_{x}\) (\(x\) = 0, 0.01, 0.02, 0.03). Standard ZrNiSn XRD pattern is also shown for comparison. negative and the absolute value almost linearly increased with temperature up to 800 K. Figure 3b shows the temperature dependence of calculated power factor (\(S^{2}\sigma\)). Peak power factor value of -3.82 mW m\({}^{-1}\) K\({}^{-2}\) was obtained at 800 K for Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{0.97}\)Sb\({}_{0.03}\). Figure 4a shows the temperature dependence of \(\kappa\) for SPSed bulks of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{1-x}\)Sb\({}_{x}\) (\(x\) = 0.01, 0.02, 0.03). To elucidate the effect of sub-micron grain structure on thermal conduction, we calculated the \(\kappa_{\rm lat}+\kappa_{\rm bp}\) by subtracting \(\kappa_{\rm ele}\) from \(\kappa\). Temperature-dependent \(\kappa_{\rm ele}\) was estimated by using Wiedemann-Franz law (\(\kappa_{\rm ele}=L\sigma T\), where \(L\) is Lorenz number) as shown in Figure 4b. The \(L\) values (inset of Figure 4b) as a function of temperature for all the samples, which ranged from 1.88 to \(2.15\times 10^{8}\) W \(\Omega\) K\({}^{-2}\), were obtained based on Equation (1) [20]. \[L=1.5+exp\Big{(}-\frac{|S|}{116}\Big{)} \tag{1}\]  
For the whole measured temperature range, \(\kappa_{\rm ele}\) of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{0.97}\)Sb\({}_{0.03}\) is higher than that of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{0.99}\)Sb\({}_{0.01}\) and of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{0.98}\)Sb\({}_{0.02}\) due to its higher \(\sigma\) (Figure 3a). Figure 4c shows the temperature dependence of \(\kappa_{\rm lat}+\kappa_{\rm bp}\) (=\(\kappa-\kappa_{\rm ele}\)) for SPSed bulks of Hf\({}_{0.35}\)Zr\({}_{0.35}\)Ti\({}_{0.3}\)NiSn\({}_{1-x}\)Sb\({}_{x}\) (\(x\) = 0.01, 0.02, 0.03).