## 3 Results & Discussion
### Thermoelectric Properties
However, the \(\lambda_{\mathrm{e}}\) calculated from the Wiedemann-Franz law seems to be overestimated for these samples, resulting in very low lattice contribution (Figure 7b). The other alloys exhibit twice lower \(\lambda(T)\) values, in the range of 0.4-0.7 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\), similar to literature reports [7; 26]. Lattice part is the main contribution to total thermal conductivity, independent of synthesis procedure (Figure 7b). Due to the included ambipolar part, values are slightly overestimated. Differences in thermal conductivity between samples after slow cooling and quenching, 5-10%, are on the level of measurement precision. One can notice extrema in the temperature dependence of Seebeck coefficient (maxima), electrical and thermal conductivity (minima), around 500 K that suggest an increase of the concentration of minority carriers--electrons, and an increase of their contribution to the electrical conductivity above 500 K. Such ambipolar conduction is observed in narrow-band-gap semiconductors [34]. Changes in the slope of \(\alpha(T)\) and \(\sigma(T)\) dependences at 420 K in Ag-rich alloys (\(x\) = 0, 0.1) are caused by polymorphic transition of Ag\({}_{2}\)Te impurities [12; 35]. The quality of synthesized materials was evaluated on the basis of the dimensionless thermoelectric figure of merit \(ZT\) (Figure 8). \(ZT\) grows monotonously with the temperature. Slowly cooled materials exhibit better TE performance compared to quenched samples. Slow cooling rate leads to crystallization of highly non-equilibrated alloys with a large number of defects and impurity phases, which effectively reduces lattice thermal conductivity. Samples \(x\) = 0.1 and \(x\) = 0.17 showed the highest values of \(ZT_{\mathrm{max}}\), 1.2 and 1.1 at 610 K, respectively. Figure 7: Temperature dependence of (**a**) total thermal conductivity and (**b**) its lattice contribution for slowly cooled Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) samples (filled symbols); for comparison, data of three quenched samples are presented with open symbols (\(x\) = 0.4—circles, \(x\) = 0.19—squares, \(x\) = 0.17—triangles). Intrinsic Properties of the \(\beta\) Phase (Ag\({}_{0.81}\)Sb\({}_{2.19}\)Te\({}_{2.19}\))  
As it was shown in previous paragraphs, the majority of Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys are multi-phase. Thus, measured physical properties reflect the intrinsic properties of the \(\beta\) phase, defect arrangement and the impurity phases. That is why it is not reasonable to present the dependence of TE properties versus lattice parameter or chemical composition. Intrinsic properties of the \(\beta\) phase were described for the quenched alloy with \(x=0.19\) only. No secondary phases were detected in this sample, within the precision of PXRD (Figure 9a) or SEM analysis (Figure 9b). Figure 8: Temperature dependence of the figure of merit \(ZT\) for slowly cooled Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) samples (filled symbols); for comparison, data of three quenched samples are presented with open symbols (\(x=0.4\)—circles, \(x=0.19\)—squares, \(x=0.17\)—triangles). Electrical conductivity, Seebeck coefficient and total thermal conductivity in the temperature range of 300-610 K equal 5.5 \(\times\) 10\({}^{3}\)\(-\) 8 \(\times\) 10\({}^{3}\) S-m, 220-280 \(\mu\)V\(\cdot\)K\({}^{-1}\) and 0.55-0.65 W\(\cdot\)m\({}^{-1}\)\(\cdot\)K\({}^{-1}\), respectively (Figure 10a,b). The dependences \(\sigma(T)\). \(\alpha(T)\) and \(\lambda(T)\) show extrema, suggesting ambipolar conduction to be an intrinsic property of the \(\beta\) phase. Charge carrier concentration is increasing from 3 \(\times\) 10\({}^{19}\) to 1 \(\times\) 10\({}^{20}\) at low temperatures (3-350 K, Figure 6b). Lattice contribution (together with ambipolar part) to thermal conductivity is higher than 90% of total \(\lambda\), showing that phonon propagation processes limit the conduction of heat in the \(\beta\) phase (Figure 10b). The highest \(ZT_{\rm max}\) value equals 0.4 at 550 K (Figure 8).