## 3 Results & Discussion
### Thermoelectric Properties  
The electrical properties were measured in several heating-cooling cycles from \(RT\) to 610 K. During subsequent measurement cycles, the decomposition process occurs and both phase composition and microstructure differ from the starting ones. This effect is discussed later. Here, we present results of the first heating cycle only. Each sample show metallic \(\sigma(T)\) dependence up to 500 K (Figure 5a). The highest values of electrical conductivity were observed for Sb-rich alloys with a notable concentration of Sb-Te impurities (\(x\) = 0.3, 0.4), independent of the cooling rate. The conductivity is higher than \(10^{5}\) S\(\cdot\)m\({}^{-1}\) at \(RT\) and resembles values typical for the Sb\({}_{2}\)Te\({}_{3}\) phase (\(1.5-2\times 10^{5}\) S\(\cdot\)m\({}^{-1}\) in the range of 300-610 K, [33]). This phase seems to contribute most to the conduction of electrical current in those samples. Samples with lower Sb content (\(x\) = 0-0.19) display similar \(\sigma(T)\) values, between \(0.5\times 10^{4}-1.3\times 10^{4}\) S\(\cdot\)m\({}^{-1}\) after slow cooling and 0.4 \(\times\) 10\({}^{4}\) - 0.9 \(\times\) 10\({}^{4}\) S\(\cdot\)m\({}^{-1}\) after quenching. The observed decrease of electrical conductivity after quenching (for \(x\) = 0-0.4) can be a consequence of pronounced carrier scattering, related to notable changes in the microstructure (Figure 4) and impurity concentration. It is also consistent with the decrease of charge carrier mobility (Figure 6a). It seems that mostly mobility influences \(\sigma\) values at \(T\) < 350 K. For \(x\) = 0.17, carrier concentrations of slowly cooled and quenched samples coincide with each other. It is worth highlighting the increase of carrier concentration with \(x\) (Figure 6b). Following the assumption that vacancies at 4\(a\) site are present in Ag-Sb-Te alloys and have an influence on hole concentration [25; 27; 28], the observed change in carrier concentration is expected. Low and high temperature data of \(\sigma\) perfectly coincide with each other, which proves the good homogeneity of the samples (inset in Figure 6a). At \(T\) < 200 K, \(\sigma\) is significantly increasing for \(x\) = 0.17, simultaneously with \(\mu\), and reaching the peak below 100 K (Figure 6a). The temperature dependence of the Seebeck coefficient reflects that of electrical conductivity, and all alloys show \(p\)-type conductivity (Figure 5b). The lowest values were observed in alloys with \(x\) = 0.4 and 0.3 due to the precipitation Sb-Te phases. The other samples show higher Seebeck coefficients in the range of 200-375 \(\upmu\)V\(\cdot\)K\({}^{-1}\). Thermal conductivity as a function of temperature is presented in Figure 7a. The electronic contribution to thermal conductivity \(\lambda_{\rm e}\) was calculated from the Wiedemann-Franz law \(\lambda_{\rm e}=L\cdot\sigma\cdot T\) (where \(L=2.44\times 10^{-8}\) W\(\cdot\Omega\cdot\)K\({}^{-2}\) is the Lorenz number). The lattice part, containing also ambipolar contribution, was then determined by subtracting the electronic part from the total thermal conductivity. Figure 5: Temperature dependence of (**a**) electrical conductivity and (**b**) Seebeck coefficient of 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). Figure 6: Temperature dependence of (**a**) charge carrier mobility and (**b**) charge carrier concentration for \(x=0.17\) (triangles), \(0.19\) (squares); inset in (**a**) presents temperature dependence of electrical conductivity in the range of 2–610 K; filled symbols—slowly cooled samples, open symbols—quenched samples. The highest values of thermal conductivity, 0.9-1.3 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\), were observed for materials with a notable concentration of Sb-Te impurities (\(x\) = 0.4 and 0.3), mainly due to their significant electronic contribution to heat conduction.