###### Abstract  
Introduction of nonstoichiometry to AgSbTe\({}_{2}\)-based materials is considered to be an effective way to tune thermoelectric properties similarly to extrinsic doping. To prove this postulate, a systematic physicochemical study of the Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys (\(0\leq x\leq 0.4\)) was performed. In order to investigate the influence of the cooling rate after synthesis on phase composition and thermoelectric performance, slowly cooled and quenched Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys (\(x=0\); 0.1; 0.17; 0.19; 0.3; 0.4) were prepared. Single-phase material composed of the \(\beta\) phase (NaCl structure type) was obtained for the quenched \(x=0.19\) sample only. The other alloys must be regarded as multi-phase materials. The cooling rate affects the formation of the phases in the Ag-Sb-Te system and influences mainly electronic properties, carrier mobility and carrier concentration. The extremely low lattice thermal conductivity is an effect of the mosaic nanostructure. The maximal value of the figure of merit \(ZT_{\rm max}=1.2\) is observed at 610 K for the slowly cooled multi-phase sample Ag\({}_{0.9}\)Sb\({}_{1.1}\)Te\({}_{2.1}\). Thermoelectric properties are repeatedly reproducible up to 490 K.  
thermoelectric properties; Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\); thermodynamic stability; nanostructure 2018 8 52 2017 2018 201  
The composition of each alloy within the diagram is described by the chemical formula Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) (\(-1\leq x\leq 1\)). A phase with the nominal composition of AgSbTe\({}_{2}\) does not exist. To emphasize the fact that the AgSbTe\({}_{2}\) formula relates only to a nominal composition, Ag\({}_{1.0}\)Sb\({}_{1.0}\)Te\({}_{2.0}\) notation was used in the whole text below. In fact, the only thermodynamically stable ternary phase in this system is the \(\beta\) phase (Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\), \(0.08<x<0.41\)[10]), which crystallizes in the NaCl structure type. However, earlier reports differ about the temperature and compositional region of the \(\beta\) phase [10; 19]. Further investigations of the Ag-Sb-Te ternary system confirmed that the \(\beta\) phase is only stable in a limited temperature range (633 K \(<T<847\) K) and it decomposes into \(\alpha\) (solid solution of Ag in Sb\({}_{2}\)Te\({}_{3}\)) and \(\varepsilon\) (solid solution of Sb in \(\beta\)-Ag\({}_{2}\)Te) phases below 633 K [11; 12; 20]. The decomposition process was additionally confirmed by temperature-dependent X-ray diffraction analysis [21] and electrochemical measurements [22]. The influence of thermal treatment on TE properties of the Ag\({}_{1.0}\)Sb\({}_{1.0}\)Te\({}_{2.0}\) alloy is easily recognizable. In a previous work, we have noticed significant changes in Seebeck coefficient and electrical conductivity during measurements that were attributed to chemical and microstructural changes of the investigated materials [12]. In the earliest report of electrical properties of Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys [23], samples with a gradual change of phase and chemical composition were obtained. It was shown that alloys with \(0<x<0.2\) possess the most prominent power factor \(PF=5\times 10^{-4}\) W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-2}\) at room temperature (\(RT\)). Single-phase alloy with the nominal composition Ag\({}_{0.875}\)Sb\({}_{1.125}\)Te\({}_{2}\) (not included in the pseudobinary Sb\({}_{2}\)Te\({}_{3}\)-Ag\({}_{2}\)Te system) was characterized by \(PF=2\times 10^{-5}\) W\(\cdot\)m\({}^{-2}\cdot\)K\({}^{-2}\) at \(RT\)[24]. High TE performance of Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys (\(ZT=1.2\)-\(1.4\) at 600 K) with \(x>\)0.25 was reported in [25; 26]. There is also a strong conviction in the literature that a small change in Ag/Sb ratio effectively enhances electrical properties, due to the formation of vacancies at the Ag/Sb site, without altering thermal conductivity [25; 27; 28].