## 4 Conclusions  
Two series of Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) samples (\(x\) = 0; 0.1; 0.17; 0.19; 0.3; 0.4) were synthesized utilizing slow cooling and quenching. All obtained materials reveal \(p\)-type conductivity with a metal-like temperature dependence of the electrical conductivity up to 500 K. Their TE properties strongly depend on the concentration of secondary phases and features of the microstructure. A higher cooling rate suppressed crystallization of secondary phases and enabled to obtain single-phase material only with \(x\) = 0.19. Due to the decrease in solidification time, the quenching procedure disrupts the formation of microstructures improving TE properties. Therefore, we regard Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys as: (i) the multi-phase materials and (ii) the materials with TE properties resulting from the combination of intrinsic properties of the \(\beta\) phase (e.g., \(x\) = 0.19) and minority phases. High level of disorder in nanoscale in the \(\beta\) phase was observed in TEM, including mosaic patterns and disorientation of grains. It plays an important role in the reduction of lattice thermal conductivity. Slowly cooled alloys with \(x\) = 0.1 and \(x\) = 0.17 exhibit the highest TE performance, showing \(ZT\) values of 1.2 and 1.1 at 610 K, respectively. It is clear that high \(ZT\) values in Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys can also be obtained without extrinsic doping as reported previously [2; 3; 4; 5; 6]. All samples reveal lack of long-term stability, which causes degradation of the \(\beta\) phase and the TE performance, in agreement with the phase diagram of the Ag-Sb-Te system. However, TE properties are reproducible up to 490 K due to kinetic hindering of the eutectoid decomposition of the \(\beta\) phase. Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) alloys show more favorable TE properties than alloys with a nominal composition Ag\({}_{1.0}\)Sb\({}_{1.0}\)Te\({}_{2.0}\). To utilize them, the suppression of the eutectoid decomposition is needed, probably by chemical substitution.  
The following are available online at [[http://www.mdpi.com/2076-3417/8/1/52/s1](http://www.mdpi.com/2076-3417/8/1/52/s1)]([http://www.mdpi.com/2076-3417/8/1/52/s1](http://www.mdpi.com/2076-3417/8/1/52/s1)), Figure S1: (a) TG-DTA analysis of slowly cooled Ag\({}_{1.0}\)Sb\({}_{1.0}\)Te\({}_{2.0}\) and (b) DTA analysis of slowly-cooled Ag\({}_{0.81}\)Sb\({}_{1.19}\)Te\({}_{2.19}\) samples; Table S1: Thermal effects observed in DTA curves with corresponding reactions; Figure S2: Optical micrographs of Ag\({}_{0.6}\)Sb\({}_{1.4}\)Te\({}_{2.4}\) and Ag\({}_{0.81}\)Sb\({}_{1.19}\)Te\({}_{2.19}\) samples; Figures S3 and S4: Backscattered-electron (BSE) images of the Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) samples; Figure S5: Real element concentration of: (a) Ag, (b) Sb, (c) Te as a function of nominal concentration in the Ag\({}_{1-x}\)Sb\({}_{1+x}\)Te\({}_{2+x}\) samples; Figure S6: HRTEM image of particle I of Ag\({}_{1.9}\)Sb\({}_{2.9}\)Te\({}_{2.5}\) sample (\(x\) = 0.19).  
The authors thank members of competence group Structure (MPI CPFS) for PXRD analysis, [PERSON] (MPI CPFS) for TG-DSC measurements, [PERSON] (MPI CPFS) for chemical analysis and [PERSON] for low-temperature thermoelectric measurements. This work was partially supported by the funds of National Science Center Poland granted on the basis of the decision No. DEC-2013/09/B/ST8/02043.  
[PERSON] and [PERSON] initiated the idea of the research. [PERSON] and [PERSON] performed synthesis, measurements of transport properties and evaluation of data. [PERSON] analyzed the microstructure. [PERSON] performed the TEM studies. [PERSON] prepared manuscript.  
The authors declare no conflict of interest.