## 3 Results & Discussion
### Nanostructure of the \(\beta\) Phase (Ag\({}_{0.81}\)Sb\({}_{1.19}\)Te\({}_{2.19}\))  
Nanostructure usually affects electronic transport properties of TE materials [34]. In the case of Ag-Sb-Te-based alloys, the presence of point and linear defects, together with different nanodomains, are believed to effectively suppress thermal conductivity to theoretically minimal values [9; 15; 25]. In this study, we performed a thorough analysis of a quenched Ag\({}_{0.81}\)Sb\({}_{1.19}\)Te\({}_{2.19}\) alloy (\(x\) = 0.19), by means of transmission electron microscopy (TEM) and selected area electron diffraction (SAED). As mentioned in the previous paragraph, the influence of a possible impurity phase on the nanostructure of this sample is minimal if any. We present, in detail, two representative particles: particle I (Figure 11a-d and Figure S6) and particle II (Figure 12a-d) with \(\sim\)0.5 um and \(\sim\)2 um size, respectively. SAED pattern ([110] zone axis) for the whole particle I consists of sharp reflections that belong to the NaCl structure type only (inset in Figure 11a). Interplanar distances for (2\(\overline{2}\)0) and (002) planes are in good agreement with values refined from PXRD data for Ag\({}_{0.81}\)Sb\({}_{1.19}\)Te\({}_{2.19}\) (2.15 A and 3.04 A respectively). Under higher magnification (\(\sim\)40 \(\times\) 40 nm field of view), well-ordered structure is visible with sharp reflections in the fast Fourier transform (FFT) pattern and correct interplanar distances (Figure S6). The well-ordered atomic arrangement within (110) plane is presented in detail in the high-resolution (HRTEM) image (Figure 11b) and is compared to the NaCl type structure model. The lattice parameter is in agreement (within the experimental error) with PXRD data. Interestingly, the chemical composition of particle I is Ag\({}_{23(1)}\)Sb\({}_{28(1)}\)Te\({}_{49(1)}\), according to EDXS analysis, and reveals a small excess of Ag, compared to the nominal composition Ag\({}_{19}\)Sb\({}_{29}\)Te\({}_{25}\). The FFT pattern from some regions of particle I contains additional reflections indicating doubling of the unit cell along [111] direction (Inset in Figure 11c). The doubling effect is clearly visible in Bragg-filtered IFFT image composed only from additional reflections along [111] direction (Figure 11d). Irregular nanodomains with well-ordered atomic arrangement (marked with dashed lines in Figure 11d) are surrounded by distorted regions. It is similar to the previously predicted and observed segregation of Ag/Sb atoms to alternating (111) planes [9; 18]. However, such forbidden reflections can also be visible due to multiple scattering processes during TEM observations. Figure 11: TEM analysis for particle I of quenched Ag\({}_{19}\)Sb\({}_{29}\)Te\({}_{2}\) sample (\(x\) = 0.19): (**a**) Particle I together with chemical composition according to EDXS analysis. Inset: an SAED pattern from the whole particle I. Doubling of each reflection is the result of rotated second crystal below; **(b)** HRTEM image of a selected area within particle I (yellow dotted circle in Figure 11a) compared with unit cell cross section along [110] plane and lattice parameter refined from PXRD (inset); (**c**) FFT filtered HR image of another region of particle I. The FFT pattern contains additional reflections, with an interplanar distance of 7 Å, which indicate doubling of the unit cell along [111] direction (inset); (**d**) Bragg-filtered IFFT image composed only from additional reflections along [111] direction. Stripe pattern corresponds to crystallographic planes normal to [111] direction with period equals 7 Å. Particle II shows a gradual increase in the level of atomic disorder. Sharp reflections of NaCl type structure are becoming diffuse, while increasing magnification from the entire particle II to smaller regions (Figure 12a-c). Two scenarios were observed: (i) intermediate state with co-existence of large well-ordered and disordered regions (Figure 12b).