## 3 Results  
By the variation of technological regulations (temperature, multiplicity, and duration of firing), optimal conditions for the phase formation of SS (1 \(-\)\(x\))BaNb\({}_{2}\)O\({}_{6}\)-\(x\)SrNb\({}_{2}\)O\({}_{6}\) are established, ensuring a practical absence (<5%) of ballast media during synthesis. The choice of optimal sintering temperatures (T\({}_{\rm sint. }\)) for a series of samples burned at (1570 \(\div\) 1670) K showed that ceramics obtained at the T\({}_{\rm sint. }\) = 1650K (Figure 1) [9] have the highest density, which was confirmed by measurements of the \(\varepsilon/\varepsilon_{0}\) dependences on T in the heat-cool regime (\(f\) = 500 kHz): the largest peaks \(\varepsilon/\varepsilon_{0}\), the smallest temperature hysteresis at temperatures below the Curie temperature (T\({}_{\rm c}\)), and its absence above T\({}_{\rm c}\) is characteristic precisely for ceramics prepared at this T\({}_{\rm sint. }\) (Figure 2a). Figure 2b shows the dielectric spectra of the studied SS, which also demonstrate the best quality of the samples at this temperature. Figure 3 shows the phase diagram of the system in which: in the interval 0.0 \(\leq x\) < 0.2 there are SS with R structure of BaNb\({}_{2}\)O\({}_{6}\)-R phase; at 0.05 \(\leq x\leq\) 0.15, the R phase and the SS with the tetragonal--tungsten bronze (TTB) structure are coexist, marked by us as the T phase and formed in the interval 0.1 \(\leq x\leq\) 0.8; at 0.7 \(\leq x\leq\) 0.8 the T phase and the SS with a monoclinic structure  
SrNb\({}_{2}\)O\({}_{6}\)-M phase are coexist; at 0.8 \(<x\leq\) 1.0 there is an M phase. Table 1 shows the symmetry and cell parameters of SS Ba\({}_{1-x}\)Sr\({}_{x}\)Nb\({}_{3}\)O\({}_{6}\)[10]. It can be seen that near the SS on the basis of BaNb\({}_{2}\)O\({}_{6}\) and SrNb\({}_{2}\)O\({}_{6}\), the parameters and the cell volume practically do not change. In the interval 0.0 \(<x\leq\) 0.1, the parameters \(a\), \(b\), and V of the R cell increase, despite the replacement of Ba\({}^{+2}\) (\(R\) = 1.38 A) with a smaller Sr\({}^{+2}\) size (\(R\) = 1.20 A). This means that the latter is built in position A1 in quadrangular channels, where there is no barium. T phase is divided into two equal concentration areas: at 0.1 \(\leq x\leq\) 0.4 the change in structural parameters has a non-monotonic character, and at 0.4 \(\leq x\leq\) 0.7 the parameters decrease monotonically. In the first region, in accordance with the dependence V(\(x\)), at \(x\) = 0.1 \(\div\) 0.2, the filling of the positions A1 is decisive, at \(x\) = 0.2 \(\div\) 0.3--the substitution of Sr\({}^{+2}\)\(\rightarrow\) Ba\({}^{+2}\) at positions A2 in pentagonal channels, and for \(x\) = 0.3 \(\div\) 0.4--re-filling positions A1. In the second region, where the cell volume decreases monotonically, it is obvious that only Sr\({}^{+2}\)\(\rightarrow\) Ba\({}^{+2}\) substitution occurs at positions A2 in pentagonal channels, which agrees with the results of the study of single crystals [11]. In this work, crystals in the interval \(0.32\leq x\leq 0.82\) were investigated and showed that in the interval \(x\approx 0.35\div 0.45\) the A1 positions are filled with strontium, respectively, from 66% to 72% and the substitution of Sr\({}^{+2}\)\(\rightarrow\) Ba\({}^{+2}\) at positions A2. At \(x>0.45\), the amount of Sr in quadrangular channels does not change, and only the replacement of ions in pentagonal channels takes place. It is interesting to note that, according to Reference [11], in the congruently melting SS, the amount of Sr and Ba in the pentagonal channels is almost identical. Thus, in BSN ceramics, as in single crystals [11], as the concentration of Sr increases, the formation of the TTB structure proceeds in two stages: positions A1 and A2 (SS1) are filled in the interval \(x=0.1\div 0.4\), but within this interval the one or the other process prevails. At \(x>0.4\), the filling of positions A1 stops and only the replacement of Sr \({}^{+2}\)\(\rightarrow\) Ba\({}^{+2}\) takes place in positions A2 (SS2).