## 3 Results  
In the course of our work, we synthesized samples in the BaF\({}_{2}\)-GdF\({}_{3}\) system doped with Yb, Ho, and Er. The nominal composition and composition determined according to the EDX data of the samples obtained, as well as the practical yield of the synthesis reaction are shown in Table 1. EDX results show that the crystal lattice of synthesized samples contains sodium in an amount of up to 8 mol. %, regardless of the content of the rare earth element. Apparently, this value corresponds to solubility limit of sodium in this solid solution. The content of rare earth elements was overestimated compared to the initial charge, and the content of barium was underestimated. Figure 1 shows the X-ray diffraction patterns of prepared samples. According to X-ray diffraction patterns, Samples 1-5 are single phase, and have a structure derived from the fluorite structure in which BaF\({}_{2}\) crystallizes. The X-ray pattern of Sample 1 is characterized by a fine splitting of the main X-ray diffraction reflexes and is indicated in the tetragonal crystallographic system in a space symmetry group (SSG) \(I\)4. X-ray pattern of Samples 2-5 also indexed in SSG \(I\)4. It is worth noting that X-ray diffraction patterns of Samples 2-5 contain superstructural peaks, which are well described when the crystal lattice parameter \"\(c\)\" is increased three times. The Supplementary Materials, Tables S2-S6, show the results of indexing of X-ray patterns. For all samples, the estimated values of the coherent scattering regions D were more than 100 nm. The lattice parameters of Samples 1-5 and the calculated X-ray density (D\({}_{\text{x}}\)) values are given in Table 2.  
SEM micrographs were obtained for all samples (Figure 2). \begin{table}
\begin{tabular}{c c c c} \hline
**Samples** & **Nominal Composition** & **Composition according to EDX Data 1,2** & **Reaction Yield, \%** \\ \hline
1 & Ba\({}_{0.69}\)Gd\({}_{0.33}\)F\({}_{2.33}\) & Ba\({}_{0.51(1)}\)Gd\({}_{0.45(1)}\)Na\({}_{0.04(2)}\)F\({}_{2.41}\) & 60.1 \\ \hline
2 & Ba\({}_{0.600}\)Gd\({}_{0.304}\)Yb\({}_{0.080}\)Ho\({}_{0.012}\)Er\({}_{0.004}\)F\({}_{2.4}\) & Ba\({}_{0.44(1)}\)Gd\({}_{0.40(1)}\)(Yb, Ho, Er)\({}_{0.11(1)}\)Na\({}_{0.05(2)}\)F\({}_{2.46}\) & 70.5 \\ \hline
3 & Ba\({}_{0.600}\)Gd\({}_{0.300}\)Yb\({}_{0.080}\)Ho\({}_{0.012}\)Er\({}_{0.008}\)F\({}_{2.4}\) & Ba\({}_{0.43(1)}\)Gd\({}_{0.38(1)}\)(Yb, Ho, Er)\({}_{0.11(1)}\)Na\({}_{0.08(2)}\)F\({}_{2.41}\) & 67.7 \\ \hline
4 & Ba\({}_{0.600}\)Gd\({}_{0.306}\)Yb\({}_{0.080}\)Ho\({}_{0.010}\)Er\({}_{0.004}\)F\({}_{2.4}\) & Ba\({}_{0.42(1)}\)Gd\({}_{0.37(2)}\)(Yb, Ho, Er)\({}_{0.13(2)}\)Na\({}_{0.08(1)}\)F\({}_{2.42}\) & 70.3 \\ \hline
5 & Ba\({}_{0.600}\)Gd\({}_{0.304}\)Yb\({}_{0.080}\)Ho\({}_{0.008}\)Er\({}_{0.008}\)Er\({}_{2.4}\) & Ba\({}_{0.40(1)}\)Gd\({}_{0.30(4)}\)(Yb, Ho, Er)\({}_{0.22(5)}\)Na\({}_{0.08(2)}\)F\({}_{2.44}\) & 74.0 \\ \hline \end{tabular} \({}^{1}\) Fluorine content was calculated by cations based on the assumption of electroneutrality of the solid solution.  
\({}^{2}\) EDX method does not have sufficient sensitivity to separate the signals of neighboring rare earth elements.  
\end{table} 
Table 1: The nominal composition of the samples, the composition according to EDX data, and the practical yield of the sample synthesis reaction. Figure 1: XRD patterns of prepared samples. \(\bullet\)–superstructural reflections. Figure 2: SEM microphotography of prepared samples. (**a**) Sample 1; (**b**) Sample 2; (**c**) Sample 3; (**d**) Sample 3 (detector of backscattered electrons was used for elemental contrast); (**e**) Sample 4; (**f**) Sample 5. All powders have submicron sizes with a bimodal particle size distribution. The first maximum is about 200 nm, and the second is about 700 nm. Histograms of particle size distribution can be found in Supplementary Materials, Figure S1. Detection of backscattered electrons showed that the particles in Sample 3 are homogeneous in composition, there is no contrast in microphotographs.