## 2 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline  & & & \multicolumn{4}{c}{Y\({}_{2}\)O\({}_{3}\); \(a\) = 10.604(1) Å} & \multicolumn{4}{c}{Sc\({}_{2}\)O\({}_{3}\); \(a\) = 9.841(4) Å} & \multicolumn{4}{c}{Y\({}_{5}\)Co\({}_{3}\); \(a\) = 10.228(1) Å} \\ \hline
**Index** & _hkI_ & \(m\) & _2\(\theta\)_ & \(d\) & \(I\) & _2\(\theta\)_ & \(d\) & \(I\) & _2\(\theta\)_ & \(d\) & \(I\) \\ \hline
1 & 211 & 24 & 20.494 & 4.3302 & 13.90 & 22.139 & 4.0121 & 19.30 & 21.261 & 4.1756 & 13.54 \\
2 & 222 & 8 & 29.162 & 3.0598 & 100.00 & 31.505 & 2.8374 & 100.00 & 30.246 & 2.9526 & 100.00 \\
3 & 004 & 6 & 33.798 & 2.6500 & 21.90 & 36.53 & 2.4578 & 8.30 & 35.065 & 2.5570 & 18.45 \\
4 & 411 & 24 & 35.918 & 2.4982 & 4.40 & 38.834 & 2.3171 & 3.50 & 37.268 & 2.4108 & 4.62 \\
5 & 332 & 24 & 39.862 & 2.2597 & 4.70 & 43.121 & 2.0962 & 11.90 & 41.372 & 2.1806 & 8.36 \\
6 & 341 & 24 & 43.51 & 2.0783 & 5.80 & 47.089 & 1.9284 & 8.60 & 45.166 & 2.0059 & 9.11 \\
7 & 251 & 24 & 46.925 & 1.9347 & 1.70 & 50.814 & 1.7954 & 3.30 & 48.724 & 1.8674 & 3.27 \\
8 & 044 & 12 & 48.556 & 1.8735 & 27.80 & 52.607 & 1.7383 & 39.10 & 50.432 & 1.8081 & 47.56 \\
9 & 433 & 24 & 50.161 & 1.8172 & 1.30 & 54.344 & 1.6868 & 1.60 & 52.098 & 1.7541 & 2.14 \\
10 & 611 & 24 & 53.245 & 1.7190 & 2.70 & 57.737 & 1.5955 & 4.10 & 55.324 & 1.6592 & 3.47 \\
11 & 541 & 24 & 56.211 & 1.6351 & 2.10 & 61.002 & 1.5177 & 3.50 & 58.429 & 1.5782 & 4.54 \\
12 & 622 & 24 & 57.657 & 1.5975 & 13.60 & 62.595 & 1.4828 & 14.20 & 59.942 & 1.5419 & 27.23 \\
13 & 631 & 24 & 59.082 & 1.5623 & 2.70 & 64.166 & 1.4503 & 4.20 & 61.433 & 1.5081 & 6.56 \\
14 & 444 & 8 & 60.478 & 1.5296 & 2.20 & 65.714 & 1.4198 & 1.20 & 62.903 & 1.4763 & 3.66 \\
15 & 721 & 24 & 64.575 & 1.4421 & 1.60 & 70.255 & 1.3387 & 2.90 & 67.205 & 1.3919 & 3.08 \\
16 & 008 & 6 & 71.123 & 1.3245 & 1.50 & & & & & 74.098 & 1.2785 & 4.70 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Miller indices (_hkI_), interplanar distances \(d\), Bragg angles _2\(\theta\)_ and Bragg peak intensities \(I\) of the Y\({}_{2}\)O\({}_{3}\), Sc\({}_{2}\)O\({}_{3}\) and YScO\({}_{3}\) with a bixbyite-type structure. Figure 1: (**a**) An image of the YScO\({}_{3}\) crystal fiber captured in backscattered electron mode (BSE). A scalebar is 0.5 mm; (**b**) Stoichiometric coefficients of Y\({}^{3+}\) (blue one) and Sc\({}^{3+}\) (red one) ions calculated based on three oxygen atoms per formula unit; (**c**) The X-ray pattern of the YScO\({}_{3}\) crystal fiber (green one) and Y\({}_{2}\)O\({}_{3}\) and Sc\({}_{2}\)O\({}_{3}\) precursors (blue and red ones, respectively). Insert: bixbyite-type crystal structure of YScO\({}_{3}\). Symmetrically diverse MO\({}_{6}\) polyhedra both centered by statistically distributed Y\({}^{3+}\) and Sc\({}^{3+}\) ions are shown as orange (C\({}_{3i}\) site) and blue (C\({}_{2}\) site); red balls are O atoms; (**d**) Raman spectra of Y\({}_{2}\)O\({}_{3}\) and Sc\({}_{2}\)O\({}_{3}\) precursors and YScO\({}_{3}\) crystal fiber (blue, red and green lines, respectively). The micro-Raman spectra have been obtained for Y\({}_{2}\)O\({}_{3}\) and Sc\({}_{2}\)O\({}_{3}\) powders and the YScO\({}_{3}\) crystal fiber (Figure 1d). The unit cell of the bixbyite-type yttrium scandate includes 40 atoms (8 formula units). Therefore, factor-group analysis leads to the following distribution of the 120 phonon modes in the Brillouin zone point \(\Gamma\) = 0:  
\[ \begin{array}{c}\Gamma=\big{(}3A_{g}+3A_{u}+3E_{g}+3E_{u}+9F_{g}+9F_{u}\big{)} \big{(}C_{1}\text{ local symmetry}\big{)}\\ +\big{(}A_{g}+A_{u}+E_{g}+E_{u}+5F_{g}+5F_{u}\big{)}\ \big{(}C_{2}\text{ local symmetry}\big{)}\\ +\big{(}A_{u}+E_{u}+3F_{u}\big{)}\ \big{(}C_{3i}\ \big{(}S_{6}\ \big{)}\ \text{ local symmetry}\big{)}\end{array}  \tag{1}\]  
After subtracting \(1F_{u}\) of the acoustic modes there remain \(16F_{u}\) of the infra-red active, \((4A_{g}+4E_{g}+14F_{g})\) of the Raman-active and \((5A_{u}+5E_{u})\) of the optically inactive phonon modes.