## 3 Materials and Methods  
To grow the YScO\({}_{3}\) crystal fiber, the laser heated pedestal growth (LHPG) method has been used [25; 30; 31]. This approach allows us to synthesize crystal in the form of a fiber and to obtain high-melting materials and compounding with disordered crystal structure. To prepare \(RE_{2}\)O\({}_{3}\)-Y\({}_{2}\)O\({}_{3}\)-Sc\({}_{2}\)O\({}_{3}\) powder, preform scandium, yttrium and rare-earth (Nd\({}^{3+}\) or Tm\({}^{3+}\)) oxides (purity of more than 99.999%, Sigma Aldrich, Burlington, MA, USA) were well mixed in a stoichiometric proportion (of mole ratio \(RE_{2}\)O\({}_{3}\)/Y\({}_{2}\)O\({}_{3}\)/Sc\({}_{2}\)O\({}_{3}\) = 0.19:9.9:100) in an agate mortar to form a homogeneous mixture. The mole ratio of 1:1 was used to prepare undoped Y\({}_{2}\)O\({}_{3}\)-Sc\({}_{2}\)O\({}_{3}\) powder preform. Then, the mixture was transferred to a platinum crucible and annealed at 1100 \({}^{\circ}\)C for 48 h in an air atmosphere to exclude the presence of H\({}_{2}\)O. The final powder mixture was pressed at 20 MPa to form a rod with about 1 mm diameter and 50 mm length.  
Visualization and chemical composition analysis of the YScO\({}_{3}\) crystal fiber were carried out on the EVO 10 scanning electron microscope (Zeiss Microscopy GmbH, Jena, Germany). The samples were examined at an accelerating voltage of 20 kV with a working distance of 9.0 mm in low vacuum operation (EP = 50 Pa) using a LaB6 cathode.  
To obtain SEM imaging of the sample, part of the crystal fiber was placed onto a carbon tape. The observations of the sample were carried out at a beam current of 85 pA. The images were captured in backscattered electron mode (BSE) to assess sample homogeneity (Figure 1a).  
The semi-quantitative estimation of the main cation (Y\({}^{3+}\) and Sc\({}^{3+}\)) ratio was based on the data of the Smart METEK EDX spectrometer. Scanning was carried out in line-scan mode at a step of 2 \(\upmu\)m and a beam current of 149 pA.  
A part of the crystal fiber has been ground in an agate mortar and characterized with X-ray phase analysis. The X-ray pattern has been recorded on the Bruker D8 Discover A25 DaVinci Design diffractometer in the range of 2\(\theta\) = 15-80\({}^{\circ}\) with a step of 0.02\({}^{\circ}\) and an exposition time of 1.0 s. The Siemens KFL X-ray tube with Cu \(K\alpha\) (\(U\) = 40 kV, \(I\) = 40 mA, \(\lambda\) = 0.154 nm) irradiation has been used as the X-ray source. The spectra have been resolved with the EVA 2.1 software and identified with the PDF-2 2011 database. The TOPAS 4.2 software has been used to index spectral peaks and to determine lattice cell parameters.  
Micro-Raman spectra of the YScO\({}_{3}\) crystal fiber and precursor (Y\({}_{2}\)O\({}_{3}\) and Sc\({}_{2}\)O\({}_{3}\)) powders have been recorded on the EnSpectr \(R\)532 express analyzer equipped with the Olympus microscope (40\(\times\) objective) at a laser excitation of 532 nm. The laser beam has been focused on a core of the fiber. Each spectrum has been obtained as the difference between the spectrum taken with the laser running and the dark spectrum. The subtraction of the first spectrum from the second one was carried out automatically using the EnSpectr Pro software. The final Raman spectra were obtained by averaging 20 runs acquired during the total time of 90 s (4.5 s for a run).  
Spectral-kinetic characteristics of the Nd\({}^{3+}\)- and Tm\({}^{3+}\)-doped YScO\({}_{3}\) crystal fibers have been obtained with the selective spectroscopy method. Luminescence spectra have been recorded on the MDR-23 monochromator. The Hamamatsu R5108 ii FEU-83 photmultipliers have been used as detectors. The LQ529B-LP 604 (Solar LS, Belarus) laser complex has been used as the excitation source.