## 2 Sample Preparation and Measurements  
Powder precursors of ternary garnets with variations in terbium concentration were produced by the reverse coprecipitation method. The precursors were calcined in corundum crucibles at the temperature of 850 \({}^{\circ}\)C for 2 h for garnet phase formation. After calcination, the powders were milled in a laboratory planetary mill (Retsch PM-100) in isopropanol media (median particle size, \(\sim\)1.5 \(\upmu\)m). Then, the powders were compacted in the shape of tablets with a diameter of 20 mm by uniaxial pressing at a pressure of 64 MPa (PLG-20 Laboratory Press by LabTools). The compacts were sintered in an air atmosphere at 1600 \({}^{\circ}\)C for 2 h using the Nabertherm LHT 02/17 LB high-temperature furnace. Ceramic samples were translucent; had \(>\)99.6% of theoretical density, which corresponds to the range of 5.84-5.89 g/cm\({}^{3}\) depending on composition; and had an optical transmission of 35-40% at 550 nm. The compositions of the samples and corresponding abbreviations are given in Table 1. Depending on terbium concentration, the elemental composition of the matrix slightly shifted. For Samples 1-4, the Gd/Y ratio in composition was chosen following the results described in [25]. Samples 5 and 6 were made to examine the possible influence of Gd/Y ratio deviation on the luminescence properties, whereas Sample 7 was solely doped with Ce. The Ce-doped sample was not codoped with Mg. Therefore, similarly to Gd\({}_{3}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\):Ce and the other quaternary garnets, it demonstrated phosphorescence [14; 26]. The pure garnet phase of the samples was confirmed by the X-ray diffraction method (2D Phaser by [PERSON] with linearly polarized Cu radiation k\(\alpha\) doublet 1.5406 and 1.5444 A), as expected. The resulting ceramic samples were single phase with a garnet structure (Figure 1). The inset shows the evolution of the main peak of the XDR spectrum, indicating a slight variation connected with the terbium content in the ceramic. \begin{table}
\begin{tabular}{c c c} \hline \hline \# & **Sample Composition** & **Abbreviation** \\ \hline
1 & Gd\({}_{1.175}\)Y\({}_{1.775}\)Tb\({}_{0.08}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) & GYAGG:Tb, Tb = 0.05 \\
2 & Gd\({}_{1.160}\)Y\({}_{1.740}\)Tb\({}_{0.1}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) & GYAGG:Tb, Tb = 0.1 \\
3 & Gd\({}_{1.120}\)Y\({}_{1.730}\)Tb\({}_{0.15}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) & GYAGG:Tb, Tb = 0.15 \\
4 & Gd\({}_{1.100}\)Y\({}_{1.700}\)Tb\({}_{0.2}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) & GYAGG:Tb, Tb = 0.2 \\
5 & Gd\({}_{1.43}\)Y\({}_{1.740}\)Tb\({}_{0.2}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) & GYAGG:Tb-2, Tb = 0.2 \\
6 & Gd\({}_{1.17}\)Y\({}_{1.710}\)Tb\({}_{0.2}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) & GYAGG:Tb-3, Tb = 0.2 \\
7 & Gd\({}_{1.175}\)Y\({}_{1.777}\)Ce\({}_{0.03}\)Al\({}_{2}\)Ga\({}_{3}\)O\({}_{12}\) & GYAGG:Ce, Ce = 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Tb- and Ce-doped samples compositions. The luminescence spectra during photoexcitation (PL) of the samples were measured with the Lumex FLUORAT-02-PANORAMA spectrofluorimeter at room temperature in the wavelength range of 360-700 nm with an excitation wavelength (dex) of 273 nm, which corresponds to the excitation in the 4\({}^{\prime\prime}\)-5d\({}^{1}\)f\({}^{\circ}\)- interconfiguration transition of Tb\({}^{3+}\)-ions. The photoluminescence kinetics of the samples were measured with the PicoQuant Fluotime 200 fluorometer. The excitation of photoluminescence during the kinetics measurement was carried out using an LED with a wavelength of 270 nm and a pulse width (FWHM) shorter than 1 ns. The scintillation intensity was evaluated at irradiation with the MIRA-2D small-size pulsed accelerator with the IMA-2-150E electron tube (150 keV; highest current density, 1 A/cm\({}^{2}\); pulse duration, \(\sim\)20 ns). The beam repetition frequency was set as 10 Hz.