## 3 Results and Discussion
Moreover, in view of the various routes of the possible energy transfer phenomena, the substantially different effects of temperature and nonradiative processes on the Tb\({}^{3+}\) and Eu\({}^{3+}\) luminescent levels decay can be explored. To verify this assumption, the experimental lifetimes of the aforementioned terbium and europium excited states were examined at room temperature and as a function of temperature up to 400 \({}^{\circ}\)C.  
The luminescence decay curves are single-exponential for both Eu\({}^{3+}\)- and Tb\({}^{3+}\)-doped samples (Figures 8a,b and 9a,b). The decay curves of the lowest emitting levels (\({}^{5}\)D\({}_{0}\) for Eu\({}^{3+}\) and \({}^{5}\)D\({}_{4}\) for Tb\({}^{3+}\)) of both rare earth dopants are similar and have time constants \(\tau\) = 1.4 ms for Eu\({}^{3+}\) and \(\tau\) = 1.7 ms for Tb\({}^{3+}\). The energy transfer from Tb to Eu was investigated by comparing the Tb\({}^{3+}\) emission decay in single-doped and co-doped samples (Figure S2). No difference was observed, and consequently, it was concluded that no energy Tb\({}^{3+}\)\(\rightarrow\) Eu\({}^{3+}\) transfer occurs in this system. The decay curve of the \({}^{5}\)D\({}_{1}\) level of Eu\({}^{3+}\) in the Eu-doped sample was recorded as single-exponential with a decay time of 35 \(\upmu\)s (Figure 8b). This observation is consistent with other Eu-doped materials, in which the decay time of \({}^{5}\)D\({}_{1}\) level is significantly shorter than that of \({}^{5}\)D\({}_{0}\)[51]. At elevated temperatures, the decay times become shorter. The decay time of the \({}^{5}\)D\({}_{0}\) level remains stable up to 250 \({}^{\circ}\)C; in higher temperatures, it becomes gradually shorter down to 0.95 ms at 400 \({}^{\circ}\)C (Figure 8c). The decay time of the \({}^{5}\)D\({}_{1}\) level is much less thermally stable due to multiphonon relaxation [32]. Figure 7: Scheme of Tb\({}^{3+}\) and Eu\({}^{3+}\) levels in germanate–tellurite glass. and decreases to 12 us at 400 \({}^{\circ}\)C (Figure 8d). The values of the decay times were fitted with Equation (12) [52]. \[\tau(T)=\frac{\tau_{R}\cdot\tanh\left(\frac{\eta_{W}}{2 kT}\right)}{1+\left(\frac {\tau_{R}\cdot\tanh\left(\frac{\eta_{W}}{kT}\right)}{\tau_{NR}}\cdot\exp\left( \frac{-\Delta E_{q}}{kT}\right)\right)} \tag{12}\]  
where \(\tau_{R}\) is the radiative lifetime at 0 K, hv is an average phonon energy for this host, \(\tau_{NR}\) is the nonradiative relaxation lifetime, \(k\) is the Boltzmann constant, and \(\Delta E_{q}\) is the activation energy of the process. The parameters of the fit are listed in Table S1. As expected, the decay time of the \({}^{5}\)D\({}_{4}\) level of Tb\({}^{3+}\) (Figure 9a,c) is much longer than that of the \({}^{5}\)D\({}_{3}\) level (Figure 9b,d), which is equal to 38 us. This is in line with other reported decay times of this level [53]. Both \({}^{5}\)D\({}_{4}\) and \({}^{5}\)D\({}_{3}\) levels in Tb-doped samples are significantly less stable than \({}^{5}\)D\({}_{0}\) and \({}^{5}\)D\({}_{1}\) of Eu\({}^{3+}\) in the same glass system, which confirms the findings of the thermal stability of emission intensity and calculated activation energies of thermal quenching. \[I=\frac{I_{0}}{1+\frac{I_{g}-\Delta E_{act}/kT}{I_{v}}} \tag{8}\]0 Decay curves of 0.2% Eu-doped sample’s emission from \({}^{5}\)D\({}_{0}\) (**a**) and \({}^{5}\)D\({}_{1}\) (**b**) levels recorded at room temperature and 400 \({}^{\circ}\)C. Decay time values of emission from \({}^{5}\)D\({}_{0}\) (**c**) and \({}^{5}\)D\({}_{1}\) (**d**) levels fitted with function (12). The impact of temperature on the values of the decay times allows for lifetime-based thermometry to be estimated.