## 3 Results and Discussion
The increase in the temperature induces a change in the emission spectrum due to a change in the Tb\({}^{3+}\) to Eu\({}^{3+}\) emission ratio, which causes the chromaticity shift (Figure 6b). The resulting chromaticity shift (\(\Delta E_{\text{C}}\)) caused by the heating of the sample from 0 up to 100 \({}^{\circ}\)C was calculated using Equation (9) and is equal to \(80\cdot 10^{-3}\), which is twice as much as found for the commercial phosphors [40], yet still within the order of magnitude for LED phosphors [41; 42]. \[\Delta E_{\text{C}}=\sqrt{\left(u_{f}-u_{i}\right)^{2}+\left(v_{f}-v_{i} \right)^{2}+\left(w_{f}-w_{i}\right)^{2}} \tag{9}\]  
where \(u=4x/(3-2x+12y)\), \(v=9y/(3-2x+12y)\) and \(w=1-u-v\). The \(x\) and \(y\) are the chromaticity in CIE 1931 color space, and the \(i\) and \(f\) indices indicate the chromaticity points before and after heating, respectively. Figure 5: (a) External quantum yield in the function of excitation wavelength for Eu- and Tb-doped samples; (b) thermal quenching curves for Eu and Tb emission in studied glass system; red curves were fitted function (8), and \(\Delta E_{\text{act}}\) is an activation energy for thermal quenching. R\({}^{2}\) (COD) of fitted curves are equal to 0.98887 and 0.98518 for Eu and Tb, respectively. The fluorescence intensity ratio (FIR) (Figure 6c) was calculated between the most intense emission lines for each co-dopant: \({}^{5}\)D\({}_{0}\)\(\rightarrow\)\({}^{7}\)F\({}_{2}\) for Eu\({}^{3+}\) (at 612 nm) and \({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{5}\) for Tb\({}^{3+}\) (at 542.2 nm). The relative sensitivity (Figure 6c) was then calculated from Equation (10) [14]:  
\[S_{r}(T)=\frac{1}{FIR(T)}\bigg{|}\frac{\partial}{\partial T}FIR(T)\bigg{|} \tag{10}\]  
The FIR profile is stably increasing in the full range of temperature, and the relative sensitivity has a maximum at 0 \({}^{\circ}\)C equal to 0.16% K\({}^{-1}\), which is similar to that reported for Tb\({}^{3+}\)/Eu\({}^{3+}\)-doped Sr\({}_{3}\)GdNa(PO\({}_{4}\))\({}_{3}\)F phosphor [43], but generally lower than that reported for Eu\({}^{3+}\)/Tb\({}^{3+}\)-co-doped crystalline (ranging from 0.37 to 5.04% K\({}^{-1}\)) [43; 18; 44; 45; 46; 47] and glass materials (ranging from 0.36 to 1.1% K\({}^{-1}\)) [48; 49]. The thermal resolution of the temperature sensor based on FIR was calculated using Equation (11),  
\[\delta T=\frac{1}{S_{r}}\cdot\frac{\Delta FIR}{FIR} \tag{11}\]  
where \(\Delta\)FIR is the uncertainty of the determination of FIR with regard to the exponential function FIR = \(B\) + _C exp_(\(-\Delta E^{\prime}/kT\)) [50]. The thermal resolution is around or below 0.2 K for  
Figure 6: (**a**) Temperature-dependent emission spectra of Eu\({}^{3+}\), Tb\({}^{3+}\)-co-doped sample; (**b**) CIE diagram of the Eu\({}^{3+}\), Tb\({}^{3+}\)-co-doped glass chromaticity shift; (**c**) fluorescence intensity ratio and relative sensitivity. The red line serves only to guide the eyes. (**d**) Thermal resolution of the temperature sensor based on FIR. The black line serves only to guide the eyes. low-temperature regions, with an increase up to 0.4 K correlating with a drop of sensitivity at 100 \({}^{\circ}\)C (Figure 6d). In fact, a relaxation of terbium and europium luminescent excited states in the studied glasses is governed by competing radiative and nonradiative processes. The nonradiative phenomena are attributed to intra-ion multiphonon relaxation and the energy transfer mechanisms involved in inter-ionic interactions promoted by the increase in rare earth concentration. The related energy levels scheme of Tb\({}^{3+}\) and Eu\({}^{3+}\) in the studied glasses is presented in Figure 7. The \({}^{5}\)D\({}_{4}\) (Tb) and \({}^{5}\)D\({}_{0}\) (Eu) excited states are characterized by a significantly larger energy gap to the lower-lying levels in relation to \({}^{5}\)D\({}_{3}\) (Tb) and \({}^{5}\)D\({}_{1}\) (Eu) manifolds.