## 4 Results and Discussion  
Figures 4 and 5 show the emission spectra of samples G and GC doped with 9% and 15%, respectively, both with and without Yb\({}^{3+}\) doping. Analyzing Figures 4a and 5a, we observe emission in the wavelength range of 450-700 nm, attributed to the electronic transitions 7\(D48 Fj(j=6,5,4,3)\)5 of Tb\({}^{3+}\) ions. The peak of maximum emission is around 543 nm, specifically corresponding to the transition 7\(D48F55\). It is noteworthy that after Yb\({}^{3+}\) co-doping, the intensity decreases significantly, indicating the presence of a down-conversion process. Some authors [25] suggest that this process is quantum cutting in glasses co-doped with Tb\({}^{3+}\) and Yb\({}^{3+}\), resulting from a cooperative energy transfer that converts a photon absorbed by Tb\({}^{3+}\) ions into two photons emitted by Yb\({}^{3+}\) ions (\(Tb3+:5D48 Yb3+:2F5/2+Yb3+:F5/2\)). The co-doped samples G and GC exhibit a broad emission band in the near-infrared range, located between 960 and 996 nm, attributed to the \(2F5/28F7/2)2 transition of Yb\({}^{3+}\), (Figures 4b and 5b). Interestingly, the maximum emission peak for GC samples is at 978 nm, whereas for G samples, it is at 981 nm. This spectral difference between G and GC samples is more pronounced in the infrared region, suggesting a change in the environment surrounding the rare-earth ions after the tempera \begin{table}
\begin{tabular}{c c} \hline
**Sample** & **Composition (mol\%)** \\ \hline
1 & 70 SiO\({}_{2}\)-30 HfO\({}_{2}\)-1.8\%Tb\({}^{3+}-7.2\%Yb^{3+}\) (G) \\
2 & 70 SiO\({}_{2}\)-30 HfO\({}_{2}\)-1.8\%Tb\({}^{3+}-7.2\%Yb^{3+}\) (GC) \\
3 & 70 SiO\({}_{2}\)-30 HfO\({}_{2}\)-3\%Tb\({}^{3+}-12\%Yb^{3+}\) (G) \\
4 & 70 SiO\({}_{2}\)-30 HfO\({}_{2}\)-3\%Tb\({}^{3+}-12\%Yb^{3+}\) (GC) \\ \hline \end{tabular}
\end{table} 
Table 1: Glass and glass-ceramic sample compositions. ture increase during the heat treatment, attributed to the appearance of HfO\({}_{2}\) nanocrystals after annealing at 1000 \({}^{\circ}\)C.  
Figure 4: **(a)** Visible emission spectra of Tb\({}^{3+}\) and **(b)** NIR emission spectra of Yb\({}^{3+}\) in 1.8%Tb\({}^{3+}-7.2\%\)Yb\({}^{3+}\) co-doped 70 SiO\({}_{2}\)-30 HfO\({}_{2}\). However, it is not possible to determine the conversion efficiency based only on photoluminescence spectra. The evaluation of the energy transfer efficiency between terbium and ytterbium is achieved by estimating the degree of energy transfer between these two ions. This assessment can be carried out by comparing the luminescence decay of terbium with and without ytterbium ion co-doping. The decay curves of Tb\({}^{3+}\) ions in the investigated system are illustrated in Figure 6.  
Almost exponential luminescent decay is observed for the samples without Yb\({}^{3+}\), whereas a faster luminescent decay with non-exponential behavior is commonly observed for the co-doped samples. This reduction in lifetime is attributed to the energy transfer from Tb\({}^{3+}:{}^{5}\)D\({}_{4}\) to Yb\({}^{3+}:2^{2}\)F\({}_{5/2}\), where the non-exponential behavior of the decay aligns perfectly with the Inokuti-Hirayama model [26]. From a graphical observation (Figure 6a,d), it is noteworthy that the GC samples exhibit a much more significant reduction in lifetime compared to the G samples. This behavior is caused by the presence of rare-earth ions in HfO\({}_{2}\) nanocrystals, which reduces non-radiative losses. The energy transfer efficiency denoted as \(\eta_{\rm{TD-Yb}}\) can be determined experimentally by dividing the integrated intensity of the decay curves observed in Tb\({}^{3+}\)-Yb\({}^{3+}\) co-doped samples by the integrated intensity of the decay curve in Tb\({}^{3+}\) single-doped samples [22]:  
\[\eta_{\rm{Tb-Yb}}=1-\frac{\int{\rm{I_{Tb-Yb}dt}}}{\int{\rm{I_{Tb}dt}}}\]  
In certain research studies, the effective quantum efficiency is described as the ratio of emitted photons to absorbed photons in a material.