## 3 Results and Discussion
### Optical and Photoluminescence Characteristics
The photoluminescence (PL) contour map clearly revealed the characteristic \({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{\rm j}\) transitions of Tb\({}^{3+}\), which dominate at higher Tb\({}^{3+}\) concentrations (5 and 10% Tb samples) due to efficient cross-relaxation processes. These transitions include emissions at 490 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{6}\)), 545 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{5}\)--the most intense green emission), 585 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{4}\)), and 620 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{3}\)) [27; 29]. These emissions were effectively excited within the 250-330 nm wavelength range. The strongest emissions, particularly the prominent 545 nm peak, were most efficiently excited at \(\sim\)270-300 nm. This excitation range corresponded to allowing for 4\({}^{6}\)\(\rightarrow\) 4\({}^{7}\)5d\({}^{1}\) transitions and charge transfer (CT) bands in Tb\({}^{3+}\), indicating that the host matrix efficiently absorbed UV light and transferred energy to the Tb\({}^{3+}\) ions. The broad excitation band (250-330 nm) made this material highly compatible with UV LEDs and suitable for X-ray scintillation. Furthermore, the intense green emission at 545 nm (\({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{5}\)) is ideal for applications in solid-state lighting (e.g., white LEDs using blue chips with green phosphors), display technologies, and radiation detection through scintillator devices [26; 27; 28; 29]. Figure 5 presents the photoluminescence (PL) decay of LuYAGG:Tb garnet crystals, at \(\lambda_{\rm ex}\) = 340 nm and \(\lambda_{\rm em}\) = 550 nm, corresponding to the green emission peak (\(\sim\)545 nm) from the \({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{5}\) transition of Tb\({}^{3+}\). The decay was recorded under pulsed excitation, with the time axis was displayed in milliseconds (ms), reflecting the typical ms-scale lifetimes of the \({}^{5}\)D\({}_{4}\) excited states. The decay profiles fit well with a single-exponential decay function: \(I(t)=A~{}exp~{}(-t/\tau)+~{}background\), where \(A\) is the initial amplitude, \(t\) is time, and \(\tau\) represents the decay lifetime. For well-isolated Tb\({}^{3+}\) ions, the decay was predominantly single exponential, corresponding to intrinsic \({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{\rm j}\) transitions. However, at higher Tb\({}^{3+}\) concentrations, non-radiative processes such as energy migration and cross-relaxation became more prominent, introducing faster decay components. This results in a decrease in \(\tau\), a characteristic feature of concentration quenching, where energy transfers non-radiatively between nearby Tb\({}^{3+}\) ions and may migrate to quenching centers (e.g., defects or impurities), thereby shortening the effective lifetime [13; 30; 31]. The observed decay lifetimes (\(\sim\)2.9-3.4 ms) are characteristic of the \({}^{5}\)D\({}_{4}\)\(\rightarrow\)\({}^{7}\)F\({}_{\rm j}\) transitions of Tb\({}^{3+}\) and are sufficiently long to support a variety of optical applications. Such millisecond-scale luminescence is advantageous for time-gated bioimaging, optical security tags, and persistent phosphor technologies, where delayed or sustained emission is desirable for contrast enhancement, data encoding, or visual persistence [32; 33; 34]. The corresponding decay lifetimes for the LuYAGG:Tb samples are summarized in Table 1. \begin{table}
\begin{tabular}{l c} \hline \hline
**Samples** & \(\tau_{1}\) **(ms)** \\ \hline LuYAGG:Tb 0.5 mol\% & 3.25 \\ LuYAGG:Tb 1 mol\% & 3.16 \\ LuYAGG:Tb 5 mol\% & 3.03 \\ LuYAGG:Tb 10 mol\% & 2.98 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Photoluminescence decay time constants for Tb-doped LuYAGG single crystals.