## 3 Results and Discussion
### Photoluminescence Analysis
The best fit to Equation (2) was reached for \(\Gamma_{0}\) equal to 1.18 meV, 1.58 meV, 1.08 meV, and 1.38 meV for the R\({}_{2}\), R\({}_{1}\), N\({}_{2}\), and N\({}_{1}\) lines, respectively, \(B\) constants of 0.6 meV, 1.2 meV, 0.4 meV, and 0.6 meV, and values of 19 meV (R\({}_{2}\), R\({}_{1}\)) and 11 meV (N\({}_{2}\), N\({}_{1}\)) for the \(\hbar\overline{\omega}\). The temperature dependence of the R- and N-lines PL intensity has been previously studied by [PERSON] et al. [46] and [PERSON] et al. [53], allowing the identification of the location of the energy diagrams, transitions from isolated Cr\({}^{3+}\) ions (R-lines), and Cr\({}^{3+}\) complexes (N\({}_{1}\) and N\({}_{2}\) lines), as well as the energy transfer processes between the different chromium optical centres present in the samples. The energy transfer process between single and exchange-coupled pairs of chromium ions (R and N lines) was also previously studied by [PERSON] [47] via lifetime measurements in low, intermediate, and highly doped samples. [PERSON] [47] proved that the energy transfer from single ions to pairs occurs nonradiatively with a fast transfer of excitation between the single ions until they are close enough for the energy to be transferred to the pairs. In addition, following the model proposed by [PERSON] [54] and [PERSON] [55], the author was able to identify that the nonradiative energy transfer is driven by electric quadrupole-quadrupole interaction, rather than exchange and magnetic dipole-dipole interactions, or electric dipole-dipole interaction, which are all weaker than the former [47]. In his studies, [PERSON] [47] found that the radiative decay of the R-lines is distinct from the N-lines, being slower in the former. Even for low-doped samples, the decay measured at 77 K for the R-lines (8.8 ms) was higher than that detected by [PERSON] et al. [9] for single chromium ions (4.2 ms) as a consequence of the luminescence-trapping dependence of the radiative recombination on the chromium concentration. Additionally, the N-lines evidenced a non-exponential lifetime at this temperature (77 K), described by a fast component in the order of 1.0 ms and a slow component with the same decay rate as the R-lines, showing that energy transfer occurs from the single chromium ions to chromium pairs [47]. Figure 8 shows the time-resolved  
Figure 3:0 Temperature dependence of the (**a**) peak position of the R-\({}^{\prime\prime}\), R-, and N-lines obtained with 3.81 eV photon excitation and (**b**) full width at half maximum of the R- and N-lines. Symbols denote the experimental values while full and dashed lines correspond to the theoretical fits of Equations (1) and (2), respectively. spectra and decay times measured at RT in the present \(\alpha\)-Al\({}_{2}\)O\({}_{3}\):Cr samples. Considering the \({}^{4}\)A\({}_{2}\)\(\rightarrow\)\({}^{4}\)T\({}_{2}\),\({}^{4}\)T\({}_{1}\) excitation, it was possible to notice that the emission intensity of the R-lines decreases at 1/e from its initial value at about 3.0 ms, following the measured single average exponential decay of 3.2 ms shown in Figure 6b. Additionally, the decay times measured at the N\({}_{2}\) line (the N-one with the highest intensity at RT) can be fitted to a multi-exponential model, with a fast lifetime of less than 0.5 ms, an intermediate one of 1.5 ms, and a slow lifetime similar to that of R-lines (-3.1 ms). It is worth mentioning that, as depicted in Figure 6b, different excitation wavelengths were employed to assess the lifetime of the mentioned emissions and all led to similar values. As above-mentioned, and in line with what was previously reported, this behavior suggests that there is energy transfer between the different chromium optical centres [47].