## 3 Results and Discussion
### Analysis of Dose\(-\)Response Graphs
#### 3.2.2 Dose\(-\)Response
As the heating rate increases from 0.5 K\(\cdot\)s\({}^{-1}\) to 4.5 K\(\cdot\)s\({}^{-1}\), the peak temperature shifts towards higher values. This directly results from the relationship between the heating rate and the thermal activation of trapped charge carriers within the material. At lower heating rates, the trapped charge carriers have more time to escape and  
Figure 6: (**A**) Analysis of dose\(-\)response graphs. (**B**) Plot of ln(I) vs. 1/T for six successive TL glow curve recorded in ZnZrO\({}_{3}\):Mn. contribute to the glow curve at relatively lower temperatures. Conversely, as the heating rate increases, there is less time for thermal excitation at lower temperatures, leading to the release of charge carriers only at higher temperatures, where the activation energy is overcome more quickly. This behavior is characteristic of TL glow peaks governed by first- and second-order kinetics, where the position of the glow peak is dependent on the rate of input of thermal energy into the system. Additionally, the figure reveals that the fluorescence intensity of the primary glow peak increases significantly, by up to 100%, as the heating rate increases. This increase in intensity can be attributed to the thermal lag that occurs at higher heating rates. At slower heating rates, the recombination of charge carriers occurs over a broader range of temperatures, leading to a spread-out glow peak with lower intensity. However, at higher heating rates, the rapid increase in temperature causes the trapped charge carriers to be released over a narrower range of temperatures, resulting in a sharper and more intense glow peak. This simultaneous shift in peak temperature and increase in peak intensity supports the TL hypothesis, as it aligns with the expected behavior for TL processes that follow first- and second-order kinetics. In such cases, the kinetics are influenced by both the activation energy and the heating rate, which together determine the peak's thermal position and the overall luminescence intensity observed. Additionally, the impact of changes in the heating rate was investigated. A peak shift to higher temperatures, a decrease in peak height, and a comparatively greater TL intensity at the final temperature of 600 K were the outcomes of an increase in heating rate (Figure 6A). This peak-shift behavior yields peaks qualitatively comparable to the TL peaks generated by a delocalized recombination process. Figure 7B, above, illustrates the thermoluminescence (TL) intensity and temperature of the glow peak as a function of the Variable Heating Rate (VHR). The relationship between these parameters reveals critical insights into the thermal behavior of the luminescent material under varying heating rates. The TL intensity (black dashed line) increases significantly as the heating rate increases. This can be attributed to the thermal lag effect, which becomes more prominent at higher heating rates. At slower heating rates, charge carriers are released and recombine gradually over a broader temperature range, resulting in a lower peak intensity. In contrast, at higher heating rates, the temperature rises more rapidly, leading to a narrower release window for trapped charge carriers. This concentrated release produces a sharper, more intense glow  
Figure 7: (**A**) TL curves produced using different variable heating rates. (**B**) TL intensity and temperature vs. VHR. peak, as seen in Figure 7B. The increase in intensity suggests that the luminescent centers are efficiently excited and recombined within the material as the heating rate increases. The blue line with square markers represents the temperature of the TL peak as a function of the heating rate. The figure demonstrates that the peak temperature shifts to higher values as the heating rate increases. This behavior is consistent with first-order and second-order kinetics in thermoluminescence, where the thermal activation of trapped charge carriers depends on the rate at which thermal energy is supplied.