The understanding of how radiative transition probabilities change with temperature is crucial for comprehending the relationship between fluorescence behavior and temperature. However, although various models have been proposed to explain the patterns of transition probabilities (A) with temperature changes, they lack consistency due to their derivation from distinct microscopic perspectives. In this study, the macroscopic law of the temperature-dependent A for the 4G5/2, 4F9/2, and 5D0 energy states in YVO4:Re3+(Re3+=Sm3+, Dy3+ and Eu3+) was obtained. Three rare earth ions (Re3+) were identified for each with unique energy level properties conducive to validating the general rules of A. These ions share a common characteristic: in the visible spectrum, their main emissions originate from the radiative transitions from the same higher energy level (4G5/2 in Sm3+, 4F9/2 in Dy3+, and 5D0 in Eu3+) to lower energy levels, respectively. The A of the main emission levels, varying with T, were obtained by fitting the fluorescence decay curves. The exponential law governing non-radiative transitions was revealed after separating the radiative transition rate (WR) from A. The macroscopic law of temperature-dependent transition probabilities of 4G5/2, 4F9/2, and 5D0 energy states in YVO4:Ln3+ (Ln3+=Sm3+, Dy3+ and Eu3+) has been found to follow the Boltzmann distribution. The results indicate that the non-radiative transitions of the main emission levels of the rare-earth ions are processes from the excited state to adjacent lower energy levels. This macroscopic pattern may serve as a foundational rule for understanding the impact of microscopic factors on A.

Temperature-dependent law of transition probability associated with main emission states in YVO4:Re3+ (Re3+=Sm3+, Dy3+ and Eu3+)