Fig. 2: Relation between the maximum phonon energy and the onset of thermal equilibrium.

a Luminescence decay curves of the ⁵D₁ emission for Y₂O₃ (top), LaPO₄ (middle), and LaBO₃ (bottom). The luminescence was excited at ⁷F₀ → ⁵D₁ and the decay curves were measured at 78 K (dark color, slower decay) and 523 K (light color, faster decay). b Decay rates of the ⁵D₁ emission at various temperatures. The solid line in the top plot and the dashed lines in the middle and bottom plots are fits of the experimental rates (dots) to Eq. 1, while the solid lines in the middle and bottom plots are fits to Eq. 3. c Intensity ratios of the ⁵D₁ and ⁵D₀ emissions for various temperatures determined from luminescence spectra upon excitation into the charge-transfer states. The solid lines are fits of the experimental ratios (dots) to the model of Eq. 4 for Y₂O₃ and Eq. 5 for LaBO₃ and LaPO₄ (lines). The onset temperatures for thermal equilibrium (T_onset) were calculated using Eq. 6 for Y₂O₃:Eu³⁺ and a numerical solution was used for LaPO₄:Eu³⁺ and LaBO₃:Eu³⁺ (see text for further details)