“…The more stable the 1 D 2 emission indicates that the larger the Δ E 2 value, the larger the IVCT energy level. Figures c–e and S4 show the Arrhenius formula – for calculating the thermal quenching activation energy Δ E 2 for LiNb 1– x Ta x O 3 :0.005Pr 3+ ( x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0). where the constants I 0 and I ( T ) are the parameters for initial temperature and any temperature ( T ) emission intensity, E represents the activation energy Δ E 2 , and A and K B (Boltzmann’s constant 8.629 × 10 –5 eV·K –1 ) are constants. With the increase of x ( x = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0), the calculated values of Δ E 2 are 0.38052, 0.41274, 0.43540, 0.46734, 0.53585, and 0.62716 eV, respectively.…”