“…The decay of Sm 3+ emissions can be fitted by exponential functions obtained from modified Arrhenius expression for a single barrier thermal quenching model: , τ T = τ 0 / ( A + B exp false( − E a / k B T false) ) where τ 0 and τ T denote the lifetimes at initial temperature ( T 0 ) and at temperature ( T ), E a is the activation energy for thermal quenching, A , B , and C are constants, and k B is the Boltzmann constant, respectively. An activation energy of 4027 ± 792 cm –1 was calculated from the exponential fit (τ T /τ 0 = 1/[0.98 + 1.05exp(−4027/(0.695 T ))]) shown in Figure f.…”