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Lanthanides in Luminescent Thermometry Chapter 281 379 and nonradiative transitions within a luminescence center. The model describes the total transition probability of an emitting level by the sum of radiative and nonradiative transition probabilities (AR and ANR, respectively). This can be evaluated by the inverse of the lifetime t of the emitting level: 11⁄41+ 1 (32) t tR tNR where tR is the radiative lifetime (assumed to be temperature indepen- dent and equal to t0, the lifetime intensity at T1⁄40K) and tNR is the nonradiative lifetime that is described by the Arrhenius dependence: tNR 1⁄4tNRð0ÞexpðDE=kBTÞ where tNR(0) stands for the nonradiative decay time at T 1⁄4 0 K and DE for the activation energy of the thermal quenching process. Solving Eq. (32), we can write: t1⁄4 t0 (33) 1+aexpðDE=kBTÞ where a1⁄4ANR/AR. When more than one quenching process is present, the above expression should be generalized including the deactivation though all the channels: t1⁄4 X t0 (34) 1+ iaiexpðDEi=kBTÞ The integrated luminescence intensity, I, may be related with t as (Duarte et al., 1999; Stalder et al., 1992): GI 1⁄4t (35) 00 where G0 is the beam intensity at T 1⁄4 0 K. Combining Eqs. (34) and (35) it follows: I1⁄4 X G0 (36) 1 + iai expðDEi=kBTÞ According to Eq. (1) (the definition of D), the temperature dependence of D is given by: 1 + 1⁄4D 1+Xia2iexpðDE2i=kBTÞ 0 1 + ia1i expðDE1i=kBTÞ X ia2i expðDE2i=kBTÞ G02 G01 1 + ia1i expðDE1i=kBTÞ D1⁄4X X (37) where D0 1⁄4 G01/G02, a1i, and a2i stand for the ratios between the nonradiative and radiative probabilities of the i deactivation channel of transitions withPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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