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380 Handbook on the Physics and Chemistry of Rare Earths intensity I1 and I2, and DE1i, and DE2i are the activation energies for the ther- mal quenching process of transitions with intensity I1 and I2, respectively. There are two particular cases of Eq. (37) that we want to discuss here: l One of the transitions (eg, I2) exhibits a temperature dependence much smaller than the other. l The exponential terms dominate the intensity of each transition, ie, 1≪aj exp DEj=kBT , j1⁄41, 2. In the first case, Eq. (37) becomes: D% X D0 (38) 1 + ia1i expðDE1i=kBTÞ The temperature dependence of this equation changes from an almost lin- ear relation (useful for a large temperature range, covering more than 100°) to a distinct S-shaped curve (of particular interest for a narrow temperature range, covering one or two tens of degrees), depending on DE1i and a1i. Although there are many luminescent thermometers presenting this functional form, eg, ZnxMn1xSe/ZnCdSe nanocrystals (Vlaskin et al., 2010), polymer dots (Gota et al., 2009; Ye et al., 2011), Tb3+/Eu3+ MOFs (Rao et al., 2013; Wei et al., 2015), and Tb3+/Eu3+ organic–inorganic hybrids (Brites et al., 2010, 2013b,c, 2016), the calibration curve was fitted to this model only in two examples (Ananias et al., 2015; Wang et al., 2015c). Ananias et al. reported a cryogenic luminescent thermometer based on the Na [(Gd0.8Eu0.1Tb0.1)SiO4] silicate exhibiting uncommon photoluminescence properties due to structural disorder and a phase transition (Ananias et al., 2015). The calibration curve was fitted using Eq. (38) for two deac- tivation channels: Tb3+-to-Tb3+ energy migration through multiple Tb3+ local sites, activation energy DE1, and Tb3+-to-Eu3+ energy transfer, with an activation energy DE2. On the other hand, Wang et al. reported the [(Tb0.914Eu0.086)2(pda)3(H2O)]2H2O nano-MOF, the first lanthanide-organic framework prepared by the spray-drying method, operating in the 10–325 K range (Wang et al., 2015c). The calibration curve was fitted using Eq. (38) with a single deactivation channel and the value obtained for the activation energy, DE 1⁄4 52.4 2.0 cm1, is in accord with the emission spectra suggest- ing that this nonradiative channel involves deactivation through the ligand levels, whose broad emission overlaps the 5D4 state. When the exponential terms dominate the intensity of each transition, Eq. (37) can be written as (assuming a single deactivation channel): 1+a expðDE=k TÞ a DE DE D1⁄4D2 2B%D2exp21(39) 0 1 + a1 expðDE1=kBTÞ 0 a1 kBT The most remarkable feature of this approximation is that Eqs. (39) and (25) have the same functional form and, thus, although we are dealing withPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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