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378 Handbook on the Physics and Chemistry of Rare Earths (D) Two Ln3+ ions indistinguishably employed as the probe or the reference, in which ion–ion energy transfer regulates the changes in the intensity ratio. Examples include Tb3+/Eu3+ (Liu et al., 2005; Sato et al., 1989) and Yb3+/Nd3+ (Marciniak et al., 2015). (E) Two Ln3+ ions embedded into a polymer or an organic–inorganic hybrid host in which changes in D are controlled by thermally activated ion-to- host energy transfer, eg, Tb3+/Eu3+ complexes incorporating into hybrid hosts (Brites et al., 2010, 2013b,c; Wang et al., 2014, 2015c). Illustrative examples of these luminescent thermometers are addressed in detail in Section 5. 4.2.1 Intensity vs Temperature: Sigmoidal Dependence Among the five classes listed earlier, examples involving direct ion!ion energy transfer and energy transfer through excited levels of the ligands or host matrix, listed as (D) and (E), respectively, show the same functional form for D(T): a S-shaped curve, which clearly deviates from an exponential inten- sity ratio profile, especially for T<200K, Fig. 16. Examples involving no-interacting Ln3+ ions, class (C), show a Boltzmann dependence for D(T), whereas those belonging to classes (A) and (B) do not present a unique trend and, thus, will not be discussed here. Similarly to what was done using the Boltzmann law in single-center- based luminescent thermometers (Section 4.1), it is also possible to rationalize the D(T) dependence for dual-center-based ones. The analysis presented next follows the discussion of Cooke et al. (1998, 2004) that extends the classical Mott–Seitz model (Mott, 1938; Seitz, 1939) for competition between radiative FIG. 16 Illustrative examples of S-shaped curves. The full circles correspond to Tb3+-to-Eu3+ energy transfer (Liu et al., 2005) in sol–gel-derived glasses, whereas the other symbols correspond to Yb3+-to-Nd3+ energy transfer in LiLa0.9x Nd0.1YbyP4O12 (Marciniak et al., 2015). The solid lines are guides to the eyes.PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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