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382 Handbook on the Physics and Chemistry of Rare Earths and the 5D4 (20,336.610.1cm1) and 5D0 (17,205.89.0cm1) emitting states, respectively. Eq. (39) yields E1 E2 1⁄4 3277 14 cm1, an energy dif- ference in accord with an energetic scheme in which the 5D4 depopulation occurs through the triplet of the acac ligand (25,3001250cm1) and the 5D0 one via the triplet of the APTES/TEOS hybrid host (20,768 2750 cm1). 4.2.2 Relative Sensitivity and Temperature Uncertainty. Illustrative Examples Whereas for the second particular case of Eq. (37), Sr and dT are given by Eqs. (29) and (30), respectively, for the first case Sr is given by (assuming a single deactivation channel): Sr 1⁄4 DE1a1 expðDE1=kBTÞ 1⁄4 DE1 kBT21⁄21+a1expðDE1=kBTÞ kBT21⁄2ð1=a1ÞexpðDE1=kBTÞ+1 (40) Typically, Sr(T) presents a bell-shaped profile that peaks at the inflection point of the S-shaped calibration curve and with a width determined by the activation energy DE1 and the kinetic constant a1. The correspondent uncer- tainty in temperature is given by: (41) which depends critically on DE1 and a1 and its general form is a U-shaped curve, with minimum at the temperature of the maximum sensitivity Sm. In order to compare the features of the single- and dual-center luminescent thermometers, we plot the calibration (Eqs. 25 and 38), sensitivity (Eqs. 29 and 40), and temperature uncertainty (Eqs. 30 and 41) curves in Fig. 18. The para- meters used are B1⁄44.0, a1⁄43000, D01⁄40.5, dD/D1⁄40.5%, and DE1⁄4600, 800, 1000cm1. Increasing or decreasing a by one order of magnitude only stretches or shrinks the profile of the S-shaped curve. Whereas dual-center ther- mometers seem to be more effective in the cryogenic range, in which values of Sm 1⁄43%K1 and dT1⁄40.2 K can be reached with portable spectrometers, single-center thermometers, however, are operative at higher temperatures (T>300 K) with Sm $0.5–1%K1 and dT$0.5 K. Furthermore, for the same DE value there is a notorious similarity of the Sr curves for higher temperatures (T > 250 K), corroborating the approximation that leads to Eq. (39) (the domi- nance of the exponential term) with the same functional form of Eq. (25). Organic–inorganic hybrids comprising [Ln(btfa)3(MeOH)(bpeta)] (Ln1⁄4Eu, Tb) complexes embedded into APTES/TEOS- and N-(triethoxysilylpropyl)-O- polyethylene oxide urethane/TEOS-based NPs and into diureasil films are examples following the temperature dependences of Eqs. (38), (40), and (41) (Fig. 19). The first excited triplet state of these three distinct hybrid hosts works as a “population storage reservoir,” as it occurs in typical E-type k T2 1 DE !dD dT1⁄4B exp 1+1 DE1a1 kBT DPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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