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Lanthanides in Luminescent Thermometry Chapter 281 373 measured with a thermocouple immersed into the suspension and the temper- ature calculated using Eq. (26). We observe a perfect match between the two temperatures indicating that the local heating induced by the laser on the NPs is unimportant at this concentration and laser power density (1.6 W cm2). 4.1.2 Boltzmann Law for Overlapped Transitions In the literature, we found several examples in which the temperature depen- dence of the intensity ratio of two-overlapped transitions was modeled through a slightly different form of Eq. (25): DE D1⁄4Bexp kBT +C (27) where C is a constant. These examples comprise either two Stark components of the same Ho3+ level (Savchuk et al., 2015) or two distinct transitions of Tm3+ (Xing et al., 2015; Xu et al., 2012; Zhou et al., 2014a), Fig. 13. In general, the arguments used to apply Eq. (27) are based on the work developed by Wade et al. for optical fiber-based thermometers (Wade et al., 2003) in which: n D1⁄4 2 Bexp n1 DE m + 1 (28) kBT n1 where ni (lower level i1⁄41 and upper level i1⁄42) defines the fraction of the total intensity of the transition originating from level i effectively measured by the detector for the i level and mi defines the fraction of the total intensity from level i which is measured by the detector for the other thermalizing level (Wade et al., 2003). We should stress, however, that Wade’s work addressed the problem of how to include intensities measured by two detectors with overlapped spectral ranges in Eq. (25), a limitation that does not occurs in the works mentioned earlier when the emission spectrum is measured by a single detector. Although the use of Eq. (27) is being increasingly disseminated, we must draw attention on the fact that it underestimates Sr, as we will show next. Tak- ing the example of NaYF4:Yb3+/Tm3+@Pr3+ core–shell NPs (Zhou et al., 2014d), we can access to the integrated intensities of each transition without the overlap contribution fitting the emission spectrum to a set of Gaussian (or Lorentzian) functions, a routine procedure that overcomes the experimen- tal difficulties in assigning precisely all the Stark components. For the spec- trum recorded at 510 K (the one in which the overlap is more evident, Fig. 13A), we used four Gaussian peaks to reproduce the envelope of the 1G4!3F4 and 3F2,3!3H6 Tm3+ transitions (Fig. 13B). The good agreement obtained between the DE value resulting from the barycenter of the deconvoluted transitions (2425 15 cm1) and that reported by Bai et al. in LaF3:Yb3+/Tm3+ (1894–2635 cm1) (Bai et al., 2012) supports the procedure.PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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