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370 Handbook on the Physics and Chemistry of Rare Earths 4.1 Single-Center Emission The ratio of the emission intensities of two distinct transitions from the same emitting center provides a robust temperature measurement approach, as men- tioned earlier. The most common examples of Ln3+-based ratiometric thermo- meters comprise Yb3+ ions as sensitizers and Er3+ (Alencar et al., 2004; Savchuk et al., 2014; Sedlmeier et al., 2012; Singh et al., 2009a, 2014; Vetrone et al., 2010a), Tm3+ (Dong et al., 2011; Lojpur et al., 2013; Pereira et al., 2015; Quintanilla et al., 2015; Sedlmeier et al., 2012), or Ho3+ (Lojpur et al., 2013; Savchuk et al., 2015; Sedlmeier et al., 2012; Xu et al., 2013) as upconverter activators. In fact, Maestro et al. demonstrated that NaYF4:Yb/Er UCNPs are the most efficient multiphoton excited fluorescent NPs developed to date, displaying larger relative multiphoton excited upcon- version efficiency (laser excitation intensities between 2 103 and 1106 W cm2) compared with those of commercial QDs (approximately 2 larger) and Au nanorods (almost 10) presently used for multiphoton fluorescence bioimaging (Maestro et al., 2010b). Less common examples involving Eu3+ (Meert et al., 2014; Yuasa et al., 2014), Nd3+, using two Stark components of the 4F3/2 multiplet (Benayas et al., 2015; Carrasco et al., 2015; Rocha et al., 2013, 2014a; Tian et al., 2014; Wawrzynczyk et al., 2012) or the 4F5/2, 4F3/2 ! 4I9/2 transitions (Balabhadra et al., 2015; Tian et al., 2014), Pr3+ (Zhou et al., 2014b), Sm3+ (Dramic ́anin et al., 2014), Dy3+ (Boruc et al., 2012; Edge et al., 2000), and Gd3+ (Zheng et al., 2013) were also reported. Illustrative examples of these luminescent thermometers are addressed in detail in Section 5. 4.1.1 Boltzmann Law The use of single-center luminescence line intensities as the thermometric parameter was described by Kusama et al. (1976) in a seminal work; for a review of the technique, see Collins et al. (1998) and Wade et al. (2003). The ratio of two energy-close emission intensities can be rationalized assum- ing the simplest model of Boltzmann thermal equilibrium between two emit- ting states, denoted by j1> and j2>, where W10 is the absorption rate from the ground state j0> to state j1> and the I0i (i1⁄41, 2) intensity (Fig. 11) is: I0i ∝ ħo0i A0i Ni (23) where A01 and A02 and o01 and o02 are, respectively, the total spontaneous emission rates and the angular frequencies of the 1!0 and 2!0 transitions, and N1 and N2 are the populations of states j1> and j2>. If these two levels are in thermal equilibrium (they are designated by “thermally coupled levels,” with separations of the order of the thermal energy), N1 and N2 are related by: g DE N1⁄4N 2 exp 21g1 kBT (24)PDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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