HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS

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HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS ( handbook-onphysics-and-chemistry-rare-earths )

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Lanthanides in Luminescent Thermometry Chapter 281 371 FIG. 11 Schematic energy-level diagram of the three-level model of a typical luminescent ion. where g1 and g2 are the degeneracies of the 1 and 2 levels, DE is the energy difference between the barycenters of the 2!0 and 1!0 emission bands. The 2!0 (I02I2) and 1!0 (I01I1) intensity ratio (D) is given by: (25) kBT B1⁄4o02A02g2: o01 A01 g1 The two levels cannot be too far apart, otherwise thermalization is no longer observed. For DE ranging from 200 to 2000 cm1 the difference in the popula- tion of the emitting levels is such that they are considered “thermally coupled.” These empirical limits guarantee that the levels are spectrally separated and not too far away so that the exponential temperature decay rate (determined by DE) is small (Khalid and Kontis, 2009). The response of the detection system in the frequency range of the two transitions was taken into account in the I1 and I2 intensities. The absolute temperature is then estimated from: T1⁄4DE 1 (26) kB lnðB=DÞ in which DE is calculated using the formal definition of the barycenter of a J–J0 transition or, when there are experimental difficulties in assigning pre- cisely the Stark–Stark transitions, by fitting the envelope of the I1 and I2 tran- sitions (Balabhadra et al., 2015). The constant B can be determined from the plot of D vs pump power extrapolating the curve (that is generally linear for laser power densities of 100–300 W cm2) to the limit of zero pump power (DD0) corresponding to room temperature (Carlson et al., 2011; Debasu et al., 2013). Fig. 12A and B illustrates how the constants DE and B are IħoANoAgDE DE D1⁄4021⁄4 02 02 21⁄4 02 02 2exp  1⁄4Bexp  I01 ħo01A01N1 o01A01g1 kBT with

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