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362 Handbook on the Physics and Chemistry of Rare Earths FIG. 6 Temperature uncertainty estimated from Eq. (19) for T 1⁄4 300 K. The gray shadowed area represents the temperature uncertainty below the minimum values resulting from the spin- boson model (Alicki and Leitner, 2015). The inset shows a magnification of the region of dT < 0.5 K where the values assigned to portable detectors and PMTs are highlighted and the corresponding numbers of particles given. and more sensitive detectors (dT<0.001K) at 300K, we find Na>3105 and Na>11011, respectively, for the minimum number of atoms constitut- ing the thermal probe (Fig. 6). The model was also tested for (Gd0.991Nd0.009)2O3 nanorods (Balabhadra et al., 2015). A temperature uncertainty of dT1⁄40.140.05 K (at 288 K) was calculated using the relative sensitivity and the dD/D value, Eq. (7), while the value estimated with Eq. (18), TD1⁄4362K and Na1⁄4(1.50.5)105, is 5 larger (Balabhadra et al., 2015). We emphasize that the number of atoms in a single nanorod is sufficient to assure, in the due time, equilibrium for any state function to be measured. Moreover, the calculus using Eq. (7) takes into account not a single NP but an ensemble of nanorods in thermal contact. In fact, considering 20–30 nanorods in contact, as shown in Fig. 2A of the refer- ence, the agreement between theoretical (0.14–0.18 K) and experimental (0.16 K) uncertainties is very good and the theoretical temperature uncertainty (Eq. 7) should be the upper limit of the experimental temperature error. 3.3 Spatial and Temporal Resolution When the temperature is measured in different spatial positions, the spatial resolution of the measurement (dx) is defined as the minimum distancePDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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