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356 Handbook on the Physics and Chemistry of Rare Earths changes in D, dT is given by the Taylor’s series expansion of the tempera- ture variation with D: dT1⁄4@TdD+ 1 @2TðdDÞ2 +⋯+ 1 @nTðdDÞn (6) where dD is the uncertainty in the determination of D. Considering that the expansion in T is dominated by the first term (Baker et al., 2005), Eq. (6) can be written in terms of Sr: dT 1⁄4 1 dD (7) Sr D pointing out that dT is dependent on the thermometer performance (quantified by the relative sensitivity) and experimental setup (that limits dD/D, as dis- cussed in Section 3.2.1). For typical portable detection systems, dD/D can reach 0.1%, at best, meaning that typical sensitivities of 1–10%K1 (Brites et al., 2012) correspond to temperature uncertainties of 0.01–0.1 K, respec- tively. With more sensitive detectors, eg, photomultiplier tubes (PMTs) and charge-coupled devices (CCDs), dD/D1⁄40.03%, and dT<0.003 K. This is an impressive temperature resolution compared with that can be achieved with other techniques, such as wired thermistors (0.01 K) and noncontact infrared cameras (1.0 K). 3.2.1 Measuring the Intensity Uncertainty The uncertainty on intensity measurements (dI) is mainly determined by the nature of the detector. Commercial detectors include, in ascending order of its sensitivity on intensity discrimination, photodiode arrays (PDAs), CCDs, and PMTs. The comparison of several detectors is not straightforward as different approaches use distinct parameters to quantify the device performance. Here we adopt the photosensitivity (SF), measured in A W1 (ampere of detection signal per Watt of incident photon). The conversion between the manufacturers’ reported quantum efficiency (QE) and SF is given by (Zalewski and Duda, 1983): SF 1⁄4 QE l (8) hc where l is the wavelength in nanometers, h is the Planck constant and c is the speed of light in vacuum. The most common PDAs are typically fabricated using Si photodiodes covering the spectral range from the UV to the near infrared (NIR). The man- ufacturers point out high-speed response, high sensitivity and low noise, as the main advantages, and they are well implemented in portable spectrometers, due to their relatively low cost when compared with other detection devices. Typically, the maximum photosensitivity in the visible spectral region is @D 2!@D2 n!@DnPDF Image | HANDBOOK ON THE PHYSICS AND CHEMISTRY OF RARE EARTHS
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