Boosting the Temperature Detection Accuracy of Luminescent

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Boosting the Temperature Detection Accuracy of Luminescent Ratiometric Thermometry via Multi–Function Fit Strategy Leipeng Li, Feng Qin, Yuan Zhou, Yangdong Zheng, Hua Zhao, and Zhiguo Zhang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06778 • Publication Date (Web): 01 Oct 2018 Downloaded from http://pubs.acs.org on October 6, 2018

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The Journal of Physical Chemistry

Boosting the Temperature Detection Accuracy of Luminescent Ratiometric Thermometry via Multi– Function Fit Strategy Leipeng Li,a Feng Qin,a,* Yuan Zhou,a Yangdong Zheng,b Hua Zhaoc and Zhiguo Zhanga,** a.

Condensed Matter Science and Technology Institute, Harbin Institute of Technology, Harbin,

150001, P.R. China. b.

Department of physics, Harbin Institute of Technology, Harbin, 150001, P.R. China.

c.

School of Materials and Engineering, Harbin Institute of Technology, Harbin, 150001, P.R.

China. Corresponding Author *([email protected]). ** ([email protected]).

ACS Paragon Plus Environment

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ABSTRACT. The influence of fit strategy on the temperature detection accuracy of luminescence ratiometric thermometry is investigated here. In the range of 303−783 K, the typical 2H11/2/4S3/2–4I15/2 upconversion emission lines of Er3+ embedded in calcium tungstate are investigated as a function of temperature. It is found that using the conventional one−function fit method over the whole temperature range leads to a mean error of 3.47 K. By contrast, the strategy, namely dividing the whole board temperature range into several narrow ones and using several fit functions over separate temperature scopes, is proposed and studied. It is demonstrated that as the number of the divided temperature scopes is increased, the measured temperature readout gradually approaches to the true value of the temperature. When the number is set to be six, the temperature error sharply goes down to 0.41 K, suggesting that the newly proposed multi−function fit strategy is superior to the traditional one−function fit method, especially when a board temperature scope is involved. The reason responsible for this phenomenon is also discussed.


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INTRODUCTION As is well known, temperature is one of the most significant parameters and plays a key role in many fields.1-10 Among various temperature measurement methods, luminescent ratiometric technology based on the Boltzmann distribution is taken as the most promising one for its non– contact pattern, relatively high thermal sensitivity, considerable spatial and temporal resolutions, etc.11-20 So far, lots of excellent reports concerning this advanced technology have been achieved.21-33 From these work, it can be concluded that boosting the temperature detection accuracy is always one of the most important goals in this field.34-38 After careful observation of the work reporting this issue, it is found that only one fit function (or calibration curve) is, in general, used to describe the luminescence intensity ratio as a function of temperature, regardless of the temperature scope.39-48 Undeniably, it works well in lots of cases where the temperature scope is relatively narrow. For instance, Vetrone et al. successfully monitored the intracellular temperature of a single living HeLa cell using the 2

H11/2/4S3/2–4I15/2 upconversion emission lines of Er3+ in the physiological temperature range

from 298 to 318 K.49 However, this strategy probably cannot ensure an accurate temperature measurement when it comes to a wide temperature scope. It is because that in addition to the Boltzmann distribution, many other mechanisms are also known to be temperature dependent. In this case, using one fit function over a wide temperature scope is likely to have an effect on the final temperature readout. Therefore, it is highly necessary to solve the problem, aiming to boost the temperature detection accuracy. In fact, if the temperature scope involved is narrow enough, other mechanisms, which do not include the Boltzmann distribution, can be neglected or taken as unchanged. It is thus followed by the confusion that to which degree the temperature scope is


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decreased, could the temperature detection accuracy be greatly increased? This issue is of great significance for luminescent ratiometric thermometry’s practical applications in the future. Therefore, in order to make a clear investigation on the issue, we elaborately design the experiments and use the 2H11/2–4I15/2 and 4S3/2–4I15/2 luminescence bands of Er3+ as examples in this work. Following the NIR irradiation by a 980 nm laser diode, the luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions of Er3+ is studied as a function of temperature between 303 and 783 K. It is demonstrated that using one–function fit method over the whole experimental temperature scope leads to a mean error of 3.47 K. To achieve the more accurate temperature measurement, here we introduce a strategy, i.e., using several functions over the different small temperature scopes. With the use of this strategy, the average temperature detection error is found to be as low as 0.41 K when the whole temperature range is divided into six parts. In addition, the reason responsible for the difference between the conventional one–function fit method and this newly used strategy is discussed. EXPERIMENTAL The CaO, WO3, Yb2O3, Er2O3 particles (>99.99%) are all of analytical purity. All involved chemicals were used as purchased without any further purification. The CaWO4:10%Yb3+– 1%Er3+ phosphors were prepared via the traditional high−temperature solid−state method, of which the specific procedures could be found elsewhere.50 The mole percentage ratio of the Yb2O3 to Er2O3 was set to be 10:1. Thepowder X-ray diffraction (XRD) patterns of the phosphors were carried out (Rigaku D/MAX-2600/PC with Cu Kα radiation, λ=1.5406 Å) at room temperature. A continuous wave 980 nm laser diode, whose current and output were controlled by the adjustor (ITC-4005,


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Thorlabs), was used as the excitation source. A spectrometer (MayaPro 2000, Ocean Optics) was used to collect the emission spectra focused by a lens with f=3.8 cm at different temperatures over the range between 303 and 783 K. The sample was heated by a home–made heating chamber with an accuracy of ±0.3 K. RESULTS AND DISCUSSION The phosphors were prepared successfully with the scheelite phase (see Figure. S1, Supporting Information).50 Following the NIR excitation by a 980 nm laser diode, the phosphors emit the characteristic upconversion (UC) green luminescence, which is presented in Figure 1(a). As can be observed, each luminescence spectrum consists of the left and right spectral parts, peaking at 525 and 550 nm, respectively. It is known that these two luminescence spectra can be ascribed to the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions of Er3+, respectively.51-55 The specific UC processes responsible for these two transitions are also depicted (see Figure. S2, Supporting Information).

Figure 1. (a) Temperature dependent UC emission spectra of the phosphors following the NIR excitation at 980 nm; (b) Luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2


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transitions of Er3+ (∆1 and ∆2) as a function of temperature in the range of 303−783 K. ∆1 is the ratio used to obtain the calibration curve and ∆2 is the ratio used to check the calibration curve. As can be observed from Figure 1(a), the 525 nm emission band increases first and then decreases as the temperature is increased from 303 to 783 K. In contrast, the 550 nm emission line decreases monotonically in the whole temperature range. By integrating the emission spectral lines, the luminescence intensity ratio between the 525 nm (the 515.63–535.79 nm range) and 550 nm band (the 535.79–560.48 nm range), ∆520/550, can be obtained (see Figure. S3, Supporting Information). It can be seen that at each selected temperature, the ratio fluctuates slightly around a mean value. Moreover, the ratio increases gradually as the temperature is increased from 303 to 783 K. This phenomenon could be expressed as follows. As is known, the luminescence intensity ratio, ∆, between the lines emanating from two closely separated excited states can be described as a function of temperature by using the Boltzmann distribution:12

∆ = A exp(-

∆E ) kT ,

(1)

where A is a constant, ∆E is the energy gap between two closely separated excited states, k is the Boltzmann constant and T is the absolute temperature. From Figure 1(a), it is known the gap that separates the 2H11/2 and 4S3/2 states is around 700 cm-1. Obviously, this value is equal to several kTs at room temperature, leaving there strong thermal excitation between the 2H11/2 and 4S3/2 states. Therefore, the populations of these two states follow the Boltzmann distribution, which means that the intensity ratio between the bands separately emanating from the 2H11/2 and 4S3/2 states would increase constantly with the rise of temperature.


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Figure 1(b) shows the ∆520/550 as a function of temperature. Note that the ratios marked as red triangles are obtained at 303, 343, 383, 423, 463, 503, 543, 583, 623, 663, 703, 743 and 783 K, which are used to obtain the calibration curve. While the blue dots, obtained at 323, 363, 403, 443, 483, 523, 563, 603, 643, 683, 723 and 763 K, are the ratios used to check the calibration curves. In the following part several fit strategies for these ratios will be discussed.

Figure 2. (a) Luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions of Er3+ and (b)the temperature errors with the use of 1–function fit strategy as a function of temperature.


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The first fit strategy is the conventional method, namely using one function to describe all the luminescence intensity ratios between the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions as a function of temperature over the whole range from 303 to 783 K. Obviously, based on this strategy, only one calibration function could be obtained through Equation (1), and the fit result is presented in Figure 2(a). The fit results are A=17.94 and ∆E/k=963.96 K. So far, there are lots of related articles reporting the temperature resolution, which is a very significant parameter to value the performance of various temperature sensors. According to the reports, the best temperature resolution based on luminescent ratiometric technology could be as low as 0.02 K.38 It indicates that luminescent ratiometric technology is a promising candidate for temperature measurement in many fields, ranging from biological domain to micro– and nano– scale circuit system. In addition to the temperature resolution, the temperature detection error (or accuracy) is also an important parameter to describe the temperature sensing ability. Compared with the former parameter, the latter one is, however, seldom investigated in the literature. The significance of temperature detection error is not difficult to be understood. For instance, we suppose that a temperature sensor owns a temperature resolution better than 0.001 K at room temperature. However, its temperature detection error is likely to be larger than 1 K. In this case, the best temperature resolution of 0.001 K seems to be meaningless. In fact, only the temperature resolution and the temperature detection error are ideal can a temperature sensor be ideal. Therefore, the temperature detection error should gain more attention in the following work concerning luminescent ratiometric thermometry. And naturally, this parameter becomes the focus in this work. Based on Equation (1), we have:


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Tmea = -

∆E / k ∆ . ln( ) A

(2)

As mentioned above, the fit parameters are A=17.94 and ∆E/k=963.96 K. The luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions, marked as blue dots presented in Figure 1(b), are then substituted into Equation (2). And the measured temperature, Tmea, can be obtained. Subsequently, the temperature error, that is, (Tmea-Treal) where Treal is the practical temperature, can be achieved. As can be observed from Figure 2(b), the maximum temperature error reaches up to 7.95 K at 643 K. Over the whole temperature range between 323 and 763 K, the average absolute temperature error is calculated to be 3.47 K. This temperature error is, obviously, too high to deviate from the goal of luminescent ratiometric thermometry, that is, accurate temperature measurement. This result largely goes beyond the expectation. It suggests that the conventional method, i.e., using one function to describe ∆525/550 and temperature over a board temperature range (here it is 303–783 K), goes against the high–accuracy thermal sensing by using luminescent ratiometric technology. In the following part, the X–function (X>1) fit strategies are used. For 2–function fit strategy, the average temperature error over the whole temperature range from 323 to 763 K is calculated to be 2.11 K (see Figure. S4 and discussion S1, Supporting Information). When the whole temperature range 303–783 K is divided into three uniform small ones, this error goes down to 1.03 K (see Figure. S5 and discussion S2, Supporting Information). In addition, if the 303–783 K range is further divided into four small temperature ranges uniformly, the mean temperature error based on this 4–function fit strategy is 0.60 K (see Figure. S6 and discussion S3, Supporting Information). Obviously, as the number of divided small temperature scopes increases, the


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measured temperature, based on the luminescence intensity ratio between the 2H11/2–4I15/2 and 4

S3/2–4I15/2 transitions, gradually tends to be the real value.

Figure 3. (a) Luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions of Er3+ and (b) the temperature errors with the use of 6–function fit strategy as a function of temperature. Figure 3(a) presents the fit results using the 6–function fit method in the range of 303–783 K. The specific procedures are as follows. Firstly, the whole temperature range, that is, the 303–783 K, is divided into six small ranges uniformly. Therefore, these small uniform ranges are 303−383, 383−463, 463−543, 543−623, 623−703 and 703−783 K, respectively. In each temperature range,


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we can obtain one fit curve with the use of Equation (1). On the basis of the 6–function fit method proposed, the following expression could be achieved:

977.56  18.79 exp(- T )  18.51exp(- 972.13 )  T  19.08exp(- 985.81)  T ∆= 19.70 exp(-1003.19 ) ,  T  923.71 17.36 exp() T   754.13 ) 13.64 exp( T Based

on

Equations

303 − 383K 383 − 463K 463 − 543K 543 − 623K .

(3)

623 − 703K 703 − 783K

(2)

and

(3),

the

temperature

errors

obtained

at

323/363/403/443/483/523/563/603/643/683/723/763 K could be calculated, which are shown in Figure 3(b). The average temperature error over the whole temperature range is calculated to be 0.41 K. For the conventional 1−function fit method, this mean error is calculated to be 3.47 K, which is nearly one order of magnitude higher than 0.41 K. Obviously, the 6–function fit strategy is able to obtain a more accurate temperature readout than the conventional one. Moreover, the 12−function fit method is also used (see Figure. S7 and discussion S4, Supporting Information). Based on this multi–function fit method, the mean temperature error further decreases to 0.35 K.


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Figure 4. Comparison of the average temperature errors with the use of X–function (X=1, 2, 3, 4, 6 and 12) fit methods. The comparison of the temperature errors obtained using the X–function (X=1, 2, 3, 4, 6 and 12) fit methods is presented (see Figure S8, Supporting Information). It can be seen that with the rise of X from 1 to 12, the temperature errors, obtained at each temperature, progressively tends to be zero. Figure 4 presents the comparison of the average temperature errors obtained based on the X–function (X=1, 2, 3, 4, 6 and 12) fit methods as a function of the function number used. As can be observed, as the function number increases gradually (or as the whole temperature range is divided into more narrow sections), the mean temperature error decreases markedly from 3.47 to 0.35 K. These facts suggest, undoubtedly, that when it comes to a board temperature scope (here it is 783-303=480 K), using the conventional 1–function fit strategy seems to be powerless for achieving an accurate temperature measurement. In stark contrast, the X–function (X>1) fit method is demonstrated to be an effective strategy to detect the temperature with a low temperature error. More importantly, according to the practical requirement, this accuracy could


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be easily adjusted by selecting a suitable function number. In addition, the Y2O3:Yb3+-Er3+ phosphors were also prepared and studied based on the same processes imposed on the CaWO4:Yb3+-Er3+ phosphors (see Figure. S9, S10 and discussion S5, Supporting Information). These results indicate that the proposed procedure is universal to some degree.

Figure 5. Comparison of the fitted energy gaps with the use of X–function (X=1, 2, 3, 4, 6 and 12) fit methods. The reason responsible for the difference among these X–function (X=1, 2, 3, 4, 6 and 12) fit methods is then analysed. Ideally, there should be only one function describing the luminescence intensity ratio between the two lines versus the temperature, regardless of the temperature scope involved. To be more specific, when the whole temperature scope studied in our work, that is 480 K (from 303 to 783 K), is divided into six narrow sections, six fit functions should be used to obtain the calibration curves. In this case, all these six fit functions should be almost the same with each other. Figure 5 shows the comparison of the fitted energy gaps with the use of X– function (X=1, 2, 3, 4, 6 and 12) fit methods. As can be observed, all these fitted energy gaps


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present the same variation tendency. For each X–function (X=1, 2, 3, 4, 6 and 12) fit method, the fitted energy gap fluctuates slightly and then decreases gradually with the temperature. It is also demonstrated that the fitted pre−exponential factors present the similar variation law with that of the fitted energy gaps depicted in Figure 5 (see Figure S11, Supporting Information). On the basis of the expectation, all these fitted energy gaps should be identical with each other. The fact presented in Figure 5 differs from the expectation to a large extent. It suggests that in addition to the thermal effect between the 2H11/2 and 4S3/2 states, other temperature dependent mechanisms may play a key role in determination of the luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions. Furthermore, considering that the fitted gap decreases gradually with the temperature, these other temperature dependent mechanisms, imposed on the 2H11/2 and 4S3/2 states, should diminish the luminescence intensity ratio between the two transitions. As is known, the lanthanides’ luminescence is sensitive to the temperature changes. Generally, their intensities, due to the thermal quenching mechanism, would decrease as the temperature is increased. Therefore, thermal quenching is likely to play a role in diminishing the luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2 transitions, thus leading to a gradually decreasing energy gap shown in Figure 5. Obviously, this issue deserves for further investigation in the future. It is known that the relative sensitivity, Sr, is a key parameter to value the performance of different temperature sensors. It could be expressed as:

Sr =

d∆ 1 dT ∆ .

(4)

Substituting Equation (1) into Equation (4), we have:


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Sr =

∆E kT 2 .

(5)

It can be concluded from Equation (5) that the larger the ∆E is, the larger the Sr is. As presented in Figure 5, the fitted ∆E is not a constant but varies with the use of the proposed multi-function fit strategy. Therefore, on the basis of Equation (5), the Sr would be affected by this fit method. Figure 6(a) shows the Sr based on the X–function (X=1, 2, 3, 4, 6 and 12) fit method. As can be observed, the Sr shows a slight dependence on the function number used. Figure 6(b), (c) and (d) present the comparison of the relative sensitivities with the use of the X-function (X=1, 2, 3, 4, 6 and 12) fit method at 323, 643 and 763 K, respectively. From the foregoing discussion we know that with the increase of the function number used, the calibration curves become closer to the experimental data points. It indicates that the calculated relative sensitivity could reflect more the practical value of the prepared material. Therefore, the relative sensitivity achieved by the 12function fit method could be regarded as the true sensitivity. As can be observed from Figure 6(b), the Sr increases gradually with the increase of the function number used, meaning that 1function fit method underestimates the relative sensitivity in relatively low temperature range. Figure 6(c) indicates that as the temperature goes higher, the sensitivity calculated by the Xfunction (X=1, 2, 3, 4, 6 and 12) fit method keeps nearly unchanged. Moreover, one can see from Figure 6(d) that in relatively high temperature range, 1-function fit method slightly overestimates the thermal sensitivity. It is not difficult to know that the absolute sensitivity, Sa, should obey the same change law with the relative one at the same temperature as Sa=∆Sr (see Figure S12, Supporting Information).


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Figure 6. (a)Comparison of the relative sensitivities with the use of the X-function (X=1,2,3,4,6,12) fit method in the experimental temperature range; (b),(c) and (d) show the comparisons of the relative sensitivities with the use of the X-function (X=1,2,3,4,6,12) fit method at 323, 643 and 763 K, respectively. CONCLUSIONS In summary, we have demonstrated that the conventional procedure, namely using one fit function to describe the luminescence intensity ratio between the 2H11/2–4I15/2 and 4S3/2–4I15/2 lines as a function of temperature from 303 to 783 K, leads to a temperature error up to 3.47 K. To achieve a more accurate temperature measurement, a strategy is introduced here, that is, using several functions over the different small temperature scopes. With the use of the 6–function fit strategy, the average temperature detection error in the range of 303–783 K is found to be as low


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as 0.41 K. Moreover, it has been confirmed that with the increase of the function number used, the measured temperature readout tends to be the practical value. Therefore, our work presents an effective strategy to boost the temperature detection accuracy for luminescent ratiometric thermometry, and it may deserve for popularization in practical applications in the future. ASSOCIATED CONTENT Supporting Information The following files are available free of charge. XRD of the phosphorS; energy level diagrams of Yb3+–Er3+ system; ∆525/550 versus temperature; X–function (where X=2, 3, 4, 12) fit results for ∆525/550 and temperature errors based on this method, and discussions for this strategy; Comparison of the temperature errors, as well as the pre-exponential factors obtained by using the X–function (X=1, 2, 3, 4, 6 and 12) fit method; Study on Y2O3:Yb3+-Er3+ phosphors with the use of same strategy; Influence of the X–function (X=1, 2, 3, 4, 6 and 12) fit method on the absolute sensitivity (PDF) AUTHOR INFORMATION Corresponding author *E-mail: [email protected]. **E-mail: [email protected]. ORCID Feng Qin: 0000-0003-4696-5142 Notes The authors declare no competing financial interests.


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ACKNOWLEDGMENT This work was supported by the National Natural Science Foundation of China (NSFC) (Grant No. 81571720 & 61505045). REFERENCES (1) Quintanilla M.; Liz-Marzán, L. M. Guiding rules for selecting a nanothermometer. Nano Today 2018, 19, 126–145. (2) Kucsko, G.; Maurer, P. C.; Yao, N. Y.; Kubo, M.; Noh, H. J.; Lo, P. K.; Park, H.; Lukin, M. D. Nanometre-scale thermometry in a living cell. Nature 2013, 500, 54–58. (3) Ke, G.; Wang, C.; Ge, Y.; Zheng, N.; Zhu, Z.; Yang, C. J. L-DNA molecular beacon: a safe, stable, and accurate intracellular nano-thermometer for temperature sensing in living cells. J. Am. Chem. Soc. 2012, 134, 18908−18911. (4) Gao, G.; Busko, D.; Kauffmann-Weiss, S.; Turshatov, A.; Howard, I. A.; Richards, B. S. Wide-range non-contact fluorescence intensity ratio thermometer based on Yb3+/Nd3+ co-doped La2O3 microcrystals operating from 290 to 1230 K. J. Mater. Chem. C 2018, 6, 4163−4170. (5) Childs, P. R. N.; Greenwood, J. R.; Long, C. A. Review of temperature measurement. Rev. Sci. Instrum. 2000, 71, 2959. (6) Wang, X.; Liu, Q.; Bu, Y.; Liu, C.; Liu, T.; Yan, X. Optical temperature sensing of rare-earth ion doped phosphors. RSC Adv. 2015, 5, 86219–86236. (7) Marciniak, L.; Waszniewska, K.; Bednarkiewicz, A.; Hreniak, D.; Strek, W. Sensitivity of a nanocrystalline luminescent thermometer in high and low excitation density regimes. J. Phys. Chem. C 2016, 120, 8877–8882. (8) Marciniak, L.; Prorok, K.; Bednarkiewicz, A. Size dependent sensitivity of Yb3+,Er3+ upconverting luminescent nano-thermometers. J. Mater. Chem. C 2017, 5, 7890–7897. (9) Cai, P.; Wang, X.; Seo, H. J. Excitation power dependent optical temperature behaviors in Mn4+ doped oxyfluoride Na2WO2F4. Phys. Chem. Chem. Phys. 2018, 20, 2028–2035.


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Table of Contents Graphic


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Boosting the Temperature Detection Accuracy of Luminescent

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