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Optical temperature sensing of NaYbF4: Tm3+ @ SiO2 core-shell micro-particles induced by infrared excitation

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Abstract

NaYbF4:Tm3+@SiO2 core-shell micro-particles were synthesized by a hydrothermal method and subsequent ultrasonic coating process. Optical temperature sensing has been observed in NaYbF4: Tm3+@SiO2 core-shell micro-particles with a 980 nm infrared laser as excitation source. The fluorescence intensity ratios, optical temperature sensitivity, and temperature dependent population re-distribution ability from the thermally coupled 1D2 /1G4 and 3F2 /3H4 levels of the Tm3+ ion have been analyzed as a function of temperature in the range of 100~700 K in order to check its availability as a optical temperature sensor. A better behavior as a low-temperature sensor has been obtained with a minimum sensitivity of 5.4 × 10−4 K−1 at 430 K. It exhibits temperature induced population re-distribution from 1D2 /1G4 thermally coupled levels at higher temperature range.

© 2013 Optical Society of America

1. Introduction

In recent years, research on rare-earth ions doped luminescence heterojunction materials has developed tremendously because of their wide applications in nanoscale biological fluorescence label, solar cells, laser materials, tricolor display technology and so on [16]. Inorganic fluorides have the advantages of intrinsic low phonon energy and high chemical stability, and thereby are often employed as core-shell host materials to obtain the desirable upconversion and downconversion luminescence emissions. Chen et al. reported a method to achieve efficient dual-mode luminescence of Eu3+ in β-NaGdF4: Yb,Tm/NaGdF4: Eu core/shell nanocrystals [7]. Capobianco and associates reported a method to enhance the Er3+ upconversion luminescence in active-core/active-shell NaGdF4:Er3+,Yb3+/NaGdF4: Yb3+ nano-particles [8]. Liu et al. reported a strategy to eliminate deleterious cross-relaxation from energy transfer between activator centre ions by gadolinium sublattice-mediated energy migration in NaGdF4:Yb,Tm/ NaGdF4:X nano-particles [9]. Prasad and associates reported the application of α-NaYbF4:Tm3+/CaF2 core/shell nanoparticles with efficient near-infrared to near-infrared upconversion in high-contrast deep tissue bioimaging [10]. Despite excellent luminescence emissions, the optical-thermal character in the core/shell fluoride nanomaterials has been reported rarely, and it remains a large area worthy of exploration in photoluminescence process.

Among fluoride materials, lanthanide ions doped fluoride nano-crystals are suitable to be as optical temperature sensing materials, due to their low phonon energy, high solubility, and high upconversion efficiency. Some trivalent rare-earth ions have a couple of adjacent thermally coupled levels with very small energy gap about 1000 cm−1, such as Er3+: 2H11/2 and 4S3/2, Tm3+: 3F2,3 and 3H4, Dy3+: 4I15/2 and 4F9/2, Eu3+: 5D1 and 5D0, Nd3+: 4F5/2 and 4F3/2, and Pr3+: 3P1 and 3P0 and so on [1119]. These adjacent energy levels can be thermally populated and depopulated through modifying the host temperature environment around the rare earth ions. The luminescence intensity ratio originated from the two adjacent energy levels will change with external temperature. This temperature dependent fluorescence intensity ratio was reported as the precise probe in optical temperature fiber sensing [19,20]. Presently, optical temperature sensors based on intensity ratios were mainly studied in the medium temperature range from 280 K to 350 K in organic dyes, thermoresponsive polymers, mesoporous silica NPs, QDs, and Ln3+-based up-converting NPs and β-diketonate complexes [2126]. The optical thermometry has been reported rarely in the low temperature range from 5 K to 300 K.

However, lanthanide ions doped fluoride nano-crystals are easy oxidized at high temperature. To overcome this, SiO2 coated fluoride nano-crystals may be a good core-shell heterojunction materials for optical temperature sensor. The SiO2 shell protects the NaYbF4:Tm3+ luminescent centre in the core from non-radiative decay caused by surface defects [8], and also from oxidization at high temperature. Among the fluoride crystals, the NaYbF4 crystals has low phonon energy and high chemical stability, and offers sufficient Yb3+ ions with long excited level life as energy-transfer donor ion to sensitize an energy acceptor Tm3+ ion under 980~1000 nm excitation [27]. It was reported that the hexagonal Tm3+-doped NaYbF4 crystals emitted strong blue luminescence and weak red luminescence [28], and the cubic Tm3+-doped NaYbF4 crystals emitted strong red luminescence and weak blue luminescence under 980 nm excitation [10]. Optical-thermal character in blue and red wavelength regions will be studied simultaneously in the hexagonal and cubic mixed Tm3+-doped NaYbF4. Thus, in this work, we synthesize the hexagonal and cubic mixed NaYbF4:Tm3+/SiO2 core-shell micro-particles, and study corresponding optical-thermal property under 980 nm excitation.

2. Experimental

All the chemicals used as received in the synthesis process were not further purified. Deionized water was used throughout. The raw materials are ethanol (AR), NaF (99.95%), 99.99% Yb2O3 and Tm2O3, hydrochloric acid (AR), tetraethoxysilane (AR).

NaYbF4:Tm3+ micro-particles were first prepared by a solvothermal method. Then tetraethoxysilane (TEOS) hydrolyzed on the surface of NaYbF4:Tm3+ to form the silica shell. At last, NaYbF4:Tm3+/SiO2 core-shell micro-particles were obtained through annealing. In a typical synthesis of cubic and hexagonal phases mixed NaYbF4:Tm3+ micro-particles, rare earth oxides Ln2O3 (Ln = Yb and Tm) were dissolved in hydrochloric acid (1mol Ln2O3: 3.5mol Hcl) to prepare 0.2 mol/L LnCl3 solution. An aqueous solution of lanthanide salt YbCl3 and TmCl3 was mixed with 27 mL deionized water and 0.2234g EDTA-2Na under thorough stirring. Then, 8 mL NaF (0.2016 g) solution was dropwise added to the mixture. After vigorous stirring at room temperature for about 30 min, the colloidal solution were transferred into a 60 mL Teflon-lined autoclave, sealed and heated at 193.5 °C for 24 h. The final products were collected, washed several times with ethanol, and purified by centrifugation.

NaYbF4:Tm3+/SiO2 core-shell micro-particles were prepared by a modified stöber method. 30 mg NaYbF4:Tm3+ micro-particles were dispersed in 80 mL 2-propanol by sonication for 30 min. Then 8.94 mL 28% ammonia, 7.5 mL deionized water, and 0.1 mL TEOS were added into the mixture. The mixture was then placed into an ultrasonic bath and kept for 2 h. The product was collected, washed and dried, and sinteringed sample at 500 °C for 2h.

Structures of the samples were investigated by X-ray diffraction (XRD) using a X'TRA (Switzerland ARL) equipment provided with Cu tube with Kα radiation at 1.54056 Å in the range of 10°≤2θ≤80°. The size and shape of the samples were observed by a transmission electron microscope (JEOL JEM-2100) equipped with an energy dispersive x-ray spectroscope (EDS). Luminescence spectra were obtained by the Edinburgh Instruments FLS920 Spectrophotometer with a photomultiplier tube equipped with one adjustable laser diode as the excitation sources. Different temperatures were obtained using a cooling power closed cyclecryo cooler (DE-202).

3. Results and discussion

Morphology and phase structure of NaYbF4:1.6%Tm3+ nano-spheres and NaYbF4: 1.6%Tm3+ active-core/SiO2 shell micro-particles are analyzed by transmission electron microscope, selected area electron diffraction, and XRD measurements. Transmission electron microscope and selected area electron diffraction observations in Fig. 1(a,b) confirm the well-dispersed polycrystal structure of NaYbF4:1.6% Tm3+ nano-spheres. The mean size of the NaYbF4:1.6%Tm3+ nano-spheres is evaluated as 140 nm. A transmission electron microscope image of silica-coated NaYbF4:1.6%Tm3+ nano-spheres is displayed in Fig. 1(c). It can be seen clearly that the NaYbF4:1.6%Tm3+ active- core/SiO2 shell micro-particles have a core-shell structure, and the thickness of the silica shell is about 100 nm. The selected area electron diffraction in Fig. 1(d) shows the single-crystalline phase structure of NaYbF4: 1.6%Tm3+ nano-spheres. The phase conversion from polycrystal to single-crystalline phase structure originated from the heat treatment at 500 °C for 2h. The XRD patterns in Fig. 2 show that diffraction peaks of NaYbF4:1.6%Tm3+ nano-spheres and NaYbF4:1.6%Tm3+ active- core/SiO2 shell micro-particles are assigned to the hybrid cubic and hexagonal phase NaYbF4, and the cubic α-NaYbF4 was main constituent.

 figure: Fig. 1

Fig. 1 Transmission electron microscope micrographs and selected area electron diffraction patterns of (a,b) NaYbF4: 1.6%Tm3+ nano-spheres, (c,d) NaYbF4: 1.6% Tm3+ active-core/SiO2 shell micro-particles.

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 figure: Fig. 2

Fig. 2 Power XRD patterns of (a) NaYbF4:1.6%Tm3+ nano-spheres, (b) NaYbF4: 1.6%Tm3+ active-core/SiO2 shell micro-particles, (c) the standard data for α-NaYbF4 (JCPDS 77-2043), (d) the standard data for β-NaYbF4 (JCPDS 27–1427).

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Figure 3(a) shows photoluminescence spectra of NaYbF4:Tm3+ nano-spheres under 980 nm excitation at room temperature. It can be seen that the photoluminescence spectra of Tm3+ ions consist of five emission peaks at 365 nm, 450 nm, 478 nm, 617 nm, 697 nm, and 798 nm, which are assigned to the 1D23H6 (365 nm), 1D23F4 (450 nm), 1G43H6 (478 nm), 1G43F4 (617 nm), 3F2,33H6 (798 nm), and 3H43H6 transitions of Tm3+ ions, respectively. The intensity of 450 nm and 478 nm blue emissions is found to increase and then decrease with increase of the Tm3+ concentration, a maximum existing at about 1.6mol%. The intensity of 697 nm and 798 nm emissions increase with increase of the Tm3+ concentration, which is orignated from the concentration quenching caused by the cross relaxation energy transfer 1D2 + 3H63F2 + 3H5 between Tm3+ ions [29,30]. Thus, NaYbF4:1.6%Tm3+ nano-spheres is chosen to be as active-core for NaYbF4:1.6%Tm3+/SiO2 core-shell micro-particles. Figure 3(b) shows photoluminescence spectra of NaYbF4:1.6%Tm3+/ SiO2 nano-spheres and core-shell micro-particles under 980 nm excitation at room temperature. The shifting of the peaks is not observed between nano-spheres and core-shell micro-particles. The intensity of 365 nm, 450 nm and 478 nm emission peaks of the NaYbF4:1.6% Tm3+/SiO2 core-shell micro-particles is a little weaker than that of the NaYbF4:1.6%Tm3+ nano-spheres. The intensity of 697 nm and 798 nm emission peaks of the NaYbF4:1.6% Tm3+/SiO2 core-shell micro-particles are much weaker than that of the NaYbF4:1.6%Tm3+ nano-spheres. The decrease of infrared emission intensity is originated from a fact that SiO2 shell changed the surface property of the NaYbF4:1.6%Tm3+ nano-spheres and inhibited the quenching from surface defect [8].

 figure: Fig. 3

Fig. 3 (a) Photoluminescence spectra of NaYbF4:xTm3+ (x = 0.4%, 0.8%,1.6%, 2.4%, and 3.2%) nano-spheres under 980 nm excitation, (b) Photoluminescence spectra of NaYbF4:1.6%Tm3+ nano-spheres and NaYbF4:1.6%Tm3+/SiO2 core-shell micro-particles under 980 nm excitation at room temperature.

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The NaYbF4:1.6%Tm3+/SiO2 core-shell micro-particles are suitable to be used as optical temperature sensor using Tm3+ upconversion emissions; because the SiO2 shell protects the NaYbF4:1.6%Tm3+ core from oxidation. To understand the properties related to optical temperature sensors, the temperature dependent Tm3+ anti-Stokes emissions from the NaYbF4:Tm3+/SiO2 core-shell micro-particles were studied in the temperature range of 100~700 K, and the pumping power of 980 nm diode laser is set at 137 mW/mm2. The emission spectra at different temperatures are shown in Fig. 4. It is interesting to observe that the intensities for these emissions are greatly decreased as temperature rises without changing the peak positions of the emissions. The intensities for 450 nm and 798 nm emissions decreased sharply and that of 478 nm and 697 nm emissions decreased slowly. In other words, the intensity decrease with temperature for different peaks in the emission spectrum is different. This change is originated from local ligand fields around Tm3+ sites, which can be expressed by the effective bandwidth from emission spectra [31]. From the emission spectra of different temperatures, the effective bandwidth Δλeff of the emission band can be obtained:

Δλeff=I(λ)dλImax,
where I(λ) is the emission intensity at wavelength λ and Imax is the emission intensity at peak emission wavelength. The effective bandwidth Δλeff usually changes with local ligand fields around Tm3+ sites. Figure 5 shows temperature dependent effective bandwidth Δλeff of anti-Stokes fluorescence emissions of NaYbF4:Tm3+/ SiO2 core-shell micro-particles. With the temperature increase from 100 k to 700K, the values Δλeff for the 697 nm (3F2,33H6) emission inhomogeneously increases from 16.76 nm to 22.94 nm, and the values Δλeff for the 798 nm emission homogeneously increases from 19.79 nm to 25.35 nm. The values Δλeff for the 450 nm (1D23F4) emission firstly increases and then decreases with the temperature increase, a maximum 11.85 nm existing at about 600 K. Similarly, the values Δλeff for the 478 nm (1G43H6) emission firstly increases and then decreases with the temperature increase, a maximum 13.82 nm existing at about 300 K. The inhomogeneous broadening of the emission spectra shows that the NaYbF4:1.6%Tm3+/SiO2 core-shell micro-particles would be suitable to be as optical temperature sensor through modifying Tm3+ upconversion emissions from thermally coupled levels.

 figure: Fig. 4

Fig. 4 Temperature dependent Tm3+ anti-stokes fluorescence emissions from the NaYbF4: Tm3+/sio2 core-shell micro-particles.

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 figure: Fig. 5

Fig. 5 Temperature dependent effective bandwidth Δλeff of anti-Stokes fluorescence emissions of NaYbF4: Tm3+ active-core/SiO2 shell micro-particles.

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In order to verify that the 1D2 and 1G4, 3F2 and 3H4 levels are thermally coupled, the upconversion emission spectra of NaYbF4:1.6%Tm3+/SiO2 core-shell micro-particles are studied as a function of temperature ranging from 100 K to 700 K under 980 nm excitation. According to the theory in Ref [19,20], the ratio of the luminescence R from each thermally coupled levels of active ions is modified as

R=IUIL=AeΔEKBT+B
where IU and IL are intensities of emissions from the upper and the lower thermally coupled levels, A and B are constants, A is a constant that depends on the experimental system and intrinsic spectroscopic parameters [20]. ΔE is the energy difference between thermally coupled levels, kB is the Boltzmann constant, and T is the absolute temperature. Figure 6(a) shows the R between 697 nm and 798 nm upconversion emissions of Tm3+ ions as a function of temperature in the range of 100~700 K under 980nm excitation. The R is obtained throughthe intensity ratio between the corresponding 697 nm and 798 nm emission spectra. The R between 697 nm and 798 nm emissions increases sharply with temperature increase. The experimental data are fitted by Eq. (2). It can be observed that the fittings agree well with the experimental data. ΔE is fitted to be 1794 cm−1, close to the experimental value 1815.9 cm−1 calculated from the emission spectra. These results confirm that the 3F2 and 3H4 are thermally coupled levels in the temperature range from 400K to 700 K [19]. Figure 6(b) shows the R between 450 nm and 478 nm upconversion emissions of Tm3+ ions as a function of temperature in the range of 100~700 K under 980 nm excitation. The R is obtained through the ratio between the integrated areas under the corresponding 450 nm and 478 nm emission spectra. Differently, the R between 450 nm and 478 nm firstly decreases sharply and then increases slowly with temperature increase. This trend suggests that it exists nonradiative relaxation between 1D2 and 1G4 in the temperature range of 100~400 K and temperature dependent population re-distribution in the temperature range of 400~700 K. The experimental data in the temperature range of 400~700 K is fitted by Eq. (2). Only at higher temperatures the behavior of the intensity ratio R shows that the population of the states is following the laws of thermalization. It can be observed that the fittings only agree with the experimental data in high temperature range. However, the ΔE is fitted to be 2268.5cm−1, deviating to the experimental value 6476.76 cm−1 calculated from the emission spectra. These results confirm that the 1D2 and 1G4 are not suitable thermally coupled levels for optical temperature sensors.

 figure: Fig. 6

Fig. 6 (a) R between the 697 nm and 798 nm, (b) R between the 450 nm and 478 nm, upconversion emissions as a function of temperature in the range of 100~700 K under 980 nm excitation.

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The mechanism on optical thermal sensing through Yb3+-Tm3+ energy transfer under 980 nm excitation is proposed in Fig. 7. If the temperature around NaYbF4:Tm3+/SiO2 core-shell micro-particles is low and keeps a constant, the population of the 1D2 level is achieved by four successive transfer processes from Yb3+ to Tm3+ ions under 980 nm excitation. The energy transfer processes from the 2F5/2 of Yb3+ to 3H 5, 1G4 and 1D2 levels of Tm3+ are non-resonant and add the amount of energy that has to be bridged producing phonons. Since the large energy mismatch (3516 cm−1) between 1G41D2 (Tm3+) and 2F5/22F7/2 (Yb3+) levels, the process 3F3 (Tm3+) + 3H4 (Tm3+) → 3H6 (Tm3+) + 1D2 (Tm3+) may alternatively play the most important role in populating 1D2 [32,33]. As a result, the 1D2, 1G4, 3F2, and 3H 4 levels are populated, and five emission peaks at 365 nm, 450 nm, 478 nm, 697 nm, and 798 nm are originated from the 1D23H6 (365 nm), 1D23F4 (450 nm), 1G43H6 (478 nm), 3F23H6 (697 nm), and 3H43H6 (798 nm) transitions of Tm3+ ions, respectively. With increase of temperature, most of ions on 3H 4 levels are excited onto upper 3F3 and 3F2 levels through thermal population [19]. The intensity 798 nm infrared emissions decreases slowly and the intensity 697 nm red emissions increases slowly with increase of temperature. As a result, the intensity ratio R between 697 nm and 798 nm emissions increases with increase of temperature, which agrees with the experimental data in Fig. 6(a). It means that temperature induced population re-distributions occurs, if the NaYbF4:Tm3+/SiO2 core-shell micro- particles is heated slowly. As for the 1D2 and 1G4 levels, the nonradiative resonant cross relaxation energy transfer 1D2 (Tm3+) + 3H6 (Tm3+) → 1G4 (Tm3+) + 3F4 (Tm3+) may be a main mechanism to depopulate the 1D2 level and populate 1G4 level at low temperature (100 K~400 K). At high temperature (400 K~700 K), cross-relaxation energy transfer 3F4 (Tm3+) + 1G4 (Tm3+) → 3H6 (Tm3+) + 1D2 (Tm3+) may be a main mechanism to populate the 1D2 level and depopulate 1G4 level.

 figure: Fig. 7

Fig. 7 The mechanism on optical thermal sensing through Yb3+-Tm3+ energy transfer under 980 nm excitation

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As for above two routes to achieve temperature induced population re-distributions, the Temperature dependent population re-distribution ability (PCA) can be defined as

PCA=IUIU+IL,
where IU and IL are fluorescence intensity generated by the radiative transitions from the upper and lower thermally coupled levels to ground level. According to Eqs. (2) and Eqs. (3) the PCA can be expressed as
PCAAA+eΔE/kBT,
where A is a fitting constant in Fig. 6, ΔE is the fitting energy difference between thermally coupled levels, kB is the Boltzmann constant, and T is the absolute temperature. Figure 8 shows the temperature dependent PCA of 1D2 /1G4 and 3F2/3H4 thermally coupled levels. It can be seen that the value of the PCA is strong dependent on absolute temperature. When the temperature is lower than 400 K, the PCA is very low. When the temperature is higher than 400 K, the PCA increases sharply, and the 1D2 /1G4 thermally coupled levels exhibit the higher PCA.

 figure: Fig. 8

Fig. 8 Temperature dependent PCA of (a) 1D2 and 1G4 and (b) 3F2 and 3H4 thermally coupled levels.

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Considering practical applications, it is also necessary to understand the change of sensitivity with temperature. The sensitivity of optical thermometry is the rate of change in the R in response to the variation of temperature [19]. To allow the comparison between the sensitivities obtained from different thermally coupled levels, the relative sensitivity SR and the absolute sensitivity SA are defined as

SR=dRdT=RΔEKBT2,
SA=1RdRdT=ΔEKBT2
where the ΔE is the energy difference between thermally coupled levels, kB is the Boltzmann constant, T is the absolute temperature, and R is the luminescence ratio between the two thermally coupled levels [19,20]. Equation (6) suggests that using pairs of levels with larger energy differences are in favor of higher sensitivity. If energy difference is too large, there won’t be any thermalization at low or room temperature. The absolute sensitivity SA decreases with the increase of temperature, shown in Fig. 9(a). The relative sensitivity SR firstly sharply decreases and then slowly increases with the increase of temperature, a minimum SR = 5.4 × 10−4 existing at T = 430 K, shown in Fig. 9(b). It means that NaYbF4:Tm3+/SiO2 core-shell micro-particles are sensitive in low temperature area.

 figure: Fig. 9

Fig. 9 (a) Sensor sensitivity SA and (b) relative sensor sensitivity SR as a function of the temperature for excitation at 980 nm.

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4. Conclusion

NaYbF4:Tm3+@SiO2 core-shell micro-particles were synthesized by combining hydrothermal process with ultrasonic coating. The optical thermometry in the rage of 100~700 K is presented using the luminescence intensity ratio technique of adjacent thermally coupled 1D2 /1G4 and 3F2 /3H4 levels under 980 nm excitation. The temperature modification of the crystal field around the Tm ions is observed through analyzing the temperature variation of the effective bandwidth. The minimum sensitivity and revolution for the optical low-temperature sensor based on NaYbF4:Tm3+@SiO2 core-shell micro-particles are 5.4 × 10−4 K−1 at 430 K. Temperature dependent population re-distribution ability from 1D2 /1G4 thermally coupled levels reaches more than 80% at higher temperature range. This work offers a new method to achieve optical temperature sensing with core-shell micro-particles.

Acknowledgments

This work was supported by National Natural Science Foundation of China (NSFC51032002, 11247033, 11274173), the key Project of the National High Technology Research and Development Program (“863” Program) of China (No. 2011AA050526), the Science and Technology Support Plan of Jiangsu Province (BE2011191), Natural Science Youth Foundation of Jiangsu Province (BK20130865).

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Figures (9)

Fig. 1
Fig. 1 Transmission electron microscope micrographs and selected area electron diffraction patterns of (a,b) NaYbF4: 1.6%Tm3+ nano-spheres, (c,d) NaYbF4: 1.6% Tm3+ active-core/SiO2 shell micro-particles.
Fig. 2
Fig. 2 Power XRD patterns of (a) NaYbF4:1.6%Tm3+ nano-spheres, (b) NaYbF4: 1.6%Tm3+ active-core/SiO2 shell micro-particles, (c) the standard data for α-NaYbF4 (JCPDS 77-2043), (d) the standard data for β-NaYbF4 (JCPDS 27–1427).
Fig. 3
Fig. 3 (a) Photoluminescence spectra of NaYbF4:xTm3+ (x = 0.4%, 0.8%,1.6%, 2.4%, and 3.2%) nano-spheres under 980 nm excitation, (b) Photoluminescence spectra of NaYbF4:1.6%Tm3+ nano-spheres and NaYbF4:1.6%Tm3+/SiO2 core-shell micro-particles under 980 nm excitation at room temperature.
Fig. 4
Fig. 4 Temperature dependent Tm3+ anti-stokes fluorescence emissions from the NaYbF4: Tm3+/sio2 core-shell micro-particles.
Fig. 5
Fig. 5 Temperature dependent effective bandwidth Δλeff of anti-Stokes fluorescence emissions of NaYbF4: Tm3+ active-core/SiO2 shell micro-particles.
Fig. 6
Fig. 6 (a) R between the 697 nm and 798 nm, (b) R between the 450 nm and 478 nm, upconversion emissions as a function of temperature in the range of 100~700 K under 980 nm excitation.
Fig. 7
Fig. 7 The mechanism on optical thermal sensing through Yb3+-Tm3+ energy transfer under 980 nm excitation
Fig. 8
Fig. 8 Temperature dependent PCA of (a) 1D2 and 1G4 and (b) 3F2 and 3H4 thermally coupled levels.
Fig. 9
Fig. 9 (a) Sensor sensitivity SA and (b) relative sensor sensitivity SR as a function of the temperature for excitation at 980 nm.

Equations (6)

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Δλ eff = I(λ)dλ I max ,
R= I U I L =A e ΔE K B T +B
PCA= I U I U + I L ,
PCA A A+ e ΔE/ k B T ,
S R = dR dT =R ΔE K B T 2 ,
S A = 1 R dR dT = ΔE K B T 2
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