- Email: [email protected]
Eliminating the “decoupling” effect of fluorescence intensity ratio thermometry for an upconversion pumped system
Journal of Luminescence 192 (2017) 184–187
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Eliminating the “decoupling” effect of fluorescence intensity ratio thermometry for an upconversion pumped system
MARK
⁎
Feng Qina, , Hua Zhaob, Moyang Lvc,d, Yuan Zhoua, Leipeng Lia, Zhengjia Wanga, ⁎ ⁎ Yangdong Zhenga, Zhiguo Zhanga,d, , Wenwu Caoa,d,e, a
Condensed Matter Science and Technology Institute and Department of Physics, Harbin Institute of Technology, Harbin 150080, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China c Harbin Medical University, The Fourth Affiliated Hospital, Harbin 150001, China d Laboratory of Sono- and Photo- Theranostic Technology, Harbin Institute of Technology, Harbin 150001, China e Department of Mathematics and Materials Research Institute, The Pennsylvania State University, PA 16802, USA b
A R T I C L E I N F O
A B S T R A C T
Keywords: Spectroscopy Thermometry Fluorescence intensity ratio Thermal population Boltzmann distribution law
To eliminate the “decoupling” effect, which causes the fluorescence intensity ratios (FIR) to deviate from the pure Boltzmann distribution law, a correcting method for an upvonversion pumped system was theoretical derived and experimentally verified. Theoretical results indicated that the double exponential decay of the lower level was entirely involved in the decay of the upper level, which could be used to determine the thermal population degree (η). Taking Tm3+ ions as examples, by analyzing the temperature dependence of the fluorescent dynamic curves originating from the thermally coupled pair, the η values at different temperatures were obtained and the corresponding correcting curve is given. The corrected FIR abides by the Boltzmann law, even in the lower temperature range.
1. Introduction The fluorescence intensity ratio (FIR) technique, based on fluorescent emissions from a thermally coupled pair of rare-earth ions in a crystal matrix, exhibits excellent potential in non–contact temperature sensing applications [1–4]. However, for some thermally coupled pairs, when there are other populating processes besides the thermal populating process, the resulting temperature dependence of FIR exhibits a deviation from the Boltzmann law [5–7]. The deviation originates from the breaking of the expected thermally populating law by a non-thermal population, which is called the “decoupling” effect [5]. For a simple downconversion populated system, such as the 5 D0 & 5D1 levels of Eu3+, which was usually pumped by a short wavelength light, a method has been established theoretically to eliminate the “decoupling” effect [6]. By introducing a correcting parameter known as the thermal population degree (η), the conventional FIR may be corrected to follow the Boltzmann law using the η factor:
ΔE ⎞ FIR* = ηFIR = A exp ⎛⎜− ⎟, ⎝ kT ⎠
(1)
where the FIR* is the Boltzmann law satisfied fluorescence intensity ratio. Further, the method of determining the η values was proposed,
⁎
and the FIR between the 5D0 & 5D1 levels of Eu3+ was accordingly corrected. Experimental results verified the effectiveness of the method for a simple downconversion populated system [8]. In this work, the correcting method for an upconversion populated system, which was usually pumped by infrared diode laser, is proposed. Tm3+/Yb3+ co-doped system, as a typical upconversion pumped system, has been extensively investigated for photoluminescence and exhibits promising potential in making optical temperature sensors [9–11]. Above all, the fluorescence efficiency is high, can reach the order of 10−3 at 800 nm by the excitation of 980 nm diode laser [12,13]. In addition, the sensitivity for the 3F2,3 & 3H4 energy level pair of Tm3+ is twice as high as that for the 2H11/2 & 4S3/2 energy level pair of Er3+ due to a larger energy gap [14]. Else, the 3F2,3 level is strongly affected by non–thermal population, which results in the deviation of the temperature dependence of FIR from the pure Boltzmann law [14]. In this study, taking the 3F2,3 & 3H4 levels of Tm3+ as an example of a thermally coupled energy level pair, a correcting method for an upconversion populated system is presented and experimentally tested. First, the temporal evolutions of population from the pair are theoretical studied and a method of obtaining thermal population degree is presented; second, the time-resolved fluorescent spectra of these pairs at different temperatures were studied and corresponding η values were
Corresponding authors. E-mail addresses: [email protected] (F. Qin), [email protected] (Z. Zhang), [email protected] (W. Cao).
http://dx.doi.org/10.1016/j.jlumin.2017.06.018 Received 24 April 2017; Received in revised form 8 June 2017; Accepted 8 June 2017 Available online 09 June 2017 0022-2313/ © 2017 Elsevier B.V. All rights reserved.
Journal of Luminescence 192 (2017) 184–187
F. Qin et al.
are labeled as 0' and 1'; the 3H6, 3F4, 3H4 and 3F2,3 levels of Tm3+ are labeled as 0, 1, 2 and 3, respectively. For decay processes, there are no pumping terms. The differential equations guiding the dynamic processes of the concerned levels in Fig. 1 can be written as:
dn1′ = −A1′ n1′, dt
(2)
dn1 = C0 n1′ n 0 − C1 n1′ n1 − A1 n1, dt
(3)
dn2 = C1 n1′ n1 − T2 n2 − A2 n2 − W2 n2, dt
(4)
dn3 = T2 n2 − W3 n3 − A3 n3, dt
(5)
where ni, Ai, Ci and Wi are the population, radiative transition probability, energy transfer rate and nonradiative relaxation probability of the state i, respectively; T2 is the thermal population probability from level 2 (3H4 level) to level 3 (3F2,3 levels) [15]. Using the initial conditions ni(t=0)=ni0, the temporal evolution of the population in these emitting levels could be obtained from above equations:
Fig. 1. The energy level diagram for Tm3+ and Yb3+ as well as the upconversion mechanisms.
n1′ (t ) = n 0 ′ e−A1′ t ,
(6)
n2 (t ) = χ0 e−A1′ t + (n20 − χ0 ) e−(A2 + W2+ T2) t ,
(7)
χ1 χ2 n3 (t ) = e−A1′ t + e−(A2 + W2+ T2) t A3 + W3 A3 + W3 χ + χ2 −(A3 + W3) t + (n30 − 1 )e , A3 + W3 with
the
parameters
χ0 =
C1 n10 n1′0 , A2 + W2 + T2 − A1′
(8)
χ1 =
(A3 + W3) T2 χ0 , A3 + W3 − A1′
(A3 + W3) T2 (n20 − χ0 ) , (A3 + W3) − (A2 + W2 + T2)
χ2 = and χ3 = n30 (A3 + W3) − χ1 − χ2 . According to Einstein's theory, the fluorescence intensity is proportional to the population of the energy level, or the depopulation rate. Therefore, the depopulation rate of the thermally coupled pair can be further deduced from Eqs. (7) and (8):
Fig. 2. Typical luminescence spectra of Tm3+ at various temperatures under the excitation of 980 nm diode laser.
dn2 (t ) = −A1′ χ0 e−A1′ t − (A2 + W2 + T2)(n20 − χ0 ) e−(A2 + W2+ T2) t , dt
(9)
A1′ χ1 −A1′ t χ (A2 + W2 + T2) −(A + W + T ) t dn3 (t ) e e 2 2 2 − χ3 e−(A3 + W3) t . =− − 2 dt A3 + W3 A3 + W3 (10) For the temporal evolution of the population in level 2, a bi-exponential decay behavior was indicated. However, the energy transfer term from level 1' to level 1 illustrated in Eq. (4) cannot be found in Eq. (9). On the other hand, for the temporal evolution of the population in level 3, a tri-exponential decay behavior was demonstrated. However, the thermally populating term from level 2 to level 3 illustrated in Eq. (5) cannot be found in Eq. (10). To clarify the physical picture, the populating term is preserved and Eqs. (9) and (10) are accordingly rewritten as
Fig. 3. Temperature dependence of FIR and fitting curves on a logarithmic scale.
dn2 (t ) = C1 n10 n1′0 e−A1′ t − (A2 + W2 + T2) χ0 e−A1′ t − (A2 + W2 + T2)(n20 dt
obtained from the decay profiles; third, the correcting curves were presented and the correcting results were evaluated. In addition, some thermal coupling related physical problems are discussed at the end.
− χ0 ) e−(A2 + W2+ T2) t ,
(11)
dn3 (t ) = T2 [χ0 e−A1′ t + n20 − χ0 e−(A2 + W2+ T2) t ] − χ1 e−A1′ t dt
(
2. Theory and method
)
− χ2 e−(A2 + W2+ T2) t − χ3 e−(A3 + W3) t .
Generally, two successive energy transfer processes are needed in the population of the 3F2,3 states of Tm3+, which results in the near infrared emission around 700 nm. A subsequential nonradiative relaxation from the 3F2,3 states populates the 3H4 state, and the intense 800 nm near-infrared emission is then produced [14]. The energy level diagrams of Tm3+ and Yb3+ as well as corresponding transitions are illustrated in Fig. 1. For simplicity, the 2F5/2 and 2F7/2 levels of Yb3+
(12)
For Eq. (11), the first positive term is the preserved populating term, whereas the two negative terms denote the radiation from the lower level (level 2) to the ground state. For Eq. (12), the first positive term is the preserved thermal populating term, whereas the three negative terms denote the radiation from the upper level (level 2) to the ground state. Therefore, the measured fluorescence decay curves from a pair of 185
Journal of Luminescence 192 (2017) 184–187
F. Qin et al.
Fig. 4. Typical luminescence dynamic curves of 5H4 (a) and 3F2,3 (b) levels under the excitation of 980 nm diode laser at 450 K and the fitting curves.
Fig. 5. Temperature dependence of the thermal population degree η and obtained correcting curve (a) and temperature dependence of FIR* on a logarithmic scale.
3. Experiment
thermally coupled energy levels should be expressed as:
I2 ∝ χ0 e−A1′ t + (n20 − χ0 ) e−(A2 + W2+ T2) t ,
(13)
I3 ∝ χ1 e−A1′ t + χ2 e−(A2 + W2+ T2) t + χ3 e−(A3 + W3) t .
(14)
Tm0.02Yb0.16Y1.82O3 ceramic samples were selected in our experiments. The precursor powders were synthesized by a simple sol-gel method and the resulting nanocrystals were pressed into smooth and flat disks under 100 MPa pressure, then sintered at 1000 °C for 12 h in air to form the ceramic [8]. The ceramic disk was then mounted inside a temperature controlled chamber and irradiated by a laser beam through a fused quartz window mounted on the chamber wall. The induced fluorescence of rare earth ions was focused onto a monochromator (Zolix SBP 300) with a resolution of 1 nm, and the dispersed luminescence was detected by a photomultiplier tube (PMT), model Zolix CR131. To measure the fluorescent dynamic profiles of the coupled pairs, the diode laser was electrically modulated and the induced time-resolved curves were recorded by a digital oscilloscope (Tektronix DPO 5054), which was triggered by a function generator. Lifetime analysis was carried out by a personal computer using Matlab.
3+
For Tm , the decay rate of level 3 and level 2 are on the order of 105 m s−1 and 104 m s−1, respectively, while that of level 1' is on the order of 102 m s−1. If these practical relationships are considered, we have
χ1 + χ2 = Tn20 ,
(15)
χ1 + χ2 + χ3 = n30 (A3 + W3).
(16)
Therefore, for an upconversion populated system, the thermal population degree η may be expressed using the three weighting parameters:
η=
χ1 + χ2 n20 T2 . = n30 (A3 + W3) χ1 + χ2 + χ3
(17) 186
Journal of Luminescence 192 (2017) 184–187
F. Qin et al.
4. Results
significant correction on the deviated FIR data confirmed the correctness of our hypothesis and method for an upvonversion pumped system. More importantly, the dynamic principle that the coupled pairs abided by verified our assumption. Our results not only provide an effective correcting method for practical applications, but also give a deeper understanding on the mechanisms of thermally coupled pairs, as well as a way of determining the populations of different origins using time–resolved fluorescent spectroscopy. In addition, we also found that the weight of the exponential component plays a significant role in the FIR.
Fig. 2 shows a typical fluorescent spectrum of the coupled pair under the excitation of a 980 nm diode laser. The two distinct near–infrared emission bands peaked at 700 and 800 nm are originated from the transitions of 3F2,3 → 3H6 and 3H4 → 3H6, respectively [14]. It could be observed from Fig. 2 that the peak positions of these two emissions are hardly changed with temperature, while the emission intensities exhibit different response to the change of temperature. The emission intensity of the 800 nm emission gradually decreases with temperature, due to the strengthening in nonradiative relaxation; while the emission intensity of the 700 nm red emission increases greatly with temperature, resulted from the enhancement of thermally population. This variation indicates the significant thermally coupled properties, which formed the base for temperature sensing using these two bands. The FIR between the fluorescent emissions of the 3F2,3 & 3H4 pair was calculated from the integrated spectral intensity. The temperature dependence of the FIR was plotted in Fig. 3 on a logarithmic scale. The pure thermal population relationship should be a straight line on a logarithmic scale according to the Boltzmann law. But the FIR values for the 3F2,3 & 3H4 pair of Tm3+ gradually deviate from the straight line as the temperature decreases. The deviation indicates the effect of “decoupling” on the temperature dependence of FIR. To eliminate the deviation, the fluorescence dynamic curves of the coupled pairs were measured at different temperatures. Since two successive energy transfer processes are involved in the populating pathway of the 3F2,3 level, the resulting dynamic curve contains more decay components. According to Eqs. (13) and (14), the fluorescent decay from the 3H4 level (the lower level) exhibits a double exponential behavior, while the fluorescent decay from 3F2,3 level (the upper level) exhibits a triple exponential behavior. A pair of typical temporal evolutions of the two fluorescence emissions is illustrated in Fig. 4. Similarly, the two slow decay components in the three exponential decay (the upper level) are consistent with that of the double exponential decay (the lower level), which indicates an intrinsic coupled relationship between the two levels. The η values at different temperatures were calculated using the weight factors in the triple exponential decay curves according to Eq. (17) and were then plotted in Fig. 5(a) as well as a proposed correcting curve. Meanwhile, the corresponding FIR* was calculated and plotted in Fig. 5(b). It is apparent from this that the deviated FIR was successfully corrected to adhere to the Boltzmann law, which is represented by a straight line in the logarithmic scale.
Acknowledgements This research was supported by National Natural Science Foundation of China (61505045, 81571720) and China Scholarship Council (201706125022). References [1] A.K. Soni, V.K. Rai, M.K. Mahata, Luminescent probes and sensors for temperature Yb3+ sensitized Na2Y2B2O7: Er3+ phosphors in enhanced frequency upconversion,.temperature sensing and field emission display, Mater. Res. Bull. 89 (2017) 116–124. [2] D. Wawrzynczyk, A. Bednarkiewicz, M. Nyk, W. Strek, M. Samoc, Neodymium (III) doped fluoride nanoparticles as non-contact optical temperature sensors, Nanoscale 4 (22) (2012) 6959–6961. [3] M. Kochanowicz, D. Dorosz, J. Zmojda, J. Dorosz, P. Miluski, Influence of temperature on upconversion luminescence in tellurite glass co-doped with Yb3+/Er3+ and Yb3+/Tm3+, J. Lumin. 151 (2014) 155–160. [4] X.N. Tian, X.T. Wei, Y.H. Chen, C.K. Duan, M. Yin, Temperature sensor based on ladder-level assisted thermal coupling and thermal-enhanced luminescence in NaYF4: Nd3+, Opt. Express 22 (24) (2014) 30333–30345. [5] S.A. Wade, S.F. Collins, G.W. Baxter, Fluorescence intensity ratio technique for optical fiber point temperature sensing, J. Appl. Phys. 94 (8) (2003) 4743–4756. [6] F. Qin, H. Zhao, M.Y. Lv, W. Cai, Z.G. Zhang, W.W. Cao, Fluorescence intensity ratio thermometer methodology of eliminating the “decoupling” effect of a pair of thermally coupled energy levels of rare-earth ions, Opt. Lett. 42 (7) (2017) 1401–1403. [7] M.G. Nikolić, D.J. Jovanović, M.D. Dramićanin, Temperature dependence of emission and lifetime in Eu3+-and Dy3+-doped GdVO4, Appl. Opt. 52 (8) (2013) 1716–1724. [8] F. Qin, H. Zhao, W. Cai, Z.G. Zhang, W.W. Cao, A precise Boltzmann distribution law for the fluorescence intensity ratio of two thermally coupled levels, Appl. Phys. Lett. 108 (24) (2016) 241907. [9] A. Kumari, A.K. Soni, V.K. Rai, Near infrared to blue upconverting Tm3+/Yb3+/Li +:Gd-2(MoO4)(3) phosphors for light emitting display devices, Infrared Phys. Technol. 81 (2017) 313–319. [10] R. Dey, V.K. Rai, Er3+-Tm3+-Yb3+:CaMoO:4 phosphor as an outstanding upconversion-based optical temperature sensor and optical heater, Methods Appl. Fluoresc. 5 (1) (2017) 015006. [11] X.F. Wang, J. Zheng, Y. Xuan, X.H. Yan, Optical temperature sensing of NaYbF4: Tm3+ @ SiO2 core-shell micro-particles induced by infrared excitation, Opt. Express 21 (18) (2013) 21596–21606. [12] J.Y. Zhang, H. Zhao, X.T. Zhang, X.Z. Wang, H. Gao, Z.G. Zhang, W.W. Cao, Monochromatic near-infrared to near-infrared upconversion nanoparticles for highcontrast fluorescence imaging, J. Phys. Chem. C 118 (5) (2014) 2820–2825. [13] A. Baride, J.M. Meruga, C. Douma, D. Langerman, G. Crawford, J.J. Kellar, W.M. Cross, P.S. May, A NIR-to-NIR upconversion luminescence system for security printing applications, RSC Adv. 5 (123) (2015) 101338–101346. [14] W. Xu, X.Y. Gao, L.J. Zheng, Z.G. Zhang, W.W. Cao, An optical temperature sensor based on the upconversion luminescence from Tm3+/Yb3+ codoped oxyfluoride glass ceramic, Sens. Actuators B 173 (2012) 250–253. [15] P. Loiko, M. Pollnau, Stochastic model of energy-transfer processes among rareearth ions. Example of Al2O3:Tm3+, J. Phys. Chem. C 120 (46) (2016) 26408–26489.
5. Conclusion In summary, using the thermally coupled pair of the 3F2,3 & 3H4 levels of Tm3+ ions, a correcting method for an upvonversion pumped system was theoretical performed and experimentally tested. Theoretical results indicated that the double exponential decay of the lower level was entirely involved in the decay of the upper level, which could be used to determine the thermal population degree (η). The η values are found to be obtainable from fitting the fluorescence dynamic curves and a correction curve has been therefore given. A clear and
187
Contents lists available at ScienceDirect
Journal of Luminescence journal homepage: www.elsevier.com/locate/jlumin
Eliminating the “decoupling” effect of fluorescence intensity ratio thermometry for an upconversion pumped system
MARK
⁎
Feng Qina, , Hua Zhaob, Moyang Lvc,d, Yuan Zhoua, Leipeng Lia, Zhengjia Wanga, ⁎ ⁎ Yangdong Zhenga, Zhiguo Zhanga,d, , Wenwu Caoa,d,e, a
Condensed Matter Science and Technology Institute and Department of Physics, Harbin Institute of Technology, Harbin 150080, China School of Materials Science and Engineering, Harbin Institute of Technology, Harbin 150001, China c Harbin Medical University, The Fourth Affiliated Hospital, Harbin 150001, China d Laboratory of Sono- and Photo- Theranostic Technology, Harbin Institute of Technology, Harbin 150001, China e Department of Mathematics and Materials Research Institute, The Pennsylvania State University, PA 16802, USA b
A R T I C L E I N F O
A B S T R A C T
Keywords: Spectroscopy Thermometry Fluorescence intensity ratio Thermal population Boltzmann distribution law
To eliminate the “decoupling” effect, which causes the fluorescence intensity ratios (FIR) to deviate from the pure Boltzmann distribution law, a correcting method for an upvonversion pumped system was theoretical derived and experimentally verified. Theoretical results indicated that the double exponential decay of the lower level was entirely involved in the decay of the upper level, which could be used to determine the thermal population degree (η). Taking Tm3+ ions as examples, by analyzing the temperature dependence of the fluorescent dynamic curves originating from the thermally coupled pair, the η values at different temperatures were obtained and the corresponding correcting curve is given. The corrected FIR abides by the Boltzmann law, even in the lower temperature range.
1. Introduction The fluorescence intensity ratio (FIR) technique, based on fluorescent emissions from a thermally coupled pair of rare-earth ions in a crystal matrix, exhibits excellent potential in non–contact temperature sensing applications [1–4]. However, for some thermally coupled pairs, when there are other populating processes besides the thermal populating process, the resulting temperature dependence of FIR exhibits a deviation from the Boltzmann law [5–7]. The deviation originates from the breaking of the expected thermally populating law by a non-thermal population, which is called the “decoupling” effect [5]. For a simple downconversion populated system, such as the 5 D0 & 5D1 levels of Eu3+, which was usually pumped by a short wavelength light, a method has been established theoretically to eliminate the “decoupling” effect [6]. By introducing a correcting parameter known as the thermal population degree (η), the conventional FIR may be corrected to follow the Boltzmann law using the η factor:
ΔE ⎞ FIR* = ηFIR = A exp ⎛⎜− ⎟, ⎝ kT ⎠
(1)
where the FIR* is the Boltzmann law satisfied fluorescence intensity ratio. Further, the method of determining the η values was proposed,
⁎
and the FIR between the 5D0 & 5D1 levels of Eu3+ was accordingly corrected. Experimental results verified the effectiveness of the method for a simple downconversion populated system [8]. In this work, the correcting method for an upconversion populated system, which was usually pumped by infrared diode laser, is proposed. Tm3+/Yb3+ co-doped system, as a typical upconversion pumped system, has been extensively investigated for photoluminescence and exhibits promising potential in making optical temperature sensors [9–11]. Above all, the fluorescence efficiency is high, can reach the order of 10−3 at 800 nm by the excitation of 980 nm diode laser [12,13]. In addition, the sensitivity for the 3F2,3 & 3H4 energy level pair of Tm3+ is twice as high as that for the 2H11/2 & 4S3/2 energy level pair of Er3+ due to a larger energy gap [14]. Else, the 3F2,3 level is strongly affected by non–thermal population, which results in the deviation of the temperature dependence of FIR from the pure Boltzmann law [14]. In this study, taking the 3F2,3 & 3H4 levels of Tm3+ as an example of a thermally coupled energy level pair, a correcting method for an upconversion populated system is presented and experimentally tested. First, the temporal evolutions of population from the pair are theoretical studied and a method of obtaining thermal population degree is presented; second, the time-resolved fluorescent spectra of these pairs at different temperatures were studied and corresponding η values were
Corresponding authors. E-mail addresses: [email protected] (F. Qin), [email protected] (Z. Zhang), [email protected] (W. Cao).
http://dx.doi.org/10.1016/j.jlumin.2017.06.018 Received 24 April 2017; Received in revised form 8 June 2017; Accepted 8 June 2017 Available online 09 June 2017 0022-2313/ © 2017 Elsevier B.V. All rights reserved.
Journal of Luminescence 192 (2017) 184–187
F. Qin et al.
are labeled as 0' and 1'; the 3H6, 3F4, 3H4 and 3F2,3 levels of Tm3+ are labeled as 0, 1, 2 and 3, respectively. For decay processes, there are no pumping terms. The differential equations guiding the dynamic processes of the concerned levels in Fig. 1 can be written as:
dn1′ = −A1′ n1′, dt
(2)
dn1 = C0 n1′ n 0 − C1 n1′ n1 − A1 n1, dt
(3)
dn2 = C1 n1′ n1 − T2 n2 − A2 n2 − W2 n2, dt
(4)
dn3 = T2 n2 − W3 n3 − A3 n3, dt
(5)
where ni, Ai, Ci and Wi are the population, radiative transition probability, energy transfer rate and nonradiative relaxation probability of the state i, respectively; T2 is the thermal population probability from level 2 (3H4 level) to level 3 (3F2,3 levels) [15]. Using the initial conditions ni(t=0)=ni0, the temporal evolution of the population in these emitting levels could be obtained from above equations:
Fig. 1. The energy level diagram for Tm3+ and Yb3+ as well as the upconversion mechanisms.
n1′ (t ) = n 0 ′ e−A1′ t ,
(6)
n2 (t ) = χ0 e−A1′ t + (n20 − χ0 ) e−(A2 + W2+ T2) t ,
(7)
χ1 χ2 n3 (t ) = e−A1′ t + e−(A2 + W2+ T2) t A3 + W3 A3 + W3 χ + χ2 −(A3 + W3) t + (n30 − 1 )e , A3 + W3 with
the
parameters
χ0 =
C1 n10 n1′0 , A2 + W2 + T2 − A1′
(8)
χ1 =
(A3 + W3) T2 χ0 , A3 + W3 − A1′
(A3 + W3) T2 (n20 − χ0 ) , (A3 + W3) − (A2 + W2 + T2)
χ2 = and χ3 = n30 (A3 + W3) − χ1 − χ2 . According to Einstein's theory, the fluorescence intensity is proportional to the population of the energy level, or the depopulation rate. Therefore, the depopulation rate of the thermally coupled pair can be further deduced from Eqs. (7) and (8):
Fig. 2. Typical luminescence spectra of Tm3+ at various temperatures under the excitation of 980 nm diode laser.
dn2 (t ) = −A1′ χ0 e−A1′ t − (A2 + W2 + T2)(n20 − χ0 ) e−(A2 + W2+ T2) t , dt
(9)
A1′ χ1 −A1′ t χ (A2 + W2 + T2) −(A + W + T ) t dn3 (t ) e e 2 2 2 − χ3 e−(A3 + W3) t . =− − 2 dt A3 + W3 A3 + W3 (10) For the temporal evolution of the population in level 2, a bi-exponential decay behavior was indicated. However, the energy transfer term from level 1' to level 1 illustrated in Eq. (4) cannot be found in Eq. (9). On the other hand, for the temporal evolution of the population in level 3, a tri-exponential decay behavior was demonstrated. However, the thermally populating term from level 2 to level 3 illustrated in Eq. (5) cannot be found in Eq. (10). To clarify the physical picture, the populating term is preserved and Eqs. (9) and (10) are accordingly rewritten as
Fig. 3. Temperature dependence of FIR and fitting curves on a logarithmic scale.
dn2 (t ) = C1 n10 n1′0 e−A1′ t − (A2 + W2 + T2) χ0 e−A1′ t − (A2 + W2 + T2)(n20 dt
obtained from the decay profiles; third, the correcting curves were presented and the correcting results were evaluated. In addition, some thermal coupling related physical problems are discussed at the end.
− χ0 ) e−(A2 + W2+ T2) t ,
(11)
dn3 (t ) = T2 [χ0 e−A1′ t + n20 − χ0 e−(A2 + W2+ T2) t ] − χ1 e−A1′ t dt
(
2. Theory and method
)
− χ2 e−(A2 + W2+ T2) t − χ3 e−(A3 + W3) t .
Generally, two successive energy transfer processes are needed in the population of the 3F2,3 states of Tm3+, which results in the near infrared emission around 700 nm. A subsequential nonradiative relaxation from the 3F2,3 states populates the 3H4 state, and the intense 800 nm near-infrared emission is then produced [14]. The energy level diagrams of Tm3+ and Yb3+ as well as corresponding transitions are illustrated in Fig. 1. For simplicity, the 2F5/2 and 2F7/2 levels of Yb3+
(12)
For Eq. (11), the first positive term is the preserved populating term, whereas the two negative terms denote the radiation from the lower level (level 2) to the ground state. For Eq. (12), the first positive term is the preserved thermal populating term, whereas the three negative terms denote the radiation from the upper level (level 2) to the ground state. Therefore, the measured fluorescence decay curves from a pair of 185
Journal of Luminescence 192 (2017) 184–187
F. Qin et al.
Fig. 4. Typical luminescence dynamic curves of 5H4 (a) and 3F2,3 (b) levels under the excitation of 980 nm diode laser at 450 K and the fitting curves.
Fig. 5. Temperature dependence of the thermal population degree η and obtained correcting curve (a) and temperature dependence of FIR* on a logarithmic scale.
3. Experiment
thermally coupled energy levels should be expressed as:
I2 ∝ χ0 e−A1′ t + (n20 − χ0 ) e−(A2 + W2+ T2) t ,
(13)
I3 ∝ χ1 e−A1′ t + χ2 e−(A2 + W2+ T2) t + χ3 e−(A3 + W3) t .
(14)
Tm0.02Yb0.16Y1.82O3 ceramic samples were selected in our experiments. The precursor powders were synthesized by a simple sol-gel method and the resulting nanocrystals were pressed into smooth and flat disks under 100 MPa pressure, then sintered at 1000 °C for 12 h in air to form the ceramic [8]. The ceramic disk was then mounted inside a temperature controlled chamber and irradiated by a laser beam through a fused quartz window mounted on the chamber wall. The induced fluorescence of rare earth ions was focused onto a monochromator (Zolix SBP 300) with a resolution of 1 nm, and the dispersed luminescence was detected by a photomultiplier tube (PMT), model Zolix CR131. To measure the fluorescent dynamic profiles of the coupled pairs, the diode laser was electrically modulated and the induced time-resolved curves were recorded by a digital oscilloscope (Tektronix DPO 5054), which was triggered by a function generator. Lifetime analysis was carried out by a personal computer using Matlab.
3+
For Tm , the decay rate of level 3 and level 2 are on the order of 105 m s−1 and 104 m s−1, respectively, while that of level 1' is on the order of 102 m s−1. If these practical relationships are considered, we have
χ1 + χ2 = Tn20 ,
(15)
χ1 + χ2 + χ3 = n30 (A3 + W3).
(16)
Therefore, for an upconversion populated system, the thermal population degree η may be expressed using the three weighting parameters:
η=
χ1 + χ2 n20 T2 . = n30 (A3 + W3) χ1 + χ2 + χ3
(17) 186
Journal of Luminescence 192 (2017) 184–187
F. Qin et al.
4. Results
significant correction on the deviated FIR data confirmed the correctness of our hypothesis and method for an upvonversion pumped system. More importantly, the dynamic principle that the coupled pairs abided by verified our assumption. Our results not only provide an effective correcting method for practical applications, but also give a deeper understanding on the mechanisms of thermally coupled pairs, as well as a way of determining the populations of different origins using time–resolved fluorescent spectroscopy. In addition, we also found that the weight of the exponential component plays a significant role in the FIR.
Fig. 2 shows a typical fluorescent spectrum of the coupled pair under the excitation of a 980 nm diode laser. The two distinct near–infrared emission bands peaked at 700 and 800 nm are originated from the transitions of 3F2,3 → 3H6 and 3H4 → 3H6, respectively [14]. It could be observed from Fig. 2 that the peak positions of these two emissions are hardly changed with temperature, while the emission intensities exhibit different response to the change of temperature. The emission intensity of the 800 nm emission gradually decreases with temperature, due to the strengthening in nonradiative relaxation; while the emission intensity of the 700 nm red emission increases greatly with temperature, resulted from the enhancement of thermally population. This variation indicates the significant thermally coupled properties, which formed the base for temperature sensing using these two bands. The FIR between the fluorescent emissions of the 3F2,3 & 3H4 pair was calculated from the integrated spectral intensity. The temperature dependence of the FIR was plotted in Fig. 3 on a logarithmic scale. The pure thermal population relationship should be a straight line on a logarithmic scale according to the Boltzmann law. But the FIR values for the 3F2,3 & 3H4 pair of Tm3+ gradually deviate from the straight line as the temperature decreases. The deviation indicates the effect of “decoupling” on the temperature dependence of FIR. To eliminate the deviation, the fluorescence dynamic curves of the coupled pairs were measured at different temperatures. Since two successive energy transfer processes are involved in the populating pathway of the 3F2,3 level, the resulting dynamic curve contains more decay components. According to Eqs. (13) and (14), the fluorescent decay from the 3H4 level (the lower level) exhibits a double exponential behavior, while the fluorescent decay from 3F2,3 level (the upper level) exhibits a triple exponential behavior. A pair of typical temporal evolutions of the two fluorescence emissions is illustrated in Fig. 4. Similarly, the two slow decay components in the three exponential decay (the upper level) are consistent with that of the double exponential decay (the lower level), which indicates an intrinsic coupled relationship between the two levels. The η values at different temperatures were calculated using the weight factors in the triple exponential decay curves according to Eq. (17) and were then plotted in Fig. 5(a) as well as a proposed correcting curve. Meanwhile, the corresponding FIR* was calculated and plotted in Fig. 5(b). It is apparent from this that the deviated FIR was successfully corrected to adhere to the Boltzmann law, which is represented by a straight line in the logarithmic scale.
Acknowledgements This research was supported by National Natural Science Foundation of China (61505045, 81571720) and China Scholarship Council (201706125022). References [1] A.K. Soni, V.K. Rai, M.K. Mahata, Luminescent probes and sensors for temperature Yb3+ sensitized Na2Y2B2O7: Er3+ phosphors in enhanced frequency upconversion,.temperature sensing and field emission display, Mater. Res. Bull. 89 (2017) 116–124. [2] D. Wawrzynczyk, A. Bednarkiewicz, M. Nyk, W. Strek, M. Samoc, Neodymium (III) doped fluoride nanoparticles as non-contact optical temperature sensors, Nanoscale 4 (22) (2012) 6959–6961. [3] M. Kochanowicz, D. Dorosz, J. Zmojda, J. Dorosz, P. Miluski, Influence of temperature on upconversion luminescence in tellurite glass co-doped with Yb3+/Er3+ and Yb3+/Tm3+, J. Lumin. 151 (2014) 155–160. [4] X.N. Tian, X.T. Wei, Y.H. Chen, C.K. Duan, M. Yin, Temperature sensor based on ladder-level assisted thermal coupling and thermal-enhanced luminescence in NaYF4: Nd3+, Opt. Express 22 (24) (2014) 30333–30345. [5] S.A. Wade, S.F. Collins, G.W. Baxter, Fluorescence intensity ratio technique for optical fiber point temperature sensing, J. Appl. Phys. 94 (8) (2003) 4743–4756. [6] F. Qin, H. Zhao, M.Y. Lv, W. Cai, Z.G. Zhang, W.W. Cao, Fluorescence intensity ratio thermometer methodology of eliminating the “decoupling” effect of a pair of thermally coupled energy levels of rare-earth ions, Opt. Lett. 42 (7) (2017) 1401–1403. [7] M.G. Nikolić, D.J. Jovanović, M.D. Dramićanin, Temperature dependence of emission and lifetime in Eu3+-and Dy3+-doped GdVO4, Appl. Opt. 52 (8) (2013) 1716–1724. [8] F. Qin, H. Zhao, W. Cai, Z.G. Zhang, W.W. Cao, A precise Boltzmann distribution law for the fluorescence intensity ratio of two thermally coupled levels, Appl. Phys. Lett. 108 (24) (2016) 241907. [9] A. Kumari, A.K. Soni, V.K. Rai, Near infrared to blue upconverting Tm3+/Yb3+/Li +:Gd-2(MoO4)(3) phosphors for light emitting display devices, Infrared Phys. Technol. 81 (2017) 313–319. [10] R. Dey, V.K. Rai, Er3+-Tm3+-Yb3+:CaMoO:4 phosphor as an outstanding upconversion-based optical temperature sensor and optical heater, Methods Appl. Fluoresc. 5 (1) (2017) 015006. [11] X.F. Wang, J. Zheng, Y. Xuan, X.H. Yan, Optical temperature sensing of NaYbF4: Tm3+ @ SiO2 core-shell micro-particles induced by infrared excitation, Opt. Express 21 (18) (2013) 21596–21606. [12] J.Y. Zhang, H. Zhao, X.T. Zhang, X.Z. Wang, H. Gao, Z.G. Zhang, W.W. Cao, Monochromatic near-infrared to near-infrared upconversion nanoparticles for highcontrast fluorescence imaging, J. Phys. Chem. C 118 (5) (2014) 2820–2825. [13] A. Baride, J.M. Meruga, C. Douma, D. Langerman, G. Crawford, J.J. Kellar, W.M. Cross, P.S. May, A NIR-to-NIR upconversion luminescence system for security printing applications, RSC Adv. 5 (123) (2015) 101338–101346. [14] W. Xu, X.Y. Gao, L.J. Zheng, Z.G. Zhang, W.W. Cao, An optical temperature sensor based on the upconversion luminescence from Tm3+/Yb3+ codoped oxyfluoride glass ceramic, Sens. Actuators B 173 (2012) 250–253. [15] P. Loiko, M. Pollnau, Stochastic model of energy-transfer processes among rareearth ions. Example of Al2O3:Tm3+, J. Phys. Chem. C 120 (46) (2016) 26408–26489.
5. Conclusion In summary, using the thermally coupled pair of the 3F2,3 & 3H4 levels of Tm3+ ions, a correcting method for an upvonversion pumped system was theoretical performed and experimentally tested. Theoretical results indicated that the double exponential decay of the lower level was entirely involved in the decay of the upper level, which could be used to determine the thermal population degree (η). The η values are found to be obtainable from fitting the fluorescence dynamic curves and a correction curve has been therefore given. A clear and
187