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Enhanced up-conversion red light emission from rare earth titanium oxide nanocrystals with pyrochlore phase

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Abstract

A facile sol-gel method combined with the post-annealing process has been used to synthesize Yb3+/Er3+ co-doped TiO2 nanocrystals. It is found that the high Yb3+ concentrations can promote the formation of TiO2 nanocrystals with pyrochlore phase. An intense up-conversion (UC) red light emission (658 nm) has been achieved under 980 nm laser excitation, which is enhanced by 108 folds compared with the reference sample. Both the luminescence intensity and the red-to-green emission intensity ratio are dependent of the annealing temperature, which can be explained as the distribution of rare-earth ions and phase change of TiO2 nanocrystals.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Recently, rare-earth (Re3+) ions doped luminescent materials have attracted great attention due to their unique luminescent characteristics [1–6]. Re3+ doped up-conversion materials refers to nonlinear optical processes, in which the low-energy light, usually near infrared (NIR), is converted into high-energy light. Furthermore, they exhibit novel and interesting fluorescence properties, which could be applied in the fields of multicolor displays, solid-state laser, photodynamic therapy, bio-imaging and luminescent solar concentrator [7–11]. Especially, Re3+ ions doped UC nanomaterials are recognized as the promising biological fluorescent labeling materials because of their low toxicity, weak background luminescence, deep-tissue penetration and minimal photo-damage to living organisms under a NIR excitation source [12]. The fluorescence of 600-1000 nm band is called “optical window” of biological tissues. Visible red emission in the range of this optical window is beneficial for bio-imaging to achieve visualization directly. Therefore, it is significant to adjust UC emission into red light emission band and enhance red fluorescence intensity for biological applications. However, one of the current challenge is to get an enhanced red light emission instead of the usually-observed strong green light emission from Yb3+/Er3+ co-doped UC nanomaterials [13–16].

Ytterbium (Yb3+) ion has a two-level structure (2F5/2 and 2F7/2 levels), large absorption cross-section near 980 nm and efficient energy transfer (ET) to other Re3+ ions. It is widely used as the sensitizer to collect 980 nm photons and subsequently transfers the photons to neighboring activators [17]. Among the various Re3+ ions, erbium (Er3+) is commonly used as the activator due to its plentiful meta-stable levels and suitable for emitting NIR to visible luminescence. In particular, Yb3+/Er3+ co-doped nanomaterials have good performance in terms of red and green UC emissions [18–21]. Up to now, a number of efforts have been made to enhance red emission in Yb3+-Er3+ system. For example, an enhanced red light emission was reported in NaGdF4:Yb/Er and NaErF4 nanocrystals by introducing Mn2+ ions due to the resonances between the Mn2+ absorption bands and metastable levels of Er3+ [22, 23]. Hu et al. demonstrated that the intensity of UC red emission was increased by 14 and 24 times in Mn2+ and Fe3+ doped NaYF4:Yb3+,Er3+ nanoparticles, respectively [24]. Ce3+/Er3+/Yb3+ tri-doped NaYF4 nanocrystals were investigated try to tune UC emission [25]. We note that most of the previous works were concentrated on introducing transition metals in fluoride. However, the transition metals, such as manganese and iron will possibly cause fatal damage to biological tissue. Oxides materials, such as TiO2, exhibiting high chemical stability, low-toxicity, low-cost and simple synthesis processes is considered to be an excellent host lattice for red light emissions [26, 27]. For instance, Zhang et al. presented red light emission of Er3+ doped TiO2 nanocrystals [28]. Intense red UC luminescence was obtained in Yb3+/Er3+ co-doped ZnO-TiO2 compound [29]. Recently, dominant red emission was achieved in pyrochlore phase rare-earth titanium oxides such as Yb3+/Er3+ co-doped Lu2Ti2O7, Gd2Ti2O7 nanocrystals [30, 31]. In our previous work, we fabricated Yb3+/Er3+ do-doped TiO2 nanocrystals, which have dominant UC red light emission [32]. However, the intensity ratio of red-to-green light emission is quite low.

In this work, TiO2 nanocrystals with high Yb3+ ions concentration doping have been prepared via previous synthesis method with some modification. It is interesting to find that the high concentration of Yb3+ doping results in the preferential formation of TiO2 nanocrystals with pyrochlore phase and the corresponding UC red light emission intensity is significantly enhanced by more than two orders of magnitude. Based on the structural characterization and dynamic luminescence measurements, the possible enhancement mechanisms are discussed.

2. Experimental section

High-purity rare-earth nitrates Yb(NO3)3·5H2O (99.99%) and Er(NO3)3·5H2O (99.9%) are purchased from Shanghai Aladdin Biochemical Technology Co., LTD. Other chemicals tetrabutyl titanate (TBOT), acetylacetone, ethanol and nitric acid (obtained from Sinopharm Chemical Reagent Co., Ltd., China) are all analytical grade. The deionized water (>18 MΩ) is prepared by a Milli-Q ultrapure water purification system. Figure 1 shows a schematic diagram of the synthesis process for the Yb3+/Er3+ co-doped TiO2 nanocrystals. In detail, firstly 38 ml ethanol, 22ml TBOT and 8ml acetylacetone are well mixed together under modest stirring to get a transparent primrose yellow solution. The mixture (PH≈2) of 3 ml deionized water, 18 ml ethanol and several drops of HNO3 is added into the above solution dropwise to form precursor solution. Then according to the molar ratio of Yb3+:Er3+:Ti4+ (0.3:0.02:0.68), Yb(NO3)3·5H2O and Er(NO3)3·5H2O are accurately weighted and dissolved in the precursor solution. The mixed solution is slightly stirred at 60 °C for 4 h, then cooled down to the room temperature and aged for 24 hours to form transparent gel. The Yb3+/Er3+ co-doped gel is transferred to a crucible, drying at 100°C to get rid of the solvent and form xerogel. Then, the obtained xerogel is annealed at different temperatures in air atmosphere for 1 hour. After annealing, the Yb3+/Er3+ co-doped TiO2 sample is collected and stored in a sealed container. The sample with 30 mol% Yb3+ doping exhibits a better UC performance than that of the samples with other Yb3+ doping concentration. Therefore, the Yb3+ concentration of the samples used in the present work is fixed at 30 mol%.

 figure: Fig. 1

Fig. 1 Schematic diagram of the synthesis procedure.

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The crystal structures and phases of the samples are determined by X-ray diffraction (XRD, Rigaku Ultima III) with Cu Kα radiation (λ = 1.5406 Å) at a step rate of 0.02° in the 10-85° range. The morphologies and microstructures are characterized using a transmission electron microscopy (TEM, Tecnai G2 F20). X-ray photoelectron spectroscopy experiment is carried out on a Thermo ESCALAB 250 system. UC emission spectra are recorded by a fluorescence spectrophotometer (Edinburgh Photonics, FLS980) equipped with a 980 nm laser with tunable power. All measurements are performed at room temperature.

3. Results and discussion

The XRD patterns of Yb3+/Er3+ (30 mol%/2 mol%) co-doped TiO2 calcined at different temperatures are given in Fig. 2(a). At low annealing temperatures (500 °C and 600 °C), amorphous structural Yb3+/Er3+ co-doped TiO2 with a very weak peak at 30.95° is detected. No anatase or rutile phase is found from the XRD patterns. For the 700 °C annealed sample, peaks at 30.95°, 35.90°, 51.70° and 61.39° are recorded, which correspond to pyrochlore phase Yb2Ti2O7 (JCPDS No.17-0454) with space group Fd-2m(227). Comparing with the XRD pattern of the un-doped TiO2 annealed at 700 °C (rutile JCPDS No.21-1276), the result indicates that Yb3+ and Er3+ ions are gradually incorporated with the TiO2 nanocrystals. Furthermore, the crystallinity of Yb3+/Er3+ co-doped TiO2 nanocrystal is improved with further increasing the annealing temperature to 800 °C, which is confirmed by TEM observations. In addition, a weak peak of rutile phase appears at 27.42° in the spectrum for the 800 °C annealed sample. The similar phenomenon was also reported by Chen et al. [34]. They prepared Yb3+/Er3+ (30 mol%/5 mol%) co-doped TiO2 films via annealing in dry oxygen atmosphere, and found a weak peak of rutile phase at 27.42° besides the peaks of pyrochlore phase when the annealing temperature higher than 800 °C.

 figure: Fig. 2

Fig. 2 (a) XRD patterns of samples annealed at different temperatures. (b) Structure models of anatase, rutile and pyrochlore phase [33].

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In general, anatase phase Re3+ doped TiO2 nanocrystals are formed firstly at low annealing temperature. Then, rutile phase TiO2 nanocrystals will be transformed from anatase phase with increasing temperature. The pyrochlore phase Re3+ doped TiO2 nanocrystals can be obtained at the annealing temperature higher than 800°C [27, 28]. However, Yb3+/Er3+ co-doped TiO2 nanocrystals with pyrochlore phase can be directly obtained even at the annealing temperature of 700 °C in our case, which suggests that the high Yb3+ doping concentration can promote the formation of pyrochlore phase TiO2 nanocrystals. Figure 2(b) shows the schematic structures of anatase, rutile and pyrochlore phase of TiO2 nanocrystal. In pyrochlore phase crystal structure, each Yb3+/Er3+ ion is surrounded by eight oxygen atoms in a distorted cubic structure, while each Ti4+ ion is six coordinated and locates at an octahedral site [33, 35]. Since the Yb3+ ion has different valence from Ti4+ ion and the ionic radii of Yb3+ (0.86 Å) is larger than that of Ti4+ (0.68 Å), TiO2 host structure will be seriously distorted by adding Yb3+ ions with high concentration [26]. Consequently, the pyrochlore phase of TiO2 nanocrystals can be easily obtained in the present work.

Typical TEM images of Yb3+/Er3+ co-doped TiO2 annealed at different temperatures are shown in Fig. 3. It can be found that the sample annealed at 600 °C is amorphous. And the crystallinity is gradually improved with increasing annealing temperature, which is consistent with the results of XRD patterns. In order to verify the crystalline structure, the High-resolution TEM (HRTEM) and corresponding Fast Fourier Transform (FFT) images are analyzed. For the sample annealed at 700 °C, the measured inter-planar spacing is 0.288 nm, which is corresponding to (222) plane of pyrochlore phase TiO2 nanocrystals (inset of Fig. 3(b)). The inter-planar spacing is about 0.578 nm for the sample annealed at 800 °C, which is corresponding to (111) plane of pyrochlore phase (inset of Fig. 3(c)). In addition, the elemental components of samples are detected by energy-dispersive X-ray (EDX) analysis. As shown in Fig. 3(d), all elemental components which are Yb, Er, Ti, O have been found.

 figure: Fig. 3

Fig. 3 TEM images of Yb3+/Er3+ co-doped TiO2 annealed at different temperatures: (a) 600 °C, (b) 700 °C, (c) 800 °C. The insets are high-resolution images and corresponding Fast Fourier Transform images. (d) EDX spectrum of the sample annealed at 700°C.

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The composition and chemical states of Yb3+/Er3+ co-doped TiO2 nanocrystals annealed at 700 °C are examined by XPS measurement. Figure 4(a) is the Ti 2p XPS spectrum, and the binding energy of the Ti 2p peaks are located at 458.22 eV and 463.83eV which correspond to Ti 2p3/2 and Ti 2P1/2, respectively. The binding energies of Ti 2p are located at lower energy compared with Ti 2p3/2 (459.1 eV) and Ti 2p1/2 (464.8 eV) of pure TiO2 [36]. This suggests a relatively poor crystal structure in the sample. Moreover, the well-fitted splitting peaks of O 1s in dash lines are shown in Fig. 4(b). There are three fitting peaks centered at 529.69, 531, and 532.21 eV, which can be assigned to the Yb-O-Ti, Ti-O and Yb-OH bonds [37, 38]. According to the XRD pattern, only pyrochlore phase is found in the 700 °C annealed sample. Therefore, the Ti-O and Yb-OH bonds might be contained in amorphous phase. Indeed, the TiO2 nanoparticles with amorphous phases are detected by TEM observations (not shown in here).

 figure: Fig. 4

Fig. 4 XPS spectra: (a) Ti 2p, and (b) O 1s, for Yb3+/Er3+ co-doped TiO2 nanocrystals annealed at 700 °C.

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The UC emission spectra of Yb3+/Er3+ co-doped TiO2 nanocrystals annealed at different temperatures are recorded by a fluorescence spectrophotometer. A 980 nm NIR laser (power density≈9 W/cm2) is used as the excitation source. The visible range of spectra are shown in Fig. 5(a). Weak green (525 and 547 nm) and relatively intense red (658 nm) emission bands of Er3+ are detected, which originate from the 2H11/24I15/2, 4S3/24I15/2 and 4F9/24I15/2 transitions, respectively. It is very clear that with the increase of the annealing temperature from 500 to 800 °C, the intensity of UC emission increases tremendously, and then decreases sharply. We also prepared the reference sample of Yb3+/Er3+ (10 mol%/2 mol%) co-doped TiO2 nanopowder annealed at 900°C in nitrogen ambient, which is prepared by the same synthesis method as reported in our previous work without spin-coating process [32]. It is found that under low concentration (10 mol%) of Yb3+ doping and nitrogen ambient, sample annealed at 900 °C exhibits the brightest UC emission compared to other annealing temperature. However, in air atmosphere, 700 °C annealed TiO2 with high concentration (30 mol%) Yb3+ doping possesses the best UC property in our present case. The UC emission intensity is about 108 times stronger than that of the reference sample as shown in Fig. 5(a). The main reason for this phenomenon is that the crystal structures are different. The anatase/rutile phase structure TiO2 is easier to form under low concentration of Re3+ doping. High concentration of Re3+ doping is beneficial to form pyrochlore phase TiO2 [34, 39]. In addition, oxygen can promote the formation of pyrochlore phase. Ting et al. observed XRD peaks of pyrochlore phase in 5 mol% Er3+ doped TiO2 annealed at 700 °C in dry oxygen atmosphere [39]. In contrary, only anatase phase was obtained in Yb3+/Er3+ (10 mol%/10 mol%) co-doped TiO2, which was annealed at 700 °C in vacuum [40]. In the present work, Yb3+/Er3+ co-doped TiO2 nanocrystals with dominant pyrochlore phase are obtained under high Yb3+ concentration doping and annealing in air atmosphere. In Yb3+/Er3+ co-doped pyrochlore phase TiO2 crystal structure, Yb3+/Er3+ ions are separated by Ti4+-O2+ octahedron, and Yb3+/Er3+ ions present a layer distribution. In principle, the two-dimensional energy migration in pyrochlore phase TiO2 structure can inhibit concentration quenching of UC fluorescence and enhance UC emission intensity [41].

 figure: Fig. 5

Fig. 5 (a) UC emission spectra of samples; (b) Integrated intensity of red emission as a function of annealing temperature, insets are the corresponding luminescent photos of the samples in ethanol solutions; (c) Double-logarithmic plot of excitation power dependent luminescence intensity of the sample annealed at 700 °C; (d) Schematic diagram of proposed UC mechanisms in Yb3+/Er3+ co-doped TiO2 nanocrystals.

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In order to visualize, the integrated intensity of red emission as a function of annealing temperature and the corresponding digital luminescent photos of UC red light in ethanol solutions (0.04 wt.%) of Yb3+/Er3+ co-doped TiO2 are shown in Fig. 5(b). The photographs are taken without using the filter either in digital camera or at the sample position and the light emission can be easily seen by naked eye. The Yb3+/Er3+ co-doped TiO2 nanocrystals annealed at 700 °C exhibit the brightest luminescence, which agrees with the spectra result. The improved UC emission can be attributed to good crystal quality and less defects states. Generally, structure with a lower crystal symmetry is benefit for UC emission [42, 43]. Rutile phase TiO2 with higher symmetric crystals symmetry may has lower UC emission efficiency compared with other phases TiO2. Moreover, high temperature annealing will cause Re3+ agglomeration, which can lead to the quenching of UC fluorescence. In addition, the mixed pyrochlore and rutile phase may cause the variation of the valence state of Ti and in turn to affect the UC emission. Therefore, the followed decreasing of UC emission for the 800 °C annealed sample can be attribute to Re3+ agglomeration in pyrochlore phase and formation of rutile phase caused by high temperature annealing. In previous literature, the fast decreasing of UC emission was also observed in the samples annealed at high temperature [26, 32, 44]. In addition, the intensity ratio of IRed/IGreen is a significant performance parameter. Although efficient UC emissions can be obtained in Yb3+/Er3+ co-doped TiO2 nanopowders by hydrothermal-assisted sol-gel method, the intensity ratio of IRed/IGreen lower than 1 [45]. In our previous work, the maximum of IRed/IGreen is about 4 [32]. Recently, Liao et al. have reported a strong red emission property in Lu2Ti2O7 nanophosphors co-doped with Yb3+ (12 at%) and Er3+ (2 at%) under the excitation of a 980nm laser (power density≈3 W/cm2) [30], in which the IRed/IGreen is estimated to be about 20. According to the data of UC emission spectra (Fig. 5(a)), the calculated intensity ratios of IRed/IGreen exceed 10. Moreover, the intensity ratio of IRed/IGreen can reach 24 under relative low power density (≈3 W/cm2).

In order to further understand the UC process, the emission spectra of samples with different pump powers are measured. In general, for unsaturated UC processes, the number of pumping photons N can be calculated through the following formula IUC∝PN, where IUC is the integrated intensity of the UC emission and P is the pumping power [46, 47]. It is found that the calculated N values of the red and green emissions in our case are approximately equal to 2 for all the 500-800 °C annealed samples. Figure 5(c) shows the power dependence of the red and green emissions by a log-log plot for 700 °C annealed sample. The slopes of the linear fitting are 1.722 and 1.922 for red and green emissions, respectively. The result indicates that two-photon excitation processes are mainly responsible for the red and green emissions in our samples.

The schematic energy level diagram of Yb3+ and Er3+ ions and possible UC processes to produce red and green emissions are depicted in Fig. 5(d). In general, for the red emission at 658 nm (Er3+: 4F9/24I15/2), the following energy transfers (ET1 and ET2) and nonradiative relaxation processes might be responsible for the population of 4F9/2 level of Er3+ ions [45],

2F5/2(Yb3+)+4I15/2(Er3+)2F7/2(Yb3+)+4I11/2(Er3+) (ET1)
2F5/2(Yb3+)+4I13/2(Er3+)2F7/2(Yb3+)+4F9/2(Er3+) (ET2)
2H11/2/4S3/2(Er3+)4F9/2(Er3+)(nonradiativerelaxation)
For the green UC emission (Er3+: 2H11/2/4S3/24I15/2), the 2H11/2/4S3/2 levels are mainly populated by sequential energy transfer ET1 and ET3 and the nonradiative relaxation, which can be expressed as [48],
2F5/2(Yb3+)+4I15/2(Er3+)2F7/2(Yb3+)+4I11/2(Er3+) (ET1)
2F5/2(Yb3+)+4I11/2(Er3+)4F7/2(Er3+)+2F7/2(Yb3+) (ET3)
4F7/2(Er3+)2H11/2/4S3/2(Er3+)(nonradiativerelaxation)
In our case, other mechanisms must be involved in for promoting dominant UC red light emission [31, 49]. For instance, the 4F9/2 level of Er3+ also can be populated by cross-relaxation CR1 process: 4F7/2(Er3+) + 4I11/2(Er3+)→24F9/2(Er3+). Additionally, cross-relaxation CR2 process: 2H11/2(Er3+) + 4I15/2(Er3+)→4I9/2(Er3+) + 4I13/2(Er3+) and back energy transfer (BET) process from Er3+ to Yb3+: 2F7/2(Yb3+) + 4S3/2(Er3+)→2F5/2(Yb3+) + 4I13/2(Er3+) will increase the population of 4I13/2 level, while depopulate the 2H11/2/4S3/2 levels of Er3+ ions. Subsequently, the populated 4I13/2 level of Er3+ ions will boost the ET2 process. The intense red and weak green emissions of Yb3+/Er3+ co-doped TiO2 nanocrystals with pyrochlore phase can be attributed to the strong CR1, CR2 and BET processes.

In order to further investigate the UC characteristics of Yb3+/Er3+ co-doped TiO2 nanocrystals. The red emission (658 nm band) decay curves of the samples annealed at different temperatures are recorded under irradiation with a 980 nm pulsed laser (see Fig. 6). All the decay curves falling edges of the samples can be well fitted to a double exponential function [50, 51]:

I(t)=Α1exp(tτ1)+Α2exp(tτ2)
where A1 and A2 are fitting constants, t is time, τ1 and τ2 are the rapid and slow lifetimes for the exponents. The average lifetime τ can be calculated as follows,

 figure: Fig. 6

Fig. 6 Transient UC spectra and decay times of 4F9/24I15/2 transition under a 980 nm pulsed laser.

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τaverage=(Α1τ12+Α2τ22)(Α1τ1+Α2τ2)

The calculated average lifetime increases to maximum 9.01μs at 700 °C annealing temperature and then decreases with further increasing annealing temperature. The change of decay curves coincides well with above spectra data (Fig. 4(a)). However, fitting with a double-exponential function means existence of some energy depletion processes. The calculated lifetimes of the red emission of Er3+ ions are lower than 10 μs, which is quite short time compared with several hundreds of microseconds of typical lifetime of Er3+ ions [45, 51, 52]. The strong cross-relaxation between the Er3+ ions, defects or quenching environment of Er3+ ions (such as OH-) could accelerate ET among the Er3+ ions in pyrochlore phase Yb3+/Er3+ co-doped TiO2 nanocrystals, resulting in a short lifetime of Er3+ UC emission. The quite short lifetimes of red UC emissions of Yb3+/Er3+ co-doped TiO2 nanocrystals are analogous to those TiO2:Er nanocrystals (<4.7 μs) and Yb3+/Er3+ co-doped perovskite KMgF3 nanocrystals (~40 μs) [50, 53].

4. Conclusion

In conclusion, Yb3+/Er3+ co-doped TiO2 nanocrystals with intense red emission are successfully synthesized via a facile sol-gel method combining with the post-annealing treatments in air atmosphere. It is found that the addition of high content of Yb3+ ions favors the formation of pyrochlore phase TiO2 nanocrystals. Under a 980 nm laser irradiation, strong UC red light emission is obtained, which is about 108 times larger than that of the reference sample. The enhanced UC light emissions can be attributed to the layer distribution structure of Re3+ ions in pyrochlore phase TiO2 structure, which can inhibit the concentration quenching of UC luminescence. The dominant UC red light emission (IRed/IGreen>10) can be attributed to the strong cross-relaxation (CR1 and CR2) processes and back energy transfer from Er3+ to Yb3+ ions. Our results indicate that the pyrochlore phase Yb3+/Er3+ co-doped TiO2 nanocrystals with intense UC red luminescence can be used as a good candidate for biological fluorescent label and other optoelectronic devices.

Funding

National Natural Science Foundation of China (No.61735008); the Higher Education Excellent Youth Talents Foundation of Anhui Province (No. gxyqZD2016329); Natural Science Foundation of Anhui Province (No. 1808085QF219).

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Figures (6)

Fig. 1
Fig. 1 Schematic diagram of the synthesis procedure.
Fig. 2
Fig. 2 (a) XRD patterns of samples annealed at different temperatures. (b) Structure models of anatase, rutile and pyrochlore phase [33].
Fig. 3
Fig. 3 TEM images of Yb3+/Er3+ co-doped TiO2 annealed at different temperatures: (a) 600 °C, (b) 700 °C, (c) 800 °C. The insets are high-resolution images and corresponding Fast Fourier Transform images. (d) EDX spectrum of the sample annealed at 700°C.
Fig. 4
Fig. 4 XPS spectra: (a) Ti 2p, and (b) O 1s, for Yb3+/Er3+ co-doped TiO2 nanocrystals annealed at 700 °C.
Fig. 5
Fig. 5 (a) UC emission spectra of samples; (b) Integrated intensity of red emission as a function of annealing temperature, insets are the corresponding luminescent photos of the samples in ethanol solutions; (c) Double-logarithmic plot of excitation power dependent luminescence intensity of the sample annealed at 700 °C; (d) Schematic diagram of proposed UC mechanisms in Yb3+/Er3+ co-doped TiO2 nanocrystals.
Fig. 6
Fig. 6 Transient UC spectra and decay times of 4F9/24I15/2 transition under a 980 nm pulsed laser.

Equations (8)

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2 F 5/2 ( Yb 3+ ) + 4 I 15/2 ( Er 3+ ) 2 F 7/2 ( Yb 3+ ) + 4 I 11/2 ( Er 3+ )
2 F 5/2 ( Yb 3+ ) + 4 I 13/2 ( Er 3+ ) 2 F 7/2 ( Yb 3+ ) + 4 F 9/2 ( Er 3+ )
2 H 11/2 / 4 S 3/2 ( Er 3+ ) 4 F 9/2 ( Er 3+ ) ( nonradiative relaxation )
2 F 5/2 ( Yb 3+ ) + 4 I 15/2 ( Er 3+ ) 2 F 7/2 ( Yb 3+ ) + 4 I 11/2 ( Er 3+ )
2 F 5/2 ( Yb 3+ ) + 4 I 11/2 ( Er 3+ ) 4 F 7/2 ( Er 3+ ) + 2 F 7/2 ( Yb 3+ )
4 F 7/2 ( Er 3+ ) 2 H 11/2 / 4 S 3/2 ( Er 3+ ) ( nonradiative relaxation )
I(t)= Α 1 exp( t τ 1 )+ Α 2 exp( t τ 2 )
τ average = ( Α 1 τ 1 2 + Α 2 τ 2 2 ) ( Α 1 τ 1 + Α 2 τ 2 )
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