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Enhanced green luminescence in Ce-Tb-Ca codoped sintered porous glass

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Abstract

We report on a new kind of green-emitting high silica luminous glass, which is fabricated by sintering of Ce3+-Tb3+ co-doped porous glass. The spectra show that there are energy transfer between Ce3+ and Tb3+, and cross-relaxation between 5D3 and 5D4 energy level of Tb3+. The energy transfer process can be adjusted by addition of Ca2+ into the Ce3+-Tb3+ co-doped porous glass, and the transfer rate can be enhanced about four times than that of Ce3+-Tb3+ co-doped porous glass. The role of Ca2+ has been discussed, and the fluorescence decay curve reveals that the Ca2+ play an important role in energy transfer.

©2010 Optical Society of America

1. Introduction

Rare earth ions doped luminescent materials have been deeply and exhaustively investigating for several decades in that these ions generally have plenty of well-shielded 4f states that can emit fluorescence covering different wavelength from ultraviolet to infrared. Therefore, these materials has generated much interest in applications such as plasma display panels, bulk lasers, fiber lasers/amplifiers, solar concentrators, displays, fluorescent lamps and transparent phosphors [13]. Recent ten years, white-LEDs have attracted lots of attention in solid state lighting for the replacement of conventional incandescent and fluorescent lamps due to their excellent advantages in energy saving and environment protection [2,4]. White-LEDs can basically classified into two types, one is multi-chip type by packaging red, green, blue LEDs together and the other one is single-chip type with one blue or ultraviolet light source coated with some phosphors. The multi-chip type must combine two or three different LEDs and the drive circuit is very complex. The single-chip type has only one type of LED and the circuit design is easier. In comparison with the commercial white LED fabricated with a blue chip coated with yellow phosphor YAG: Ce3+, the white LED based on near ultraviolet (NUV) chip coated with tri-phosphor fluorescent powder has higher color stability and better color index because all of the colors are determined by the phosphors [1,5]. Luminescent glass has many advantages, and widely used as fluorescent material. There is plenty of investigation on rare earth ion-doped luminescent glass excited by LED; most of them are limited in non-silicate glass system such as borate and phosphate glass. Compared to the non-silicate glass systems, the silica glass has some advantages such as higher mechanical, thermal and chemical stability [57]. The silica glass is rarely used as fluorescent materials other than optical fiber, because there is a natural tendency for rare-earth ions with higher concentration to form clusters and quench the luminescence in the silica glass [69]. Recently we developed a new method to overcome these drawbacks mentioned above. The method is primarily dependent on sintering of porous glass impregnated with rare-earth ions to prepare high-silica luminous glass. The component of the porous glass is very close to that of silica glass; therefore the sintered high-silica glass has excellent mechanical, thermal and chemical properties similar to silica glass [6,10,11]. Optically active elements such as metal ions and nanocrystals can be incorporated into the nano pores and channels in the porous glass. The sintered porous glasses can tolerate a higher concentration of dopants than traditional melt glasses without apparent concentration quenching [10,11]. By this route, we fabricated a series of transparent high-silica luminous glass with different emission. In this manuscript, we report on a new kind of Ce3+-Tb3+-Ca2+ co-doped green-emitting high silica luminous glass. The luminescence spectra show that there are energy transfers between Ce3+ and Tb3+, and also between 5D3 and 5D4 energy level of Tb3+. The excitation wavelength can be tuned from short-wavelength ultraviolet (238nm) towards long-wavelength ultraviolet (310nm) by energy transfer processes. Furthermore, the energy transfer process can be adjusted by addition of Ca2+ into the porous glass, and the transfer rate can be enhanced about four times than that of Ce3+-Tb3+ co-doped porous glass.

2. Experiment

Preparation of the rare earth ions doped porous glass followed the process described in earlier work of Chen and Yang et al [6,10,11]. We prepared the samples by sintering of the porous glass impregnated with Tb3+, Ce3+, and Ca2+ ions. In this system Ce3+ acts as sensitizer transferring energy to activator Tb3+ and Ca2+ acts as a modifier to this process. The ions were introduced into the glasses by immersing the porous glass into 0.2−1.7 mol% solutions containing corresponding nitrate compounds. After drying in air for 1 hour, the glasses were sintered at 1120°C in a reduced atmosphere for 2 hours. Finally, a series of compact, transparent and colorless glasses were fabricated. Then the large surfaces of glasses were optically polished for subsequent measurements with thickness of 1mm. Excitation and emission spectra in the ultra-violet and visible wavelength ranges were recorded on a JASCO FP-6500 fluorescence spectrophotometer equipped with a tunable excitation source range from 200nm to 750nm. Photoluminescence decay measurements of Ce3+ and Tb3+ were performed by using an FLS920 fluorescence spectrophotometer. Decay curves for Tb3+was recorded at 379nm under 238nm excitation and that of Ce3+ was recorded at 395nm with the excitation at 307nm. In order to reduce the test error, we put every sample at the same position and keep them on same angle related to excitation light. All of measurements were carried out at room temperature.

3. Results and discussion

Figure 1 shows the emission spectra of Tb3+ doped, Ce3+ doped,Tb3+–Ce3+ co-doped, and Tb3+–Ce3+–Ca2+ co-doped sintered porous glasses. For the Tb3+ doped porous glass (a), there is almost no emission under 310nm excitation and for the Ce3+ doped porous glass (b) there is only one broad emission bands around 375 nm. However, for the Tb3+–Ce3+ co-doped glass (c) and the Tb3+–Ce3+–Ca2+ co-doped glass (d), there are a broad emission band around 375 nm, and several narrow peaks centered at 488, 543, 588, and 622 nm. The broad emission band can be ascribed to the 5d→4f transition of Ce3+ and the narrow emission peaks are due to 5D47FJ transitions of Tb3+ [48].The narrow emission peaks from Tb3+ indicates presence of energy transfer from Ce3+ to Tb3+. It was shown that by co-doping of a small amount of Ce3+ with Tb3+ into glass, the emission of Tb3+ can be significantly increased due to energy transfer from Ce3+ to Tb3+. Furthermore, it is amazing that compared with the Tb3+–Ce3+ co-doped glass, the Tb3+ ions in the Tb3+–Ce3+–Ca2+ co-doped glass have stronger emission whose intensity is enhanced at least three times than that in Tb3+–Ce3+ co-doped glass. It is obvious that Ca2+ plays an important role in increasing the emission of Tb3+, and the energy transfer processes can be adjusted by addition of Ca2+. The left inset shows the photographs of luminous glasses under 312nm excitation. It can be seen the glasses exhibit gradually increased green emission from sample c to sample d, which corresponds to the Tb3+–Ce3+ co-doped, Tb3+–Ce3+–Ca2+ co-doped glasses.

 figure: Fig. 1

Fig. 1 Emission spectra of Tb3+ doped (a),Ce3+ doped (b), Tb3+–Ce3+ co-doped (c), and Tb3+– Ce3+–Ca2+ co-doped (d) sintered porous glasses. The excitation wavelength is 310 nm. Tb3+ doped glass has a Tb3+ concentration of 0.235 mol%. Tb3+–Ce3+ co-doped glass has a Tb3+ concentration of 0.235 mol% and a Ce3+ concentration of 0.08 mol%. Tb3+– Ce3+–Ca2+ co-doped glass has a Tb3+ concentration of 0.235 mol%, a Ce3+ concentration of 0.08 mol% and a Ca2+ concentration of 1.2 mol%. The left inset gives the photographs of luminous glasses exhibiting blue and green emission under 310nm irradiation. The a, b, c, and d samples correspond to Tb3+ doped glass, Ce3+ doped glass, Tb3+-Ce3+ co-doped glass, Tb3+-Ce3+-Ca2+ co-doped glass, respectively.

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To investigate the actual role of Ca2+ in the glass, we prepared a series of glass samples with the same Tb3+ and Ce3+ concentration and different Ca2+ concentrations. Figure 2 exhibits the 5D4 emission spectra and the corresponding excitation spectra of Tb3+. The excitation and monitoring wavelengths is 310nm and 544nm respectively.

 figure: Fig. 2

Fig. 2 (A) describes the 5D4 emission spectra of Tb3+-Ce3+-Ca2+-co-doped glasses under 310nm excitation. All of the glasses have Tb3+ concentration of 0.235 mol% and Ce3+ concentration of 0.08 mol% respectively. The concentration of Ca2+ is changed from 0.4 mol%, 0.6 mol%,0.8 mol%, 1.0 mol% to 1.2 mol%. Figure 2(B) shows the excitation spectra of the corresponding glasses monitored at 544 nm.

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Figure 2(A) shows the 5D4 emission spectra of Tb3+-Ce3+-Ca2+ co-doped glasses under 310 nm excitation, the concentration of Tb3+ and Ce3+ are constant but the concentration of Ca2+ is varied from 0.4 mol% to 1.2 mol%. It can be seen that the emissions from 5D4-7Fj transitions of Tb3+ increased with increased Ca2+ concentration. Corresponding to the 5D4 emission spectra, Fig. 2(B) shows increased excitation band with increased Ca2+ concentration. The excitation band centered at 320 nm is due to the 4f-5d absorption of Ce3+, and the weaker band centered at 238 nm is contribute to the absorption of Tb3+.

The above results imply that Ca2+ promote the energy transfer from Ce3+ to Tb3+. For the porous glass, there are some non-bridging oxygen (NNO) atoms at the internal surface of pores and channels and the rare-earth ions have high coordination numbers so the doped ions accumulated to share the limited non-bridging oxygen atoms [8,11]. Therefore in the sintered glass, parts of Tb3+ and Ce3+ tend to be clustered and have no contribution to emission. At low RE concentrations, the dopants can be distributed uniformly, bound to NNO atoms in RE–O–Si bonds. As the RE concentration is increased, clusters are formed through RE–O–RE bonding [8]. Clustering facilitates energy migration and fluorescence quenching. It is suggested from the above results that the Ca2+ can prevent the cluster formation because addition of Ca2+ can provide more non-bridging oxygen. Addition of Ca2+ facilitates the break-up of silica tetrahedron network; this will generate more non-bridging oxygen. At the same time, the lower coordination number of Ca2+ increases the probability of forming Ca–O–RE bond, so Ca2+ can substitute parts of clustered REs and make them free. Therefore there will be more rare-earth ions contributing to emission, and this will also decrease the distance between free Ce3+ and Tb3+ which can promote the energy transfer efficiency.

Furthermore, we also prepared Tb3+-Ca2+-codoped glasses with different Ca2+ concentration. Figure 3 shows the 5D3 and 5D4 emission spectra and excitation spectra of Tb3+. The excitation and monitoring wavelength is 238nm and 379 nm for 5D3 emission,and 238 and 544 nm for 5D4 Emission. Figure 3(A) shows the 5D3 emission spectra, there are several emission peaks at 379, 415, 438, and 458 nm corresponding to 5D37FJ (J = 6, 5, 4, and 3) transitions, respectively. It is shown that the emission intensity of 5D3 gradually decreases with increased Ca2+ concentration. However, for the 5D4 emission [Fig. 3(B)] peaked at 488, 544, 588, and 622 nm, the intensity can be greatly increased with increased Ca2+. Corresponding to the 5D3 and 5D4 emission spectra, Fig. 3(C) and 3(D) show the excitation spectra of Tb3+ obtained by monitoring 379nm (5D37F6) and 543nm (5D47F5)emissions, respectively [4,1012]. The excitation band of 379nm decreases when increasing of Ca2+ concentration. However, the excitation band of 544nm increases with the increasing of Ca2+ concentration. The two excitation spectra just like the corresponding emission spectra have absolutely contrary tendency, this implies more and more energy of 5D3 were transferred to 5D4 with the increase of Ca2+. All above results implies the occurrence of cross-relaxation processes among Tb3+ ions, and Ca2+ play an important role in this process [13,14]. The cross-relaxation process can be represented as (5D3, 7F6) →(5D4,7F0), and was facilitated for the closely matched energy level difference between 5D4 and 5D3 levels and the 7F6 and 7F0 levels [8]. The energy transfer rate of this process strongly depends on the inter-ion distance, which is determined byTb3+ concentration.

 figure: Fig. 3

Fig. 3 (A) and (B) are 5D3 and 5D4 emission spectra of Tb3+–Ca2+ co-doped glasses under 238-nm excitation. (C) and (D) are the excitation spectra of 5D3 and 5D4 emission of Tb3+ obtained by monitoring 379nm and 544nm emissions, respectively. All of the glasses have Tb3+concentration of 0.235 mol%. The concentration of Ca2+ is changed from 0.4 mol%, 0.6mol%, 0.8mol% to 1.0 mol%.

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The fluorescence decay curves of 5D37F5 emission are examined for the samples with different Ca2+ concentration. Figure 4 represents the decay curves of 5D37F5 emission for these samples. The cross relaxation between 5D3 and 5D4 leads to the decrease in 5D3 decay with increased Ca2+ concentration and produces a nonexponential component in the initial regime of the decay curves. As can be observed in Fig. 4, the cross relaxation is inconspicuous at lower Ca2+ concentration, and the decay are nearly in the form of single exponential and the variation of decay with Ca2+ concentration can be hardly observed. The decay curves are getting more nonexponential as Ca2+ concentration increase. In order to give a reasonable interpretation to the nonexponential behavior, a fundamental approach is adopted based on the multipolar interaction scheme.

 figure: Fig. 4

Fig. 4 Decay curves of the Tb3+ (5D37F5, 379nm) transition in the sintered porous silica glasses with different Ca2+ concentration under 238nm excitation. The concentration of Ca2+ is 0 mol% (a), 0.4 mol% (b), 0.6 mol% (c) and 0.8 mol% (d) respectively. The Tb3+ concentration is 0.235 mol%. The lines in colors are fitted lines of decay curves corresponding to sample a, b, c, and d, respectively.

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Assuming that the interaction is multipolar type and no migration takes place, the 5D3 decay curves could be analyzed using the well-known direct quenching mechanism. There is no energy migration effect or less energy migration effect in the 5D3 level because it is obviously suppressed by faster cross relaxation. Usually, the interaction scheme of 5D3 emission involves both the dipole-dipole and the dipole-quadrupole interactions, which can be described by Inokuti-Hirayama formula [8,13,14]. The rare earth ions doped in porous glass tend to accumulate at the internal surface of the pores and channels of porous glass, therefore the concentration of rare-earth ions is different everywhere. During subsequent sintering process, partsk of rare-earth ions tend to cluster in the glass matrix. Therefore parts of Tb3+ ions doped in porous glass clustered and these ions have no or less contribution to the emission. The non-clustered Tb3+ ions can efficiently emit fluorescence from the 5D3 and 5D4 levels, and can be classified into two types due to the distance between Tb3+ ions, one isolated and with no interaction with other ions, another with cross-relaxation by multipolar interaction. Therefore, the fluorescence from the former should decay exponentially and the latter should decay according to Inokuti-Hirayama formula. So the resultant fitting equation could be formulated as [11,15]:

I(t)=Aexp(tτ0)+(1A)exp[tτ0π(CC0)(tτ0)1/2]

The fitting equation consists of the emission without cross-relaxation and the emission taking account of the cross-relaxation. Where, A is the contributive parameter; τis the intrinsic lifetime of a single ion (0.85msec for our samples measured for a sample with very low Tb3+ concentration of 0.05mol%); C is the number of acceptors per unit volume; C0−1 is the volume of donor’s sphere of influence ( = 4πR0 3/3, R0 is the critical separation between donor and acceptor, at which the nonradiative rate equals that of the internal single ion relaxation); the ratio of C/C0 means the number of acceptors in donor’s sphere of influence. The fitted curves are depicted in Fig. 4 and the contributive parameter (A) values and the resultant C/C0 values are given in Table 1. The overall fitting result shows that the analysis using the multipolar interaction scheme produces a relatively good fit between the theoretical calculation and the measured data. From the Table 1, it is shown that the contributive parameter A gradually decrease with the increasing of Ca2+ concentration which means that the increased Ca2+ concentration facilitated the cross-relaxation. The ratio of C/C0 has a increasing tendency with increased Ca2+ concentration. C is the number of acceptors per unit volume, that is, Tb3+ concentration itself in this case. According to our previous assumption, it refers in particular to the concentration of non-clustered Tb3+ with cross-relaxation. The addition of Ca2+ facilitates the cross-relaxation process and results in the increase of 5D4 emission. Furthermore, we calculated the mean lifetime (τm) and the energy transfer efficiency (ηET) as follows [4]:

τm=t0I(t)tdt/t0I(t)dt
and
ηET=1-τm-xCa/τ0
where I(t) is the luminescence intensity as a function of time t. The energy transfer efficiency ηET is defined as the ratio of donors that are depopulated by energy transfer to the acceptors over the total number of donors being excited. In our system, the 5D3 energy level of Tb3+ acts as the donor and 5D4 energy level of Tb3+ as the acceptor. By dividing the mean lifetime of the 5D3 emission of Ca2+ doped glass over the Ca2+ free glass, the transfer efficiency is obtained as a function of Ca2+ concentration

The calculated lifetime (τm-xCa) and energy transfer efficiency (ηET) is also exhibited in Table 1.

Tables Icon

Table 1. Parameters for the fitted equation, decay life time and energy transfer efficiency of samples with different Ca2+ concentration

The mechanism of the energy transfer between Ce3+ and Tb3+ can also be analyzed using the approach of Dexter’s theory or Inokuti-Hirayama formula. Usually the interaction between Ce3+ and Tb3+ is an electric dipole-dipole nature for lower acceptor concentrations.

Figure 5 compares the Ce3+ fluorescence decay for several samples doped with different Ca2+ concentration. With increased Ca2+ the decay curves are non-exponential and the tendency is getting more prominent as Ca2+ concentration increase. The deviation from the single exponential behavior is due to the radiationless process involving energy transfer. Assuming a dipole-dipole radiationless energy transfer and without energy migration occurs over the donor subsystem, the decay can be fitted by such a formula [11,15]:

 figure: Fig. 5

Fig. 5 Decay curve of Ce3+ emission at 395nm in the sintered porous silica glasses with different Ca2+ concentration under 307nm excitation. The concentration of Ca2+ is 0.2 mol% (a), 0.8 mol% (b) and 1.4 mol% (c), respectively. The concentration of Ce3+ is 0.08 mol% and Tb is 0.235 mol%. The red lines are fitted lines of decay curves corresponding to sample a, b, and c, respectively.

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I(t)=I(0)exp[tτ0π(CC0)(tτ0)12]

Where I(0) represents the initial intensity of the emission, τ0 is the intrinsic lifetime measured with very low Ce3+ concentration (56ns for our samples) and other parameters have the same meaning with Eq. (1) mentioned above. From Fig. 5, it is seen that there is a good fit between measured data and the fitted curves. Therefore, the energy transfer between Ce3+ and Tb3+ is based on dipole-dipole interaction. We also calculated the mean lifetime (τ) and the energy transfer efficiency (ηET) according to formula (2) and formula (3).

The parameter C/C0, calculated mean lifetime (τ) and energy transfer efficiency (ηET) are show in Table 2.

Tables Icon

Table 2. Parameters for the fitted equation, decay life time and energy transfer efficiency of Ce3+-Tb3+-Ca2+ co-doped samples with different Ca2+ concentration. CTCx mol% represent Ce3+-Tb3+-Ca2+ co-doped glasses with Ca2+ concentration of x mol%

The fitting of Tb3+ decay and Ce3+ decay by formula (1) and formula (4) is successful respectively. The Ce3+ decay cannot be fitted by formula (1), which means there is no isolated Ce3+, and almost all of the non-clustered Ce3+ ions have interaction with Tb3+. The above result is also approved by the fact that the critical distance of cross-relaxation between Tb3+ ions is usually shorten than that of Ce3+-Tb3+ dipolar-dipolar interaction [1618].

It is obvious that the rare earth ions of Ce3+ and Tb3+ doped in porous glass results in Ce3+,Tb3+ and Ce3+-Tb3+ clusters as well as non-clustered Ce3+ and Tb3+ ions. In porous glasses, ion clustering occurs because the rare earth ions have large coordination number and must share the limited non-bridging oxygen, therefore the local concentration of non-clustered ions is low and the distance between non-clustered Ce3+ and Tb3+ is large, so the energy transfer efficiency between non-clustered ions is low and the emission intensity of Tb3+ is weak. Addition of Ca2+ into Ce3+-Tb3+ co-doped glass can increase the emission intensity of Tb3+ greatly, because the Ca2+ ions lead to more non-network oxygen and replace clustered Ce3+ and Tb3+. On the one hand, the more non-network oxygen results in more dispersed rare earth ions, on the other hand, the replaced Ce3+ and Tb3+ will increase the local concentration non-clustered Ce3+ and Tb3+. Therefore the local concentration of non-clustered Ce3+ and Tb3+ is greatly increased. The distance among non-clustered rare earth ions can be greatly shortened. Therefore, the addition of Ca2+ facilitates the energy transfer between Ce3+ and Tb3+ and the cross-relaxation between the 5D3 and 5D4 levels of Tb3+. Therefore, the 5D4 emission of Tb3+ can be enhanced greatly.

4. Conclusions

In conclusion, the sintered porous glasses impregnated with Tb3+ ions were successfully prepared as intense green emitters under long wavelength ultraviolet excitation. Luminescence spectra and fluorescence decay of Tb3+-Ca3+ co-doped glasses and Ce3+-Tb3+ co-doped glasses were measured and studied. It is suggested that the addition of optically inert glass network modifier oxides (such as Ca2+) play an important role in facilitating the energy transfer between non-clustered sensitizers and activators. Due to their strong emissions under long wavelength ultraviolet excitation, the colorless transparent green-emitting glasses have a potential for application in lasers, solar concentrators, LED displays and fluorescent lamps.

Acknowledgments

We would like to thank the Hubei Optoelectronics Testing Center and Huazhong University of Science and Technology Analytical and Testing Center for sharing their equipments.

References and links

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Figures (5)

Fig. 1
Fig. 1 Emission spectra of Tb3+ doped (a),Ce3+ doped (b), Tb3+–Ce3+ co-doped (c), and Tb3+– Ce3+–Ca2+ co-doped (d) sintered porous glasses. The excitation wavelength is 310 nm. Tb3+ doped glass has a Tb3+ concentration of 0.235 mol%. Tb3+–Ce3+ co-doped glass has a Tb3+ concentration of 0.235 mol% and a Ce3+ concentration of 0.08 mol%. Tb3+– Ce3+–Ca2+ co-doped glass has a Tb3+ concentration of 0.235 mol%, a Ce3+ concentration of 0.08 mol% and a Ca2+ concentration of 1.2 mol%. The left inset gives the photographs of luminous glasses exhibiting blue and green emission under 310nm irradiation. The a, b, c, and d samples correspond to Tb3+ doped glass, Ce3+ doped glass, Tb3+-Ce3+ co-doped glass, Tb3+-Ce3+-Ca2+ co-doped glass, respectively.
Fig. 2
Fig. 2 (A) describes the 5D4 emission spectra of Tb3+-Ce3+-Ca2+-co-doped glasses under 310nm excitation. All of the glasses have Tb3+ concentration of 0.235 mol% and Ce3+ concentration of 0.08 mol% respectively. The concentration of Ca2+ is changed from 0.4 mol%, 0.6 mol%,0.8 mol%, 1.0 mol% to 1.2 mol%. Figure 2(B) shows the excitation spectra of the corresponding glasses monitored at 544 nm.
Fig. 3
Fig. 3 (A) and (B) are 5D3 and 5D4 emission spectra of Tb3+–Ca2+ co-doped glasses under 238-nm excitation. (C) and (D) are the excitation spectra of 5D3 and 5D4 emission of Tb3+ obtained by monitoring 379nm and 544nm emissions, respectively. All of the glasses have Tb3+concentration of 0.235 mol%. The concentration of Ca2+ is changed from 0.4 mol%, 0.6mol%, 0.8mol% to 1.0 mol%.
Fig. 4
Fig. 4 Decay curves of the Tb3+ (5D37F5, 379nm) transition in the sintered porous silica glasses with different Ca2+ concentration under 238nm excitation. The concentration of Ca2+ is 0 mol% (a), 0.4 mol% (b), 0.6 mol% (c) and 0.8 mol% (d) respectively. The Tb3+ concentration is 0.235 mol%. The lines in colors are fitted lines of decay curves corresponding to sample a, b, c, and d, respectively.
Fig. 5
Fig. 5 Decay curve of Ce3+ emission at 395nm in the sintered porous silica glasses with different Ca2+ concentration under 307nm excitation. The concentration of Ca2+ is 0.2 mol% (a), 0.8 mol% (b) and 1.4 mol% (c), respectively. The concentration of Ce3+ is 0.08 mol% and Tb is 0.235 mol%. The red lines are fitted lines of decay curves corresponding to sample a, b, and c, respectively.

Tables (2)

Tables Icon

Table 1. Parameters for the fitted equation, decay life time and energy transfer efficiency of samples with different Ca2+ concentration

Tables Icon

Table 2. Parameters for the fitted equation, decay life time and energy transfer efficiency of Ce3+-Tb3+-Ca2+ co-doped samples with different Ca2+ concentration. CTCx mol% represent Ce3+-Tb3+-Ca2+ co-doped glasses with Ca2+ concentration of x mol%

Equations (4)

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I ( t ) = A exp ( t τ 0 ) + ( 1 A ) exp [ t τ 0 π ( C C 0 ) ( t τ 0 ) 1 / 2 ]
τ m = t 0 I ( t ) t d t / t 0 I ( t ) d t
η ET = 1- τ m-xCa / τ 0
I ( t ) = I ( 0 ) exp [ t τ 0 π ( C C 0 ) ( t τ 0 ) 1 2 ]
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