1. Introduction

Persistent luminescence is defined as emission obtained after the removal of an excitation source. The phenomenon is a special case of thermally stimulated luminescence at room temperature. Persistent luminescence materials function by collecting energy from ambient sunlight and/or artificial lighting to trapping sites. The energy is then gradually released as visible emission [1]. Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ [2] with the blue persistent emission at 475 nm lasting for 24+ hours is one of the most efficient persistent luminescence materials. With the long persistence and emission color at the sensitivity maximum of the human eye in the dark [3], this material is ideally suited for lighting applications in dark environments, e.g. in self-lit emergency signalization or luminescent paints.

The mechanism of persistent luminescence in Eu²⁺ doped materials is rather well established, but some details are still missing and/or contested. It is known that Eu²⁺ is the emitting center and that structural defects act as the trapping sites. However, the nature of the traps (vacancy, co-dopant, interstitial) is not clear [4]. For the other emitting species, not much work has been done to establish the persistent luminescence mechanism(s), but recently the mechanisms of Eu³⁺ in Y₂O₂S [5], Tb³⁺ in CdSiO₃ [6], Ti³⁺ in ZrO₂ [7] and Cu⁺ in the Bologna Stone [8] have been presented. The elucidation of the mechanism is essential to allow for the development of more efficient persistent luminescence materials.

Previous thermoluminescence (TL) results for the Sr₂MgSi₂O₇:Eu²⁺,R³⁺ (R: rare earth) materials [4] have shown that the shallowest, and simultaneously the main trap for every Sr₂MgSi₂O₇:Eu²⁺,R³⁺ material above room temperature is at ca. 0.7 eV below the conduction band. This corresponds to a strong TL maximum at ca. 80 °C. The combined results for the trap level energies, obtained from the experimental data and density functional theory (DFT) calculations, suggested that the main trap responsible for the persistent luminescence of Sr₂MgSi₂O₇:Eu²⁺,R³⁺ is created by charge compensation lattice defects. These are induced by the R³⁺ co-dopants. The defects were tentatively identified as oxygen vacancies [4]. In this work, the fading of persistent luminescence from Sr₂MgSi₂O₇:Eu²⁺,R³⁺ (R: Y, La-Nd, Sm-Lu) was studied based on the TL and room temperature luminescence measurements to gain more information on the persistent luminescence mechanism. The Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ material was used as a model due to its strong persistent luminescence and uncomplicated glow curve.

2. Experimental

The polycrystalline Sr₂MgSi₂O₇:Eu²⁺,R³⁺ (R: Y, La-Nd, Sm-Lu) materials were prepared by a solid state reaction between stoichiometric amounts of SrCO₃ (Merck, Pro Analysi), Mg(NO₃)₂·6H₂O (Merck, Pro Analysi), fumed SiO₂ (Sigma, 99.8%) and rare earth oxides (99.9 to 99.99%). The starting materials were ground and heated first for 1 h at 700 °C and then for 10 h at 1350 °C in a reducing N₂ + 10% H₂ gas sphere. The materials were doped and co-doped with one mole-% by the Eu²⁺ and R³⁺ ions (of the Sr amount), respectively. The purity of the materials was checked by routine X-ray powder diffraction measurements. Traces of Sr₃MgSi₂O₈ were occasionally observed as an impurity.

The TL glow curves were measured with an upgraded Risø TL/OSL-DA-12 system using a constant heating rate of 5 °Cs⁻¹ in the temperature range from 25 to 500 °C. The global TL emission from UV to 650 nm was monitored. Prior to the TL measurements, the samples were irradiated with a combination of the Philips TL 20W/05 (emission maximum @ 360 nm) and TL 20W/03 (@ 420 nm) UV lamps. Selected irradiation times between 15 s and 30 min were used to test the kinetic order of the glow curve bands. A delay of 3 min between the irradiation and measurement was then used. For the fading measurements, an irradiation time of 5 min was used with selected delay times from 3 min to 4 h. The heating rates were 1, 3, 5, 10 and 20 ^oCs⁻¹.

The analysis of the TL glow curves was carried out by the deconvolution fitting method with the program TLanal v.1.0.3 [9]. The program allows the choice of different kinetic models (1^st, 2^nd, general and mixed order, general approximation and full iteration) for the generation of a calculated glow curve. In the fitting procedure, the calculated glow curve is compared to the experimental one. The former is repeatedly recalculated by adjusting parameter values until the best fit is obtained in terms of least squares [10]. The fitting parameters depend on the kinetic model used. In the first order case, these are n₀ (trap density, i.e. initial number of electrons trapped), s (frequency factor, i.e. the easiness with which the electron can escape from the trap) and E_t (trap depth, i.e. the energy required to bleach the trap). For the second order kinetics, s’ – defined as s/N (N: concentration of available traps with the depth E_t) – is used instead of s. s’ can be converted to s” = n₀s’, which is then comparable to the first order frequency factor, since s” = s(n₀/N). Although s” strictly equals s only with the trap close to saturation, the s” value can nevertheless give information on the ease of detrapping. For the general order, the program yields s” as the frequency factor and also the order b is obtained. More details on these models can be found elsewhere [10–12]. Regardless of the kinetic order, all these parameters are strongly correlated, if the peak shape methods as deconvolution are used for the analysis. Thus, in the present work, data sets were collected with different heating rates (1, 3, 5, 10 and 20 ^oCs⁻¹) and used simultaneously for the fits in order to minimize the correlation.

The persistent emission spectra of the materials were measured with a Varian Cary Eclipse spectrometer using selected delays from 1 min to 6 h after ceasing the irradiation. The irradiation was carried out with a 4 W UV lamp at 254 nm.

3. Results and discussion

3.1 Considerations of kinetic order

The TL glow curve bands are usually modeled based on single trap models assuming no interactions between traps. In that case, thermal energy raises electrons trapped to lattice defects to the conduction band from where they move further to recombine with the emitting center producing luminescence. If it is further assumed that negligible retrapping takes place during the emptying of the traps, the process is of the first order. Then, the band shape is asymmetric with the low-temperature side wider than the high-temperature one. If retrapping dominates and the trap can be assumed to be far from saturated, the process is of second order and the bands are symmetric. If these simple assumptions are not valid, the TL band will not fit to either the first or second order kinetics but a general order approach must be adapted [12].

For the Sr₂MgSi₂O₇:Eu²⁺,R³⁺ (R: Y, La-Nd, Sm-Lu) materials, the TL bands appear to be symmetric (Fig. 1 ) thus suggesting second order kinetics. To verify this, TL measurements were carried out for Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ with different irradiation times between 15 s and 30 min. Increasing irradiation time should increase the n₀ value and introduce a shift of the TL band maximum, T_max, to lower temperatures, if the band is of the second order. For the first order kinetics, no such shift will occur.

 

Fig. 1 TL glow curves of selected Sr₂MgSi₂O₇:Eu²⁺,R³⁺ materials. Note that the signal for R: Dy has been multiplied by 0.2. Inset: effect of irradiation time on the glow curve of Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺.

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In the present work, the irradiation time had practically no effect on the T_max of Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺, which varied randomly between 75.9 and 77.0 °C (Fig. 1). The temperature shift predicted by the second order kinetics for a similar variation in (sample mass weighted) TL band intensity is ca. 6 °C as calculated with TLAnal. Moreover, the variation in the band height (within 30%) and width (7%) was rather small. This indicates that the trap is not far enough from saturation for the second order kinetics to apply even with the lowest irradiation time of 15 s. On the other hand, with the trap close to saturation, general order kinetics predict very small changes of ca. 1 °C in T_max for a 30% change in TL band height. With much lower trap occupancies as 1%, T_max shifts of 6 °C or greater can be expected [13].

3.2 Persistent luminescence fading

The fading of persistent luminescence in the Sr₂MgSi₂O₇:Eu²⁺,R³⁺ materials is typically manifested as a decrease of the main TL signal at ca. 80 °C. This is accompanied by a simultaneous shift to higher temperatures (Fig. 2 ). The latter behavior may suggest that within the main TL band there are, in fact, two traps. The first is an intense one corresponding to the T_max of the glow curve at short delay times and the other a weaker one visible at longer decay times. The apparent band position would then shift as the stronger shallower trap is emptied during the fading of persistent luminescence. On the other hand, it is also possible that there is only one trap, whose density and frequency factors change with the delay time thus causing a shift in the T_max.

 

Fig. 2 Persistent luminescence fading of the Sr₂MgSi₂O₇:Eu²⁺,R³⁺ materials (R: Dy and Tm) as evidenced by the TL glow curves.

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The fading in Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ was first modeled based on the general order kinetics as suggested by the results of section 3.1. The trap then assumes the same depth during all of the fading, but the general order frequency factor s” and the trap density n₀ change. The results suggest that the order of the kinetics is slowly decreasing from 2.03 to 1.63 (Table 1 ). The trap density and frequency factor decrease with increasing fading time (Fig. 3 , Table 1), as well. This indicates the emptying of the trap and the accompanying decrease of probability for the electrons to escape from the trap with time, i.e. the number of electrons escaping from the trap will decrease as the trap occupancy decreases. This corresponds to that predicted by the Boltzmann distribution. The persistent luminescence intensity decreases in a very similar manner as do the s” and n₀ values (Fig. 3). Moreover, since the fading of persistent luminescence slows down with increasing time, the s” value decrease suggested by the general order kinetics model seems well justified.

Table 1. Results for General Order Fits for Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ (E_t: 0.60 eV)

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Fig. 3 Effect of persistent luminescence fading on the n₀ and s” parameter values of the general order kinetic model for Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺. Inset: Persistent luminescence fading for the same material. Note that all but the time axes are presented in a logarithmic scale.

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Since the observed persistent luminescence fading curve was clearly not exponential, the possibility of the first order kinetics was definitely ruled out. In fact, the hyperbolic shape of the persistent luminescence intensity fading curve for Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ should serve as a straightforward indication of higher than the first order kinetics, even if no dependence of the T_max on n₀ was observed.

The possibility of the second order kinetics was tested next. This model has one parameter less than the general one and is thus less prone to strong correlation between the parameters. This could thus serve as a better option to describe the fading, even if the condition of n₀ being far from saturation seems not to be fulfilled. With one trap at the main TL band, the trap densities (Table 2 ) are equal to those obtained from the general order model (Table 1). The trap depth varies smoothly from 0.60 to 0.76 eV. This could be an indication of a continuous trap depth distribution, but it seems more probable that there are two traps with constant depths and a smoothly varying intensity ratio. This would then result in an apparent trap depth shift if modeled with one trap only. The evolution of the frequency factor s” values (Table 2) does not follow the persistent luminescence fading well. The value decreases fast in the first 15 minutes and then assumes an almost constant – although slowly decreasing – one. At 15 min, the persistent luminescence intensity still decreases rather fast (Fig. 3) suggesting that the second order one trap model does not describe the fading well enough.

Table 2. Results for Second Order Fits for Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺

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If two traps (at 0.60 and 0.79 eV) are accounted for, the density of the first one decreases rather similarly to the general order model, while the second trap depth decreases until 15 min and thereafter increases (Table 2). However, with fading times of 30 min and over, the fitting of the two traps into one symmetric peak becomes increasingly difficult as they are expected to be close to equal in depths. The number of refined parameters is then too high considering their strong correlation. As for the one trap case, the shallower (main) trap (0.60 eV) shows a too fast decrease to be consistent with the observed persistent luminescence fading (Fig. 3).

3.3 Modeling persistent luminescence fading based on TL data

Persistent luminescence fading was calculated for Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ based on the results obtained from the TL data. The emission intensity during the fading, I(t), is obtained for the general (Eq. (1)) and second order kinetics (Eq. (2)) as follows [11]:

For the second order kinetics model, the values obtained for one trap and 3 min delay (Table 2) were used. The calculated curve follows the experimental ones obtained after irradiation times of 15 s and 30 min only for the first minute and thereafter fades much faster (Fig. 4 ). For the general order, the Eq. (2) should not be used as such, since it is derived for constant order (parameter b). In the present case, the fits suggested changing order (Table 1). Thus, the calculated fading curve was obtained by splitting the curve to time intervals corresponding to the delay times used for obtaining the general order parameter values (Table 1). Then, the values for the delay time of 3 min were used for calculating fading between 3 and 5 min, parameters for 5 min for fading between 5 and 15 min etc. The fit with the experimental data is not good, either (Fig. 4). Again, the calculated curve decreases too fast, although slower than for the second order. All in all, the general order does not seem to fulfill the good expectations set on it by the TL fits.

 

Fig. 4 Comparison of the observed and calculated persistent luminescence fading for Sr₂MgSi₂O₇:Eu²⁺,Dy³⁺ with two different irradiation times. General and second order as well as Becquerel decay were used for the calculated curves.

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Finally, it was found that the experimental fading of persistent luminescence actually shows the following behavior (Eq. (3)):

Similar to the first (b: 1) and second order (b: 2, Eq. (2)) decays, the Becquerel type behavior is included in the general order formula (Eq. (1)). However, as the exponent b/(b-1) (Eq. (1)) can assume only values of two or less for the Becquerel decay, this model describes solely kinetic orders of two or more. In the present case with b/(b-1) = 1 (Eq. (3)), the order b (Eq. (1)) is approaching infinity. This suggests that the fading is controlled by multiple detrapping and retrapping. In fact, the exponent b/(b-1) is strongly dependent on the ratio between the probabilities of retrapping and recombination. With b/(b-1) = 2, which corresponds to second order kinetics, retrapping and recombination are equally probable, whereas for b/(b-1) = 1, retrapping is ca. 70 times as probable as recombination [14].

3.4 Conclusions

The first, second and general order kinetics were tested to model the persistent luminescence fading of the Sr₂MgSi₂O₇:Eu²⁺,R³⁺ materials. The latter two models yielded good fits for the TL glow curve deconvolutions. The general order model with one trap for the main TL band seemed to describe the TL results better than the second order one. The persistent luminescence fading could not be simulated based on these models, however. In contrast, the Becquerel decay model proved to produce the experimental fading curve very well suggesting that the retrapping clearly dominates over recombination. The fading of persistent luminescence can thus be predicted with fairly good accuracy by using the E, n₀ and s’ parameter values obtained by deconvoluting the main TL band with second or general order kinetics. In the future, the study will be extended to materials with more complex trap structures.