Research Article  Open Access
Analysis of Eu^{3+} Emission from Mg_{2}TiO_{4} Nanoparticles by JuddOfelt Theory
Abstract
Eu^{3+} doped Mg_{2}TiO_{4} (2 at% of Eu) nanoparticles which are 5 to 10 nm in diameter are prepared by Pechinitype polymerized complex route followed with the calcination in the temperature range from 400°C to 700°C. Emission spectra display characteristic (, 1, 2, 3, and 4) spin forbidden ff electronic transitions of the Eu^{3+} ions with the most pronounced emission coming from transition and with the emission decays varying between 0.57 and 0.87 ms for samples prepared at different temperatures. JuddOfelt theoretical analysis of the emission spectra of Eu^{3+} ions was performed, which allowed calculating radiative and nonradiative emission probabilities, JuddOfelt intensity parameters, and the quantum efficiency of the Eu^{3+} emission in the Mg_{2}TiO_{4} nanoparticles. The analyses showed the existence of high asymmetry around the metal ion sites. Also, the largest quantum efficiency of emission of 58.5% is found in nanoparticles prepared at 600°C.
1. Introduction
Magnesiumorthotitanate (Mg_{2}TiO_{4}) is a dielectric for microwave technology, a heat resistor, a capacitor for temperature compensation, and a refractory material. Strong, deepred emission can be achieved by incorporation of Mn^{4+} ions in its structure [1, 2], and the emission is used to improve the colorrendering index of phosphorconverted whitelightemitting diodes. Luminescence from Mg_{2}TiO_{4} can be also realized with the incorporation of trivalent rare earth (RE) ions in its structure since the band gap of the material is large enough (Eg ~ 3,7 eV) to accommodate RE energy levels. Then, Mg_{2}TiO_{4} can serve as a phosphor of different colors depending on the RE ion used as an activator. In this sense, nanoparticles of Mg_{2}TiO_{4} can be of particular interest since internal light scattering in nanophosphors is negligible compared to bulk counterparts [3]. Also, nanophosphors show stronger luminescence emission compared to bulk ones due to the modification of radiative lifetimes [4].
So far no data on the radiative and nonradiative transition probabilities and quantum efficiencies of emission of RE impurities in Mg_{2}TiO_{4} nanoparticles have been reported. These important emission characteristics are needed to compare luminescence performance of the RE ions in Mg_{2}TiO_{4} with their performance in other, well established hosts. Therefore, we aimed in this work at an analysis of the Eu^{3+} ion emission in the Mg_{2}TiO_{4} nanoparticles prepared with Pechinitype polymerized complex route [2, 5] at different, low temperatures. In addition to the experimental studies, the JuddOfelt analysis of the emission spectra of Eu^{3+} ions was performed, which allowed calculating radiative and nonradiative transition probabilities, JuddOfelt intensity parameters, and the quantum efficiency of the Eu^{3+} emission in the Mg_{2}TiO_{4} nanoparticles. At low temperatures Mg_{2}TiO_{4} structure is metastable; however, literature results indicate that crystallites of nanoscale dimensions may lead to a higher stability of some cubic phases [6, 7]. Therefore, the analysis should also provide the temperature that delivers Mg_{2}TiO_{4} nanoparticles with best luminescence properties.
2. Experimental Part
2.1. Synthesis of Eu^{3+} Doped Mg_{2}TiO_{4} Nanoparticles
Eu^{3+} doped Mg_{2}TiO_{4} (2 at% of Eu) was synthesized with Pechinitype polymerized complex route which is essentially based on the polyesterification between citric acid (CA) and ethylene glycol (EG) [2, 5]. Molar ratio of precursor components was magnesium oxide : titanium (IV)isopropoxide : citric acid : ethylene glycol = 2 : 1 : 5 : 20. In the first step, titanium (IV)isopropoxide (Alfa Aesar, 97%) was dissolved in ethylene glycol (LachNer, 99%) under constant magnetic stirring at room temperature. Then, citric acid (Kemika, 99.5%) was added to the solution and stirred until complete dissolution was achieved. The appropriate amount of MgO and Eu_{2}O_{3} were dissolved in concentrated nitric acid at 130°C, evaporated to dryness, and joined with titanium (IV)isopropoxide/EG/CA mixture. In the next step, the mixture was stirred for 1 hour at 60°C until it becomes transparent and further stirred at 130°C for few hours. During this heating process, the formation of the polymer was promoted. As the colloidal solution was condensed and the excess of solvents removed, it became highly viscous, and this viscous polymeric product was decomposed at 350°C in 30 minutes to a dark mass precursor. This mass precursor was powdered and further calcined at 400°C, 450°C, 500°C, 550°C, 600°C, 650°C, and 700°C to obtain pure phase of Eu^{3+} doped Mg_{2}TiO_{4} nanoparticles.
2.2. Instruments and Measurements
Xray diffraction measurements were performed with Rigaku SmartLab diffractometer and data were recorded in a 2θ range from 15° to 120°, counting 0.7°/minute in 0.02° steps. Transmission electron microscopy was performed using JEOLJEM 2100 LaB6 operated at 200 kV. Photoluminescence measurements were performed at room temperature on Fluorolog3 Model FL3221 spectrofluorometer system (Horiba JobinYvon), utilizing 450W Xenon lamp as an excitation source for emission measurements and Xenon–Mercury pulsed lamp for lifetime measurements. The emission spectra were scanned in the range of wavelengths from 430 to 790 nm. The TBX04D PMT detector is used for both lifetime and steady state acquisitions. The line intensities and positions of the measured spectra were calibrated with a standard mercuryargon lamp.
3. Results and Discussion
3.1. Microstructural Analysis
Mg_{2}TiO_{4} crystallize in a cubic, inverse spinel structure (Fd3m space group) [8–10]. In this structure, Mg^{2+} ions are located in tetrahedral and octahedral sites while the Ti^{4+} ions occupy only octahedral sites, as shown in Figure 1(a). Arrangement of Ti^{4+} and Mg^{2+} ions in the octahedral sites is random.
(a)
(b)
Xray diffraction patterns of samples calcined at different temperatures from 400°C to 700°C are presented in Figure 1(b). The main diffraction peaks are indexed according to ICDD010726968 card. Pure phase of Mg_{2}TiO_{4} is present in the samples annealed in the temperature range from 400°C to 650°C. In the sample calcined at 700°C ilmenite (MgTiO_{3}) phase is presented along with Mg_{2}TiO_{4}.
TEM image in Figure 2 shows morphology of particles of Mg_{2}TiO_{4} doped Eu^{3+} sample annealed at 600°C for 1 hour. The sample is composed of loosely agglomerated nanoparticles of 5 to 10 nm in diameter.
3.2. Photoluminescence Emission Spectra and Lifetime Measurements
The emission spectra of Mg_{2}TiO_{4} samples doped with 2 at% Eu and annealed in the 400–650°C temperature range are presented in Figure 3. Due to even number of electrons in the 4f shell (4f^{6} configuration), the crystalfield perturbation by the host matrix lifts partly or completely the degeneracies of the Eu^{3+} levels [11]. Therefore, emission spectra show five characteristic bands centered around 17271, 16892, 16287, 15290, and 14245 cm^{−1} that originate from ( = 0, 1, 2, 3, and 4) spin forbidden ff electronic transitions of the Eu^{3+} ions. The transition is magnetic dipole in nature and follows the selection rule . Its intensity is independent of the host matrix. On the other hand, the are “the forced” (induced) electric dipole transitions, known to be forbidden by the Laporte selection rule and may occur due to the mixing of the 4f orbitals with opposite parity at the low symmetry sites. The is known as a hypersensitive transition because it is easily affected by the local environment around europium ion, and its intensity depends on the symmetry of crystal field around the europium ion. The intensity of transition is the most intense across the emission spectra. The transition is not allowed since 0–0 transitions are forbidden by the selection rule . The appearance of this transition is mainly due to the mixing effect [12] and indicates that Eu^{3+} ion is located in a site without an inversion center. Low energy transitions, and , are also clearly visible. Emissions from (12990–13510 cm^{−1}) and (11900–12350 cm^{−1}) transitions could not be detected due to the instrument limitations.
From emission spectra (Figure 3) one can notice that the emission intensity increases with the increase of annealing temperature and that there is no significant change in the emission spectra’s shape. The emission decays of the ^{5}D_{0} emitting level are obtained under 394 nm excitation. Average lifetime values are calculated using the following equation: where represents the luminescence intensity (corrected for the background) at time . The results are presented in Table 1.

In all samples the highest emission intensity is observed for transition. The intensity of this transition, Figure 2, and the lifetime values, Table 1, enlarge with the rise of the annealing temperature up to 650°C. These values, however, decrease in the sample prepared at 650°C.
3.3. JuddOfelt Calculations and Results
The JuddOfelt theory [13, 14] describes intensities of transitions of lanthanides and actinides in solids and solutions, whereas JuddOfelt parameters characterize local structure and bonding in the vicinity of rare earth ions. This theory provides information about oscillator strengths, radiative lifetime, and emission probabilities. The analysis also provides values of quantum efficiency.
According to JO theory [13, 14] theoretical expression for the oscillator strength of an induced electric dipole transition from the ground state to an excited state is where denotes Planck constant (6.626 × 10^{−34} J·s; 4.135 × 10^{−15} eV·s), is the degeneracy of the initial state, is the refractive index, are the JuddOfelt parameters, and terms are the double reduced matrix elements of unit tensor operators whose values are independent of the local environment of the ion. According to the JuddOfelt theory radiative transition probability, , is related to its dipole strength according to the following equation:where and represent the electric and magnetic dipole strengths, respectively. Transition probabilities of the rare earths are composed mainly of the electric dipole contribution ( = 2, 4) and to a much lesser extent by the magneticdipole contribution . The transition is forbidden according to JuddOfelt theory, both in magnetic and induced electric dipole scheme, and this transition can only gain intensity via mixing [15, 16]. Also, the transition is strictly forbidden according to the standard JuddOfelt theory. Therefore, these two transitions will not be considered in determining transition probabilities. The intensity of magnetic dipole transition is largely independent of the environment and can be considered in a first approximation to be constant [17]. The magnetic dipole transition can be calculated by theory [15, 18]:The strength of all induced electric dipole transitions is where squared reduced matrix elements have values independent of the host matrix. For the case of Eu^{3+} these values are tabulated in [18–20], and JuddOfelt intensity parameters can be evaluated solely from the emission spectrum because nondiagonal elements of the matrix have zero values according to the following equation:For the calculations, the value of refractive index of 1.691 for Mg_{2}TiO_{4} is taken from the literature [21]. According to [22] radiative emission probability of magnetic dipole transition, (), has value of 57.34 s^{−1} for the 50(NaPO_{3})_{6} + 10TeO_{2} + 20AlF_{3} + 19LiF + 1Eu_{2}O_{3} glass with a refractive index of 1.591. Taking this value as a reference, and with the wellknown correction factor of , which can be derived from the general equations for the magnetic dipole transition probability rates [23, 24], () = 68.85 s^{−1} is calculated for the radiative emission probability of magnetic dipole transition of Eu^{3+} in Mg_{2}TiO_{4}. The intensity of this transition can be considered as a reference for all transitions originating from the ^{5}D_{0} excited state [11]. Then, it is possible to calculate radiative emission probabilities of all transitions originating from the ^{5}D_{0} excited state from the ratios of areas under corresponding emission bands in Figure 3 [20, 22]:Total radiative emission probability, , defined as the sum of all radiative emission probabilities:can be further used to calculate nonradiative probability (which includes relaxation by multiphonon emission and effective energy transfer rates arising from ionion interactions [11]) and emission quantum efficiency (the ratio between the number of photons emitted by the Eu^{3+} ion to the number of those absorbed):The intensity parameter describes hypersensitivity of transition since it is affected by the symmetry of local surrounding around the Eu^{3+} site. and parameters are associated with the viscosity and rigidity of the host material. Several reports [25–28] used to assess the magnitude of covalence between Eu^{3+} and surrounding ligands (the larger the , the stronger the covalence); however one should note that there are number of competing mechanisms for induced electric dipole transitions, so the dominant mechanism could not be determined from the single parameter. Luminescence intensity ratio is also known as asymmetry ratio [29]. Higher values of indicate lower symmetry around the trivalent europium ions [30, 31]. and reveal similar physical information on the bonding nature between Eu^{3+} ion and the surrounding anions and explain the short range effects in local structure around Eu^{3+} ions [28]. intensity parameter could not be determined because emission in this sample could not be detected due to the instrumental limitations.
Calculated JuddOfelt parameters show variation with the annealing temperature, and their values are presented in Table 2 along with the values of radiative and nonradiative emission probabilities, quantum efficiencies, and asymmetry ratios.

and dependence on temperature is displayed in Figure 4(a), and asymmetric ratio is presented in Figure 4(b). One can notice that the values of and increase with the increase of annealing temperature until 600°C. Eu^{3+} emission from the sample prepared at 650°C has lower values of and than in the case of sample prepared at 600°C. This result indicates that local environment of the Eu^{3+} ion changes at temperatures higher than 600°C. In the complete temperature range is larger than . The relatively high value of and the observed trend indicate a relatively high asymmetry at the Eu^{3+} site. These results are in agreement with the values of luminescence intensity ratio: 3.23, 5.46, 6.65, 7.10, 7.75, and 7.60. One should notice the trend of value increase with the annealing temperature up to 600°C and decrease for 650°C. A high value of this ratio indicates low symmetry of the crystal field around the europium ion due to distortion of the surrounding bonds [32]. The start of reverse trend of change of JuddOfelt parameters and asymmetric ratio at temperature of 650°C indicates the beginning of material structural disorder since at that temperature the decrease of quantum efficiency is also observed.
(a)
(b)
Figure 5(a) shows changes of radiative and nonradiative emission probabilities of Eu^{3+} emissions in samples prepared at different temperatures. Until 600°C radiative emission probability increases and nonradiative decreases. The trend reverses for sample prepared at 650°C. The quantum efficiency of emission, Figure 5(b), increases from 17.75% in sample annealed at 400°C to 58.53% for a sample prepared at 600°C. The quantum efficiency of Eu^{3+} emission in sample prepared at 650°C is 55.70%, lower than for sample prepared at 600°C.
(a)
(b)
One should note that the values of quantum efficiency are slightly underestimated, since calculation does not account emissions. However, the trend of quantum efficiency change with annealing temperature is unaffected by this deficiency. Also, refraction index is wavelength dependent physical property, so taking the constant value into calculation introduces error into results; however, the error is small since the refractive index changes are small over the wavelength region of interest [20]. These simplifications are justified for the sake of comparison of JO parameters and emission parameters between samples, since small errors cannot change observed trends. It is acknowledged that JuddOfelt theory estimates transition probabilities with accuracy generally not worse than 10% [33].
4. Conclusion
To conclude, Eu^{3+} doped Mg_{2}TiO_{4} nanoparticles of about 5 to 10 nm in size can be prepared with Pechinitype polymerized complex route after annealing in the lowtemperature range from 400°C to 650°C. The best luminescence properties showed nanoparticles prepared at 600°C exhibiting quantum efficiency of emission of 58.5% and emission lifetime of 872 μs. In all samples JuddOfelt intensity parameter was larger than , and relatively high values of and asymmetry ratio are observed. The latter indicate relatively high asymmetry at the Eu^{3+} sites.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
Acknowledgments
The authors acknowledge the financial support of the Ministry of Education and Science of the Republic of Serbia (Project no. 45020) and the support from the APV Provincial Secretariat for Science and Technological Development of the Republic of Serbia through Project no. 1144511850/201403.
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Copyright © 2015 Katarina Vuković et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.