# Analysis of Eu3+ Emission from Mg2TiO4 Nanoparticles by Judd-Ofelt Theory

Authors: Katarina Vuković; Mina Medić; Milica Sekulić; Miroslav D. Dramićanin
Journal: Advances in Condensed Matter Physics
 (2015)

---

## Abstract

Eu3+ doped Mg2TiO4 (2 at% of Eu) nanoparticles which are 5 to 10 nm in diameter are prepared by Pechini-type polymerized complex route followed with the calcination in the temperature range from 400°C to 700°C. Emission spectra display characteristic D
0
5
→
F
7
J (J
=
0, 1, 2, 3, and 4) spin forbidden f-f electronic transitions of the Eu3+ ions with the most pronounced emission coming from D
0
5
→
F
7
2 transition and with the emission decays varying between 0.57 and 0.87 ms  for samples prepared at different temperatures. Judd-Ofelt theoretical analysis of the emission spectra of Eu3+ ions was performed, which allowed calculating radiative and nonradiative emission probabilities, Judd-Ofelt intensity parameters, and the quantum efficiency of the Eu3+ emission in the Mg2TiO4 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.


---

## Body

## 1. Introduction

Magnesium-orthotitanate (Mg2TiO4) is a dielectric for microwave technology, a heat resistor, a capacitor for temperature compensation, and a refractory material. Strong, deep-red emission can be achieved by incorporation of Mn4+ ions in its structure [1, 2], and the emission is used to improve the color-rendering index of phosphor-converted white-light-emitting diodes. Luminescence from Mg2TiO4 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, Mg2TiO4 can serve as a phosphor of different colors depending on the RE ion used as an activator. In this sense, nanoparticles of Mg2TiO4 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 Mg2TiO4 nanoparticles have been reported. These important emission characteristics are needed to compare luminescence performance of the RE ions in Mg2TiO4 with their performance in other, well established hosts. Therefore, we aimed in this work at an analysis of the Eu3+ ion emission in the Mg2TiO4 nanoparticles prepared with Pechini-type polymerized complex route [2, 5] at different, low temperatures. In addition to the experimental studies, the Judd-Ofelt analysis of the emission spectra of Eu3+ ions was performed, which allowed calculating radiative and nonradiative transition probabilities, Judd-Ofelt intensity parameters, and the quantum efficiency of the Eu3+ emission in the Mg2TiO4 nanoparticles. At low temperatures Mg2TiO4 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 Mg2TiO4 nanoparticles with best luminescence properties.


## 2. Experimental Part

### 2.1. Synthesis of Eu3+ Doped Mg2TiO4 Nanoparticles

Eu3+ doped Mg2TiO4 (2 at% of Eu) was synthesized with Pechini-type 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 (Lach-Ner, 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 Eu2O3 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 Eu3+ doped Mg2TiO4 nanoparticles.


### 2.2. Instruments and Measurements

X-ray 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 JEOL-JEM 2100 LaB6 operated at 200 kV. Photoluminescence measurements were performed at room temperature on Fluorolog-3 Model FL3-221 spectrofluorometer system (Horiba Jobin-Yvon), 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 TBX-04-D 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 mercury-argon lamp.


## 2.1. Synthesis of Eu3+ Doped Mg2TiO4 Nanoparticles

Eu3+ doped Mg2TiO4 (2 at% of Eu) was synthesized with Pechini-type 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 (Lach-Ner, 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 Eu2O3 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 Eu3+ doped Mg2TiO4 nanoparticles.


## 2.2. Instruments and Measurements

X-ray 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 JEOL-JEM 2100 LaB6 operated at 200 kV. Photoluminescence measurements were performed at room temperature on Fluorolog-3 Model FL3-221 spectrofluorometer system (Horiba Jobin-Yvon), 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 TBX-04-D 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 mercury-argon lamp.


## 3. Results and Discussion

### 3.1. Microstructural Analysis

Mg2TiO4 crystallize in a cubic, inverse spinel structure (Fd-3m space group) [8–10]. In this structure, Mg2+ ions are located in tetrahedral and octahedral sites while the Ti4+ ions occupy only octahedral sites, as shown in Figure 1(a). Arrangement of Ti4+ and Mg2+ ions in the octahedral sites is random.Figure 1
Crystal structure of Eu3+ activated Mg2TiO4: (a) schematic of the unit cell; (b) X-ray diffraction patterns of nanoparticles prepared at different temperatures from 400°C to 700°C.
(a)
(b)X-ray diffraction patterns of samples calcined at different temperatures from 400°C to 700°C are presented in Figure1(b). The main diffraction peaks are indexed according to ICDD01-072-6968 card. Pure phase of Mg2TiO4 is present in the samples annealed in the temperature range from 400°C to 650°C. In the sample calcined at 700°C ilmenite (MgTiO3) phase is presented along with Mg2TiO4.TEM image in Figure2 shows morphology of particles of Mg2TiO4 doped Eu3+ sample annealed at 600°C for 1 hour. The sample is composed of loosely agglomerated nanoparticles of 5 to 10 nm in diameter.Figure 2
TEM image of the Eu3+ activated Mg2TiO4 nanoparticles prepared at 600°C.


### 3.2. Photoluminescence Emission Spectra and Lifetime Measurements

The emission spectra of Mg2TiO4 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 (4f6 configuration), the crystal-field perturbation by the host matrix lifts partly or completely the degeneracies of the Eu3+ levels [11]. Therefore, emission spectra show five characteristic bands centered around 17271, 16892, 16287, 15290, and 14245 cm−1 that originate from D
0
5
→
F
7
J(J = 0, 1, 2, 3, and 4) spin forbidden f-f electronic transitions of the Eu3+ ions. The D
5
0
→
F
7
1 transition is magnetic dipole in nature and follows the selection rule Δ
J
=
1. Its intensity is independent of the host matrix. On the other hand, the D
0
5
→
F
7
2,4
,
6 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 D
0
5
→
F
7
2 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 D
0
5
→
F
7
2 transition is the most intense across the emission spectra. The D
0
5
→
F
7
0 transition is not allowed since 0–0 transitions are forbidden by the selection rule J
=
0
→
J
′
=
0. The appearance of this transition is mainly due to the J-mixing effect [12] and indicates that Eu3+ ion is located in a site without an inversion center. Low energy transitions, D
0
5
→
F
7
3 and D
0
5
→
F
7
4, are also clearly visible. Emissions from D
0
5
→
F
7
5 (12990–13510 cm−1) and D
0
5
→
F
7
6 (11900–12350 cm−1) transitions could not be detected due to the instrument limitations.Figure 3
The emission spectra of the Eu3+ activated Mg2TiO4 nanoparticles prepared at different temperatures from 400°C to 650°C.From emission spectra (Figure3) 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 5D0 emitting level are obtained under 394 nm excitation. Average lifetime values are calculated using the following equation: (1)
τ
avg
=
∫
0
∞
t
I
t
d
t
∫
0
∞
I
t
d
t
,where I
(
t
) represents the luminescence intensity (corrected for the background) at time t. The results are presented in Table 1.Table 1
Lifetimes of the5D0 emission level of Eu3+ in Mg2TiO4 nanoparticles prepared at different temperatures.
Mg2TiO4 doped 2at% Eu3+
Annealing temperature (°C)
Lifetime (µs)
400
573
450
741
500
818
550
853
600
872
650
851In all samples the highest emission intensity is observed forD
0
5
→
F
7
2 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. Judd-Ofelt Calculations and Results

The Judd-Ofelt theory [13, 14] describes intensities of transitions of lanthanides and actinides in solids and solutions, whereas Judd-Ofelt 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 J-O theory [13, 14] theoretical expression for the oscillator strength of an induced electric dipole transition from the ground state to an excited state is (2)
f
=
8
π
2
m
c
ν
3
h
2
J
+
1
n
2
+
2
2
9
n
∑
λ
=
2,4
,
6
Ω
λ
Ψ
J
U
λ
Ψ
J
′
2
,where h denotes Planck constant (6.626 × 10−34 J·s; 4.135 × 10−15 eV·s), 2
J
+
1 is the degeneracy of the initial state, n is the refractive index, Ω
λ are the Judd-Ofelt parameters, and Ψ
J
U
(
λ
)
Ψ
J
′ 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 Judd-Ofelt theory radiative transition probability, A, is related to its dipole strength according to the following equation:(3)
A
Ψ
′
J
′
;
Ψ
′
J
′
=
65
π
4
e
2
3
h
2
J
′
+
1
λ
3
n
n
2
+
2
2
2
D
ED
+
n
2
D
MD
,where D
ED and D
MD represent the electric and magnetic dipole strengths, respectively. Transition probabilities of the rare earths are composed mainly of the electric dipole contribution D
5
0
→
F
7
J (J = 2, 4) and to a much lesser extent by the magnetic-dipole contribution D
5
0
→
F
7
1. The D
5
0
→
F
7
3 transition is forbidden according to Judd-Ofelt theory, both in magnetic and induced electric dipole scheme, and this transition can only gain intensity via J-mixing [15, 16]. Also, the D
5
0
→
F
7
0 transition is strictly forbidden according to the standard Judd-Ofelt theory. Therefore, these two transitions will not be considered in determining transition probabilities. The intensity of  D
5
0
→
F
7
1 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]:(4)
D
MD
=
9.6
×
10
-
42
esu
2
cm
2
=
0.96
×
10
-
54
J
·
m
3
=
5.99
×
10
-
36
eV
·
m
3
.The strength of all induced electric dipole transitions is (5)
D
ED
J
,
J
′
=
e
2
∑
λ
=
2,4
,
6
Ω
λ
Ψ
J
U
λ
Ψ
J
′
2
,where squared reduced matrix elements Ψ
J
U
(
λ
)
Ψ
J
′
2 have values independent of the host matrix. For the case of Eu3+ these values are tabulated in [18–20], and Judd-Ofelt intensity parameters can be evaluated solely from the emission spectrum because nondiagonal elements of the Ψ
J
U
(
λ
)
Ψ
J
′
2 matrix have zero values according to the following equation:(6)
Ω
λ
=
D
MD
ν
1
3
e
2
ν
λ
3
9
n
3
n
n
2
+
2
2
Ψ
J
U
λ
Ψ
′
J
′
2
∫
I
λ
ν
λ
∫
I
1
ν
1
.For the calculations, the value of refractive index of 1.691 for Mg2TiO4 is taken from the literature [21]. According to [22] radiative emission probability of magnetic dipole transition, A (D
5
0
→
F
7
1), has value of 57.34 s−1 for the 50(NaPO3)6 + 10TeO2 + 20AlF3 + 19LiF + 1Eu2O3 glass with a refractive index of 1.591. Taking this value as a reference, and with the well-known correction factor of n
/
1.591
3, which can be derived from the general equations for the magnetic dipole transition probability rates [23, 24], A (D
5
0
→
F
7
1) = 68.85 s−1 is calculated for the radiative emission probability of magnetic dipole transition of Eu3+ in Mg2TiO4. The intensity of this transition can be considered as a reference for all transitions originating from the 5D0 excited state [11]. Then, it is possible to calculate radiative emission probabilities of all transitions originating from the 5D0 excited state from the ratios of areas S under corresponding emission bands in Figure 3 [20, 22]:(7)
A
D
5
0
⟶
F
7
2,4
=
A
D
5
0
⟶
F
7
1
S
D
5
0
⟶
F
7
2,4
S
D
5
0
⟶
F
7
1
.Total radiative emission probability, A
R, defined as the sum of all radiative emission probabilities:(8)
A
R
=
∑
λ
=
1,2
,
4
A
λ
,can be further used to calculate nonradiative probability A
NR (which includes relaxation by multiphonon emission and effective energy transfer rates arising from ion-ion interactions [11]) and emission quantum efficiency η (the ratio between the number of photons emitted by the Eu3+ ion to the number of those absorbed):(9)
A
NR
=
1
τ
-
A
NR
,
η
=
A
R
A
R
+
A
NR
.The Ω
2 intensity parameter describes hypersensitivity of D
5
0
→
F
7
2 transition since it is affected by the symmetry of local surrounding around the Eu3+ site. Ω
4 and Ω
6 parameters are associated with the viscosity and rigidity of the host material. Several reports [25–28] used Ω
2 to assess the magnitude of covalence between Eu3+ and surrounding ligands (the larger the Ω
2, 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 R
=
(
D
5
0
→
F
7
2
)
/
(
D
5
0
→
F
7
1
) is also known as asymmetry ratio [29]. Higher values of R indicate lower symmetry around the trivalent europium ions [30, 31]. Ω
2 and R reveal similar physical information on the bonding nature between Eu3+ ion and the surrounding anions and explain the short range effects in local structure around Eu3+ ions [28]. Ω
6 intensity parameter could not be determined because D
5
0
→
F
7
6 emission in this sample could not be detected due to the instrumental limitations.Calculated Judd-Ofelt parameters show variation with the annealing temperature, and their values are presented in Table2 along with the values of radiative and nonradiative emission probabilities, quantum efficiencies, and asymmetry ratios.Table 2
Intensity parameters, radiative and nonradiative emission probabilities, quantum efficiencies, and asymmetry ratios of Eu3+ emission from Mg2TiO4 nanoparticles prepared at different temperatures from 400°C to 650°C.
T (°C)
Ω
2 (10−20 cm−2)
Ω
4 (10−20 cm−2)
A (s−1)
A
NR (s−1)
η (%)
R
400
5.23
2.94
309.68
1435.51
17.75
3.22
450
8.80
4.50
487.37
862.15
36.11
5.46
500
10.71
5.08
577.53
644.96
47.24
6.65
550
11.42
5.30
609.79
562.53
52.01
7.10
600
12.46
6.23
671.20
475.58
58.53
7.75
650
12.24
5.88
654.54
520.54
55.70
7.60Ω
2 and Ω
4 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 Ω
2 and Ω
4 increase with the increase of annealing temperature until 600°C. Eu3+ emission from the sample prepared at 650°C has lower values of Ω
2 and Ω
4 than in the case of sample prepared at 600°C. This result indicates that local environment of the Eu3+ ion changes at temperatures higher than 600°C. In the complete temperature range Ω
2 is larger than Ω
4. The relatively high value of Ω
2 and the observed trend indicate a relatively high asymmetry at the Eu3+ 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 R 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 Judd-Ofelt 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.Figure 4
(a)Ω
2 (black squares) and Ω
4 (red circles) intensity parameters and (b) asymmetric ratio of Eu3+ emission in Mg2TiO4 nanoparticles prepared at different temperatures.
(a)
(b)Figure5(a) shows changes of radiative and nonradiative emission probabilities of Eu3+ 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 Eu3+ emission in sample prepared at 650°C is 55.70%, lower than for sample prepared at 600°C.Figure 5
(a) Radiative (black squares) and nonradiative transition rates (red circles) and (b) quantum efficiency of Eu3+ emission in Mg2TiO4 nanoparticles prepared at different temperatures.
(a)
(b)One should note that the values of quantum efficiency are slightly underestimated, since calculation does not accountD
5
0
→
F
7
3,5
,
6 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 Judd-Ofelt theory estimates transition probabilities with accuracy generally not worse than 10% [33].


## 3.1. Microstructural Analysis

Mg2TiO4 crystallize in a cubic, inverse spinel structure (Fd-3m space group) [8–10]. In this structure, Mg2+ ions are located in tetrahedral and octahedral sites while the Ti4+ ions occupy only octahedral sites, as shown in Figure 1(a). Arrangement of Ti4+ and Mg2+ ions in the octahedral sites is random.Figure 1
Crystal structure of Eu3+ activated Mg2TiO4: (a) schematic of the unit cell; (b) X-ray diffraction patterns of nanoparticles prepared at different temperatures from 400°C to 700°C.
(a)
(b)X-ray diffraction patterns of samples calcined at different temperatures from 400°C to 700°C are presented in Figure1(b). The main diffraction peaks are indexed according to ICDD01-072-6968 card. Pure phase of Mg2TiO4 is present in the samples annealed in the temperature range from 400°C to 650°C. In the sample calcined at 700°C ilmenite (MgTiO3) phase is presented along with Mg2TiO4.TEM image in Figure2 shows morphology of particles of Mg2TiO4 doped Eu3+ sample annealed at 600°C for 1 hour. The sample is composed of loosely agglomerated nanoparticles of 5 to 10 nm in diameter.Figure 2
TEM image of the Eu3+ activated Mg2TiO4 nanoparticles prepared at 600°C.


## 3.2. Photoluminescence Emission Spectra and Lifetime Measurements

The emission spectra of Mg2TiO4 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 (4f6 configuration), the crystal-field perturbation by the host matrix lifts partly or completely the degeneracies of the Eu3+ levels [11]. Therefore, emission spectra show five characteristic bands centered around 17271, 16892, 16287, 15290, and 14245 cm−1 that originate from D
0
5
→
F
7
J(J = 0, 1, 2, 3, and 4) spin forbidden f-f electronic transitions of the Eu3+ ions. The D
5
0
→
F
7
1 transition is magnetic dipole in nature and follows the selection rule Δ
J
=
1. Its intensity is independent of the host matrix. On the other hand, the D
0
5
→
F
7
2,4
,
6 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 D
0
5
→
F
7
2 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 D
0
5
→
F
7
2 transition is the most intense across the emission spectra. The D
0
5
→
F
7
0 transition is not allowed since 0–0 transitions are forbidden by the selection rule J
=
0
→
J
′
=
0. The appearance of this transition is mainly due to the J-mixing effect [12] and indicates that Eu3+ ion is located in a site without an inversion center. Low energy transitions, D
0
5
→
F
7
3 and D
0
5
→
F
7
4, are also clearly visible. Emissions from D
0
5
→
F
7
5 (12990–13510 cm−1) and D
0
5
→
F
7
6 (11900–12350 cm−1) transitions could not be detected due to the instrument limitations.Figure 3
The emission spectra of the Eu3+ activated Mg2TiO4 nanoparticles prepared at different temperatures from 400°C to 650°C.From emission spectra (Figure3) 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 5D0 emitting level are obtained under 394 nm excitation. Average lifetime values are calculated using the following equation: (1)
τ
avg
=
∫
0
∞
t
I
t
d
t
∫
0
∞
I
t
d
t
,where I
(
t
) represents the luminescence intensity (corrected for the background) at time t. The results are presented in Table 1.Table 1
Lifetimes of the5D0 emission level of Eu3+ in Mg2TiO4 nanoparticles prepared at different temperatures.
Mg2TiO4 doped 2at% Eu3+
Annealing temperature (°C)
Lifetime (µs)
400
573
450
741
500
818
550
853
600
872
650
851In all samples the highest emission intensity is observed forD
0
5
→
F
7
2 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. Judd-Ofelt Calculations and Results

The Judd-Ofelt theory [13, 14] describes intensities of transitions of lanthanides and actinides in solids and solutions, whereas Judd-Ofelt 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 J-O theory [13, 14] theoretical expression for the oscillator strength of an induced electric dipole transition from the ground state to an excited state is (2)
f
=
8
π
2
m
c
ν
3
h
2
J
+
1
n
2
+
2
2
9
n
∑
λ
=
2,4
,
6
Ω
λ
Ψ
J
U
λ
Ψ
J
′
2
,where h denotes Planck constant (6.626 × 10−34 J·s; 4.135 × 10−15 eV·s), 2
J
+
1 is the degeneracy of the initial state, n is the refractive index, Ω
λ are the Judd-Ofelt parameters, and Ψ
J
U
(
λ
)
Ψ
J
′ 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 Judd-Ofelt theory radiative transition probability, A, is related to its dipole strength according to the following equation:(3)
A
Ψ
′
J
′
;
Ψ
′
J
′
=
65
π
4
e
2
3
h
2
J
′
+
1
λ
3
n
n
2
+
2
2
2
D
ED
+
n
2
D
MD
,where D
ED and D
MD represent the electric and magnetic dipole strengths, respectively. Transition probabilities of the rare earths are composed mainly of the electric dipole contribution D
5
0
→
F
7
J (J = 2, 4) and to a much lesser extent by the magnetic-dipole contribution D
5
0
→
F
7
1. The D
5
0
→
F
7
3 transition is forbidden according to Judd-Ofelt theory, both in magnetic and induced electric dipole scheme, and this transition can only gain intensity via J-mixing [15, 16]. Also, the D
5
0
→
F
7
0 transition is strictly forbidden according to the standard Judd-Ofelt theory. Therefore, these two transitions will not be considered in determining transition probabilities. The intensity of  D
5
0
→
F
7
1 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]:(4)
D
MD
=
9.6
×
10
-
42
esu
2
cm
2
=
0.96
×
10
-
54
J
·
m
3
=
5.99
×
10
-
36
eV
·
m
3
.The strength of all induced electric dipole transitions is (5)
D
ED
J
,
J
′
=
e
2
∑
λ
=
2,4
,
6
Ω
λ
Ψ
J
U
λ
Ψ
J
′
2
,where squared reduced matrix elements Ψ
J
U
(
λ
)
Ψ
J
′
2 have values independent of the host matrix. For the case of Eu3+ these values are tabulated in [18–20], and Judd-Ofelt intensity parameters can be evaluated solely from the emission spectrum because nondiagonal elements of the Ψ
J
U
(
λ
)
Ψ
J
′
2 matrix have zero values according to the following equation:(6)
Ω
λ
=
D
MD
ν
1
3
e
2
ν
λ
3
9
n
3
n
n
2
+
2
2
Ψ
J
U
λ
Ψ
′
J
′
2
∫
I
λ
ν
λ
∫
I
1
ν
1
.For the calculations, the value of refractive index of 1.691 for Mg2TiO4 is taken from the literature [21]. According to [22] radiative emission probability of magnetic dipole transition, A (D
5
0
→
F
7
1), has value of 57.34 s−1 for the 50(NaPO3)6 + 10TeO2 + 20AlF3 + 19LiF + 1Eu2O3 glass with a refractive index of 1.591. Taking this value as a reference, and with the well-known correction factor of n
/
1.591
3, which can be derived from the general equations for the magnetic dipole transition probability rates [23, 24], A (D
5
0
→
F
7
1) = 68.85 s−1 is calculated for the radiative emission probability of magnetic dipole transition of Eu3+ in Mg2TiO4. The intensity of this transition can be considered as a reference for all transitions originating from the 5D0 excited state [11]. Then, it is possible to calculate radiative emission probabilities of all transitions originating from the 5D0 excited state from the ratios of areas S under corresponding emission bands in Figure 3 [20, 22]:(7)
A
D
5
0
⟶
F
7
2,4
=
A
D
5
0
⟶
F
7
1
S
D
5
0
⟶
F
7
2,4
S
D
5
0
⟶
F
7
1
.Total radiative emission probability, A
R, defined as the sum of all radiative emission probabilities:(8)
A
R
=
∑
λ
=
1,2
,
4
A
λ
,can be further used to calculate nonradiative probability A
NR (which includes relaxation by multiphonon emission and effective energy transfer rates arising from ion-ion interactions [11]) and emission quantum efficiency η (the ratio between the number of photons emitted by the Eu3+ ion to the number of those absorbed):(9)
A
NR
=
1
τ
-
A
NR
,
η
=
A
R
A
R
+
A
NR
.The Ω
2 intensity parameter describes hypersensitivity of D
5
0
→
F
7
2 transition since it is affected by the symmetry of local surrounding around the Eu3+ site. Ω
4 and Ω
6 parameters are associated with the viscosity and rigidity of the host material. Several reports [25–28] used Ω
2 to assess the magnitude of covalence between Eu3+ and surrounding ligands (the larger the Ω
2, 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 R
=
(
D
5
0
→
F
7
2
)
/
(
D
5
0
→
F
7
1
) is also known as asymmetry ratio [29]. Higher values of R indicate lower symmetry around the trivalent europium ions [30, 31]. Ω
2 and R reveal similar physical information on the bonding nature between Eu3+ ion and the surrounding anions and explain the short range effects in local structure around Eu3+ ions [28]. Ω
6 intensity parameter could not be determined because D
5
0
→
F
7
6 emission in this sample could not be detected due to the instrumental limitations.Calculated Judd-Ofelt parameters show variation with the annealing temperature, and their values are presented in Table2 along with the values of radiative and nonradiative emission probabilities, quantum efficiencies, and asymmetry ratios.Table 2
Intensity parameters, radiative and nonradiative emission probabilities, quantum efficiencies, and asymmetry ratios of Eu3+ emission from Mg2TiO4 nanoparticles prepared at different temperatures from 400°C to 650°C.
T (°C)
Ω
2 (10−20 cm−2)
Ω
4 (10−20 cm−2)
A (s−1)
A
NR (s−1)
η (%)
R
400
5.23
2.94
309.68
1435.51
17.75
3.22
450
8.80
4.50
487.37
862.15
36.11
5.46
500
10.71
5.08
577.53
644.96
47.24
6.65
550
11.42
5.30
609.79
562.53
52.01
7.10
600
12.46
6.23
671.20
475.58
58.53
7.75
650
12.24
5.88
654.54
520.54
55.70
7.60Ω
2 and Ω
4 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 Ω
2 and Ω
4 increase with the increase of annealing temperature until 600°C. Eu3+ emission from the sample prepared at 650°C has lower values of Ω
2 and Ω
4 than in the case of sample prepared at 600°C. This result indicates that local environment of the Eu3+ ion changes at temperatures higher than 600°C. In the complete temperature range Ω
2 is larger than Ω
4. The relatively high value of Ω
2 and the observed trend indicate a relatively high asymmetry at the Eu3+ 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 R 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 Judd-Ofelt 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.Figure 4
(a)Ω
2 (black squares) and Ω
4 (red circles) intensity parameters and (b) asymmetric ratio of Eu3+ emission in Mg2TiO4 nanoparticles prepared at different temperatures.
(a)
(b)Figure5(a) shows changes of radiative and nonradiative emission probabilities of Eu3+ 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 Eu3+ emission in sample prepared at 650°C is 55.70%, lower than for sample prepared at 600°C.Figure 5
(a) Radiative (black squares) and nonradiative transition rates (red circles) and (b) quantum efficiency of Eu3+ emission in Mg2TiO4 nanoparticles prepared at different temperatures.
(a)
(b)One should note that the values of quantum efficiency are slightly underestimated, since calculation does not accountD
5
0
→
F
7
3,5
,
6 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 Judd-Ofelt theory estimates transition probabilities with accuracy generally not worse than 10% [33].


## 4. Conclusion

To conclude, Eu3+ doped Mg2TiO4 nanoparticles of about 5 to 10 nm in size can be prepared with Pechini-type polymerized complex route after annealing in the low-temperature 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 Judd-Ofelt intensity parameter Ω
2 was larger than Ω
4, and relatively high values of Ω
2 and asymmetry ratio are observed. The latter indicate relatively high asymmetry at the Eu3+ sites.



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*Source: 736517-2015-07-27.xml*