Journal of Molecular Structure 1041 (2013) 100–105
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Optical absorption and photoluminescence properties of Dy3+ doped heavy metal borate glasses – Effect of modifier oxides M.V. Sasi kumar, D. Rajesh, A. Balakrishna, Y.C. Ratnakaram ⇑ Department of Physics, Sri Venkateswara University, Tirupati 517 502, India
h i g h l i g h t s The effect of modifier oxides on J–O intensity parameters and radiative properties are studied. 4
Decay curves of F9/2 state exhibits non-exponential nature in all the glasses. 3+
Dy
doped different modifiers in zinc borate glasses exhibits white light emission under 450 nm excitation.
a r t i c l e
i n f o
Article history: Received 17 January 2013 Received in revised form 5 March 2013 Accepted 5 March 2013 Available online 13 March 2013 Keywords: Thermogram Absorption Emission Lifetime Branching ratio Decay curve
a b s t r a c t The present paper aims at reporting the optical absorption and emission properties of Dy3+ doped alkali (Li, Na, K) and mixed alkali (Li–Na, Li–K, Na–K) heavy metal borate glasses. For these glasses X-ray diffraction (XRD), differential scanning calorimetry (DSC), optical absorption, emission and lifetime decay measurements were carried out. Glass transition temperatures are obtained from the DSC spectra. Judd–Ofelt theory has been used to derive the spectral intensities (f), Judd–Ofelt intensity parameters (O2, O4 and O6) and certain radiative properties. Using the Judd–Ofelt intensity parameters, radiative lifetimes (sR), branching ratios (b), integrated absorption cross-sections (R) and emission cross-sections (rP) were obtained. The variations in these parameters with the variation of glass matrix are discussed in detail. The decay lifetime of the 4F9/2 level has been measured from the decay profiles and compared with calculated lifetimes. From the emission spectra, chromacity color coordinates are calculated and indicated the white light emission for potassium glass matrices. It was observed that among various glass matrices, potassium glass matrix has exhibited large emission cross-section for 6F9/2 ? 6H13/2 transition. Crown Copyright Ó 2013 Published by Elsevier B.V. All rights reserved.
1. Introduction Glass hosts activated with trivalent rare earth ions possess broad emission bands that afford enhanced prospect of tuning, Q-switching of lasers and production of fiber amplifiers [1]. Oxide based glasses such as silicate, phosphate, borate, germinate, vanadate and tellurite are found to be promising for photonic applications. Among all these glass families’ borate glasses are the most suitable ones for rare earth ion doping due to their high transparency, low melting point, high thermal stability and good rare earth ion solubility [2]. Among trivalent lanthanides, Dy3+ ions were incorporated in several glasses [3] and crystals [4] for obtaining the three primary colored luminescent bands. Dysprosium doped solid state systems can be quite easily excited because their excitation spectra exhibit several 4f–4f electronic bands.
⇑ Corresponding author. Tel.: +91 9440751615. E-mail address:
[email protected] (Y.C. Ratnakaram).
Luminescence spectrum of Dy3+ consists two relatively intense bands in the visible spectral region that correspond to 4 F9/2 ? 6H15/2 (blue) and 4F9/2 ? 6H13/2 (yellow) transitions along with the sickly red luminescence band which corresponds to 4 F9/2 ? 6H11/2 transition. Thus, the Dy3+ doped several glasses are studied to obtain two primary colored luminescent materials as well as white light emitting material. An appropriate combination of these luminescence bands leads to generation of white light in the glass [5]. The spectroscopic and luminescence properties of trivalent rare-earth (RE) ions are strongly influenced by the presence of highly polarizable Pb2+ ions due to the strong and direct nature of Pb–O bond [6,7]. Recently, Vijaya kumar et al. [8] reported the optical absorption and fluorescence studies of Dy3+ doped lead telluroborate glasses. Luminescence quenching of Dy3+ ions in lead bismuth glasses were studied by Pisarski et al. [9]. The luminescence spectra of Dy3+ ions in heavy metal glasses and glass ceramics were reported by Mohan Babu et al. [10] and Babu et al. [11]. Tanabe et al. [12] have made a systematic study of yellow and blue luminescence in Dy3+ doped borate glasses. Laser action in Dy3+ in
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M.V. Sasi kumar et al. / Journal of Molecular Structure 1041 (2013) 100–105
NIR and visible regions were reported by Kaminski et al [13,14]. In the present work, thermal and spectroscopic properties of Dy3+ doped certain heavy metal borate glasses were investigated and reported. The purpose of present study is to investigate the photoluminescence characteristics of Dy3+ doped alkali and mixed alkali lead zinc borate glasses using the absorption, emission and decay measurements in order to know their utility for various device applications. Judd–Ofelt (J–O) theory has been used to evaluate various spectroscopic properties such as spectral intensities (f), intensity parameters Ok (k = 2, 4 and 6), spontaneous transition probabilities (AR), radiative lifetimes (sR) and branching ratios (b). From the emission spectra it is proposed that the CIE chromaticity co-ordinates (x, y) from which light emission could be obtained for using in lighting applications. 2. Experimental The following molar compositions were used for the preparation of dysprosium doped alkali and mixed alkali heavy metal borate glasses using melt quenching technique. Glass A: 54 B2O3 + 15 PbO + 10 ZnO + 20 Li2O + 1Dy2O3. Glass B: 54 B2O3 + 15 PbO + 10 ZnO + 20 Na2O + 1Dy2O3. Glass C: 54 B2O3 + 15 PbO + 10 ZnO + 20 K2O + 1Dy2O3. Glass D: 54 B2O3 + 15 PbO + 10 ZnO + 10 Li2O + 10 Na2O + 1Dy2O3. Glass E: 54 B2O3 + 15 PbO + 10 ZnO + 10 Li2O + 10 K2O + 1Dy2O3. Glass F: 54 B2O3 + 15 PbO + 10 ZnO + 10 Na2O + 10 K2O + 1Dy2O3.
101
fluorometer in the wavelength range of 400–700 nm under excitation 450 nm.
3. Results and discussion 3.1. XRD and DSC studies Fig. 1 shows the X-ray diffraction patterns of the Dy3+ doped sodium and lithium–sodium heavy metal borate glass matrices. As the diffractograms of other glass matrices were found similar in shape, they were not shown in the figure. The spectra did not show any sharp peaks which indicate the amorphous nature of glass samples. Fig. 2 shows the DSC thermograms of different alkali and mixed alkali heavy metal borate glass matrices doped with Dy3+ ions. It is observed from Fig. 2 that the glass transition temperatures for lithium, sodium, potassium, lithium–sodium, lithium–potassium and sodium–potassium glass matrices were 365, 336, 343, 335, 334 and 329 °C respectively. The data on transition temperatures reveal that lithium glass has the highest glass transition temperature (365 C). 3.2. Absorption spectra
All the compounds were thoroughly crushed in an agate mortar in order to mix the chemicals homogeneously. The mixture was taken in silica crucible and melted in an electric furnace at 960 °C for about half an hour. The melt was quenched between two well polished brass plates for obtaining the smooth surfaced bubble free glasses. The glasses so formed were then annealed at 300 °C for 2 h. The non-crystalline nature of synthesized glasses was tested using XRD 3003 TT Scifert diffractrometer with Cu Ka radiation. By employing the Archimedes principle, the glass densities were measured with xylene as an immersion liquid. The refractive indices of these glasses were measured at 589.3 nm on an Abbe refractrometer with 1-monobromonaphthalene as the contact layer between sample and prism of the refractometer. The UV–VIS–NIR absorption spectra were recorded at room temperature using JASCO V-570 spectrometer in the range of 500–1900 nm. The emission spectra of these glasses were recorded on JOBINYVON Fluorolog-3
The absorption spectra of Dy3+ doped (1 mol%) alkali and mixed alkali heavy metal borate glasses recorded at room temperature in the wavelength region 500–1900 nm are shown in Fig. 3. Because of strong absorption in the visible region, no absorption bands are observed in that region. All these absorption bands correspond to the transitions from the ground state, 6H15/2 to different excited states, 6F3/2, 6F5/2, 6F7/2 + 6H5/2, 6F9/2 + 6H7/2, 6F11/2 + 6H9/2 and 6H11/2 of Dy3+ ion [8]. The spectral intensities (fexp) of the absorption bands are obtained using the relation given in Refs. [15,16]. The Judd–Ofelt theory is applied to evaluate the calculated spectral intensities (fcal) and Judd–Ofelt intensity parameters (X2, X4 andX6) are obtained from the experimental spectral intensities using least square analysis [17,18]. Table 1 gives the experimental and calculated spectral intensities along with the rms deviations (drms) between experimental and calculated spectral intensities and Judd–Ofelt intensity parameters for all the glasses studied. Small rms deviations (drms) indicate a good fit between experimental and calculated values. From Table 1, it is observed that the spectral intensity of the hypersensitive transition (6F11/2 + 6H9/2) has been increasing with the increase of atomic number of modifier cation in the glass matrix (i.e., Li < Na < K). It is also observed that the spectral intensities are intermediates for lithium–potassium and sodium–potassium glass matrices between lithium and
Fig. 1. X-ray diffraction (XRD) patterns of sodium and lithium–sodium heavy metal borate glasses doped with Dy3+ ions.
Fig. 2. DSC thermograms of different alkali and mixed alkali heavy metal borate glasses doped with Dy3+ ions.
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Fig. 3. Optical absorption spectra of alkali and mixed alkali heavy metal borate glasses doped with Dy3+ ions.
(b) which indicates the covalency of RE–O bond [21]. The degree of covalency of Dy–O bond decreases/increases with the shift of the peak wavelength of hypersensitive transition towards lower/higher wavelength due to nephelauxetic effect. In the present work, the peak wavelengths (kp) (nm) of the hypersensitive transition in lithium, sodium, potassium, lithium–sodium, lithium–potassium and sodium–potassium glass matrices are observed as 1265.4, 1263.7, 1264.7, 1265.0,1266.7 and 1263.4 nm respectively. From the data, a shift in the peak wavelength of hypersensitive transition towards shorter wavelength for lithium to sodium glass matrix is observed but the X2 parameter is found increasing (5.72–6.46) which indicates some structural changes. For potassium to lithium–sodium and lithium–potassium to sodium–potassium, there is a shift in the peak wavelength towards longer and shorter wavelengths, but the X2 parameter decreases and increases respectively indicating some structural changes that are present in the glass matrices. 3.3. Radiative properties
potassium and sodium and potassium respectively. It is found that for lithium–sodium glass the spectral intensity of hypersensitive transition has been decreasing. The three Judd–Ofelt intensity parameters exhibit a common trend (X2 > X4 > X6) for all the glass matrices. The magnitude of X2 parameter is higher in potassium and sodium–potassium glass matrices among the three alkali and mixed alkali glass matrices respectively indicating higher covalency of Dy–O bond in these two glass matrices. The magnitude of X4 and X6 parameters are related to the bulk properties such as viscosity and rigidity of the medium in which the rare earth ions are situated [19]. In the present work, X4 and X6 parameters are higher in potassium and lithium–potassium glass matrices among the three alkali and mixed alkali glasses respectively. It indicates higher rigidity of the medium in these two glass matrices. The ratio between X4 and X6 parameters is known as spectroscopic quality factor and it characterizes the lasing properties of the material concerned [20]. The X4/X6 values for all the studied glass matrices are also presented in the Table 1. It is observed that among the three alkali heavy metal borate glass matrices, sodium and lithium glass matrices have higher and lower spectroscopic quality factors respectively. In the case of mixed alkali glass matrices, when lithium is mixed with sodium and potassium, the spectroscopic quality factor is in between lithium and sodium and lithium and potassium glass matrices. When sodium is mixed with potassium, spectroscopic quality factor is decreased. For Dy3+ ion, the transition, 6H15/2 ? 6F11/2 + 6H9/2 is hypersensitive transition. The spectral intensity and spectral profile of this transition are very sensitive to the environment. Hypersensitivity of a transition has shown to be proportional to nephelauxetic ratio
To understand the luminescence properties of Dy3+doped glass matrices, Judd–Ofelt theory has been employed and various radiative properties like radiative transition probabilities (A), lifetimes (sR), branching ratios (b) and integrated absorption cross-sections P ( ) are studied. All the above properties are studied using the formulae given in Ref [22]. In the present work, the radiative lifetimes (sR) of certain excited states, 4I15/2, 4I9/2, 6F3/2, 6F5/2 and 6F11/2(6H9/2) of Dy3+ are estimated in all the glass matrices and are presented in Table 2. From the table it is observed that the lifetimes of all the excited states are found higher in lithium glass matrix and lower in potassium glass matrix among the three glass matrices (Li, Na, and K). In the case of mixed alkali glass matrices lithium–sodium glass matrix shows higher radiative lifetimes (sR). The branching P ratios (b) and absorption cross-sections ( ) for certain transitions which have higher magnitudes are also presented in Table 2. Among the five transitions presented in Table 2, the branching ratios of the transitions 6F11/2 (6H9/2) ? 6H15/2 and 4F9/2 ? 6H13/2 have higher magnitudes. 3.4. Excitation and emission spectra Fig. 4 shows excitation spectra of the Dy3+ doped potassium heavy metal borate glass matrix using the emission wavelength 570 nm. The excitation spectra consists six bands corresponding to the transitions from 6H15/2 to different excited states, 6P7/2 (350 nm), 4P3/2 (365 nm), 4I13/2 (389 nm), 4G11/2 (426 nm), 4I15/2 (453 nm) and 4F9/2 (472 nm). The excitation spectra of all the remaining glasses are similar to Fig. 4. In the present investigation,
Table 1 Experimental and calculated spectral intensities (f 106) of certain excited states and Judd–Ofelt intensity parameters (O2, O4 and O6) (1020 cm2) of Dy3+ doped alkali and mixed alkali heavy metal borate glasses. S. No
Energy level
Li fexp
1 2 3 4 5 6
6
F3/2 6 F5/2 6 F7/2, 6H5/2 6 F9/2, 6H7/2 6 F11/2, 6H9/2 6 H11/2 rms deviation X2 X4 X6 X4/X6 Trend
0.15 1.21 0.96 2.04 6.11 0.84 ±0.32 5.72 2.00 1.24 1.61 X2 > X4 > X6
Na fcal 0.10 0.55 1.33 1.96 6.11 0.84
fexp 0.17 1.33 1.42 2.04 6.87 0.65 ±0.34 6.46 2.26 1.21 1.87 X2 > X4 > X6
K fcal 0.10 0.54 1.35 2.08 6.84 0.88
fexp 0.17 1.19 1.78 2.09 7.64 0.65 ±0.32 7.34 2.36 1.28 1.84 X2 > X4 > X6
Li–Na fcal 0.11 0.57 1.42 2.20 7.60 0.96
fexp 0.18 1.23 1.31 1.99 6.00 0.64 ±0.30 5.43 2.14 1.19 1.80 X2 > X4 > X6
Li–K fcal 0.10 0.53 1.32 2.00 5.98 0.81
fexp 0.19 1.35 1.18 2.13 6.45 0.76 ±0.34 5.94 2.24 1.26 1.78 X2 > X4 > X6
Na–K fcal 0.11 0.56 1.39 2.11 6.44 0.87
fexp 0.16 1.13 1.38 1.99 7.00 0.74 ±0.23 6.79 2.09 1.23 1.70 X2 > X4 > X6
fcal 0.10 0.54 1.34 2.01 6.78 0.90
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Table 2 P Radiative lifetimes (sR) (ls) of certain excited states, branching ratios (b) and absorption cross-sections ( , cm) of certain transitions of Dy3+ doped alkali and mixed alkali heavy metal borate glass matrices. S. No
Glass
4
6
6
6
2560 2419 2231 2620 2454 2391
1115 1023 925 1151 1068 997
1232 1203 1138 1259 1186 1223
1058 1015 954 1067 1013 1024
1039 924 832 1059 986 905
I15/2
1 2 3 4 5 6
Li Na K Li–Na Li–K Na–K
4
Lifetimes 4
F9/2
F3/2
F5/2
6
F11/2, ( H9/2)
I15/2 ? 6H15/2 P b
4
F9/2 ? 6H13/2 P b
6
F3/2 ? 6H13/2 P b
F5/2 ? 6H15/2 P b
F11/2(6H9/2) ? 6H15/2 P b
0.63 0.61 0.61 0.62 0.62 0.62
0.71 0.72 0.72 0.70 0.71 0.72
0.43 0.41 0.41 0.42 0.42 0.42
0.44 0.42 0.42 0.43 0.43 0.43
0.93 0.93 0.93 0.93 0.93 0.93
0.24 0.25 0.27 0.24 0.25 0.26
Fig. 4. Excitation spectra of Dy3+ doped potassium heavy metal borate glass monitored at 570 nm.
the luminescence spectra were carried out by exciting the samples with 450 nm wavelength. The emission spectra were recorded in the spectral region 450– 700 nm for all Dy3+ doped glasses and are shown in Fig 5. The spectra exhibits two strong luminescence bands, 4F9/2 ? 6H15/2 (blue) and 4F9/2 ? 6H13/2 (yellow) and one weak luminescence band, 4 F9/2 ? 6H11/2 (red). The shapes of the emission peaks are similar in all the glass matrices except in small variations in the intensity of the emission transition. Table 3 presents peak wavelengths (kp), branching ratios (b), effective bandwidths (Dteff) and peak emission cross-sections (rp) of Dy3+ in all the heavy metal borate glass matrices. From the table it is observed that among the three transitions 4F9/2 ? 6H13/2 transition consists higher branching ratios and peak emission cross-sections. Among all the glass matrices studied, r and b values are found higher for potassium glass for the above transition.
3.5. Luminescence decay analysis In general, the non-exponential behavior of decay curves of rare earth doped materials arises from the ion–ion interactions would be governed mainly by the dopent concentration. The decay curves
0.98 1.08 1.2 0.94 1.02 1.11
1.74 1.71 1.8 1.68 1.77 1.72
6
1.29 1.27 1.33 1.24 1.31 1.28
6
6.93 7.79 8.68 6.78 7.31 7.96
Fig. 5. Emission spectra of alkali and mixed alkali heavy metal borate glasses doped with Dy3+ ions.
Table 3 Emission peak wavelengths (kP, nm), branching ratios (bexp and bcal), effective bandwidths (Dteff, cm1) and peak stimulated emission cross-sections (rp 1020 cm2) of certain transitions of Dy3+ doped alkali and mixed alkali heavy metal borate glass matrices. Transition
Parameter
Li
Na
K
Li–Na
Li–K
Na–K
4
kP bexp bcal Dteff
486 0.49 0.14 730 0.21
486 0.51 0.13 687 0.22
486 0.54 0.13 703 0.22
486 0.59 0.15 707 0.21
486 0.57 0.14 725 0.21
486 0.56 0.13 685 0.22
578 0.50 0.71 490 2.11
577 0.48 0.72 467 2.43
578 0.45 0.72 469 2.71
578 0.41 0.70 470 2.12
577 0.42 0.71 472 2.27
578 0.43 0.72 465 2.53
666 0.01 0.07 228 0.62
667 0.01 0.7 327 0.48
669 0.01 0.08 288 0.62
668 0.01 0.07 257 0.52
668 0.01 0.07 303 0.49
667 0.01 0.08 361 0.46
F9/2 ? 6H15/2
rp 4
F9/2 ? 6H13/2
kP bexp bcal Dteff
r 4
F9/2 ? 6H11/2
kP bexp bcal Dteff
rp
exhibit single exponential nature at lower concentrations (<1.0 mol%) and non- exponential behavior at higher concentration
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M.V. Sasi kumar et al. / Journal of Molecular Structure 1041 (2013) 100–105 Table 4 Experimental and calculated lifetimes (sexp and sR) (ls), non-radiative transition rates (WNR) (s1) and quantum efficiencies (g) (%) of 4F9/2 state of Dy3+ doped alkali and mixed alkali heavy metal borate glasses.
Fig. 6. Decay profiles of 4F9/2 emission level of Dy3+ doped different alkali and mixed alkali heavy metal borate glasses.
(P1.0 mol%) of Dy3+ ion [23,24]. The luminescence decay curves for the excited level, 4F9/2 of Dy3+ ion gives additional information on the luminescence properties of Dy3+ doped glasses. Fig. 6 shows the decay profiles of 4F9/2 excited state recorded at room temperature upon 450 nm excitation by monitoring the emission wavelength at 570 nm. All the decay curves show bi-exponential behavior as per formula given in Ref. [25]
t t þ A2 exp IðtÞ ¼ A1 exp
s1
s2
ð1Þ
where A1 and A2 are constants and s1 and s2 are the lifetimes of two channels responsible for the decay. The experimental lifetimes (sexp) has been evaluated using the relation
sexp
A1 s21 þ A2 s22 ¼ A1 s1 þ A2 s2
W NR ¼
1
sexp
1
sR
ð3Þ
where sexp and sR are the experimental and calculated radiative lifetimes obtained from the decay curves and Judd–Ofelt theory respectively. The quantum efficiency (g) of the excited state, 4F9/2 is obtained from
g¼
sexp sR
Glass
sexp
sR
WNR
g
1 2 3 4 5 6
Li Na K Li–Na Li–K Na–K
333 376 372 331 487 432
1115 1023 925 1151 1068 997
2106 1682 1607 2152 1117 1312
30 37 40 29 46 43
Fig. 7. Representation of color coordinate of Dy3+ doped potassium heavy metal borate glass in CIE chromaticity color diagram.
presence of non-radiative channels. From the table it is also observed that lithium–potassium and sodium–potassium glass matrices show higher quantum efficiencies. 3.6. Color analysis The color of any light source can be described by three variables xðkÞ, yðkÞ and zðkÞ which are dimensionless quantities [26]. To estimate the emission color of the glass matrices, the Commission International deI’Eclairage (CIE) chromacity coordinates are determined from the tristimulus values using the following relations.
x¼
X XþY þZ
ð5Þ
y¼
Y XþY þZ
ð6Þ
ð2Þ
The discrepancy between the sexp and sR may be due to the nonradiative relaxation (WNR) of excited Dy3+ ions which are calculated from the relation
S. No
ð4Þ
Table 4 represents the experimental and calculated lifetimes (sexp and sR), non-radiative relaxation rates (WNR) and quantum efficiencies (g) for 4F9/2 state of Dy3+ doped alkali and mixed alkali heavy metal borate glass matrices. From the data, it observed that experimental lifetimes (sexp) are lower than the calculated lifetimes (sR) in all the glass matrices. This is mainly due to the
The locus of all monochromatic color coordinates makes the perimeter of CIE 1931 chromaticity diagram. All the multi-chromatic wavelengths lie within the area of chromaticity diagram. In the present investigation, the color coordinates x and y of all the alkali and mixed alkali heavy metal borate are found almost the same (0.44 and 0.42). Fig 7 represents the chromaticity diagram of lithium heavy metal borate glass doped with Dy3+ ion. In the present study, the color coordinates fall on the white light region on the chromaticity diagram for all the prepared glasses. From these results it is predicted that all the prepared glasses can be used for white light emitting devices with blue excitation. 4. Conclusions The present research work explains the properties of optical absorption and luminescence spectra of alkali and mixed alkali heavy metal borate glasses doped with Dy3+ ion. The amorphous
M.V. Sasi kumar et al. / Journal of Molecular Structure 1041 (2013) 100–105
nature of the prepared glasses was confirmed by the XRD studies. The glass transition temperatures were obtained from the DSC studies. From the Judd–Ofelt intensity parameters, the covalency and rigidity of the glass matrices were discussed. The X2 parameter was found larger for potassium and sodium–potassium glass matrices among the three alkali and mixed alkali glass matrices respectively which indicate the stronger covalency of Dy–O bond in these two glass matrices. Potassium and lithium–potassium glass matrices have shown higher X4 value indicating higher rigidities of the glass matrices among all the glass matrices studied. For potassium to lithium–sodium and lithium–potassium to sodium– potassium, a shift in the peak wavelength of hypersensitive transition towards longer and shorter wavelengths is observed, but the X2 parameter was found decreasing and increasing respectively indicating some structural changes. The emission transition, 4 F9/2 ? 6H13/2 of Dy3+ showed higher peak emission cross-section in potassium glass matrix among all the glass matrices studied indicating for laser excitation. The decay curves were found bi-exponential for all the glass matrices. The quantum efficiency and experimental lifetimes were found larger for lithium–potassium glass matrix among all the studied glass matrices. From the chromaticity diagram, it was observed that all the chromaticity color coordinates fell on the white light region. Acknowledgement The author Y.C. Ratnakaram expresses his thanks to the University Grants Commission for providing the financial assistance in the form of major research project (No. F.40-443/2011 (SR)). References [1] L. Nagli, D. Bunimovich, A. Katzir, O. Gorodetsky, V. Moley, J. Non-Cryst. Solids 217 (1997) 208. [2] R.T. Karunakaran, K. Marimuthu, S. Surendra Babu, S. Arumugam, J. Lumin. 130 (2010) 1067.
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