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Judd-Ofelt analysis and temperature dependent upconversion luminescence of Er3 þ /Yb3 þ codoped Gd2(MoO4)3 phosphor Hongyu Lu a, Yachen Gao b, Haoyue Hao a, Guang Shi a, Dongyu Li c, Yinglin Song a, Yuxiao Wang a,n, Xueru Zhang a,n a

Department of Physics, Harbin Institute of Technology, Harbin 150001, China College of Electronic Engineering, Heilongjiang University, Harbin 150080, China c Department of Physics, Lingnan Normal University, Zhanjiang 524048, China b

art ic l e i nf o

a b s t r a c t

Article history: Received 14 January 2016 Received in revised form 28 July 2016 Accepted 3 February 2017 Available online 6 February 2017

Although lanthanide doped luminescent materials have been extensively investigated, a quantitative analysis of how temperature affects upconversion luminescence is still incomplete. The Gd2(MoO4)3:Er3 þ /Yb3 þ phosphor is synthetized by sol-gel method. Based on the absorption spectra of Er3 þ ions, J-O intensity parameters and radiative transition probabilities are computed to estimate the optical properties. In view of ion-phonon interaction, the phonon-assisted energy transfer and multiphonon relaxation are responsible for the temperature dependent luminescence. Additionally, cross relaxation probability for 4I11/2 þ 4I11/2-4I15/2 þ 4F7/2 is determined to be 240 s 1 through quantitative simulation of ion-ion interaction. These meaningful results are of vital values for the ﬁeld of laser crystal and optical temperature sensing. & 2017 Elsevier B.V. All rights reserved.

Keywords: Phonon J-O intensity parameters Energy transfer Multiphonon relaxation Cross relaxation Rare earth

1. Introduction Recently, enormous attention has been paid to lanthanide doped luminescent materials because of their broad applications, such as remote sensing, biological labeling, and display devices [1– 6]. The unique upconversion luminescence depends on intra-4f electronic transition of lanthanide ions, which can convert low energy photons to high energy photons via multiphoton processes. Photon upconversion involves multiple mechanisms, such as ionphoton, ion-ion and ion-phonon interactions. For ion-photon interactions, the Judd-Ofelt (J-O) theory is an effective method to investigate the radiative transition within the 4fN conﬁguration of lanthanide ions based on their optical absorption measurement [7–11]. In view of ion-ion interactions, the energy transfer (ET) and cross relaxation (CR) are extremely sensitive to the distance of lanthanide ions [12–14]. In the case of ion–phonon interactions, phonon-assisted ET and multiphonon relaxation strongly depend on the phonon energy of materials, energy gap (to the adjacent levels) and temperature [15–17]. Among the variety of available phosphors, Gd2(MoO4)3 doping with Er3 þ ions and Yb3 þ ions has n

Corresponding authors. E-mail addresses: [email protected] (Y. Wang), [email protected] (X. Zhang).

http://dx.doi.org/10.1016/j.jlumin.2017.02.009 0022-2313/& 2017 Elsevier B.V. All rights reserved.

been extensively investigated since not only does Gd2(MoO4)3 have high chemical durability and low phonon energy, but also the Er3 þ ion has abundant energy levels whose emissions almost include the whole visible range [18,19]. Huang et al. investigated radiative transition properties of the Tm3 þ doped Gd2(MoO4)3 crystal using J-O theory and concluded that it could be a promising blue phosphor due to relatively larger radiative transition probability and ﬂuorescence branching ratio [20]. Skrzypczak et al. quantitative analyzed ion-ion interactions (ET and CR processes) of the Nd3 þ doped ceramic using rate equation system [21]. Jin et al. reported the inﬂuence of the phonon on upconversion process for the Yb3 þ and Er3 þ codoped NaYF4 phosphor [22]. To the best of our knowledge, a fundamental understanding of the overall mechanism of upconversion process has not been reported in the literature so far. Here, we quantitatively investigate the upconversion luminescence processes that the population and depopulation of the excited states are responsible for temperature dependent emission in Er3 þ and Yb3 þ codoped Gd2(MoO4)3 phosphor. In addition, the J-O theory is adopted to calculate radiative transition probabilities and predict the material properties. Using a steady-state rate equation system, we develop a comprehensive theoretical model including resonant or phonon-assisted ET, radiative, multiphonon relaxation

H. Lu et al. / Journal of Luminescence 186 (2017) 34–39

35

and CR, which collectively accounts for the variation of luminescent intensity.

2. Experimental The Gd2(MoO4)3:1%Er3 þ /9%Yb3 þ phosphor was prepared using a sol-gel method. Firstly, an appropriate amount of (NH4)6Mo7O24 was dissolved in 15 mL 2-methoxyethanol with 5 mL acetic acid glacial under constant magnetic stirring. 10 mL 2-methoxyethanol solution containing Gd(NO3)3 (1.8 mmol), Yb(NO3)3 (0.18 mmol) and Er(NO3)3 (0.02 mmol) was slowly added into the solution. Subsequently, the citric acid (4.5 mmol) was added to this solution which acts as chelating agent, and then a yellowish transparent solution was obtained by stirring a few minutes. Finally, the wet gel was dried at 60 °С for 8 h, and then the product was sintered 800 °С for 2 h in air atmosphere. The luminescent spectra were measured in the wavelength range 450–650 nm under 980 nm excitation by a Spectrometer (HORIBA Jobin Yvon iHR550). Powder X-ray diffraction (XRD) pattern was recorded using Panalytical Empyrean diffractometer with Cu-Ka radiation (λ ¼1.5406 Å). The absorption spectrum was inspected by a spectrophotometer (Hitachi UV–vis-NIR U4100).

3. Results and discussion The XRD pattern of Gd2(MoO4)3:1%Er3 þ /9%Yb3 þ phosphor is presented in Fig. 1. The pattern reveals that the sample are pure phase, which is well consistent with the standard value of orthorhombic Gd2(MoO4)3 (JCPDS No. 70-1397). The lattice constants are a¼ 10.3881 Å, b¼10.4194 Å, c¼10.7007 Å, α ¼ β ¼ γ ¼90° and the space group is Pba2 [23]. 3.1. Judd-Ofelt analysis The absorption spectrum of Gd2(MoO4)3:Er3 þ /Yb3 þ powder in the Vis-NIR region is shown in Fig. 2. Eight absorption bands arising from the ground (4I15/2 for Er3 þ ) to the upper levels transitions are selected to determine the phenomenological experimental oscillator strengths (ƒexp), which can be determined from the below given expression [24]:

Fig. 2. Absorption spectrum of Gd2(MoO4)3:1%Er3 þ /9%Yb3 þ powder.

(

)

fexp J → J ′ =

mc2 Nπe2

2

c ∫ ε ( v) dν = 2.303m ∫ A ( v ) dν Nπe2cb Δx

4.318 × 10−9 cb Δx

=

∫ A ( v ) dν

(1)

where c (¼ 2.998 1010 cm/s) is the light velocity, N is the Avogadro's number, m (¼ 9.1 10–28 g) is the electron mass, e ( ¼4.8 10 10 esu) is the electron charge, ν (cm 1) is the wavenumber of the absorption band, ε(ν) (L/(mol cm)) is the molar extinction coefﬁcients (ε(ν)¼ 2.303 A(v)/cbΔx), A(ν) is wavenumber dependent absorbance, cb (mol/L) is the amount of substance concentration of Er3 þ , and Δx (cm) is the path-length of the light, respectively. ed The theoretical oscillator strengths of the electric ( f cal ) and md ) dipole transition from the initial J state to the ﬁnal J′ magnetic ( f cal state can be represented as [25]:

2

(

)

ed f cal J → J′ =

2 8π 2mcν ( n + 2) 9n 3h ( 2J + 1)

×

∑

Ωt 4f N (αSL ) J‖U t‖4f N (α′S ′L′) J ′

2

(2)

t = 2,4,6

md

f cal

( J → J ) = 6mch(2νnJ + 1) ′

×

(

fcal J → J ′

)

(

)

4f N ( αSL ) J‖L + 2S‖4f N α′S ′L′ J ′

(

ed = f cal J → J′

)

(

md + f cal J → J′

2

(3)

)

(4) 27

Fig. 1. XRD pattern of Gd2(MoO4)3:1%Er3 þ /9%Yb3 þ phosphor and the standard date of orthorhombic phase Gd2(MoO4)3 (JCPDS No. 70-1397).

2

where n is medium refractive index, h (¼6.63 10 g cm /s) is Plank's constant, J (J′) is the total angular momentum of initial (ﬁnal) state, Ωt is the J-O intensity parameters, and ║U t║2 is the squared reduced matrix elements of the unit tensor operator which is independent of the chemical environment of the ion and was given in Ref. [26], respectively. The wavelength dependent refractive indexes of Gd2(MoO4)3 were reported by Jaque et al. [27]. For powder material of random orientations, the optical anisotropy is averaged. Therefore, the refractive index of Gd2(MoO4)3 powder can be expressed as n¼(2no þne)/3 [28]. The radiative transition probability arising from the J′ to the J state transition is calculated by using the following formulas [29]:

36

H. Lu et al. / Journal of Luminescence 186 (2017) 34–39

Fig. 3. Luminescence decay curve of 4I13/2-4I15/2 transition for Gd2(MoO4)3: Er3 þ /Yb3 þ phosphor under 980 nm excitation.

2

(

)

A ed J ′ → J =

2 64π 4e2v 3 n ( n + 2) ′ 9 3h 2J + 1

(

×

)

(

)

Ωt 4f N α′S ′L′ J ′ ‖U t‖4f N ( αSL ) J

∑

2

t = 2,4,6

(

)

Amd J ′ → J =

4π 2e2hv 3n3

( ) ( α′S L ) J ‖L + 2S‖4f ( αSL) J

3m2c2 2J ′ + 1 × 4f N

(

(5)

)

(

′ ′

)

′

N

(

A J ′ → J = A ed J ′ → J + Amd J ′ → J

2

)

(6)

(7)

where Aed and Amd are electric and magnetic dipole radiative transition probability, respectively. In view of Er3 þ , the transition between 4I13/2 and 4I15/2 involves electric and magnetic dipole transition. The radiative lifetime is related to radiative probability, which can be expressed as [30]:

1/τ = A ed + Amd

(8)

For 4I13/2-4I15/2 transition, radiative lifetime is obtained from the luminescence decay curve (Fig. 3) and determined to be 2.46 ms. In terms of diffuse reﬂectance absorption spectra, the actual path-length (Δx) is unknown. An effective method is used to calculate the three J-O intensity parameters (Ωt), which is reported by Toma et al. [28]. The three J-O intensity parameters (Ωt) can obtain from the least squares ﬁtting between the experimental (ƒexp) and the theoretical (ƒcal) oscillator strengths with the help of Eq. (8). Meanwhile, the relation between three J-O intensity parameters (Ωt) and ﬂuorescence intensity ratio (FIR) (Eq. (9)) is taken into account. As a result, the three J-O intensity parameters (Ωt) are determined to be Ω2 ¼ 11.74 10 20 cm2, 20 2 20 Ω4 ¼8.16 10 cm and Ω6 ¼2.05 10 cm2, respectively. Since the relative population of thermal coupling levels follows the Boltzmann distribution, based on measurement of temperature dependent luminescence, the FIR can be related to the J-O intensity parameters (Ωt) as follows [31]:

FIR =

⎤ ⎡ −ΔEHS ⎤ v 4 ⎡ 0.7158Ω 2 + 0.4138Ω 4 IH = H4 ⎢ + 0.4166⎥ exp ⎢ ⎣ kT ⎥⎦ ⎦ IS 0.2225Ω 6 vS ⎣

(9)

where IH and IS are the integral intensity of luminescence arising

Fig. 4. (a) The upconversion emission spectra of Gd2(MoO4)3:Er3 þ /Yb3 þ phosphor at different temperature (323, 453 and 633 K). (b) Temperature dependent luminescence and FIR.

from 2H11/2 and 4S3/2 to the 4I15/2 transition, νH and νS are the wavenumber of corresponding emission band, k is the Boltzmann constant, T is the absolute temperature, and ΔEHS is the energy gap between the 2H11/2 and 4S3/2 levels, respectively. According to Eq. (9), the theoretical FIR is plotted in Fig. 4(b) as a function of temperature. In addition, the root-mean-square deviation of the experimental and calculated oscillator strengths represents the validity of the J-O intensity parameters, which is deﬁned as [32]:

⎡ N−1 f exp − fcal ⎢ δ rms = ⎢ ∑ N−q ⎣ i=0

(

)

2 ⎤1/2

⎥ ⎥ ⎦

(10)

Table 1 The calculated and experimental oscillator strengths, and radiative transition probabilities for Gd2(MoO4)3: Er3 þ /Yb3 þ phosphor. Transition

Energy (cm 1)

fcal (J, J) ( 10 6)

fexp (J, J) ( 10 6)

A (J, J) (s 1)

4

22,222 20,408 19,083 18,315 15,290 12,531 10,204 6631

1.85 11.24 27.27 2.66 12.42 2.15 3.04 7.14

5.33 11.09 27.18 5.68 11.92 4.24 4.70 6.67

2937 10,831 28,339 (A60) 2857 (A50) 7800 (A40) 1159 (A30) 416 (A20) 406 (A10)

F5/2-4I15/2 F7/2-4I15/2 2 H11/2-4I15/2 4 S3/2-4I15/2 4 F9/2-4I15/2 4 I9/2-4I15/2 4 I11/2-4I15/2 4 I13/2-4I15/2 4

H. Lu et al. / Journal of Luminescence 186 (2017) 34–39

37

Table 2 The J-O intensity parameters (Ωt 10 20 cm2) and quality factor (Ω4/Ω6) of Er3 þ doped typical hosts. Crystal

Ω2

Ω4

Ω6

Ω4/Ω6

Ref.

Er:NaYF4 Er:YAG Er/Yb:GdVO4 Er/Yb:NaY(WO4)2 Er/Yb:LiLa(WO4)2 Er/Yb:Gd2(MoO4)3

2.11 0.45 6.47 18.1 9.03 11.74

1.37 0.98 1.51 2.59 2.02 8.16

1.22 0.62 0.91 1.21 0.59 2.05

1.12 1.58 1.66 2.14 3.42 3.98

[36] [37,38] [37] [39] [39] This work

where N (¼8) is the number of absorption bands analyzed, q (¼ 3) is the number of parameter. The value of δrms is calculated to be 2.40 10 6. The experimental (ƒexp) and the theoretical (ƒcal) oscillator strengths and the radiative transition probability A (J, J) are listed in Table 1, respectively. In general, the Ω2 reﬂects the asymmetry of the local environment and the degree of covalence between rare earth ions and the vicinity ligands [33,34]. The higher the values of Ω2 is, the more asymmetric the ion site and the stronger the covalent chemical bond. The spectroscopic quality factors (Ω4/Ω6) of typical phosphors are summarized in Table 2, which is a signiﬁcant laser characteristic in predicting the stimulated emission [35]. The spectroscopic quality factor of Gd2(MoO4)3: Er3 þ /Yb3 þ crystal is determined to be 3.98, which is much higher than that of YAG host, implying that is a promising laser crystal. 3.2. Temperature dependent theoretical model Under 980 nm excitation, the upconversion spectrum of Gd2(MoO4)3:Er3 þ /Yb3 þ phosphor are shown in Fig. 4(a). The characteristic emissions arising from 2H11/2 and 4S3/2 to 4I15/2 transitions of the Er3 þ ions are observed. Since lanthanide ions can be affected by the surrounding crystal ﬁeld environment according to the crystal ﬁeld theory [40], upconversion emission spectrum splits to several obvious emission peaks. Signiﬁcant changes in the luminescent intensity are found with the temperature rising. In order to investigate more clearly temperature (Fig. 4(b)) dependent behavior, the upconversion process of Er3 þ and Yb3 þ codoped system is explained using the model portrayed in Fig. 5. Firstly, a ﬁrst ET process occurs between the 2F5/2 level (Yb3 þ ) and the 4I15/2 level (Er3 þ ), promoting the latter to the 4I11/2 level [ET1: 2 F5/2(Yb3 þ )þ 4I15/2(Er3 þ )-2F7/2(Yb3 þ )þ 4I11/2(Er3 þ )] [41]. Subsequently, a second ET process occurs between the 2F5/2 level (Yb3 þ ) and the 4I13/2 level (Er3 þ ), which derives from multiphonon relaxation of the 4I11/2 level, promoting the latter to the 4F9/2 level [ET2: 2 F5/2(Yb3 þ )þ 4I13/2(Er3 þ )-2F7/2(Yb3 þ )þ 4F9/2(Er3 þ )]. Meanwhile, the third ET step occurs between the 2F5/2 level (Yb3 þ ) and the 4I11/2 level (Er3 þ ) promoting the latter to the 4F7/2 level which quickly relaxes its population to the 2H11/2 level through nonradiative decay [ET3: 2 F5/2(Yb3 þ )þ 4I11/2(Er3 þ )-2F7/2(Yb3 þ )þ 4F7/2(Er3 þ )] [22]. For above the three ET processes, the energy of corresponding transition is matched. Owing to energy mismatching ( 1100 cm 1), however, the phonon assisted ET process occurs between the 2F5/2 level (Yb3 þ ) and the 4I11/2 level (Er3 þ ) ion promoting the latter to the 2H11/2 level, which is greatly dependent on temperature [ET4: 2 F5/2(Yb3 þ )þ 4I11/2(Er3 þ )-2F7/2(Yb3 þ )þ 2H11/2(Er3 þ )] [42]. The phonon-assisted ET theory is presented by Dexter, which was applied to characterize the ion-ion interactions between these dopants, and the phonon-assisted ET probability is given by [43]

WET ( T ) = W0

e−βΔE ⎡ 1 ⎣

− exp ( −Ephonon/kT ) ⎤⎦

−p

where W0 is the probability of resonant ET,

(11)

β is a host parameter,

Fig. 5. Schematic energy levels diagram of Er3 þ and Yb3 þ ions and upconversion processes under 980 nm excitation.

Ephonon is the phonon energy of Gd2(MoO4)3, ΔE is the energy mismatch, and p is the number of phonon, respectively. For the multiphonon relaxation, each level is taken into account except the 2F5/2 (Yb3 þ ) and 4I13/2 (Er3 þ ) level, since energy gaps between their adjacent levels are extremely large, which means the corresponding multiphonon relaxation is extremely small. The multiphonon relaxation probability can be related to the temperature through [44] −p Wij ( T ) = Wij0 ⎡⎣ 1 − exp ( −Ephonon/kT ) ⎤⎦

(12)

Wij0 = Cm exp ( −αΔEij )

(13)

where Wij0 is multiphonon relaxation probability at T ¼0 K, Cm is a host dependent constant and α is dependent on electron-phonon coupling constant, and ΔEij is energy gaps from i level to j level of Er3 þ , respectively. Due to long lifetimes of the 4I11/2 level, we only consider the most inﬂuential CR process [Er3 þ : 4I11/2 þ 4I11/24 I15/2 þ 4F7/2]. In this model, only optical absorption through Yb3 þ ions and ET from Yb3 þ to Er3 þ are considered, because the absorption cross section of Yb3 þ is an order of magnitude higher than Er3 þ at 980 nm and the high concentration ratio is 9(Yb3 þ ):1(Er3 þ ). Under these assumptions, the sets of phenomenological rate equations which describe the model are listed below as:

dNa P = σab Na − ( WET 1 + WET 2 + WET 3 + WET 4 − Ab ) Nb = 0 dt Sε

(14)

dN1 = W21N2 − WET 2 Nb − A10 N1 = 0 dt

(15)

dN2 = W32 N3 − A20 N2 − W21N2 + ( WET 1 − WET 3 − WET 4 ) Nb dt − 2CR N2 N2 = 0

(16)

38

H. Lu et al. / Journal of Luminescence 186 (2017) 34–39

4. Conclusions

Table 3 Parameters involved in the rate equations, and their sources are also labeled. Symbols

Values

Sources

Symbols

Values

Sources

Ephonon (cm 1) sab (10–25 m2) Ab (s 1) WET1 (s 1) WET2 (s 1) WET3 (s 1)

970 11.7 438 758 118 150

[45] [46] [47] [48] [48] This work

W0 (s 1) β (10 3 cm) Cm (108 s 1) α (10 3 cm) S (10 6 m2) CR (s 1)

120 2.75 4.13 3.45 3.5 240

This This This This This This

work work work work work work

dN3 = W43 N4 − A30 N3 − W32 N3 = 0 dt

(17)

dN4 = W54 N5 − W43 N4 − A 40 N4 + WET 2 Nb = 0 dt

(18)

d ( N5 + N6 ) dt

= ( WET 3 + WET 4 ) Nb − A 60 N6 − A50 N5 − W54 N5 + CR N2 N2 = 0

N6/N5 = 3 × exp ( −ΔE65/kT )

(19)

(20)

N0 + N1 + N2 + N3 + N4 + N5 + N6 = 1

(21)

Na + Nb = 9

(22)

where Aij are the radiation transition probability (calculated by the J-O theory), Ni are the population densities of i level, P is the exciting power, S is the spot size, ε is the exciting photon energy, and CR is the cross relaxation probability between neighbor Er3 þ pairs, respectively. For Eq. (20), the populations of N6 and N5 follow Boltzmann distribution. The Cm, α and β were estimated from typical values observed for similar compounds. The roughly estimated values of resonant ET probability WET3 and W0 were 150 and 120 (s 1), respectively. Using the calculated radiative transition probabilities (Aij), multiphonon relaxation probability (Wij) and other parameters listed in Table 3, temperature dependent luminescence (2H11/2/4S3/2-4I15/2) has been investigated and the theoretical result is shown in Fig. 4(b). It is found that the luminescent intensity arising from 2H11/2 to 4I15/2 transition (525 nm) increases a factor of 2 when the sample was heated from 295 to 490 K, and then continuously decreases in the range of 490–660 K. The electronphonon coupling increases with the temperature rising, resulting in improving multiphonon relaxation probability (Wij) and the phonon-assisted ET probability. The competition between the phonon-assisted ET and multiphonon relaxation accounts for variation of luminescent intensity. The above mentions demonstrate that the phonon-assisted ET makes a major contribution to improving luminescence initially. Further increasing the temperature, however, the multiphonon relaxation becomes dominant, which is responsible for reduction of luminescent intensity. In view of 4S3/2 to 4I15/2 transition (545 nm), the luminescent intensity gradually decreases over the whole temperature range (295–660 K), indicating that multiphonon relaxation is dominant. In addition, the CR probability is determined as 240 s 1 based on the theoretical simulation. The theoretical simulation is well agreement with experimental results, demonstrating that theoretical model and analysis are reasonable.

In summary, we have successfully prepared Gd2(MoO4)3: Er3 þ /Yb3 þ phosphor. Employing the J-O theory, a series of photophysical parameters such as J-O intensity parameters and radiative transition probabilities are calculated and analyzed. The spectroscopic quality factor (Ω4/Ω6 ¼3.98) is found to be much higher than previous reports, indicating that Gd2(MoO4)3:Er3 þ /Yb3 þ crystal is a promising laser crystal. Using a simpliﬁed steady-state rate equation model, the temperature dependent luminescence is quantitatively interpreted by ion–phonon interactions. The variation of luminescence arising from 2H11/2 to 4I15/2 indicates a competitive behavior between the phonon-assisted ET and multiphonon relaxation with the temperature rising. Initially, the phonon-assisted ET made a major contribution to the luminescence increasing, and then the multiphonon relaxation is dominant, which is responsible for the decrease of luminescence. Additionally, for ion-ion interaction, the CR probability ( 240 s 1) is obtained through quantitative simulation data. These results are of signiﬁcant value for understanding temperature dependent upconversion luminescence of Gd2(MoO4)3:Er3 þ /Yb3 þ phosphor.

Acknowledgments This work has been supported by the Grant of National Natural Science Foundation of China (Nos. 11374079, 11474078, 61275117 and 11404283).

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H. Lu et al. / Journal of Luminescence 186 (2017) 34–39

[18]

[19]

[20] [21]

[22]

[23]

[24]

[25]

[26]

[27]

[28] [29] [30]

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