Standard and modified Judd-Ofelt theories in Pr3+-doped calcium aluminosilicate glasses: A comparative analysis

Accepted Manuscript Standard and modified Judd-Ofelt theories in Pr glasses: A comparative analysis

3+

-doped calcium aluminosilicate

G.A.S. Flizikowski, V.S. Zanuto, L.A.O. Nunes, M.L. Baesso, L.C. Malacarne, N.G.C. Astrath PII:

S0925-8388(18)34436-0

DOI:

https://doi.org/10.1016/j.jallcom.2018.11.308

Reference:

JALCOM 48534

To appear in:

Journal of Alloys and Compounds

Received Date: 28 August 2018 Revised Date:

5 November 2018

Accepted Date: 22 November 2018

Please cite this article as: G.A.S. Flizikowski, V.S. Zanuto, L.A.O. Nunes, M.L. Baesso, L.C. Malacarne, 3+ N.G.C. Astrath, Standard and modified Judd-Ofelt theories in Pr -doped calcium aluminosilicate glasses: A comparative analysis, Journal of Alloys and Compounds (2018), doi: https://doi.org/10.1016/ j.jallcom.2018.11.308. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Standard and modified Judd-Ofelt theories in Pr3+ -doped calcium aluminosilicate glasses: a comparative analysis G. A. S. Flizikowskia , V. S. Zanutoa,b,∗, L. A. O. Nunesb , M. L. Baessoa , L. C. Malacarnea, N. G. C. Astratha

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a Departamento b Instituto

de F´ısica, Universidade Estadual de Maring´a, Maring´a, PR 87020-900, Brazil de F´ısica de S˜ao Carlos, Universidade de S˜ao Paulo, S˜ao Carlos, SP 13560-590, Brazil

Abstract

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The small energy difference between the fundamental level and the first opposite parity configuration of Pr3+ -doped hosts is particularly challenging for the characterization of radiative transitions using the Judd-Ofelt theory, although modified versions of the theory have been proposed in the past for the investigation of praseodymium doped materials. Here, we present a detailed spectroscopic investigation on two sets of calcium aluminosilicate glasses, with 34 wt.% of SiO2 (CAS) and with 7 wt.% of SiO2 (LSCAS), doped with different concentrations of Pr3+ (0.5, 1.0 and 2.0 wt.%). We use the standard Judd-Ofelt theory to characterize the glasses and the results and derived spectroscopic quantities — such as transition probabilities, radiative lifetimes and branching ratios — are compared to results obtained by the modified Judd-Ofelt theories. The analysis showed that the modified theories could lead to smaller values of root mean square deviations. However, a better agreement between experimental data and the standard theory was achieved when the derived spectroscopic quantities are taken into account. Moreover, the branching ratios of the 3 P0 → 3 H4 and 1 D2 → 3 H4 transitions were over 60% for both glass hosts, suggesting its potential use as solid-state laser devices.

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Keywords: Aluminosilicate glass, CAS:Pr3+ , LSCAS:Pr3+ , Standard Judd-Ofelt theory, Modified Judd-Ofelt theory

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1. Introduction

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The great potentiality of rare earth elements as optically active ions in a wide variety of host materials is, in part, accounted by the minimal influence that the host crystal field has on the intraconfigurational 4f electron distribution as it is shielded by the outer electronic shells. In this context, the third ionized state of praseodymium (Pr3+ ) makes this ion an interesting element among other rare earths as a consequence of its variety of optical transitions. Ultraviolet (UV) emission can be provided by either direct excitation of 4f5d level or via upconversion mechanisms. In the visible (Vis) range, Pr3+ presents several optical transitions in blue, green [1], orange-red and in the red part of the spectrum [2]. Besides, a broad band emission in the infrared region, around 1.5 µm, suggests its applicability in devices for telecommunications [3]. Pr3+ has been studied in many different hosts, such as fluoride [4–6], borate [7–9], borosilicate [3, 10], phosphate [11, 12], fluorotellurite [13, 14], and aluminosilicate glasses [15]. However, studies on Pr3+ -doped calcium aluminosilicate glasses (CAS) were only reported when co-doped with ytterbium (Yb3+ ) [16], in which the authors investigated the occurrence of energy transfer processes from Pr3+ to Yb3+ . Recently, an investigation on the upconversion and hypersensitive transitions of Pr3+ -doped CAS glasses was reported [17]. Such glasses have attracted interest due to their appropriate thermo-optical ∗ Corresponding

author: [email protected]

Preprint submitted to Journal of Alloys and Compounds

and mechanical properties compared to silicates and phosphates [18], elevated transition temperature, and transparency up to 5 µm [19, 20]. Investigations have also been performed with regard to the compositional dependence of the physical properties of the calcium aluminosilicate glasses [18, 21]. When doped with rare earth elements, studies have shown that these glasses are potential candidates for optical devices such as tunable white light systems [21, 22] and solid state lasers [21, 23, 24]. The luminescent properties of trivalent rare earth elements have been described with reasonable success by the Judd-Ofelt (J-O) theory [25, 26]. However, the description of the spectroscopic properties of Pr3+ is particularly challenging due to the low energy difference between the fundamental level and the first opposite parity excited configuration, 4f2 and 4f5d, respectively. The drawback related to this feature includes relatively large values of the root mean square, which measures the agreement between experimental and calculated line strengths, and eventual negative values for the phenomenological Judd-Ofelt parameters Ωk , which are not consistent with the fundamental theoretical definitions [27]. These issues, specially concerning the Pr3+ , demonstrate there are some aspects in the theory of the 4f-4f transitions that are not yet fully understood. In essence, the present study investigates the spectroscopic properties of calcium aluminosilicate glasses with two different compositions: CAS and low-silica CAS (LSCAS) glasses with 34 and 7 wt.% of SiO2 concentration, respectively. Both compositions were doped with three different Pr3+ concentrations. November 23, 2018

ACCEPTED MANUSCRIPT optical transitions. Low values of root mean square deviation denote high quality J-O parameters. The J-O parameters allow the determination of the spectroscopic properties of the samples. For instance, the radiative emission probabilities from an excited state level J ′ to a lower state J is given by

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The Judd-Ofelt parameters were calculated using the standard and modified theories in order to get a better insight of the effectiveness of these alternative theories applied to Pr3+ -doped calcium aluminosilicate glasses. Moreover, radiative transition probabilities, radiative lifetime and branching ratios were calculated and compared with the experimental data.

AJ′ J =

2. Judd-Ofelt Theory The J-O theory describes the optical intensities of the 4f-4f transitions of rare earth elements. The theory was independently developed by Judd [25] and Ofelt [26] in 1962. Essentially, they demonstrated that the electric dipole transitions between states are allowed when the rare earth element is inserted in a medium. The reason of this behavior is the admixing of the first opposite parity configuration 4fN−1 5d and the fundamental level 4fN [9]. The experimental line strength Sexp represents the intensity of the absorption band of a particular transition, which is obtained from the absorption spectrum as [9] Z 3hc (2J + 1) Sexp = 3 2 α(λ)dλ, (1) 8π e χ λm N

64π4 e2 ν3 χemi Scal , 3h(2J ′ + 1)

(4)

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where χemi = n(n2 + 2)2 /9 is the local field correction and ν the transition energy in cm−1 . The radiative lifetime of an excited level is related to the sum of all possible decays from that level and is defined as τ=P

1 . A J ′ ,J

(5)

A J ′ ,J . J ′ A J ′ ,J

(6)

J′

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The branching ratio is given by βJ′ J = P

2.2. Modified theories

where h is the Planck’s constant, c is the speed of light in vacuum, e is the elementary electric charge, and χ = (n2 + 2)2 /9n is the Lorentz local field correction, in which n is the medium refractive index. The total angular momentum of the ground state is represented by J. The mean wavelength of the absorption band in nanometer is represented by λm , N is the number of Pr3+ per unit of volume in ions/cm3 and α(λ) is the absorption coefficient as a function of the wavelength.

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For Pr3+ , the energy of the 4f5d configuration, which is approximately 50 × 103 cm−1 , is very close to that of the 4f states when compared to other rare earth elements. Therefore, the energy difference between the 4f5d and 4f states, assumed to be constant in the standard theory, is not suitable when analyzing Pr3+ [29]. Hence, the approximation used to derive Eq. (2) is unreliable and could lead to negative intensity parameters [4, 5, 7, 11, 12, 30], which have no physical meaning. Consequently, a modified theory must be considered. Alternative approaches have been developed in the past. In this work, we compare the results of the standard J-O theory with the method of Kornienko et al. [31, 32] and Fl´orez et al. [33, 34]. Third order perturbation theory was employed by Kornienko et al. resulting in the calculated line strength X Scal = Ωk [1 + 2A(E J + E J ′ − 2E4 f )]

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2.1. Standard theory Since the magnetic dipole component for Pr3+ may be neglected [12], the calculated line strength according to the standard J-O theory is given by the electric dipole line strength, X  2 Scal = Ωk h4 f S LJ| U (k) 4 f S ′ L′ J ′ , (2) k=2,4,6

k=2,4,6

where Ωk is the intensity parameter of rank k. The set of all Ω ’s are the so-called J-O parameters, and k 2 h4 f S LJ| U (k) |4 f S ′ L′ J ′ i is the squared reduced matrix elements of the unit tensor U (k) . The intensity parameters can be evaluated minimizing the difference between the experimental line strengths (Eq. (1)) of certain amount of absorption bands, and the calculated line strengths (Eq. (2)), usually by least squares method. The quality of the results are determined by the root mean square deviation between experimental and calculated line strengths using the definition [28], v u u   t i i 2 X S exp − S cal δrms = , (3) Nt − Np i

×

 2 h4 f S LJ| U (k) 4 f S ′ L′ J ′ ,

(7)

in which A = 1/2E4 f 5d , and E4 f 5d is the energy of the 4f5d configuration, which for Pr3+ is approximately 50 × 103 cm−1 . E J ′ , E J and E4 f are the energies of the upper, lower states and barycenter of the 4f configuration, respectively. Thus, the parameter A is expected to be ∼ 10−5 cm for Pr3+ , although it has been often used as a fitting parameter. Additional odd rank operators have been considered by Fl´orez et al. and the calculated line strength is written as

Scal

=

X

k=2,4,6

where Nt and Np are the number of transitions and the number of parameters, respectively. The sum is performed over all

+

X

k=1,3,5

2

 2 Ωk h4 f S LJ| U (k) 4 f S ′ L′ J ′

 2 ξ2 Ωk h4 f S LJ| U (k) 4 f S ′ L′ J ′ ,

(8)

ACCEPTED MANUSCRIPT where ξ = ν/∆E, and ∆E refers to the energy difference between ground state and the first opposite parity excited configuration. Regardless the modified theory, the expressions for the spectroscopic properties remain the same only with a different Scal .

3

3

P

H

4

3

P

2

3

P

1

1

1

D

0

G

2

3

4

3

F + F 4

3

3

3+

Two sets of Pr -doped calcium aluminosilicate glass samples were prepared accordingly to the procedure described in Refs. [23, 24]. The compositions are (in wt.%) 34CaO + (27.9 − x/2)Al2O3 + (34 − x/2)SiO2 + 4.1MgO + xPr6 O11 , referenced as CAS:xPr3+ ; and (47.4 − x/2)CaO + (41.5 − x/2)Al2O3 + 7SiO2 + 4.1MgO + xPr6 O11 , referenced as LSCAS:xPr3+ , where x = 0.5, 1.0 and 2.0 for both sets. The reagents (with over 99.99% of purity) were mixed in a ball mill for 12 hours then melted at approximately 1600 ◦ C under vacuum atmosphere (10−3 atm) for 2 hours to remove completely OH− molecules from glass structure. The glasses were cut and polished for optical measurements. Refractive index n was determined using the Brewster’s angle method [35] at 442 and 632.8 nm, using a He-Cd laser (Kimmon Koha, model IK5652R-G) and a He-Ne laser (Newport, model R-32734), respectively. Mass density (ρ) was determined by the Archimedes method [36] using a digital balance (Shimadzu, model AUW220D) and distilled water as the immersion liquid. Absorption spectra were obtained using an UV–Vis–NIR double beam spectrophotometer (Perkin-Elmer, model Lambda 900) in the spectral range of 300–2500 nm. Photoluminescence spectra were obtained using a He-Cd (Kimmon Koha, model IK5652R-G) tuned at 442 nm as excitation. Emission in visible region was collected by an optical fiber coupled to a monochromator (Newport, model 77780) and detected by a photomultiplier (Hamamatsu, model R1477). The signal was analyzed by a lock-in amplifier (Stanford Research System, model SR830). In the infrared region, two quartz lenses collected the emission to the monochromator. The emission was detected by an InGaAs detector (Newport, 70328NS). Luminescence decay measurements were carried out using the same photoluminescence experimental arrangement, using instead an optical parametric oscillator (OPO) (Surelite/Continuum) pumped by the third harmonic (355 nm) of a Nd-YAG laser (Surelite II/Continuum, 10 Hz, 5 ns) as excitation source. The emission signal was acquired by a digital oscilloscope (Tektronix, model DPO 4102B).

6

CAS

1.8 1.2 0.6 0.0

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-1

Absorption coefficient (cm )

3.1. Glass synthesis and characterization

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2

2.4

3. Materials and Methods

3

F

3+

wt.% of Pr

1.8

LSCAS

2.0 1.0

1.2

0.6

0.0

450

500

550

SC

400

0.5

600

1200

1600

2000

2400

Wavelength (nm)

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Figure 1: Optical absorption spectra of Pr3+ -doped CAS and LSCAS glasses in the UV–Vis–NIR range. Transitions are indicated. Table 1: Experimental line strengths Sexp (10−20 cm2 ) for CAS and LSCAS glasses for different concentrations of Pr3+ in wt.%.

Transition

CAS:xPr3+

LSCAS:xPr3+

0.5

1.0

2.0

0.5

1.0

2.0

8.06 3.63 3.29 2.05 0.75 23.91 18.52

7.40 3.29 3.02 1.83 0.55 21.73 14.61

7.32 3.64 3.00 1.75 0.42 23.55 16.96

7.76 4.21 4.33 1.53 0.25 20.70 17.14

8.26 4.23 4.44 1.82 0.14 19.19 14.88

6.80 3.88 3.82 1.72 0.65 20.29 16.32

3

H4 → P2 3 P1 3 P0 1 D2 1 G4 3 F4 +3 F3 3 F2 +3 H6

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excited states. In the range of 900 to 2500 nm, five absorption bands are observed corresponding to transitions from 3 H4 to 1 G4 (999 nm), 3 F4 (1421 nm), 3 F3 (1504 nm), 3 F2 (1906 nm), and 3 H6 (2371 nm) states. The absorption coefficient presented a linear increase as the dopant concentration increases. Additionally, the band widths have not shown any displacement as dopant concentration increases, meaning all dopant inserted in the samples are homogeneously distributed in the host. Experimental line strengths for the transitions were calculated according to Eq. (1) and the results are presented in Table 1. The Sellmeier’s equation [37] was used to determine the refractive index as a function of the wavelength. The refractive indexes presented no significant variation with the Pr3+ concentration. The values obtained for CAS samples were 1.63 and 1.61 at 442 and 632.8 nm, respectively, while for LSCAS samples were 1.68 and 1.66 at 442 and 632.8 nm, respectively. Low concentrations of Pr3+ presented transitions with very low absorption coefficient values. For instance, the transitions 3 H4 → 1 G4 and 3 H4 → 3 H6 are barely noticeable, as presented in Fig. 1. As the calculation of experimental line strength is related to the area of absorption band, low absorption values

4. Results and Discussion 4.1. Absorption spectra The absorption spectra of Pr3+ -doped CAS and LSCAS glasses for different concentrations of Pr3+ are shown in Fig. 1. In the range of 400 to 650 nm, the samples present four absorption bands related to transitions from the ground state 3 H4 to the 3 P2 (442 nm), 3 P1 (472 nm), 3 P0 (483 nm), and 1 D2 (588 nm) 3

3+

LSCAS

2.0 1.0 0.5

500

550

600

650

700

1 2

D

2

D

1

1

3

4

G

4

3

F

4

G

1 0

P

2

1

30 15 0 45

1 0

3+

wt. of Pr

2.0

LSCAS

3

1.0

30

0.5

15 0

750

2

CAS

SC

100 0

3

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Emission intensity (a.u.)

50

200

4

45

100

wt.% of Pr

D

3

CAS

0

2

F

4

3

F

3

F

P

60

3

150 Emission intensity (a.u.)

0

5

H

3

P

3

3

0

2

F

D

1

2

6

3

P

3

0

H

4 0

P

2

3

D

1

3

3

H

5

0

3

H

4

P

3

0

3

P

3

H

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800

900

1000

1100

2 1 1400

1600

0

Wavelength (nm)

Wavelength (nm)

Figure 3: Emission spectra of Pr3+ -doped CAS and LSCAS glasses in the infrared range under excitation at 442 nm. Transitions are indicated.

have direct influence in the uncertainty of the calculated value. Thus, absorption spectrum of high concentration provides most reliable values for Sexp [6].

Notice that the CAS2 and LSCAS2 sets present lower error compared to CAS1 and LSCAS1 for all the concentrations, as shown in Table 2. The same occurred to the modified theories. Consequently, all the following results correspond to the CAS2 and LSCAS2 sets. Calculations using the Kornienko et al. method exhibited the same behavior for all concentrations. The results for the samples with 2.0 wt.% of Pr3+ are shown in Table 2. Some authors suggest fixing A = 10−5 cm [4, 12, 32]. With this consideration, the results differ from those of standard theory, presenting deviations δrms up to three times greater. On the other hand, better fitting results were achieved with A ∼ 10−7 cm for all samples, leading to fairly good agreement between experimental and calculated line strengths. The deviations δrms are about the same as those of standard theory. However, such magnitude of A is rather unrealistic since it corresponds to an energy of the 4f5d configuration of 5 × 106 cm−1 . In general, this modified theory can lead to reasonable agreement between experimental and calculated line strengths, although the use of an additional parameter leads to nonphysical results. Using the Fl´orez et al. approach, several sets of parameters were calculated and the best set would be the one which obeys the following requirements: (i) all intensity parameters must be positive and (ii) the root mean square must be the lowest. Differently from the work of Fl´orez et al. [33], where only one combination of parameters produced positive values for all intensity parameters Ωk , results in this work presented a considerable amount of parameters with all positive Ωk . Table 2 shows the calculated line strengths and respective values of Ωk for the combination with lowest root mean square, which is k = 2, 3, 4, 6 for both glass hosts. The inclusion of the odd parameter has led to a significant better agreement between experimental and calculated line strengths. The deviations δrms were at least two times lower than that of the standard theory, although the contribution of the odd parameter Ω3 is rather high.

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Figure 2: Emission spectra of Pr3+ -doped CAS and LSCAS glasses in the visible range under excitation at 442 nm. Transitions are indicated.

4.2. Emission spectra

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The emission spectra in the visible range for both CAS and LSCAS Pr3+ -doped samples are shown in Fig. 2. Several emission bands were identified: blue emission band centered around 487 nm, assigned to the 3 P0 → 3 H4 transition; green emission around 531 nm corresponding to the 3 P0 → 3 H5 transition; and broader orange-red band from 575 to 660 nm and from 680 to 755 nm related to the 1 D2 → 3 H4 , 3 P0 → 3 H6 , 3 P0 → 3 F2 , 1 D2 → 3 H5 , 3 P0 → 3 F3 and 3 P0 → 3 F4 transitions. Figure 3 shows the emission spectra in the IR region. Three emission bands were observed around 890, 1060 and 1500 nm assigned to the 1 D2 → 3 F2 , 3 F4 and 1 G4 transitions, respectively. For higher concentrations, an additional band around 930 nm was noticed due to the 3 P0 → 1 G4 transition. 4.3. Judd–Ofelt analysis

Using the experimental line strengths values, the matrix elements for Pr3+ [33] and employing least squares method, the J-O parameters were derived from the standard and modified theories. Calculations were performed considering two approaches: the 3 H4 → 1 I6 transition is convoluted in the band associated to the (i) 3 H4 → 3 P1 and (ii) 3 H4 → 3 P2 transitions [33], referred to as CAS1/LSCAS1 and CAS2/LSCAS2, respectively. Results from the standard J-O theory are presented in Table 2. All the calculated intensity parameters presented positive values and reasonable values for δrms [9, 14, 38]. Nevertheless, reports have indicated the standard theory is not optimal for Pr3+ -doped materials, which makes it necessary to examine the accuracy of these results comparing it with the modified theories. 4

ACCEPTED MANUSCRIPT Table 2: Results for the calculated line strength Scal , intensity parameters Ωλ and root mean square deviation δrms (all in units of 10−20 cm2 ) for the CAS and LSCAS hosts using the standard theory and the Fl´orez et al. and Kornienko et al. modified theories for different concentrations of Pr3+ in wt.%.

Standard Scal Transition

Fl´orez et al. Scal CAS2:xPr3+

CAS2:xPr3+

1.0

Kornienko et al. Scal CAS2:xPr3+

0.5

1.0

2.0

0.5

1.0

2.0

0.5

3

2.53 3.95 2.80 1.00 0.27 24.62 18.40

2.34 3.58 2.56 0.91 0.24 22.37 14.51

2.51 3.81 2.70 0.98 0.26 24.16 16.86

3.84 3.84 3.82 1.00 0.27 24.53 18.50

3.50 3.50 3.48 0.91 0.24 22.29 14.59

3.75 3.64 3.62 0.98 0.26 24.06 16.94

7.98 3.48 3.46 0.73 0.21 23.99 18.51

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CAS1:xPr3+

7.33 3.17 3.15 0.66 0.18 21.79 14.61

7.26 3.34 3.32 0.75 0.21 23.60 16.95

3.76 3.64 3.62 0.98 0.26 24.12 17.00

Ω2 Ω4 Ω6 Ω3

14.91 16.35 14.14

8.96 14.96 13.13

12.38 15.79 14.12

10.90 22.30 12.33

5.34 20.33 11.5

8.76 21.14 12.48

15.31 20.22 7.31 767.91

9.41 18.40 6.87 709.04

12.49 19.38 8.23 649.89

8.84 21.13 12.53

δrms

2.86

2.61

2.46

2.23

0.84

0.72

0.65

1.87 A = 10−7 cm Kornienko et al. Scal LSCAS2:xPr3+

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H4 → P2 3 P1 3 P0 1 D2 1 G4 3 F4 +3 F3 3 F2 +3 H6

2.04

1.87

Standard Scal LSCAS1:xPr3+ LSCAS2:xPr3+ Transition

0.5

1.0

2.0

0.5

2.16 4.78 3.54 0.87 0.23 21.40 17.02

2.03 4.82 3.62 0.82 0.21 19.97 14.75

2.12 4.34 3.19 0.85 0.23 20.89 16.22

Ω2 Ω4 Ω6 Ω3

10.4 20.7 10.3

6.14 21.12 9.23

δrms

2.88

0.5

1.0

2.0

2.0

3.55 4.65 4.62 0.87 0.23 21.30 17.11

3.40 4.77 4.74 0.82 0.21 19.88 14.85

3.40 4.16 4.14 0.85 0.22 20.79 16.30

7.70 4.29 4.27 0.60 0.17 20.76 17.13

8.18 4.35 4.33 0.50 0.14 19.26 14.88

6.73 3.87 3.85 0.63 0.18 20.35 16.32

3.41 4.16 4.14 0.85 0.23 20.84 16.35

10.51 18.63 10.54

6.18 27.00 8.36

1.70 27.70 7.24

6.77 24.16 8.85

10.60 24.90 3.33 769.33

6.79 25.29 1.45 886.35

10.31 22.49 4.81 617.25

6.85 24.15 8.89

2.44

2.17

2.52

1.80

0.55

0.77

0.69

1.80 A = 10−7 cm

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3.22

Fl´orez et al. Scal LSCAS2:xPr3+

2.0

EP

H4 → P2 3 P1 3 P0 1 D2 1 G4 3 F4 +3 F3 3 F2 +3 H6

2.0

1.0

3 3

2.0

SC

3

Concerning the radiative lifetimes, the standard theory also presents a better agreement with the experimental lifetimes τexp . From luminescence decay curves [17], after offset correction, the 1 D2 level experimental lifetime values obtained for CAS are 80.9, 41.5 and 14.1 µs for the samples doped with 0.5, 1.0 and 2.0 wt.% of Pr3+ , respectively. LSCAS presented the lifetime values: 87.8 (0.5Pr3+), 44.1 (1.0Pr3+) and 16.5 µs (2.0Pr3+ ). For the 3 P0 level, the experimental lifetime values for CAS are 2.5 (0.5Pr3+ ), 2.3 (1.0Pr3+ ) and 2.1 µs (2.0Pr3+), and for LSCAS, the obtained values are 4.1 (0.5Pr3+), 3.9 (1.0Pr3+) and 3.4 µs (2.0Pr3+). The emission quantum efficiency can also be calculated and it is given by

Nevertheless, a better insight about the consistency of these results is obtained comparing the spectroscopic properties from both the standard theory and the Fl´orez et al. modified theory. Results for the emission transition probabilities, branching ratios and radiative lifetimes for CAS and LSCAS with 2.0 wt.% of Pr3+ are shown in Table 3. Emission spectra in Figs. 2 and 3 show a significant better agreement to the standard J-O theory rather than the modified theory of Fl´orez et al. For instance, the two most intense emission transitions in visible range, according to standard theory, would be 3 P0 → 3 H4 and 3 P0 → 3 F2 for both glass hosts, while for the modified theory, results suggest the 3 P0 → 3 F3 and 3 H4 transitions would be the two most intense for both hosts, which is in disagreement with the experimental emission spectra.

η= 5

τexp , τ

(9)

ACCEPTED MANUSCRIPT Table 3: Emission transition probabilities, A (s−1 ), branching ratios, β, and radiative lifetimes, τ (µs), from standard and Fl´orez et al. J-O theory and experimental radiative lifetimes, τexp (µs), for CAS and LSCAS with 2.0 wt.% of Pr3+ .

CAS2:2.0Pr3+ Standard Fl´orez et al. Transition

A

A

β

β

LSCAS2:2.0Pr3+ Standard Fl´orez et al. A

110920 0.669 103230 0.117 0 0 0 0 8232 0.050 4475 0.005 22148 0.134 33752 0.038 0 0 718186 0.814 19661 0.119 18299 0.021 4917 0.030 4577 0.005 τ = 6.03 µs τ = 1.13 µs τexp = (3.4 ± 0.1) µs

10873 0.654 10759 0.046 82 0.005 5516 0.023 2390 0.144 9507 0.04 2570 0.155 156820 0.666 697 0.042 52918 0.225 τ = 60.19 µs τ = 4.25 µs τexp = (14.1 ± 0.2) µs

12688 0.7 12571 0.053 97 0.005 5590 0.024 2627 0.145 10096 0.042 2081 0.115 156234 0.657 627 0.035 53210 0.224 τ = 55.18 µs τ = 6.87 µs τexp = (16.5 ± 0.1) µs

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D2 → H4 3 H5 3 F2 3 F4 1 G4

β

88851 0.610 81438 0.098 0 0 0 0 10785 0.074 7111 0.009 26144 0.180 37286 0.045 0 0 684601 0.826 15868 0.109 14544 0.018 3905 0.027 3580 0.004 τ = 6.87 µs τ = 1.21 µs τexp = (2.1 ± 0.2) µs

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P0 → H4 3 H5 3 H6 3 F2 3 F3 3 F4 1 G4 3

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Additionally, from Table 3, the transitions 3 P0 → 3 H4 and D2 → 3 H4 presented a branching ratio greater than 60% for both glass hosts, which added to the reasonably good emission quantum efficiencies of these levels, specially the 3 P0 → 3 H4 transition of LSCAS host, suggests its potential use as solid state laser [42].

with τ the theoretical and τexp the experimental lifetimes. Considering the values obtained by the standard theory, the emission quantum efficiencies of CAS:2.0Pr3+ for the 1 D2 and 3 P0 levels, for instance, are 0.24 and 0.31, respectively, while for LSCAS:2.0Pr3+ the values are 0.30 and 0.56, respectively. On the other hand, the quantum efficiencies obtained with the modified theory of Fl´orez et al. for the CAS:2.0Pr3+ are 3.32 and 1.75 for 1 D2 and 3 P0 levels, respectively, and 2.48 and 3.00 for LSCAS:2.0Pr3+ , respectively, for the same levels. Emission quantum efficiency values over 1 are, in general, related to energy transfer mechanisms, which may be the case of the samples doped with 0.5 wt.% of Pr3+ . However, the concentration of 2.0 wt.% of Pr3+ should be close to quenching concentration, which decreases the emission quantum efficiency. With this consideration, the results obtained with the theory of Fl´orez et al. presented values that are higher than the physically expected for these hosts. Table 2 shows that the J-O intensity parameters follow the trend Ω4 > Ω6 > Ω2 for all Pr3+ concentration, for both glass hosts. In fact, Ω2 parameter is correlated to the asymmetry and degree of covalency of the ion surroundings, which means that higher values of Ω2 result in more asymmetric glass network and the ligand field at the ion site is more covalent [9, 39, 40]. The glasses studied in this work presented higher value of Ω2 than aluminosilicate [15], borate [8, 9], and phosphate [11] glasses. This demonstrates a highly asymmetrical and covalent environment in this glasses. The Ω6 is inversely proportional to the covalency degree between the bond of oxygen and Pr3+ . The Ω4 and Ω6 parameters are related to the rigidity degree of the host [41].

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5. Conclusion

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In this study, three Judd-Ofelt theories were applied in Pr3+ doped CAS and LSCAS glasses, the standard and two modified approaches. Results using the Kornienko et al. modified theory had two outputs: (i) when the value of the parameter A was fixed to 10−5 cm: results were inferior than those presented by the standard theory and the deviation δrms value was up to three times greater than standard theory. (ii) When the parameter A was let to vary, better results were achieved with A ∼ 10−7 cm and the deviation δrms was about the same as for the standard theory. However, such magnitude corresponds to an energy of the 4f5d level of about 5 × 106 cm−1 , which is not reasonable for Pr3+ . Using the modified theory of Fl´orez et al., there were several sets with all positive intensity parameters. The set with smallest deviation was the Ω2,3,4,6 , presenting δrms about two times smaller than that of the standard theory, for both hosts. Spectroscopic properties were derived using the standard theory and the modified theory of Fl´orez et al. When compared to the experimental data, the emission transition probabilities showed a better agreement with the standard theory. Similar results are observed with the radiative lifetime. Although the root mean square deviation was used as a relative parameter of 6

ACCEPTED MANUSCRIPT the quality of results, additional indicators must be taken into account, such as the agreement between experimental and derived spectroscopic quantities. In this sense, the standard theory gives more realistic results for the hosts studied in this work, even though the standard theory is known to be less effective on Pr3+ in some hosts. Overall, some real improvement can be seen with the modified theories developed so far. However, results can be also quite inconsistent as demonstrated in this work, indicating there are some aspects in the theory of the 4f4f transitions that are not completely understood yet. For this reason, additional investigations are necessary. Finally, by the standard theory, the branching ratio was found to be over 60% for the 3 P0 → 3 H4 and 1 D2 → 3 H4 transitions, for both hosts, suggesting these glasses as potential candidates for solid-state laser devices.

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[22] S. M. Lima, L. H. C. Andrade, A. C. P. Rocha, J. R. Silva, A. M. Farias, A. N. Medina, M. L. Baesso, L. A. O. Nunes, Y. Guyot, G. Boulon, J. Lumin. 143 (2013) 600–604. [23] L. H. C. Andrade, S. M. Lima, A. Novatski, P. T. Udo, N. G. C. Astrath, A. N. Medina, A. C. Bento, M. L. Baesso, Y. Guyot, G. Boulon, Phys. Rev. Lett. 100 (2008) 027402. [24] A. Steimacher, M. J. Barboza, F. Pedrochi, N. G. C. Astrath, J. H. Rohling, M. L. Baesso, A. N. Medina, Opt. Mater. (Amst). 37 (2014) 531–536. [25] B. R. Judd, Phys. Rev. 127 (1962) 750–761. [26] G. S. Ofelt, J. Chem. Phys. 37 (1962) 511–520. [27] R. D. Peacock, Struct. Bond. 22 (1975) 83–122. [28] M. J. Weber, T. E. Varitimos, B. H. Matsinger, Phys. Rev. B 8 (1973) 47–53. [29] M. P. Hehlen, M. G. Brik, K. W. Kr¨amer, J. Lumin. 136 (2013) 221–239. [30] R. Hakim, K. Damak, A. Toncelli, M. Fourati, R. Maalej, J. Lumin. 143 (2013) 233–240. [31] A. A. Kornienko, A. A. Kaminskii, E. B. Dunina, Phys. status solidi B 157 (1990) 261. [32] A. A. Kornienko, A. A. Kaminskii, E. B. Dunina, Phys. status solidi B 157 (1990) 267. [33] A. Fl´orez, O. L. Malta, Y. Messaddeq, M. A. Aegerter, J. Non. Cryst. Solids 213-214 (1997) 315–320. [34] A. Fl´orez, M. Fl´orez, Y. Messaddeq, M. A. Aegerter, P. Porcher, J. Non. Cryst. Solids 247 (1999) 215–221. [35] S. Schutzmann, M. Casalboni, F. De Matteis, P. Prosposito, J. Non. Cryst. Solids 351 (2005) 1814–1818. [36] A. B. Spierings, M. Schneider, R. Eggenberger, Rapid Prototyp. J. 17 (2011) 380–386. [37] E. Grace, A. Butcher, J. Monroe, J. A. Nikkel, Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers, Detect. Assoc. Equip. 867 (2017) 204–208. [38] R. T. G´enova, I. R. Mart´ın, U. R. Rodr´ıguez-Mendoza, F. Lahoz, A. D. Lozano-Gorr´ın, P. N´un˜ ez, J. Gonz´alez-Platas, V. Lav´ın, J. Alloys Compd. 380 (2004) 167–172. [39] C. K. Jørgensen, R. Reisfeld, J. Less-Common Met. 93 (1983) 107–112. [40] M. El Okr, M. Farouk, M. El-Sherbiny, M. A. K. El-Fayoumi, M. G. Brik, J. Alloys Compd. 490 (2010) 184–189. [41] G. Lakshminarayana, J. Qiu, M. G. Brik, G. A. Kumar, I. V. Kityk, J. Phys. Condens. Matter 20 (2008). [42] V. Ravi Kumar, N. Veeraiah, B. Appa Rao, S. Bhuddudu, J. Mater. Sci. 33 (1998) 2659–2662.

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6. Acknowledgments The authors acknowledge the support from the Brazilian agencies CAPES, CNPq, Fundac¸a˜ o Arauc´aria, FINEP and FAPESP (processo 2017/16392-6). The authors are also thankful to Prof. A. Fl´orez for supplying the matrix elements of Pr3+ . References

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Highlights (for review)

Comparation between three different Judd-Ofelt theories for Pr3+-doped glasses.

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Spectroscopic properties were derived and compared with the theories.

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Branching ratio suggests a potential candidate for solid-state laser devices.

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