Sử dụng lý thuyết Judd-Ofelt để phân tích phổ về cấu trúc mạng của thủy tinh lithium-sodium aluminoborate glass pha tạp ion Dy+3

 Tran Ngoc / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(45) (2021) 109-116 109 
 02(45) (2021) 109-116
 Using the Judd-Ofelt theory to analyze the lattice structure of the Dy+3 
 ions doped lithium-sodium aluminoborate glass 
 Sử dụng lý thuyết Judd-Ofelt để phân tích phổ về cấu trúc mạng của thủy tinh 
 lithium-sodium aluminoborate glass pha tạp ion Dy+3 
 Tran Ngoca,b* 
 Trần Ngọca,b* 
 aInstitute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam 
 aViện Nghiên cứu và Phát triển Công nghệ Cao, Trường Đại học Duy Tân, Đà Nẵng 
 bFaculty of Natural Sciences, Duy Tan University, Da Nang, 550000, Vietnam 
 bKhoa Tự nhiên, Trường Đại học Duy Tân, Đà Nẵng 
 (Ngày nhận bài: 23/3/2021, ngày phản biện xong: 10/4/2021, ngày chấp nhận đăng: 15/4/2021) 
Abstract 
 3+ 3+
Dy doped lithium-sodium aluminoborate glass (60-x) B2O3-10Al2O3-15Na2O-15Li2O-xDy2O3 (ABLN: Dy ) are 
prepared by the conventional melting procedure. Optical absorption and luminescence spectra have been measured at 
room temperature. Using the Judd - Ofelt (JO) theory, the intensity parameters Ωλ (λ = 2,4,6) have been evaluated for 
 3+
ABLN: Dy glass. These intensity parameters are used to predict radiative properties that include electric (Sed) 
magnetic (Smd) dipole line strength, radiative transition probabilities (AR), lifetime (τR), branching ratios (βR) for the 
 3+
excited levels of Dy . In addition, the stimulated emission cross – sections (σλp) have been predicted for the transitions 
4 6
 F9/2 → HJ (J=15/2, 13/2, 9/2). 
 Keywords: Aluminoborate glasses; Judd-Ofelt theory; luminescence. 
Tóm tắt 
 3+ 3+
Thủy tinh lithium-sodium aluminoborate pha tạp Dy (60-x) B2O3-10Al2O3-15Na2O-15Li2O-xDy2O3 (ABLN: Dy ) 
được chế tạo bằng phương pháp nung nóng chảy. Phổ hấp thụ và phổ huỳnh quang được đo tại nhiệt độ phòng. Sử dụng 
 3+
lý thuyết Judd – Ofelt (JO), các thông số cường độ Ωλ (λ = 2, 4, 6) đã được xác định cho thủy tinh ABLN: Dy . Các 
thông số cường độ này được sử dụng để dự đoán các đặc tính bức xạ bao gồm lực vạch lưỡng cực điện (Sed), lưỡng 
cược từ (Smd), xác suất chuyển dời bức xạ (AR), thời gian sống (τR), tỷ số phân nhánh (βR) cho các mức kích thích của 
 3+ 4 6
Dy . Ngoài ra, tiết diện phát xạ (σλp) đã được dự đoán cho quá trình các chuyển dời bức xạ: F9/2 → HJ 
(J=15/2,13/2,9/2). 
 Từ khóa: Thủy tinh aluminoborate; lý thuyết Judd-Ofelt; huỳnh quang. 
* Corresponding Author: Tran Ngoc; Institute of Research and Development, Duy Tan University, Da Nang, 550000, 
Vietnam; Faculty of Natural Sciences, Duy Tan University, Da Nang, 550000, Vietnam 
Email: daotaoqb@gmail.com 
110 Tran Ngoc / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(45) (2021) 109-116 
1. Introduction transition and the blue band at 470 - 500 nm 
 4 6
 Rare-earth (RE) ions doped borate glasses corresponding to the F9/2 - H15/2 transition. 
gained intensive attention from the researchers Dysprosium doped glasses and crystals emit 
for various technological applications, such as intense discrete radiation in the yellow (570 - 
solid-state lasers, optical fiber amplifiers, 600 nm) and NIR (1,35 mm and 3,0 mm) 
radiation dosimetry, high quality laser regions that have potential technological 
illuminators, white-LED (W-LEDs), and applications in commercial displays and 
scintillators [1, 2, 3] etc. Borate glasses possess telecommunications [12, 13, 14]. The intensity 
 4 6
good RE ion solubility, high spectral of the F9/2- H13/2 hypersensitive transition 
transparency, low melting temperature, thermal strongly depends on the host, in contrast to a 
 4 6 3+
stability and high mechanical stability, ease of less sensitive F9/2- H15/2 transition of Dy and 
synthesis, may be fabrication in different results in different yellow to blue luminescence 
shapes and low manufacturing cost [2, 3, 4, 5]. intensity ratios that largely change with 
Further, RE ions offer excellent emission concentration and/or glass composition. 
efficiency because of their characteristic 4f–4f In this work, we prepared and studied 
and 4f–5d transitions, and these 4f-4f spectroscopic properties of Dy3+ ions in lithium-
transitions can give luminescence covering sodium aluminoborate glasses. Judd - Ofelt theory 
wide spectral range starting from ultraviolet has been used to evaluate intensity parameters 
(UV) to infrared (IR) as the 4f orbitals are very Ωλ (λ = 2, 4, 6) by analyzing the absorption 
effectively protected from the interaction with spectrum of ABLN: Dy3+ glass, and calculated 
external fields by 5s2 5p6 shells [1, 3, 6]. the radiative transition probabilities, branching 
 4
However, high phonon energy (~1300–1500) ratios, radiative lifetimes of F9/2 excited level, 
cm−1 of borates increases the multi-phonon stimulated emission cross - section for selected. 
relaxation rates of the RE emission transitions, Besides that, the potential application of the 
that decreases the luminescence and qu ... 6 4
 P3/2, M17/2 30864 30892 3.14 2,02 
  1.0063; 1.63 rms = 1.09×10-6 
 Nephelauxetic effect- Bonding parameter 
 The bonding parameter (δ) is defined where α is molar extinction coefficient at 
 -1
as  1  /  100 [1, 4, 5], energy ν (cm ). The α(ν) values can be 
where  ()/ n and nephelauxetic ratio β = calculated from absorbance A by using Lambert 
νc/νa, (νc and νa are energies of the – Beer’s law: A = α(ν)Cd, C is concentration 
corresponding transitions in the complex and [dim: L-3; units: mol-1], d is the optical path 
aquo-ion, respectively, and n to refers to the length [dim: L; units: cm]. n is the refractive 
number of levels that are used to compute  index of the material, J is the total angular 
values) [1, 2]. Depending on the field 
 momentum of the ground state, Ωλ are the JO 
 2
environmental, the bonding parameter (δ) can intensity parameters and U  are the squared 
be received the positive or negative value doubly reduced matrix of the unit tensor 
indicating covalent or ionic bonding. In our operator of the rank λ = 2, 4, 6 is calculated 
sample, the values of  and δ bonding from intermediate coupling approximation for a 
parameter are 1.0063 and -1.63, respectively. transition JJ ''. These reduced matrix 
 3+
Thus, the bonding of Dy ions with the local elements did not nearly depend on host matrix 
host is ionic bonding [17, 19, 20]. as noticed from earlier studies [15, 17]. All 
 Oscillator strengths and JO parameters thirteen absorption bands have been analyzed 
 using JO theory and were least squared fitted to 
 The experimental (fexp) and calculation 
 yield the best fit values for the JO parameters. 
oscillator strengths (fcal) of absorption bands are 
determined using Eq [15, 16, 18]: The results of the parameters a, b, c, for the 
 transitions of Dy in the glass ABLN are: Ω2 = 
 9
 fd 4,318.10 (  )  (1) -20 -20 2 -20
 exp 16,30×10 ± 0.82×10 cm , Ω4 = 5,81×10 
 -20 2 -20 -20
 ± 0.77×10 cm , Ω6 = 5.28×10 ± 0.48×10 
 222 2
 82 mc n 2 cm . Table 2 compared the JO intensity 
 f  n U () (2) 
 cal   3+ 
 3h (2 J 1) 3 n  parameters obtained for ABLN: Dy glass with 
 some of the reports on systems: Dy3+ [15 - 22]. 
 Table 2: The JO parameters of Dy3+ ions doped various hosts 
 -20 2 -20 2 -20 2
 Host matrix 2(×10 cm ) 4(×10 cm ) 6(×10 cm ) 4/6 Ref. 
 ABLN: Dy3+ glass 16,30 5,81 5.28 1,10 Present 
 LYB: Dy3+ glass 12,83 3,47 3,43 1,01 [7] 
 PKBFA: Dy3+ glass 10,41 2,29 2,07 1,10 [21] 
 NaLTB: Dy3+ glass 9,86 3,39 2,41 1,41 [20] 
 NaLTB: Dy3+ glass 9,25 2,87 2,29 1,25 [22] 
 LiLTB: Dy3+ glass 8,75 2,62 2,07 1,26 [22] 
 PKMAF: Dy3+ glass 7,04 1,73 1,57 1,10 [21] 
 Tran Ngoc / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(45) (2021) 109-116 113 
 The Table 2 shows the values of Ω2 and Ω6 
in ABLN glass are larger than those of the 
different hosts. The characteristic feature of the 
Ω2 is that it is sensitive to the local environment 
of the RE3+ ions and is often related with the 
asymmetry of the coordination structure, 
polarizability of ligand ions or molecules and 
bonding nature [15, 16, 19, 23, 24]. The larger 
 3+ 
of Ω2 parameter in ABLN: Dy glass than other 
hosts can be attributed to lower symmetry of 
the coordination structure surrounding the RE3+ 
ion. The Ω6 parameter related to the rigidity of 
the medium in which the RE3+ ions are Fig. 2. The emission spectrum of ABLN: Dy3+ glass 
embedded. Rigid matrices show low values for under excitation by 365 nm 
the Ω parameter [15, 18]. The larger of Ω 
 6 6 As shown in Fig. 2, which illustrates the 
parameter in ABLN: Dy3+ glass than other hosts 
 emission spectrum using the 365 nm excitation 
suggests that the rigidity of the surrounding 
 wavelength of xenon lamp source, 4 emission 
environment Dy3+ in ABLN glass is lower than 
 bands at 481, 575, 664 and 755 nm which are 
other hosts. The spectroscopic quality factor χ = 4 6
 attributed to transitions from F9/2 to H15/2, 
Ω4/Ω6, is one of the ABLN important lasing 6 6 6
 H13/2, H11/2 and H9/2 and states, respectively, 
characteristic parameters which is used to 
 of Dy3+ions. But among of them, the yellow 
predict the stimulated emission in any active 
 3+ (Y) band (575 nm) corresponds to the 
medium. The Dy doped glass hosts 4 6
 hypersensitive transition F9/2 → H13/2, and the 
possessing spectroscopic quality factors in the 
 blue (B) band (481 nm) corresponds to the 
range 0.42–1.92 are the good candidates for 4 6
 F9/2 → H15/2 transition are the dominant bands 
laser active media [12, 13, 14, 19]. The 
 in the emission spectrum. The intensity ratio of 
observed value of χ in ABLN: Dy3+ glass is 
 yellow emission to blue emission (Y/B) of the 
1.10, which suggests that ABLN: Dy3+ glass is 
 Dy3+ions dependents on the asymmetry of the 
good material for various optical devices. 
 ligand. With the ABLN: Dy3+, the Y/B ratio is 
3.2. Fluorescence spectra and radiation 1.27 and higher than other hosts [19-21]. The 
properties higher value of Y/B indicates that the higher 
 From the JO parameters, the radiative degree of covalence between dysprosium and 
properties such as the electric (Sed) and oxygen ions. From the JO parameters and 
magnetic (Smd) dipole line strengths, the refractive index, the radiative properties such as 
radiative transition rates (AR), radiative lifetime the electric (Sed) and magnetic (Smd) dipole line 
(τR), branching ratios (βR) were calculated for strengths, the radiative transition rates (AR), 
 4
excited levels F9/2. The results are showed in radiative lifetime (τR), branching ratios (βR) 
 4
Table 3. were calculated for F9/2 excited levels. The 
 results are showed in table 3. 
114 Tran Ngoc / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(45) (2021) 109-116 
 Table 3. Transition energies (ν), radiative transition probabilities (Sed, Smd, A and AT), radiative 
 lifetime (ιR) and branching ratios (βR) for excited levels. 
 -1 2 2 -1
 SLJ S’L’J’ ν (cm ) Sed (cm ) Smd (cm ) A (s ) βR (%) 
 4 6
 F9/2 F1/2 7,296 4.90E-42 0.00E+00 1.94E-01 8.01E-03 
 6
 F3/2 7,908 4.00E-42 0.00E+00 1.97E-01 8.16E-03 
 6
 F5/2 8,552 2.59E-42 0.00E+00 1.71E+01 7.09E-01 
 6
 F7/2 9,944 1.03E-41 4.00E-41 1.13E+01 4.67E-01 
 6
 H5/2 10,901 6.13E-40 0.00E+00 8.11E+00 3.35E-01 
 6
 H7/2 11,962 2.30E-40 1.76E-41 4.06E+01 1.68E+00 
 6
 F9/2 12,065 1.07E-41 1.59E-41 1.94E+01 8.01E-01 
 6
 F11/2 13,257 2.09E-40 2.26E-42 5.10E+01 2.11E+00 
 6
 H9/2 13,398 1.61E-41 1.65E-40 4.46E+01 1.84E+00 
 6
 H11/2 15,209 4.34E-40 3.13E-41 1.59E+02 6.59E+00 
 6 
 H13/2 17,628 2.89E-39 0.00E+00 1.62E+03 6.69E+01 
 6 
 H15/2 21,182 4.64E-40 0.00E+00 4.48E+02 1.85E+01 
 -1
 AT(4F9/2) = 2423 s ; τR(4F9/2) = 414 μs 
 3+
 From the emission spectrum of ABLN: Dy and integrated emission cross – section (Σif) to 
 4 6
glass, the emission peak positions (λp), effective have calculated for F9/2 → HJ (J = 15/2, 13/2, 
line width (Δλeff), measured branching ratios 11/2, 9/2) transitions. The results are displayed 
(βexp), stimulated emission cross – section σ(λP) in Table 4. 
 Table 4. Emission peak positions (λp), effective line width (∆λeff), radiative transition 
 probabilities (A), branching ratios (βexp), stimulated emission cross – section σ(λP) and integrated 
 4 6 3+ 
 emission cross – section (Σif) for F9/2 → HJ transitions of Dy in ABLN glass. 
 4 -1 -22 2 -18
 F9/2 → λp (nm) ∆λeff (nm) A (s ) σ(λp) (×10 cm ) Σif (× 10 cm) βR (%) 
 exp cal 
 6 
 H11/2 661.3 26.1 160 6,52 0,39 4,62 6,59 
 6 
 H13/2 570.7 16.3 1626 59,8 2,99 56,32 66,80 
 6 
 H15/2 480.4 18.7 450 7,26 0,62 40,63 18,53 
 In general, the luminescence branching ratio than 10-18 cm, laser emission is probable [13]. 
 4 6
is a critical parameter to the laser designer, In our case, with the F9/2 → H13/2 transition, 
because it characterizes the possibility of the integrated emission cross – section is 
attaining stimulated emission from any specific 2.99×10-18 cm. The stimulated emission cross – 
transition. In this work, the predicted branching section σ(λP), which is an another of the most 
 4 6
ratio of F9/2 → H13/2 transition get a maximum important parameter that affects the potential 
value and be 66,8 %, while that the measured laser performance and its value signifies rate of 
ratio is 56.32 %. Thus, there is a good energy extraction from the lasing material. It is 
 4 6
agreement between experimental and calculated found that F9/2 → H13/2 transition exhibits 
 -22 2
branching ratios [19]. maximum σ(λP) (59,8×10 cm ). The large 
 values of branching ratio, integrated emission 
 The integrated emission cross–section, Σif, 
was an important parameter when considering cross – section and stimulated emission cross 
 4 6
the laser emission of the material. When the section suggest that the F9/2 → H13/2 transition 
integrated emission cross–section is greater can give rise to lasing action. 
 Tran Ngoc / Tạp chí Khoa học và Công nghệ Đại học Duy Tân 02(45) (2021) 109-116 115 
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