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Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids
journal homepage: www.elsevier.com/locate/jnoncrysol
Structural and optical properties of TeO2-Li2O-ZnO-Nb2O5-Er2O3 glass
system
⁎
N. Elkhoshkhanya, , Samir Y. Marzoukb, Nourhan Moataza, Sherif H. Kandila
a
b
Department of Material Science, Institute of Graduate Studies and Researches, Alexandria University, 163 Horreya Avenue, Shatby 21526, Egypt
Department of Basic and applied science, Faculty of Engineering and Technology, Arab Academy of Science and Technology, Egypt
A R T I C LE I N FO
A B S T R A C T
Keywords:
Tellurite glasses
Optical properties
Er3+ ions
Judd-Ofelt
Quinary tellurite glass system in the percentages of 75TeO2–5Li2O–10ZnO–(10–x) Nb2O5–xEr2O3 where
(x = 0.0, 0.5, 1.0, 1.5, 2.0, and 2.8 mol%) have been prepared and characterized. Both Fourier-transform-infrared (FTIR) and Raman spectroscopies were performed to study the structural changes correlated with the glass
network. The thermal characteristics of the system were specified which showed a higher thermal stability
(> 100 °C) due to the formation of more bridging oxygen's (BO's) revealed by (FTIR) and Raman spectroscopies.
The optical absorption spectra within near UV–visible regions were performed, and exhibited nine absorption
bands centered around 1536, 977, 798, 653, 545, 524, 490, 450, and 443 nm corresponding to the 4I15/2 ground
state to the various excited states 4I13/2, 4I11/2, 4I9/2, 4F9/2, 4S3/2, 2H11/2, 4F7/2,4F5/2, and 4F3/2 respectively. The
same measurement also showed increasing values of the optical band gap (Eg) form 2.70 to 2.90 (eV) and
decreasing the refractive index (n) from 2.48 to 2.42. Both the extinction coefficient data and the complex
dielectric functions of the glasses were estimated. The different optical parameters were distinctly affected by
increasing the Er2O3 (mol %) and the structural changes. The radiative properties of the glass were calculated
using J-O parameters. The Branching ratio (β) of 4I13/2 → 4I15/2 transition peaked at 1520.48 nm for Er3+ ions
has the highest value (1.000) also, the radiative lifetime (τ) of the same transition changed from 1.4510 to
1.8483. The gain cross-section of the laser transition level from 4G11/2 → 4I15/2 changed from 1.44 × 10−20 to
1.92 × 10−20 cm−1 in the existing glass system. The acquired results exhibited that the existent glass can be a
good candidate in the fiber drawing and laser, non-linear optical applications.
1. Introduction
TeO2-based glasses have been recently the subject of many types of
research according to their promising mechanical, electrical, physical,
optical, and magnetic properties as well their chemical durability;
lower manufacturing temperatures, large refractive indices, high dielectric characteristics, and good optical transmission [1, 2]. All of
these unique properties made the TeO2-glass a suitable material for
optical applications like laser materials and nonlinear applications [3].
The TeO2-glasses are distinguished by their ability to have two structural units, one is TeO4 with the Te element positioned in trigonal bipyramids (tbps) and the other is TeO3 with the Te element positioned in
trigonal pyramids (tps) with a lone pair in both [4]. The TeO2 cannot be
vitrified on its own but it can with the aid of a network modifier such as
alkaline earth metal, transition metal or rare earth oxides to easily form
a glass. It was reported that the insertion of Nb2O5 in tellurite
glass stabilizes the glass matrix and it may have a dual modification
⁎
role, one as a network former and the other as a network modifier [5]
thereby enhances the thermal stabilization (as proved previously [6]).
The inclusion of Er3+ (as a rare earth metal) increases the chemical
durability of the glass due to its lower oxidizing in the air as well its
stability. Its addition makes the glass possess specific applications in the
optoelectronics, glass fibers and also the medical field [7, 8]. The addition of ZnO increases both the tendency of glass formation, refractive
index while decreases the optical energy band gap [9]. Insertion of
alkali oxides M2O (where M = Li, Na or K) to TeO2 based glasses create
more non-bridging oxygen's (NBO's) which result in decreasing the
coordination number of the glass forming units and hence decreasing
the glass strength [10]. The present system was chosen due to these
oxides and doped with Er3+ due to its advanced applications especially
in photonics and laser [11, 12]. This research aims to report our results
on the structural, optical properties of the prepared erbium-doped
tellurite glass. All the results will be discussed with respect to increasing
Er2O3.
Corresponding author.
E-mail address: Elkhoshkhany@alexu.edu.eg (N. Elkhoshkhany).
https://doi.org/10.1016/j.jnoncrysol.2018.08.011
Received 27 May 2018; Received in revised form 8 August 2018; Accepted 9 August 2018
0022-3093/ © 2018 Elsevier B.V. All rights reserved.
Please cite this article as: Elkhoshkhany, N., Journal of Non-Crystalline Solids (2018), https://doi.org/10.1016/j.jnoncrysol.2018.08.011
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Fig. 1. Shape of the prepared TLZNE glass samples.
Fig. 3. The FTIR absorption spectra of TLZNE glasses (the inset figure is the
transmittance spectra for the glass).
Fig. 2. XRD charts of TLZNE glasses.
Table 2
Band position (cm−1) and its corresponding peak assignments of the FTIR
spectra of the TLZNE glasses according to Fig. 4
2. Experimental work
Band position
A glass system 75TeO2–5Li2O–10ZnO–(10 − x)Nb2O5–(x)Er2O3;
(x = 0.0, 0.5, 1.0, 1.5, 2.0, 2.8 mol%) was prepared using meltquenching method by initially mixing appropriate amounts of
Tellurium dioxide (TeO2), Lithium oxide (Li2O), Zinc oxide (ZnO),
Niobium pentoxide (Nb2O5), and Erbium oxide (Er2O3) which all of
them were +99.99% purity, Sigma-Aldrich. The powder admixtures
were then placed in a platinum crucible and heated in a muffle furnace
at 950 °C for 10 min. The mixtures were then whiskered to get homogeneous melts. The melts were poured on a stainless-steel mold in the
room temperature which was previously preheated at 340 °C. The
glassy nature of the samples was checked using the X-ray diffraction
(XRD) recording with a Schimadzu 7000 diffractometer, (Japan) system
with Cu as a radiation source (λ = 1.54060 A), 30 kV accelerating
potential and 30.0 mA tube current. The scanning was made from 4 to
90° at a step width of 0.02°. The characteristics temperatures like glass
transition (Tg) and crystallization (Tc) temperatures were estimated by
DSC (TA Instruments, SDT Q600) by heating 15 mg of the samples in an
−1
906 cm
760–788 cm−1
646–660 cm−1
470–450 cm−1
421 cm−1
Assignments
Stretching vibration of NbeO in NbO6
(TeeO) symmetrical and (TeeO) asymmetrical vibrational
modes of TeO3/TeO3+1units
Axial symmetrical stretching vibrational of (TeeO) of
tetrahedral (TeO4) unit
Symmetrical stretching or bending vibration of (Te-O-Te)
linkages
ZnO4 tetrahedra group
open platinum pan heated with a rate of 10 °C/min from the room
temperature up to about 800 °C in a nitrogen atmosphere with a flow
rate of 15 Psi. The infra-red (IR) spectra were performed at the room
temperature with the help of an FTIR system, type spectrum BX
(PerkinElmer) using the KBr pellet technique within the region of
350–4400 cm−1. Raman analysis was used also to characterize the glass
which carried out using a Senterra Raman microscope (Bruker Optik,
Table 1
Glass code, composition, density (ρ), molar volume (Vm) and oxygen packing density (O.P.D) of the TLZNE glasses.
Glass sample code
TLZNE1
TLZNE2
TLZNE3
TLZNE4
TLZNE5
TLZNE6
Composition (mol %)
TeO2
Li2O
ZnO
Nb2O5
Er2O3
75
75
75
75
75
75
5
5
5
5
5
5
10
10
10
10
10
10
10
9.5
9.0
8.5
8.0
7.2
0.0
0.5
1.0
1.5
2.0
2.8
2
ρ ± 0.02 (gm/cm3)
Vm ± 0.2 (cm3/mol)
O.P.D ± 0.3 (mol/l)
4.12
4.21
4.24
4.53
4.71
4.83
37.84
37.11
36.98
34.77
33.57
32.96
43.02
57.66
57.59
60.98
62.85
63.53
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
polishing the samples to produce two parallel faces through which the
beam can be easily passed. The thickness-which is a significant parameter in calculating the attenuation and the absorption coefficient - was
measured accurately by a micrometer. The small parts and the residues
were then ground to be powder form to agree with the needs of (XRD),
(FTIR), (Raman), and (DSC).
3. Results and discussion
All the synthesized glasses were bubble free, transparent and light
pink color as in Fig. 1. The XRD patterns for all the prepared TLZNE
glasses were observed to have no sharp peaks which confirm the glassy
nature of the samples as in Fig. 2.
3.1. Density, molar volume, and oxygen packing density
The density (ρ), the molar volume (Vm), and the oxygen packing
density (O.P.D) were obtained according to the relations in Ref [13]
and their values are in Table 1. The density and molar volume values
vary from 4.12 to 4.83 ± 0.02 (g/cm3) and from 37.84 to 32.96 ± 0.2
(cm3/mol) respectively. The density values increase with increasing
Er2O3 because of the heavy molecular mass of Erbium (III) oxide
(382.52 g/mol) rather than the Niobium (V) pentoxide (265.81 g/mol);
this makes the glass becomes denser when more Er3+ ions are added
[7]. Decreasing the molar volume presented by the glass was due to the
variance of the ionic radii between the two oxides (i.e Nb2O5 and
Er2O3). The (O.P.D) increases from 43.02 to 63.53 ± 0.3 mol/L as in
Table 1 due to the excess of the oxygen atoms number per unit composition [14].
3.2. FTIR and Raman spectroscopy
Fig. 4. De-convolution of Raman spectra of (a) TLZNE1 and (b) TLZNE6 glasses.
The FTIR spectra of the present TLZNE glasses are represented in
Fig. 3 inside the region 400–1000 cm−1. There are five major IR absorption bands that were observed at 421, 470–450, 646–660, 760–788
and 906 cm−1. The FTIR bands positions of the current glasses and their
assignments are in Table 2. The tellurium oxide may be found in two
forms of structural configuration units namely trigonal bipyramids
(tbps) (TeO4) and trigonal pyramid (tps) (TeO3) [4]. The bands appear
in the region 450–470 cm−1 are assigned to the symmetrical stretching
or the bending vibrations of TeeOeTe linkages [15] which were
formed by corner-sharing of TeO4, TeO3+1 polyhedra and TeO3 units
[16]. These bands were shifted from higher to lower wave number with
increasing Er2O3 (mol %) which indicate the cleavage of TeeOeTe
linkages. This can be understood as; the insertion of Er2O3 to TeO2 glass
network may forms EreTeeO, EreOeTe and/or EreOeEr bonds instead of TeeOeTe linkages. The bands which appear inside the regions
646–660 and 760–788 cm−1 are ascribed to the axial symmetrical
stretching vibrational modes of (TeaxeO)s of TeO4 tetrahedra and the
(TeeO)s, (TeeO) as vibrational modes of TeO3+1 polyhedra or TeO3
trigonal bipyramid units [17]. These bands were shifted from higher to
lower wavenumber due to the structural changes that took place in the
glass network. It was suggested that the addition of Er2O3 could break
the axial TeeO bonds of TeO4 units then transform it into TeO3 (tps) via
TeO3+1 but still the ratio of TeO4 units is larger [18, 19]. This means
that more (BO's) are present within the network which causes the
density of the glass to increase and the molar volume to decrease. The
bands appear around 906 cm−1 are specified to NbeO bonds stretching
vibrations in NbO6 octahedra. These bands were shifted toward higher
wavenumber due to the deformation of the NbO6 octahedra because of
the addition of Er2O3 [20]. The bands which appear around 421 cm−1
are assigned to ZnO4 tetrahedra groups [21].
The experimental and de-convoluted Raman spectra of TLZNE1 and
TLZNE6 glasses by using Gaussian function are indicated in Fig. 4 and
the peaks centers and their assignments are in Table 3. The Raman
spectrum consists of three spectral regions, the first one is the low
Table 3
De-convolution result of Raman spectra of TLZNE1 and TLZNE6 glasses according to Fig. 5.
Peak
symbol
Peak position in cm−1
TLZNE1
TLZNE6
A
___
367
B
423
434
C
474
510
D
___
569
E
658
690
F
736
805
G
884
835
Assignments
TeO3 tps units with two or three nonbridging oxygen
Vibrations of lithium cations and ZnO4
tetrahedra group
Symmetrical stretching or bending
vibration (TeeOeTe)
(OeTeeO) linkages are replaced by
(OeTeeEr)
Axial Symmetric stretching vibrations of
(TeeO) of tetrahydral (TeO4) units
Stretching vibration of (TeeO) from
TeO3 tp units or TeO3+1 polyhedra
Stretching vibration of NbeO in NbO6
Ettlingen, Germany) with a laser excitation line of 785 nm and a power
at the surface of the sample 50 mW. The data were collected across
three spectral windows that together spanned (40–4450 cm−1) at a
spectral resolution of (3–5 cm−1). The optical spectra within the visible
and near ultraviolet (UV) regions were recorded at the room temperature. Computer-aided two-beam spectrophotometer (JASCO Corp, v570, Rel-00 Japan) in 200–2500 (nm) region has been used to record
the absorption. A resolution of 0.2 nm and a distance of 2 nm were
performed for 1155 measuring points. Sample preparation was made to remove the surface irregularities and other impediments to the
transmission which may cause scattering to the incident light beam - via
3
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Fig. 5. DSC curves of TLZNE glasses (the inset figure represents the DSC curve of the sample TLZNE1).
884–850 cm−1 is regarded to the stretching of Nb and its neighboring
non-bridging oxygen's in NbO6 octahedra [28]. This band shifts to
lower wave number likely due to the deformation of NbO6 octahedra
with growing Er2O3.
Table 4
Glass transition temperature (Tg), onset of the crystallization temperature (Tx),
temperature of the crystallization (TC), and thermal stability (ΔT) of the TLZNE
glasses.
Sample
Tg (°C)
Tx (°C)
TC (°C)
ΔT = Tx − Tg(°C)
TLZNE1
TLZNE2
TLZNE3
TLZNE4
TLZNE5
TLZNE6
348.45
347.81
352.20
355.03
356.07
360.00
525.47
541.00
522.70
510.00
519.30
516.29
559.03
598.70
581.70
542.00
541.00
533.70
177.02
193.19
170.50
154.97
163.23
156.29
3.3. DSC measurements
The Thermal behavior of TLZNE glasses is represented by the DSC
curves in Fig. 5. The temperature of the glass transition (Tg), the onset
of the crystallization temperature (Tx), the temperature of the crystallization (Tc), and the thermal stability ΔT = (Tx–Tg) of the present
glasses are mentioned in Table 4. The large glass thermal stability is a
significant factor in the fiber manufacturing operation [29] also, large
ΔT provides a strong inhibition of the nucleation and hence crystallization. From the results, the temperature Tg changes from 347.81 to
360.00 °C with increasing the concentration of Er3+ ions in the glass
as well the higher ΔT values (> 100 °C) (which are higher than other
Er3+doped-tellurite glasses [6]) which indicate increasing the bond
strength and hence the rigidity of the glass matrix. This result was also
confirmed by the formation of more (BO's) as indicated form IR
spectra.
frequency part (> 300 cm−1) which is specified to the combined modes
of local structures and heavy metals vibrational modes, the second intermediate region (300–665 cm−1) which is ascribed to deformation of
the vibrational modes of the glass network with bridged oxygen's (BO's)
while the third is the high-frequency region (< 665 cm−1) which is
ascribed to the stretching vibrational modes of the glass network former
[22]. The Raman spectra intensity increase with increasing Er2O3 from
0.5 to 2.8 (mol%). The structures of these glasses were investigated as;
the band labeled as (A) around 367 cm−1 is assigned to the TeO3 trigonal pyramids units with two or three non-bridging oxygen's [23]. The
band that labeled as (B) around 423–434 cm−1 is assigned to the vibrations of lithium cations [24] and/or ZnO4 tetrahedra groups [19].
The band (C) around 474–510 cm−1 is assigned to the symmetrical or
bending vibrations of (TeeOeTe) linkages at corner sharing sites [25].
The band labeled as (D) which resonated at 569 cm−1 is regarded to the
asymmetrical stretching of the continuous network composed TeO4
(tbps) and (OeTeeO) linkages replaced by (OeTeeEr) [26]. The band
labeled as (E) around 658–690 cm−1 is ascribed to the asymmetrical
stretching of the continuous network composed of TeO4 (tbps) [13].
The band that labeled as (F) around 736–805 cm−1 is regarded to the
stretching vibrations of (TeeO) bonds containing (NBO's) in TeO3 (tps)
and TeO3+1 polyhedra [13, 27]. The band labeled (G) around
3.4. Optical absorption spectra
The optical spectra of the rare earth doped glasses are the result of
two absorptions; the first one is the intrinsic absorption which occurs at
the short and long wavelengths, while the second is the extrinsic absorption which is correlated to the internal electronic transitions
especially within the 4f-shell of the rare earth ions [30]. The spectra of
the synthesized TLZNE glasses are presented in Fig. 6. Energy levels
higher than 4F3/2 were not noticed because of the intrinsic absorption
band gaps. The absorption bands correlated to the 4f–4f transitions of
the Er3+ ions coincided with the 4I15/2 ground state to different excited
states. The spectra consist of nine absorption bands centered around
1536, 977, 798, 653, 545, 524, 490, 450, and 443 nm coincide to the
4
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Fig. 6. Absorption spectra of TLZNE glasses.
increase of the electronic absorption edge [31]. The absorption coefficient (α) can be determined via using Relation (1)
I˳
α (λ ) = Ln ⎛ ⎞/ d (cm − 1)
⎝I⎠
(1)
where, Io and I are the intensities of the incident and the transmitted
radiations respectively, and (d) is the thickness of the sample [9].
Practically, the optical band gap (Eg) evaluation is based on the
optical absorption coefficient measurement near the absorption edge. It
was reported that, glasses with high refractive indices and low energy
gaps are favorable for the strong optical field [34]. For the amorphous
materials, Tauc [35], Davis and Mott [36] presented the computation of
the optical energy gap. For the absorption by indirect transition, the
absorption coefficient α (ν) can be calculated through Relation (2)
(αhν )1/2 = A(hν − Eg (eV))
(2)
where, A is a constant, and hν is the incident radiation photon energy.
The optical band gap can be acquired through extrapolation from the
linear parts in the figures that represent (αhν)1/2 versus hν as in Fig. 7.
From Table 5 one can observe that, Eg values increase from 2.7 to
2.9 eV. Increasing the Er2O3 (mol %) led to this increase of Eg which is
usually coincide to the excess of bridging oxygen's (BO's) in the network
of the glass as deduced from IR results. Actually, pure TeO2 consist
mainly of TeO4 trigonal bipyramid polyhedral (tbp) units which may
transform to TeO3 through TeO3+1 with the addition of the modifier to
TeO2 [30].
Urbach energy (ΔE) is a measure of the disorder in amorphous solids
(i.e. the larger is the ΔE, the more disorder there is) [37]. ΔE can be
estimated from the slopes of the linear parts of representing Ln(α)
against hν corresponding to Relation (3) and as represented in Fig. 8
Fig. 7. Representation of (αhν)1/2 Vs (hν) of TLZNE glasses.
4
I15/2 ground state to the various excited states 4I13/2, 4I11/2, 4I9/2, 4F9/2,
S3/2, 2H11/2, 4F7/2,4F5/2, and 4F3/2 respectively [31–33]. The absorption bands < 300 nm could not be measured because of the rapid
4
5
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Table 5
Values of optical band gap (Eg), Urbach energy (ΔE), refractive index (n), molar refraction (RM), molar polarizability (∝m), metallization (M), electronic polarizability
of the oxide ion (∝°2 − ), the optical basicity (Λ) and Cauchy coefficients (A, B) of TLZNE glasses.
Sample
Eg (eV)
ΔE (eV)
n
RM (cm3/mol)
∝m×10−24 (cm3/mol)
M
∝°2 − (Å3)
Ʌ
A
B × 10−14 (m2)
TLZNE1
TLZNE2
TLZNE3
TLZNE4
TLZNE5
TLZNE6
2.70
2.75
2.76
2.76
2.80
2.90
0.208
0.231
0.249
0.279
0.287
0.302
2.48
2.47
2.46
2.46
2.45
2.42
23.94
23.34
23.23
21.83
21.01
20.40
9.49
9.25
9.21
8.65
8.33
8.09
0.367
0.371
0.372
0.372
0.374
0.381
3.82
3.72
3.71
3.46
3.30
3.20
1.23
1.22
1.22
1.19
1.16
1.15
2.26
2.07
2.05
2.03
2.04
2.04
2.28
2.21
1.40
1.20
2.70
0.50
Fig. 8. Representation of Ln(α) Vs (hν) of TLZNE glasses.
Fig. 10. Dependence of the refractive index (n) on the wavelength of TLZNE
glasses.
hν ⎞
Ln (α ) = ⎛
−C
⎝ ΔE ⎠
(3)
where C is a constant [38]. The Urbach energies are found to increase
from 0.208 to 0.302 eV with increasing Er2O3 as in Table 5. Increasing
ΔE values means increasing the level of the disorder with increasing of
Er2O3 (mol %) which is compatible with XRD results. The refractive
index (n) values can be gained using Relation (4) [39].
2
⎛n − 1⎞ = 1 −
2 + 2
n
⎠
⎝
⎜
⎟
Eg
20
(4)
Table 5 shows the decreasing of (n) from 2.48 to 2.42 with increasing Er2O3 (mol %) from 0 to 2.8 mol%. The higher values of (n) are
expected due to the higher polarization of the TeO2 network [39].
The molar refraction (RM) can be calculated using Relation (5) [39].
n2 − 1 ⎞
Vm (cm3/mol)
RM = ⎛ 2
n
⎝ + 2⎠
⎜
⎟
(5)
where Vm represents the molar volume. The RM of TLZNE glasses decrease from 23.94 to 20.40 (cm3/mol) with increasing of Er2O3 as in
Table 5. The RM is correlated to the molar electronic polarizability of a
material (∝m) as indicated by Relation (6) [40].
Fig. 9. Dependence of the extinction coefficient (k) on the wavelength of
TLZNE glasses.
3
⎞ RM (cm3/mol)
∝m = ⎛
⎝ 4π N ⎠
6
(6)
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Fig. 12. Representation of the refractive index factor (n2−1)
TLZNE glasses.
−1
Vs (E2) of
where, ∝i is the cation polarizability, P and q denote the numbers of
cations and oxide ions respectively. The calculated oxide ions polarizability values (∝°2 −) are mentioned in Table 5 which decrease from 3.82
to 3.20 Å3 across increasing Er2O3 from 0 to 2.8 mol%. This decrease of
(∝°2 −) is due to the difference in the cation polarizability between Te4+
cation (1.595 Å3) and Er3+ cation (0.89 Å3), and this also proves the
opposite relationship between (∝°2 −) and the energy gap (Eg).
The optical basicity (Λ) depending on the polarizability of oxide ion
can be computed using Relation (9) [40].
1
Λ = 1.67 ⎛1 − 2 − ⎞
∝° ⎠
⎝
Fig. 11. (a) The real (ε') and (b) the imaginary (ε″) optical dielectric constant Vs
the wavelength of TLZNE glasses.
Values of Λ are in Table 5 which decrease from 1.23 to 1.15 with
growing Er2O3 mol%. These values of Λ confirm the direct correlation
between the optical basicity and the polarizability of the oxide ion
where both decrease with increasing Er2O3 [44].
where N is the number of the polarizable ions per mole which assumed
to be equal to the Avogadro's number. The resultant values of (∝m)
decrease from 9.49 to 8.09 × 10−24 (cm3/mol) with increasing Er2O3
as tabulated in Table 5. Accordingly, decreasing the RM is in direct
relation with reducing the glass polarizability [41]. The metallization
criterion (M) can be gained by Relation (7) [37].
M=1−
Rm
Vm
3.5. Determination of the optical constants
The real refractive index part (n) of the complex refractive index as
a function of the reflectance (R) and coefficient of the extinction (k) can
be given by Relation (10) which is regarding Fresnel's theory where, the
appropriate root of the equation is considered as the refractive index
[45].
(7)
Values of (M) of TLZNE glasses are mentioned in Table 5 and fell in
the range of 0.367–0.381. The existence of (M) in this region confirms
the applicability of the existing glass to the non-linear optical applications [42]. The oxygen ion electronic polarizability (∝°2 − ) based on the
energy gap can be given from the optical absorption data by using
Relation (8) [43].
⎡ V
∝°2 − = ⎢ m ⎛⎜1 −
2.52 ⎝
⎣
Eg ⎞
⎟ −
20 ⎠
⎤
∑ P ∝i ⎥ q−1
i
⎦
(9)
R=
(n − 1)2 + k 2
(n + 1)2 + k 2
(10)
The coefficient of extinction (k) can be given by Eq. (11) [45] which
represents a relation between the absorption coefficient (α) and the
extinction coefficient.
k=
(8)
αλ
4π
(11)
Fig. 9 represents the variance of (k) with the wavelength (λ) of the
7
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Table 6
Values of Wemple–DiDomenico dispersion parameters (Eo) and (Ed), the average cation coordination number(Nc), linear refractive index n(0), lattice oscillator
strength (El), wavelength at zero material dispersion (λc), Abbe dispersion number (νd), second-order index of refraction (n2), third-order nonlinear optical susceptibility (χ3) of TLZNE glasses.
Samples
Eo
Ed
Nc
n(0)
El (eV)
λc ± 0.03 (μm)
νd
n2 ± 0.04 × 1013
χ3×10−13
TLZNE1
TLZNE2
TLZNE3
TLZNE4
TLZNE5
TLZNE6
10.10
10.20
11.64
12.29
9.56
16.97
45.20
38.02
39.77
40.66
36.33
54.05
7.63
6.42
6.71
8.86
6.13
9.13
2.33
2.17
2.10
2.07
2.19
2.05
0.016
0.015
0.014
0.011
0.010
0.009
5.89
5.79
5.50
5.97
7.36
5.57
33
28
26.8
26
24
23.5
6.52
6.79
6.86
7.19
8.00
8.02
0.40
0.38
0.38
0.40
0.44
0.44
where E is the energy of the incident photon in (eV), Eo is the singleoscillator energy (related to the optical band gap) and Ed is the dispersion energy. According to this form, drawing a relation between
(n2–1)−1 against photon energy squared (E2) ought to be a direct line
with a slope equal to (EoEd)−1 and an intercept on the y-axis of (Eo/Ed)
as represented in Fig. 12. It is observed that, values of Eo and Ed change
from 9.56 to 16.97 and from 36.33 to 54.05 respectively with increasing Er2O3 mol% in the studied glasses as in Table 6.
The dispersion energy (Ed) relates to other physical parameters of
the material can be given by the empirical Relation (17) [49].
prepared glasses. It is well known that (k) determines the absorption of
the light wave at any wavelength and aids in the computation of the
dielectric constant components (real and imaginary).
The attenuation coefficient η(λ) can be calculated by Relation (12)
based on the thickness (d) of the sample
η (λ ) = e α (λ) d
(12)
The variation of refractive index (n) as a function of wavelength (λ)
is represented in Fig. 10. It can be observed that the refractive index of
studied glass decreases with increasing both wavelength and Er2O3
(mol %) which confirm increasing the number of (BO's) as indicated by
IR spectra. Portions of the dispersion curve in-between the anomalousdispersion branches are known to represent a normal dispersion which
obeys the Cauchy dispersion Relation (13) [46, 47].
n=A+
B
C
+ 4
λ2
λ
Ed = βNc Ne Za
where, β is a constant with two-values either an ionic or a covalent
value (βi = 0.26 ± 0.03 eV) or/and (βc = 0.37 ± 0.04 eV), Nc is the
effective coordination number of the cation nearest neighbor to the
anion, Ne is the number of valence electrons per anion and Za is the
solemn chemical valency of the anion. The calculated values of Nc of the
present glasses are in Table 6 which change from 6.13 to 9.13 with
growing Er2O3 mol%.
Value of the linear refractive index (n(0)) related to Eo and Ed at
longer wavelength can be estimated through Relation (18) with the
value of the incident photon energy E approach zero [50].
(13)
where, A, B, and C are known as Cauchy coefficients which are characteristic to the material. The coefficient C can be canceled as a consequence of its small value in the material transparency region. Values
of the Cauchy's coefficients were estimated by fitting the curve of n(λ)
as in Table 5.
The optical complex dielectric function describes the interaction of
electromagnetic waves with the matter which reflects by that the underlying molecular mechanisms. The complex dielectric constant components (ε) of the material are ε (λ) = ε' (λ) + j ε″ (λ) which are correlated to the wavelength (λ). The real (ε') and the imaginary (ε″) parts
in terms of the constants (n) and (k) are presented by the Relations (14
and 15).
ε′ = n2 − k 2
(14)
ε″ = 2nk
(15)
E
n (0) = ⎛ d + 1⎞
⎝ E0
⎠
⎜
Eo Ed
Eo2 − E 2
0.5
⎟
(18)
Table 6 confirms the reverse relation between both (Eo and Ed) and n
(0) by looking to their corresponding values within the table.
The lattice contribution for wavelengths much shorter than the
phonon resonances is presented by Relation (19) [51]
n2 − 1 =
Both the real (ε') and the imaginary parts (ε″) of the dielectric
constant versus the wavelength for the present glasses are represented
in Fig. 11 (a, b). The imaginary part (ε″) could be employed in the
determination of the optical relaxation time of glasses [45]. The dielectric constants for all samples have an exponential fixed decrease
with the wavelength and a decrease with increasing the Er2O3; this
suggests that for all glasses the free carrier concentration changes in the
same way with the change of Er2O3 mol% [47].
S. H. Wemple and M. DiDomenico [48] established the WempleDoDomenico dispersion model (WDD) by analyzing the refractive index
dispersion data below the inter-band absorption edge in the ionic and
covalent materials and have shown that a single - oscillator fit of the
Relation (16)
n2 − 1 =
(17)
E˳Ed
E2
− l2
2
2
E˳ − E
E
(19)
2
where, El represents the lattice oscillator strength. At E < < Eo2 where
the long wavelength, drawing (n2–1) against 1/E2 should approach a
straight line. Applying this relation to Eq. (19) yields Eq. (20).
n2 − 1 =
Ed
E2
− l2
E0
E
(20)
Ed
E0
El 2 ).
where the intercept is the ratio
and the slope is (−
Values of El
are in Table 6. The material dispersion effect parameter M(λ) can be
given by using the parameters Eo, Ed and El as given by Eq. (21) [51].
M(λ) = 1.54 × 10 4
Ed
λ
− 2.17 × 103El 2
n
2λ2E03
(21)
The wavelength λc at zero material dispersion (M = 0) can be
computed from Relation (22) [48].
(16)
8
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
4.3578
0.8248
0.3896
2.0525
5.0098
1.8448
10.961
2.0232
2.1009
2.1272
2.1562
2.2032
2.2234
2.3752
8.6897
1.7341
2.6499
1.4482
⎜
4
⎟
(22)
The wavelength λc values of TLZNE glasses are fluctuating with
increasing Er2O3 as in Table 6 from 5.50 to 7.36 (μm). The Abbe
number (νd) measures the material's dispersion (changing of refractive
index vs. the wavelength) which can be given by Relation (23) [52].
νd =
4.173
1.1854
0.4496
2.0719
3.4218
1.9394
4.3965
fexp
n
4.1666
1.2929
1.0528
2.1522
7.152
1.915
9.203
1
E
λ c = 1.63 ⎛ 3d 2 ⎞
⎝ E0 El ⎠
nd − 1
n f − nc
(23)
1.9879
2.0660
2.0919
2.1199
2.1644
2.1832
2.3209
3.5758
1.5041
2.7428
1.7510
4.9031
1.4825
1.0116
2.4671
6.982
2.255
8.9821
5.1596
0.994
0.3776
2.3763
7.7108
2.0353
8.5077
1.9672
2.0471
2.0733
2.1015
2.1458
2.1645
2.3009
8.2980
1.8848
3.1573
0.6163
n
where K is an empirical constant. Based on this semi-empirical relation,
the third-order non-linear optical susceptibility (χ3) of the glass is
fundamentally concerning (n2) index and the linear index (n) as given
by Eq. (25) [54].
fexp
n2 (10−13esu) = K
fcal
4.3335
0.8252
0.3977
2.0345
6.1759
1.8189
2.2739
where, nd, nf and nc are the refractive indices at the wavelengths of the
yellow He d-line and F-and C-lines of hydrogen (587.56 nm, 486.13 nm
and 656.27 nm respectively) in VIS region. The higher dispersion
glasses have νd < 55 whereas the lower ones have larger Abbe numbers.
From Table 6, the Abbe dispersion number decreases from 33 to 23.5
with increasing Er2O3 mol % which shows that the existing glasses
provide a high dispersion. Boling et al. [53] derived a relation for the
second-order refraction index (n2) concerning the glass from the linear
refractive index (n) which is given from Relation (24)
χ3 =
n
TLZNE4
TLZNE5
fexp
fcal
TLZNE6
fcal
N. Elkhoshkhany et al.
n−1
ν5/4
(24)
nn2
12π
(25)
Values of χ change by increasing Er2O3 (mol %) from 0.38 to 0.44
across the existing glasses as in Table 6.
5.6984
1.631
0.6176
2.649
4.5461
2.6135
5.8424
fcal
3
5.8421
1.0953
0.3983
2.5158
9.1445
2.7056
2.3161
1.9714
2.0511
2.0771
2.1051
2.1492
2.1678
2.3030
4.9110
1.6919
3.7748
2.9139
5.3186
1.646
1.3284
2.7695
9.0539
2.4497
11.65
5.0642
0.9531
0.3778
2.3096
9.169
3.7938
11.710
1.9697
2.0510
2.0770
2.1045
2.1472
2.1651
2.2951
10.9614
2.2569
3.3807
0.9332
n
fcal
fexp
n
Numerical integration of the identical absorption bands was utilized
to realize the experimental oscillator strengths of the transitions from
the ground 4I15/2 level to the different excited states. Judd-Ofelt theory
was performed to figure out the transition prospects of Er2O3 excited
levels. Determining the experimental oscillator strengths fexp associated
with the transitions can be accomplished by integration the absorption
bands for each spectrum [55, 56] according to Formula (26)
fexp = 2.303
mc 2
LNπe 2
∫ ODdλ(λ2) dλ
6536
10,225
12,500
15,267
19,120
20,449
26,597
8π 2mc
(n2 + 2)2
×
×
3hλ (2J + 1)
9n
U λ ‖ 〈 (S´. L´) J ´〉 ‖2
λ
∑
Ωλ 〈 (S. L) J 〉
λ = 2.4.6
(27)
I13/2
I11/2
I9/2
4
F9/2
2
H11/2
4
F7/2
4
G11/2
Ω 2 ×10−20 cm2
Ω 4 ×10−20 cm2
Ω 6 ×10−20 cm2
RMS
1530
978
800
655
523
489
376
where, m, h, c, λ, n and U are; the mass of electron, Planck's constant,
the velocity of light, mean wavelength of the transition, refractive index
of the glass forming unit, and doubly reduced matrix elements of the
unit tensor that have been taken from Weber [57] respectively. Table 7
includes all values of both experimental and calculated oscillator
strengths of the studied glasses. It was obvious that the values of fcal are
the highest for 4I15/2 → 4G11/2 transition in all glasses. From the experimental UV intensities and by using the least squares fit approach,
values of Ω2, Ω4, and Ω6 can be predicted as in Table 7. The Judd-Ofelt
intensities and strength parameters are remarkable for checking of local
structure and bonding in the neighborhood of rare-earth ions where the
4
4
(26)
where, e, L, N, and OD(λ) are the electron charge, sample thickness, the
number of the active ions, and optical density respectively. The calculated oscillator strength fcal can be gained by the isolation of both
electric-dipole and magnetic-dipole contribution from fexp [55, 56] according to Relation (27)
fcal [(S. L)J; (S´ . L´)J´] =
4
TLZNE2
Energy (cm−1)
Wavelength nm
Transition 4I15/2→
Table 7
The experimental (fexp) and calculated (fcal) oscillator strengths for Er3+ of TLZNE glasses.
TLZNE3
fexp
3.6. Oscillator strengths and Judd–Ofelt parameters
9
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Table 8
Calculated branching ratio (β) and lifetime (τ) of TLZNE glasses.
Transition 4I15/2→
4
I13/2
I11/2
4
I9/2
4
F9/2
2
H11/2
4
F7/2
4
G11/2
4
TLZNE2
TLZNE3
TLZNE4
τ (ms)
β
τ (ms)
β
τ (ms)
β
τ (ms)
β
τ (ms)
1.0000
0.9362
0.6792
0.9188
0.9561
0.8521
0.9004
1.5472
1.0425
1.3059
0.1371
0.0239
0.0428
0.0052
1.0000
0.9328
0.5965
0.9210
0.9394
0.8791
0.8713
1.4510
1.0479
1.4728
0.1436
0.0466
0.0412
0.0100
1.0000
0.9334
0.6559
0.919
0.9531
0.8606
0.8961
1.6690
1.1619
1.5060
0.1548
0.0310
0.0470
0.0067
1.0000
0.9268
0.6368
0.9223
0.9355
0.8671
0.8700
1.8483
1.3943
1.7586
0.1790
0.0601
0.0533
0.0128
1.0000
0.9298
0.6717
0.9169
0.9557
0.8542
0.9038
1.7378
1.2046
1.5344
0.1607
0.0274
0.0496
0.0058
3.7. Emission spectra, absorption and emission cross-sections
Depending on the emission and absorption properties and the threelevel nature on their spectral shape and population inversion, the potential performance of the erbium-glass laser can be obtained. The
absorption cross-section σabs(λ) has been established by Eq. (32)
σabs (λ ) = 2.0303
(28)
U λ ‖ 〈 (S´. L´) J ´〉 ‖2
∑
σemis (λ ) = σabs (λ )
Ωλ 〈 (S. L) J 〉
λ = 2.4.6
(29)
(33)
(34)
G (λ ) = σems (λ ) NP − σabs (λ ) N (1 − P )
(30)
where, P is population inversion rate for G11/2 → I15/2 laser transition,
N is the concentration of Er3+ ions. Values of G(λ) are in Fig. 14 where
the values of P are: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0
respectively. The emission profile of TLZNE samples (Fig. 14) shows
that, the peaks of the gain coefficient are shifted toward the shorter
wavelength. In the end, G(λ) at 1531 nm transition 4G11/2 → 4I15/2
changes from 1.44 × 10−20 to 1.92 × 10−20 cm−1 in the existing glass
system.
4
For whole likely transitions, the radiative lifetimes can be located
from the upper J manifolds 4I13/2, 4I11/2, 4I9/2, 4F9/2, 4F7/2, and 2H11/2
to all lower lying states of the Er3+ ions in the existing glasses. The
radiative lifetimes of the 4G11/2 state of the glass samples are in Table 8
which are higher other than Er3+doped zinc boro-tellurite glasses
synthesized by Z.A. Said Mahraz et al. [59]. The current glasses are in
good harmony and tuning inside the region of latest laser host glasses
doped with Er3+ [60].
The fluorescence branching ratio β(J. J´) can be presented by
Relation (31)
A (J . J ´)
β (J . J ´) =
∑J ´ A (J . J ´)
EZ − hcλ−1 ⎤
Zl
exp ⎡ l
⎢
⎥
Zu
KB T
⎣
⎦
where Zl and Zu are the partition function for lower and upper levels
concerned in the measured optical transition, T is the room temperature
and Ezl is the zero-line energy which is the energy segregation among
the lowest components of the upper and lower states. Fig. 13 explains
the predicted absorption and emission cross sections of the synthesized
glasses. Values of the stimulated emission cross sections σemis(λ) are
about 1.65 × 10−20, 1.95 × 10−20, 1.7 × 10−20, 1.45 × 10−20 and
1.5 × 10−20 cm−2 for TLZNE2 to TLZNE6 glasses respectively.
From both the absorption and emission cross sections for the transitions between two laser operating states, the optical gain coefficient
G(λ) - that drive to an estimation of the probable operating laser wavelength - can be gained by Eq. (34) [65].
The lifetime of the radiative excited levels is given by the reverse of
the sum of A(J, J') values calculated over all the terminal levels [58].
1
A (J . J ´)
(32)
ions in each glass
where N is the concentration of the respective Er
sample. The stimulated emission cross-section σemis(λ) of Er3+ for 4G11/
4
2 → I15/2 transition was calculated by McCumber method [63] which
can be detected from their matching ground state absorption crosssection σabs(λ) through Eq. (33) [64].
where P is the number of the significant transitions in the absorption
spectra. The parameters Ω2, Ω4 and Ω6 can be applied in the Eq. (29) to
obtain the radiative transition probabilities for the electric dipole
transitions between the excited states and the lower-lying level of Er3+
[58].
64π 2e 2
n (n2 + 2)2
×
×
3hλ3 (2J + 1)
9n
OD (λ )
Nl
3+
1
(f − fmeas )2 ⎤2
⎡
r . m . s = ⎢∑ cal
⎥
P−3
⎣ P
⎦
τrad =
TLZNE6
β
value of Ω2 is related to the coincidence of the glass hosts. Ω6 is related
the covalence nature of the EreO bonds in inverse relation and influenced by the overlap integrals of 4f orbitals rather than Ω2 and Ω4 [58].
Both Ω4 and Ω6 are parameters related to characteristics such as rigidity. From Table 7, decreasing both Ω2 from 10.9614 × 10−20 to
8.6897 × 10−20 and Ω6 from 3.3807 × 10−20 to 2.6499 × 10−20 with
increasing Er2O3 (mol %) confirms increasing the covalency of bonds
and also increasing the thermal stability and the energy gaps as indicated from IR results. To obtain the quality of fitting of the calculated
oscillator strengths to the experimental one Relation (28) the rootmean-square (r. m. s) can be used
A (J . J ´) =
TLZNE5
4
4. Conclusion
The glass system 75TeO2–5Li2O–10ZnO–(10–x)Nb2O5–xEr2O3 with
(x = 0.0, 0.5, 1.0, 1.5, 2.0, and 2.8 mol%) was synthesized and characterized by XRD, FTIR, Raman, DSC, and optical absorption studies.
Increasing the density from 4.12 to 4.83 ± 0.02 (g/cm3) and decreasing the molar volume from 37.84 to 32.96 ± 0.2 (cm3/mol) was
due to the increase in the packing of the glass, which in turn caused an
increase of the transformation temperature and the thermal stability of
the glass. Both FTIR and Raman spectroscopes showed a presence of a
mix of (BO's) and (NBO's) but the dominated effect was attributed to
(BO's). The optical measurements showed an increase of the band gap
energy from 2.7 to 2.9 eV by the action of the (BO's) with increasing
(31)
The ratio of branching can be used to characterize the transition in
the emission spectra. The value of β is larger than 0.5, which implies
that the emission radiation is stronger relative to transition and shows
the possible application of this transition for laser creation [61]. The
highest β is founded in the 4I13/2 → 4I15/2 transition peaked at
1520.48 nm for Er3+ ions in all glasses as in Table 8 which is greater
than other Er3+ doped tellurite glasses [62].
10
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Fig. 13. Absorption cross-sections σabs(λ) and stimulated emission Cross section σemis(λ) of TLZNE glasses.
exponential fixed decrease with the wavelength and a decrease with
increasing the Er2O3. The Judd-Ofelt parameter (Ω2, Ω4, Ω6) were
calculated. Both Ω2 and Ω6 decreased with increasing Er2O3 (mol %)
which confirmed increasing the covalency of bonds and also increasing
the thermal stability and the energy gaps as indicated from IR results.
The present system opposed higher branching ratio (1.000) and radiative lifetime (1.8483 ms) compared to other tellurite glasses.
Er2O3 mol %. Decreasing the molar refraction from 23.94 to 20.40
(cm3/mol) was related to decreasing of the glass polarizability. Both the
oxide polarizability and the optical basicity of the present glass were in
direct relation where both decreased with increasing Er2O3. The glass
became optically more dispersive with a higher refractive index with
increasing Er2O3 mol% due to the higher polarization of the TeO2
network. The complex dielectric constants for all samples have an
11
Journal of Non-Crystalline Solids xxx (xxxx) xxx–xxx
N. Elkhoshkhany et al.
Fig. 14. Gain coefficient for 4G11/2 → 4I15/2 transitions of TLZNE glasses.
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