Hindawi Publishing Corporation
ISRN Ceramics
Volume 2013, Article ID 419183, 11 pages
http://dx.doi.org/10.1155/2013/419183
Research Article
Physical, Optical, and Spectroscopic Studies on MgO-BaO-B2O3
Glasses
Samdani,1 Md. Shareefuddin,2 G. Ramadevudu,3 S. Laxmi Srinivasa Rao,4
and M. Narasimha Chary2
1
Department of Physics, Muffakham Jah College of Engineering & Technology, Hyderabad 500034, India
Department of Physics, Osmania University, Hyderbad, Andhra Pradesh 500007, India
3
Department of Physics, Vasavi College of Engineering, Ibrahimbagh, Hyderabad 500031, India
4
Department of Physics, Bhawan’s New Science College, Narayanaguda, Hyderbad, Andhra Pradesh 500029, India
2
Correspondence should be addressed to G. Ramadevudu; [email protected]
Received 8 September 2013; Accepted 3 November 2013
Academic Editors: K. L. Bing, D. Jia, and O. P. Thakur
Copyright © 2013 Samdani et al. This is an open access article distributed under the Creative Commons Attribution License, which
permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The mixed alkaline effect in double alkaline borate glasses MgO-BaO-B2 O3 containing small proportions of copper oxide
(CuO) has been studied. The glass samples are characterized by optical absorption, electron paramagnetic resonance (EPR), and
Fourier transform infrared spectroscopy (FTIR). A red shift in optical absorption peaks with increasing MgO (decreasing BaO)
concentration has been observed. The values of “𝑔” tensor and hyperfine “𝐴” tensor have shown inflections with glass composition.
The number of spins (𝑁) and paramagnetic susceptibility (𝜒) also exhibited mixed alkaline effect. The broadening of glass network
with increase in MgO concentration is found from the FTIR spectra. Interestingly both density and molar volume have shown
decreasing trend with glass composition. The optical band gaps exhibited a nonlinear compositional dependence. As expected, the
glass samples possessed higher values of optical basicity (Λ), molar electronic polarizability (𝛼𝑚 ), and Urbach energy (ΔE).
1. Introduction
Binary alkali and alkaline borate glasses R2 O-B2 O3 (R = Li,
Na, K, Cs, Ca, Mg, Ba, etc.) have been studied extensively
by several authors [1, 2]. It is known that boric acid forms
stable glasses with alkaline earth oxides (R = MgO, CaO, SrO,
BaO) and at the same time alkaline earth oxides improve
glass forming ability. These oxides act as glass network
formers (GNF) at low concentrations and behave as glass
network modifiers (GNM) at higher concentrations [3].
Several researches reported mixed alkali effect (MAE) in
borate glasses containing alkali oxides in varying proportions
using several experimental techniques such as EPR, Optical
absorption, and impedance measurements [4]. The studies on
mixed alkali effect (MAE) suggested [5] that alkali ions tend
to preserve their local structural environment in the glass
system. Liu et al. [6] suggested that alkaline earth ions can also
show similar effect, namely, mixed alkaline effect. Miyoshi et
al. [7] observed similar behavior of CaO as that of Na2 O in
their glass systems.
The mixed alkaline earth effect is exhibited when one
alkaline earth ion is substituted progressively with another
one in the glass network. It is of great importance to look into
the mixed alkaline effect in glasses as it changes the properties
(such as electrical conductivity, 𝑇𝑔 , microhardness, refractive
index, and density) in a nonpredictive manner [8].
Many researchers focused mainly on mixed alkali borate
glasses, but little efforts have been put in to study mixed
alkaline effect. In this paper, we have made an attempt to
study this effect by incorporating two divalent (MgO and
BaO) oxides in B2 O3 -CuO glass network. MgO and BaO
are chosen for investigation purpose (as the difference in
their ionic radii is more). Also, glasses containing heavy
metal oxides such as BaO and PbO found applications in
plasma displays, gamma ray radiation shields [9], and so
forth in addition to exhibiting good chemical durability and
higher refractive indices. Addition of MgO and BaO to borate
network stabilizes the glasses [9]. In this paper, we report
optical, physical, and structural properties of 𝑥MgO-(30 −
𝑥)BaO-69B2 O3 -1CuO mixed alkaline glass systems.
2
ISRN Ceramics
Table 1: Composition, average molecular weight (𝑀), measured density (𝜌), theoretical density (𝜌th ), molar volume (𝑉𝑀 ), molar refraction
(𝑅𝑚 ), and metallization criterion (𝑀𝑐 ) of the glasses.
Glass code
MBBC-0
MBBC-1
MBBC-2
MBBC-3
MBBC-4
MBBC-5
Composition in (mol %)
MgO BaO B2 O3
CuO
0.0
30.0
69
1
5.0
25.0
69
1
7.5
22.5
69
1
10.0
20.0
69
1
12.5
17.5
69
1
15.0
15.0
69
1
𝑀 (g/mole)
𝜌cal (g/cc) ± 0.001
𝜌th (g/cc) ± 0.001
𝑉𝑀 (cc/mol) ± 0.01
𝑅𝑀
𝑀𝑐
145.32
137.47
133.54
129.62
125.69
121.76
3.49
3.48
3.40
3.35
3.29
3.19
3.45
3.30
3.23
3.16
3.08
3.00
41.63
39.45
39.26
38.69
38.20
38.11
26.03
24.65
24.50
24.12
23.71
23.61
0.6252
0.6248
0.6240
0.6234
0.6206
0.6195
Mixed alkaline earth borate glasses 𝑥MgO-(30 − 𝑥)BaO69B2 O3 -1CuO were prepared by conventional melt quenching technique. In the present glass system, the concentration
of MgO was gradually increased from 0 to 15 mol% while
BaO concentration was decreased from 30 to 15 mol%. The
concentrations of alkaline earth oxides MgO and BaO were
varied to study the mixed alkaline earth oxide effect. The
analar grade boric acid (H3 BO3 -99% purity), magnesium
oxide (MgO-99.9%), barium oxide (BaO-99%), and copper
oxide (CuO-99.9%) were used as the starting materials.
The appropriate mole concentrations were weighted and
grounded in a mortar. These materials were taken in porcelain
crucible and placed in an electrically heated furnace maintained at 1000∘ C. These mixtures took nearly 40–50 minutes
to melt congruently; further, these mixtures were stirred
occasionally to achieve homogeneity. The melt was then
quenched by pouring it on to a preheated (around 200∘ C)
stainless steel plate and pressing with another steel plate. The
glasses formed were clear, transparent, bubble free with light
blue tint. These glasses were annealed at that temperature
to relieve the mechanical stresses. The thicknesses of the
glass samples were around 0.5 to 1 mm. The compositions (in
mol%) of the glasses studied in the present investigation were
presented in Table 1.
XRD measurements were carried on Philips X-ray
diffractometer PW/1710 with Cu-K𝛼 radiation with angle
2𝜃 ranging from 10 to 80 degrees. The optical absorption
measurements were carried on polished glass samples using
Shimadzu UV-1800 spectrophotometer in the wavelength
region 300–1200 nm at room temperature. EPR spectra were
recorded on dry and perfectly powdered glass samples at
room temperature (310 K) using EPR spectrometer (JEOL
FEIX) operating at X-band frequency (9.205 GHz) with a
modulation frequency of 100 kHz. Uncertainties in the measurement of “𝑔” and “𝐴” values were about ±0.002 and ±2
× 10−4 cm−1 , respectively. The Fourier infrared absorption
spectra of the samples were recorded at room temperature
in the wave number range 4000–400 cm−1 on Bruker model
TENSOR 27 spectrometer using KBr disc technique. Density
measurements were carried out at room temperature using
the Archimedes method with xylene as the immersion liquid.
The density values were reproducible to ±0.02 g/cm3 .
Intensity (a.u.)
2. Materials and Method
MBBC-5
MBBC-4
MBBC-3
MBBC-2
MBBC-1
MBBC-0
10
20
30
40
50
60
70
80
90
2𝜃 (deg)
Figure 1: X-ray diffractograms of the glass samples at room
temperature.
3. Results and Discussion
3.1. XRD, Density, and Molar Volume. The X-ray diffraction
spectra (Figure 1) of the present glass samples did not show
any peaks. The peak free X-ray diffractograms indicated
amorphous nature of the glass samples. The molar volume
(𝑉𝑀) is calculated using the formula
𝑉𝑀 =
𝑀𝑇
,
𝜌
(1)
where 𝑀𝑇 is the total molecular weight of the multicomponent glass and 𝜌 is the density. The measured density (𝜌)
values along with molar volume values of the present glass
system are given in Table 1. Figure 2 shows the compositional
dependence of density and molar volume with MgO content
in the glass. It is found that both density and molar volume
decreased nonlinearly with increase in MgO content in the
base glass.
The decrease in density of the glass samples is due
to decrease in the mol% of BaO that has relatively high
molecular mass. The density values of present glass samples
are in good agreement with those of the values reported
3
3.6
3.55
3.5
3.45
3.4
3.35
3.3
3.25
3.2
3.15
3.1
1.2
43
41
40
39
38
37
36
5
7.5
10 12.5
MgO (mole%)
0.8
MBBC-2
0.6
MBBC-3
0.4
15
MBBC-4
0.2
Density
Figure 2: Variation of density and molar volume as a function of
MgO content.
0.0
400
3.2. Optical Band Gap and Urbach Energy. The optical
absorption spectra (Figure 3) of pure glass samples revealed
only one broad absorption band. It is clear from this figure
that the absorption edges were not sharp which is an indication of amorphous nature of the samples. Figure 4 shows
transmittance and reflectance spectra of the glass samples in
the wavelength range of 300–1200 nm.
The optical absorption coefficients (𝛼) are evaluated from
the optical transmittance (𝑇), reflectance (𝑅), and thickness
“𝑡” of the samples using the relation
𝛼 (]) =
1
(1 − 𝑅)
ln [
],
𝑡
𝑇
(2)
800
Wavelength (nm)
1000
1200
Figure 3: Optical absorption spectra of Cu2+ ions of glass samples.
0.9
0.35
0.8
MBBC-0
0.30
MBBC-5
0.25
0.7
Transmission (%)
in the literature for other barium borate glasses [10, 11]. In
general, it was observed that the density and molar volume
show quite opposite behavior to each other in many glass
systems. However, in the present glass system both density
and molar volume have shown decrease with increasing MgO
content in the glass network. This kind of behavior was
also observed in other alkali borate and bismuthate glasses
[12–15]. This might be due to the action of both MgO and
BaO as network modifiers causing the metaborate network
to further degrade and form (chain terminating) pyroborate
units. In this process there must be a decrease in number of
nonbridging oxygen atoms and thus led to decrease in the
molar volume. On the contrary, an increase in molar volume
would have been possible only if MgO and BaO play a role
of network formers. Thus, variation of molar volume in the
present investigation suggests that the MgO and BaO are
acting as network modifiers rather than network formers [16].
The observed mixed alkaline effect both in case of density
and molar volume of present glasses is negative. The decrease
in molar volume can be attributed to tighter binding of oxygen to magnesium as it has larger field strength and smaller
size when compared to barium. According to Kjeldsen et al.
a smaller molar volume does not mean a denser structure.
Therefore, the structure becomes loose which in turn gives
rise to a decrease in the refractive index as observed in the
present glass system [8].
600
0.6
0.5
MBBC-0
0.4
0.20
0.3
MBBC-5
0.2
0.1
Reflectance (%)
0
1.0
Absorbance
42
Molar volume (cm3 /mol)
Density (g/cm3 )
ISRN Ceramics
0.15
0.10
0.0
400
600
800
1000
1200
Wavelength (nm)
Figure 4: Transmittance and reflectance spectra of some glass
samples.
and the relation between 𝛼(]) and photon energy (ℎ]) of the
incident radiation is given by [17, 18]
𝛼 (𝜔) =
𝑟
const
(ℎ𝜔 − 𝐸opt ) ,
ℎ𝜔
(3)
where 𝐸opt is the optical energy band gap and “𝑟” is the index
which determines the type of electronic transitions causing
the absorption and takes the values 1/3, 1/2, 2, and 3 for direct
forbidden, direct allowed, and indirect allowed, indirect
forbidden transitions. By plotting (𝛼ℎ])1/r as a function of
photon energy h] (i.e., Tauc’s plot), one can find optical
energy band gap (𝐸opt ). The values of optical band gap energy
(𝐸opt ) can be obtained by extrapolating the linear portion of
Tauc’s plots to intersect the 𝑥-axis at (𝛼ℎ])1/r = 0. Figure 5
shows Tauc’s plots between (𝛼ℎ])1/2 and ℎ]. The optical band
gap energy thus evaluated for the glass samples for different
values of 𝑟 is listed in the Table 2. It is observed that the
measured absorption data best fits to (3) for 𝑟 = 2 which
corresponds to indirect allowed transitions.
4
ISRN Ceramics
Table 2: Oxygen packing density (OPD), refractive index (𝑛), molar electronic polarizability (𝛼𝑚 ), oxide ion polarizability (𝛼o 2− ), Urbach
energy (ΔE), energy gap (Eopt ), theoretical basicity (Λ th ), experimental basisity (Λ exp ), and theoretical interaction parameter (Ath ) of the glass
samples.
Glass code
MBBC-0
MBBC-1
MBBC-2
MBBC-3
MBBC-4
MBBC-5
OPD (g⋅atm/L)
𝑛
𝛼𝑚 (×10−24 )
𝛼o 2−
ΔE (eV)
57
60
60
61
62
62
2.450
2.449
2.446
2.443
2.437
2.419
10.32
9.78
9.72
9.57
9.40
9.36
2.81
2.67
2.66
2.62
2.57
2.48
0.59
0.74
0.37
0.46
0.44
0.61
asf
𝐸opt
(eV)
2.808
2.814
2.824
2.833
2.852
2.916
𝑟=2
2.849
2.846
2.853
2.856
2.844
2.918
Eopt (eV)
𝑟 = 1/2 𝑟 = 2/3
3.137
2.942
3.060
2.938
3.390
3.195
3.180
2.999
3.120
2.933
3.190
2.946
Λ th
Λ exp
Ath
0.66
0.64
0.62
0.61
0.59
0.58
1.075
1.044
1.042
1.032
1.020
0.996
0.169
0.177
0.181
0.184
0.188
0.192
0.040
0.035
1/2
0.030
3
(a𝜆−1 )
(𝛼h)1/2 (eV/cm)1/2
4
MBBC-0
MBBC-3
2
0.020
0.015
MBBC-5
2.5
MBBC-3
0.025
MBBC-5
0.010
3.0
3.5
0.0020
h (eV)
0.0025
𝜆−1 (nm−1 )
Figure 5: Tauc’s plot (𝛼ℎ])1/2 versus (ℎ]) for some glass samples.
Figure 6: (𝑎𝜆)1/𝑟 versus (1/𝜆) (ASF) plots of some glass samples.
Optical band gap energy cannot be determined accurately
by alone using absorbance measurements. Escobar-Alarcón
et al. [19] and Souri and Shomalian [20] proposed absorption
spectrum fitting (ASF) method to find optical band gap more
accurately. Accordingly (3) can be rewritten as a function of
wavelength as
can be obtained by extrapolating the linear region of (a/𝜆)1/r
versus (1/𝜆) curve at (a/𝜆)1/r = 0. The best fit is observed for
𝑟 = 2. This value of band gap, designated as (𝐸asf
opt ) in eV, is
calculated from the parameter 𝜆 𝑔 using the expression
𝑎 (𝜆) = const(ℎ𝑐)𝑟−1 𝜆(
𝑟
1
1
),
−
𝜆 𝜆𝑔
(4)
where 𝜆 𝑔 , ℎ, and 𝑐 are wavelengths corresponding to the optical gap, Plank’s constant, and speed of the light, respectively.
Incorporating Beer-Lambert’s law into the above equation,
the absorbance a(𝜆) can be expressed as
𝑎 (𝜆) = 𝐾1 𝜆 (
1
1
−
) + 𝐾2 ,
𝜆 𝜆𝑔
(5)
where 𝐾1 = [const(ℎ𝑐)𝑟−1 𝑡/2.303] and 𝐾2 is a constant which
takes into account the reflection of the incident light lost,
assuming that the amount of fraction reflected or dispersed
light is small. Using (5) optical band gap can be calculated
from the absorbance spectrum fitting method without the
need of thickness of the glass sample. The value of band gap
asf
(𝐸opt
)=
1239.83
.
𝜆𝑔
(6)
The variation of (a/𝜆)1/r versus (1/𝜆) is shown in Figure 6. The
values of optical band gaps (𝐸asf
opt ) of the present glass samples
calculated using ASF method are reported in Table 2. It is
observed that the values of optical band gap energies calculated from transmittance and reflectance spectra (𝐸opt ) match
the values of optical band gap energies (𝐸asf
opt ) calculated from
ASF method.
For lower photon energies (ℎ𝜔) lying between 102 and
4
10 cm−1 , absorption coefficient 𝛼(𝜔) follows Urbach law
given as
𝛼 (𝜔) = (const) × e(ℎ𝜔/Δ𝐸) ,
(7)
ISRN Ceramics
5
evaluated from the optical band gap values (𝐸asf
opt ) using the
relation proposed by Dimitrov and Sakka [25]
3.00
2.95
(𝑛2 − 1)
(𝑛2 + 2)
asf
Eopt
(eV)
2.90
=1−√
asf
𝐸opt
20
.
(9)
The refractive index values calculated from (9) are given
in Table 2. The refractive index values quoted correspond
to the respective 𝜆 𝑔 values of the present glass samples.
However, there are chances of creeping small errors in the
refractive index “𝑛” values owing to extrapolation (𝑎𝜆−1 )1/2
versus (𝜆−1 ) plots in estimating (𝐸asf
opt ). One of the parameters
related to the structure of the glass called molar refraction 𝑅𝑚
(in cm3 ) is given by the Lorentz-Lorentz equation as
2.85
2.80
2.75
0
2
4
6
8
10
12
14
16
xMgO (mole%)
𝑅𝑚 =
Figure 7: Variation of (𝐸asf
opt ) with MgO content in glass system.
where Δ𝐸 is the Urbach energy and is interpreted as the width
of the tail of the localized energy states in the band gap. The
above relation can be expressed as
ln 𝛼 (𝜔) = (
ℎ𝜔
) − const.
Δ𝐸
3.3. Refractive Index, Electronic Polarizability, and Molar
Refraction. The refractive indices (n) of the samples are
(𝑛2 + 2)
𝑉𝑚 ,
(10)
where “𝑛” is the refractive index, 𝑉𝑚 is molar volume and the
term (𝑛2 −1)/(𝑛2 +2) represents the reflection loss. According
to Clausios-Mossotti, the molar electronic polarizability 𝛼𝑚 is
given by the relation
𝛼𝑚 = (
(8)
The plots of natural logarithm of absorption coefficients ln(𝛼)
versus photon energy (ℎ𝜔) are called Urbach plots. The values
of Urbach energy (Δ𝐸) were estimated from the reciprocals
of slopes of linear regions of Urbach plots. Urbach energy
(Δ𝐸) values of the present glass samples are given in Table 2.
There is an increase in the band gap values with increasing
MgO content. The values of optical band gaps of present
glasses are in good agreement with other glass systems found
in the literature [21, 22]. The variation of optical band gap
with MgO content in the glass system is shown in Figure 7.
The Urbach energy values of the present glasses varied from
0.37 to 0.74 eV in a nonlinear manner with increasing MgO
content in the glass.
The increase in optical band gap in the present glass
system indicates decease in nonbridging oxygen content
since the bridging oxygen (BOs) atoms are less excited than
NBOs. Hence, with increase in MgO content in the glass,
the number of nonbridging oxygen ions decreased [21]. The
increment in optical band values means that there are less
tails in the localized states. The variation in optical bands with
the increasing MgO in the glass matrix is small and therefore
rigorous structural changes might have not occurred in the
glass network.
According to Urbach’s rule, optical absorption coefficient
near the absorption edge is an exponential function of photon
energy. The Urbach energies are attributed to phonon assisted
indirect electronic transitions. The nonlinear increase of 𝐸opt
and Urbach energy (Δ𝐸) with MgO can be attributed to
mixed alkaline effect [23, 24].
(𝑛2 − 1)
3
) 𝑅𝑚 ,
4𝜋𝑁A
(11)
where 𝑁A is Avogadro’s number. Dimitrov and Sakka [25] had
derived the relationship between 𝛼o 2− and (𝐸asf
opt ) using the
relationship proposed by Duffy et al. [26]. This relationship
has been modified by Banu et al. [27] and is given by
asf
𝛼o 2− ((𝐸opt
))
𝑉
= [( 𝑀 ) (1 −
2.52
[
1/2
asf
))
((𝐸opt
1.23
− 0.98
) − ∑𝑃𝛼𝑖 ] 𝑞−1 ,
𝑖
]
(12)
where 𝛼𝑖 is molar cation polarizability and 𝑞 is the number
of oxide ions in the chemical formula. For one of the glass
samples, namely, 10MgO-20BaO-69B2 O3 -1CuO, the value of
𝛼𝑖 is calculated as [0.1𝛼Mg + 0.2𝛼Ba + (0.69)2𝛼B + 0.01𝛼Cu ].
The molar cation polarizabilty values of Mg2+ , Ba2+ , B3+ , and
Cu2+ ions 𝛼Mg = 0.094 Å3 , 𝛼Ba = 1.55 Å3 , 𝛼B = 0.003 Å3 , 𝛼Cu
= 0.437 Å3 are, respectively, taken from Dimitrov and Sakka
[25]. Here 𝛼o 2− (𝐸asf
opt ) represents the electronic polarizability
of oxide ion calculated using optical band gap values. Average
oxide ion polarizability (𝛼o 2− ) values B2 O3 = 1.345 Å3 , MgO =
1.678 Å3 , BaO = 3.741 Å3 , and CuO = 2.90 Å3 are taken from
the literature [25]. The cation polarizability values of Mg2+ ,
Ba2+ , B3+ , and cu2+ are moderately high. Hence, the present
glass samples have shown high electronic polarizability 𝛼o 2−
as expected. The values of molar refraction (𝑅𝑚 ), molar
polarizabilty (𝛼𝑚 ), and electronic polarizability of oxide ions
𝛼o 2− are given in Table 1. The values 𝑅𝑚 , 𝛼𝑚 , and 𝛼o 2− have
shown decreasing trend with increasing MgO content in the
glass.
6
ISRN Ceramics
3.4. Optical Basicity and Interaction Parameter. Theoretical
optical basicity (Λ th ) of a glass is related to the electron
density carried by oxygen. Oxides with less electron donor
abilities are termed as acids and those with high electron
donor abilities are called bases. The theoretical optical basicity (Λ th ) values are determined by using the relation
Λ th = 𝑋MgO Λ MgO + 𝑋BaO Λ BaO + 𝑋B2 O3 Λ B2 O3
+ 𝑋CuO Λ CuO ,
(13)
where 𝑋MgO , XBaO , 𝑋B2 O3 , and 𝑋CuO are the equivalent
fractions of the different oxides, that is, the proportion of
oxide atoms that they contribute to the stoichiometry of the
glass. The values of optical basicity for individual oxides are
taken from Dimitrov and Komatsu [28] where Λ MgO = 0.67,
Λ BaO = 1.23, Λ B2 O3 = 0.42, and Λ CuO = 1.11 are used in the
calculations. The theoretical basicity values of present glass
system are given in Table 2. For oxide glasses, Duffy [29]
proposed the following relationship between the oxide ion
polarizability (𝛼o 2− ) and optical basicity:
asf
Λ (𝐸opt
) = 1.67 [1 − (
1
𝛼o
2−
)] .
(14)
The optical basicity values calculated using (13) and (14) using
𝛼o 2− (𝐸asf
opt ) are designated as Λ asf and are given in Table 2. The
values of Λ asf are higher than those of Λ th .
The polarizability state of an average oxide ion is
described by the interaction parameter (𝐴 th ) as proposed by
Yamashita and Kurosawa [30]. The interaction parameter is a
quantitative measure of interionic interaction of negative ions
such as F− and O2− with the nearest neighbors. It represents
the charge overlapping of the negative ions with its nearest
×103
1
First derivative of absorption (a.u.)
The decrease in refractive index is a result of increase in
optical band gap values. At the same time, molar refraction
decreased with decrease in refractive index, which in turn
decreased both oxide ion polarizability and electronic polarizability. The decreasing values of density and molar volume
correspond to loosening of glass network and as a result
the refractive index of present glass system has exhibited a
decrease in refractive indices. This decrease is also due to
decrease in the concentration of BaO which has higher cation
polarizability and average oxide polarizability than MgO in
the glass composition.
The slight decrement in refractive indices can be
attributed to the replacement of alkaline earth oxide of
decreasing mass (MgO → BaO). The observed variation in
refractive index (𝑛) values is small indicating less significant
structural changes in the basic glass network with the replacement of alkaline earth oxides.
The prediction of glasses as metallic or insulator is based
on metallization criterion 𝑀 = 1 − 𝑅𝑚 /𝑉𝑚 . If 𝑅𝑚 /𝑉𝑚 > 1
and the material exhibits metallic nature and if 𝑅𝑚 /𝑉𝑚 < 1,
the material is treated as insulating nature. The metallization
parameter of the present glass system is given in Table 2. From
these values, it is concluded that the present glasses have
insulating behavior.
MBBC-5
MBBC-4
MBBC-3
0
−1
−2
MBBC-2
MBBC-1
MBBC-0
−3
−4
−5
−6
−7
−8
225
250
275
300
Magnetic field (mT)
325
350
Figure 8: EPR spectra of Cu2+ ions.
positive neighbors. The theoretical interaction parameter 𝐴 th
is calculated using the following equation
𝐴 th = 𝑋MgO 𝐴 MgO + 𝑋BaO 𝐴 BaO + 𝑋B2 O3 𝐴 B2 O3
+ 𝑋CuO 𝐴 CuO .
(15)
The interaction parameter (𝐴 th ) values are presented in
Table 2 for the present glasses. It is observed from Table 2
that the values of optical basicity, oxide ion polarizability
of the present glass samples decreased, whereas interaction
parameter is increased with increasing MgO content.
It is understood that lower the oxide ion polarizability
value more is the interaction parameter value. The oxide
ion polarizability depends on molar volume. Hence, the
decrement in 𝛼o 2− is due to decrease in molar volume. As a
result, there is a decrement in optical basicity and an increase
in the interaction parameter.
The higher values of molar polarizability (𝛼𝑚 ) and electronic polarizability of oxide ions (𝛼o 2− ) observed in these
glass systems can be attributed to the presence of Ba2+ ions.
The decline in both the parameter values could be attributed
to decrease in BaO content which in turn decreases Ba2+ ions
in the glass. The higher values of optical basicity (Λ) are most
probably due to formation of higher valence states by Ba2+
ions.
3.5. EPR Spectra of Cu2+ Ions. The EPR spectra of Cu2+ in
𝑥MgO-(30 − 𝑥)BaO-69B2 O3 -1CuO (where 𝑥 = 0, 5, 7.5, 10,
12.5, and 15 mol%) are shown in Figure 8. The Cu2+ ion, with
effective spin S = 1/2, has a nuclear spin 𝐼 = 3/2 for both
63
Cu and 65 Cu. Hence, (2I + 1), that is, four parallel and four
perpendicular hyperfine (hf) components, are expected.
In the present work, three weak parallel components are
observed in the lower field region and the expected fourth
parallel component was overlapped with the perpendicular
components. The perpendicular components in the high field
region are not resolved. The EPR spectra of all the glass
samples containing Cu2+ ions are similar to those reported
ISRN Ceramics
7
Table 3: Spin-Hamiltonian parameters of Cu2+ ion in xMgO-(30−x)BaO-69B2 O3 -1CuO glass system.
Glass code
MBBC-0
MBBC-1
MBBC-2
MBBC-3
MBBC-4
MBBC-5
𝑔||
2.343
2.351
2.340
2.350
2.347
2.350
𝑔⊥
2.090
2.082
2.082
2.082
2.082
2.083
𝐴 || × 104 (cm−1 )
147
142
150
136
141
144
𝐴 ⊥ × 104 (cm−1 )
37
26
53
23
25
29
ΔE𝑥𝑦 (cm−1 )
13263
13184
13038
12970
12853
12853
𝑁 (×1020 kg−1 )
2.440
0.815
0.845
3.465
6.407
2.354
𝜆 𝑝 (nm)
754
759
767
771
778
778
Table 4: Optical absorption bands and bonding parameters of Cu2+ ions in the glass systems.
Glass code
MBBC-0
MBBC-1
MBBC-2
MBBC-3
MBBC-4
MBBC-5
𝛼2
0.829
0.820
0.831
0.804
0.814
0.825
𝛽2
0.927
0.937
0.925
0.956
0.944
0.931
𝛽12
0.821
0.847
0.798
0.846
0.821
0.816
ΔE𝑥𝑦,𝑦𝑧
14408
15958
15939
15939
15919
15800
for Cu2+ ions in other glass systems [31–33]. An axial spinHamiltonian is employed in the analysis of EPR spectra [34]
which is given as
𝜏𝜎 %
37
39
37
43
40
38
𝜒 (×10−5 m3 kg−1 )
0.790
0.263
0.272
1.190
2.067
0.760
𝜏𝜋 %
36
31
40
31
36
37
2.352
152
2.35
148
+𝐴 ‖ 𝐼𝑧 𝑆𝑧 + 𝐴 ⊥ (𝐼𝑋 𝑆𝑋 + 𝐼𝑌 𝑆𝑌 )] ,
(16)
where 𝑧 is the symmetry axis, 𝛽 the Bohr magneton, S and
𝐼 are the electron and nuclear spin operators, 𝐻𝑋 , 𝐻𝑌 , and
𝐻𝑍 the static magnetic field components, 𝑔‖ and 𝑔⊥ the
parallel and perpendicular components of “𝑔” tensor while
𝐴 ‖ and 𝐴 ⊥ are parallel and perpendicular components of the
hyperfine tensor 𝐴. Here nuclear quadruple contribution is
neglected [35]. The solution to the spin-Hamiltonian gives
the following expressions for the peak position related to the
principal values of 𝑔 and 𝐴 tensors [36], for the parallel and
perpendicular hyperfine peaks, respectively:
ℎ] = 𝑔‖ 𝛽𝐻 + 𝑚𝐴 ‖ + {
𝐴2⊥
15
− 𝑚2 }
,
4
2𝑔‖ 𝛽𝐻
𝐴2⊥ + 𝐴2‖
15
.
ℎ] = 𝑔⊥ 𝛽𝐻 + 𝑚𝐴 ⊥ + { − 𝑚2 }
4
2𝑔‖ 𝛽𝐻
(17)
Here 𝑚 is the nuclear magnetic quantum number of the
copper nucleus with the values +3/2, +1/2, –1/2 and –3/2,
and ] is the microwave frequency. The spin-Hamiltonian
parameters have been evaluated and are presented in Table 3.
It was observed that, 𝑔‖ > 𝑔⊥ > 𝑔𝑒 = 2.0023.
From the “𝑔” values and the shape of the EPR spectra, it
can be concluded that the ground state of Cu2+ ions is 𝑑𝑥2−𝑦2
orbital (2 B1𝑔 state) and Cu2+ ions are located in tetragonally
distorted octahedral sites [37]. The high “𝑔” values indicate
the presence of a CuO6 chromophore. It can be observed from
2.346
144
2.344
140
g‖
𝐻 = 𝛽 [𝑔‖ 𝐻𝑧 𝑆𝑧 + 𝑔⊥ (𝑆𝑋 𝐻𝑋 + 𝑆𝑌 𝐻𝑌 )
A‖
2.348
2.342
136
2.34
132
2.338
0
5
7
10
MgO (mole%)
12
15
g‖
A‖
Figure 9: Variation of 𝑔‖ and 𝐴 ‖ with MgO content.
Figure 9 that the variation of 𝑔‖ and 𝐴 ‖ is nonlinear with
MgO content. This may be due to change in the tetragonal
distortion. Variation in 𝑔 and 𝐴 values may be associated with
the change in the environment around Cu2+ ion, that is, the
ligand field strength at the site of Cu2+ .
The ratio of 𝑔‖ /𝐴 ‖ that represents the interaction of copper (Cu2+ ) ion with the oxygen ligands gives an estimation of
tetragonal distortion. For the present glass samples, the value
of 𝑔‖ /𝐴 ‖ ratio is around 164. However, this ratio has shown a
nonlinear variation because of presence of two alkaline earth
oxides with increasing and decreasing concentration in the
glasses.
3.6. Number of Spins Taking Part in Resonance. Using the
expression given by Weil et al. [38] the number of spins (𝑁)
8
ISRN Ceramics
1.0 MBBC-4
0.8
0.6
MBBC-5
8
2
6
1.5
4
1
2
0.5
N (×1020 kg−1 )
690
961
1398
1270
1.6 MBBC-0
MBBC-1
1.4
MBBC-2
1.2 MBBC-3
2.5
𝜒 (×10−5 m3 kg−1 )
Transmittance (%)
1.8
0
0
0
0.4
5
7
10
12
MgO (mole %)
15
𝜒
N
0.2
4000
3000
2000
1000
0
Figure 11: Variation of 𝑁 and 𝜒 with MgO mole%.
Wave number (cm−1 )
Figure 10: FTIR spectra of glass samples.
taking parting in the resonance is estimated by comparing the
area under the absorption curve of present glass samples with
that of CuSO4 : 5H2 O (as standard)
𝑁
2
=
2
𝐴 𝑥 (Scan𝑥 ) 𝐺std (𝐵𝑚 )std (𝑔std ) (𝑃std )
2
2
1/2
1/2
𝐴 std (Scanstd ) (𝑔𝑥 ) 𝐺𝑥 (𝐵𝑚 )𝑥 (𝑃𝑥 )
[𝑆 (𝑆+1)]std
[𝑆 (𝑆+1)]𝑥
[std] ,
(18)
where “𝐴” is the area under the absorption curve that was
obtained by double integrating the first derivative absorption
curve, “Scan” is the magnetic field corresponding to the unit
length of the chart, “𝐺” is the gain, 𝐵𝑚 is the modulation
filed width, “𝑔” is the 𝑔-factor, 𝑆 is the spin of the system
in its ground state, and 𝑃 is the microwave power applied.
Here the subscripts “std” and “𝑥”, respectively represent the
corresponding quantities of the samples and the standard.
The values of 𝑁 are presented in Table 3.
Interestingly, the number of spins taking part in the
resonance with decreasing MgO concentration in the glass
has shown inflections indicating a sort of mixed alkaline
effect. This variation is due to slight modification of boron
network by the alkaline oxides.
nonlinear variations were observed in mixed alkali borate
glasses [40].
3.8. Optical Absorption Spectra. The optical absorption spectra of all the glasses containing Cu2+ ions resulted in a
broad absorption band. The observed peak positions of
the optical absorption spectra of the glasses are listed in
Table 4. The observed broad band is assigned to the 2 B1𝑔 →
2
B2𝑔 transition of Cu2+ ions [32]. With increasing MgO
content, the absorption peak is found to shift towards longer
wavelength (754 nm to 778 nm).
The variation of peak position of the optical absorption
band with MgO content is shown in Figures 11 and 12.
The shift in absorption peak with increasing MgO content
towards longer wavelengths can be attributed to decrease in
ligand field strength around Cu2+ ion.
The optical absorption spectrum is influenced by the host
structure into which the TM ions are incorporated. In oxide
glasses, the TM ions mostly form coordination complexes
with doubly charged oxygen as the ligands. However Cu2+ ,
being as d9 ion, experiences a strong John-Teller distortion,
which leads to the splitting of energy levels [41] and causes
predominantly an elongated octahedral coordination with
four short in-plane bond lengths and longer axial bond
lengths. Accordingly three transitions, namely, 2 B1𝑔 → 2 A1𝑔 ,
2
3.7. Paramagnetic Susceptibility from EPR Data. The paramagnetic susceptibility (𝜒) values of the samples presented in
Table 4 are calculated using the following relation [39]:
𝜒=
𝑁𝑔2 𝛽2 𝐽 (𝐽 + 1)
,
3𝑘𝐵 𝑇
(19)
where 𝑁 is number of spins per Kg calculated using (18), 𝐽 is
the total angular momentum, 𝛽 is the Bohr magneton, 𝑘𝐵 is
the Boltzmann constant, 𝑇 is the absolute temperature (here
room temperature), and 𝑔 is the 𝑔-factor.
Figure 10 gives the variation of 𝑁 and 𝜒 with MgO mol%
in the glass samples. It is clear from the figure that both
the parameters have exhibited mixed alkaline effect. Such
B1𝑔 → 2 B2𝑔 , and 2 B1𝑔 → 2 E𝑔 , are expected. However,
only a single optical absorption maximum was observed in
most of the cases [42]. Most of the authors [43, 44] assigned
the observed optical peak to the 2 B1𝑔 → 2 B2𝑔 transition
(Δ𝐸𝑥𝑦 ) and used this value in the calculation of the bond
parameters. Therefore, in the present case also the optical
absorption band was assigned to 2 B1𝑔 → 2 B2𝑔 (Δ𝐸𝑥𝑦 )
transition.
The calculated values (Table 4) of 𝛼2 and 𝛽12 indicated inplane 𝜎-bonding as well as in-plane 𝜋-bonding as moderately
ionic while out of plane 𝜋-bonding 𝛽2 as ionic. The cupric ion
is a network modifier along with MgO and BaO in the B2 O3
glass network. The competition between the glass former
cations and cupric ion in attracting neighboring alone pairs
ISRN Ceramics
9
where 𝑠 is the overlapping integer (𝑠oxy = 0.076). The
normalized covalency of the Cu2+ –O of in-plane bonding of
𝜋 symmetry (𝜏𝜋 ) indicates the basicity of the oxide ion. The
calculated values of 𝜏𝜎 and 𝜏𝜋 are presented in Table 4.
780
775
𝜆p (nm)
770
765
760
755
750
0
2
4
6
8
10
12
14
16
xMgO (mole%)
Figure 12: Variation of peak position of the optical absorption band
with MgO content.
of intervening oxygen ions can be known from 𝛽12 . The value
of 𝛽12 strongly depends on network former.
3.9. Cu2+ Ligand Bond Nature. The EPR and optical absorption spectra data can be correlated to evaluate the bonding
coefficients of Cu2+ [43, 44]. The bonding parameters are
evaluated using the following [43]:
𝛼2 = [− (
𝐴‖
3
) + (𝑔‖ − 2) + ( ) (𝑔⊥ − 2) + 0.04] ,
𝑃
7
𝛽2 = [(
Δ𝐸𝑥𝑦,𝑦𝑧
𝑔⊥
− 1)] [
],
𝑔𝑒
828𝛼2
𝛽12 = [(
(20)
Δ𝐸𝑥𝑦
𝑔‖
− 1)] [
],
𝑔𝑒
3312𝛼2
where 𝑃 is the dipolar hyperfine coupling parameter
(= 0.036 cm−1 ), Δ𝐸𝑥𝑦 , Δ𝐸𝑥𝑧,𝑦𝑧 are the heights of 𝑑𝑥𝑦 , and
𝑑𝑥𝑧,𝑦𝑧 molecular orbital levels above the ground state 𝑑𝑥2−𝑦2 ,
respectively. Here, 𝛼2 describes the in-plane 𝜎-bonding with
copper 𝑑𝑥2−𝑦2 orbital, 𝛽2 describes the out-of-plane 𝜋bonding with the 𝑑𝑥𝑧 and 𝑑𝑦𝑧 orbital, and 𝛽12 is a measure of
in-plane 𝜋-bonding with 𝑑𝑥𝑦 orbital. The positions of optical
peak indicate the value of Δ𝐸𝑥𝑦 . The corresponding value of
Δ𝐸𝑥𝑧,𝑦𝑧 was calculated using the approximate relation [32]
Δ𝐸𝑥𝑦,𝑦𝑧 =
1257.12
.
𝑔𝑒 − 𝑔⊥
(21)
The normalized covalency of Cu2+ –O in-plane bonding 𝜎 and
𝜋 symmetries (resp., 𝜏𝜎 and 𝜏𝜋 ) can be expressed in terms of
bonding coefficients 𝛼2 and 𝛽2 as follows:
𝜏𝜎 =
200 (1 − 𝑠) (1 − 𝛼2 )
(1 − 2𝑠)
𝜏𝜋 = 200 (1 −
𝛽12 ) %,
%,
(22)
3.10. FTIR Spectra. The FTIR absorption spectra of all the
glass samples are illustrated in Figure 10. The overall spectrum consists of distinctive absorption bands centered in
the mid-region extending from 500 to 1500 cm−1 . The IR
spectrum shows a sharp band around 690 cm−1 , followed by
a broad absorption band around 961 cm−1 , a prominent kink
around 1270 cm−1 and followed by a broad absorption band
around 1398 cm−1 are observed.
The broad band at ∼1398 cm−1 can be attributed to B–O−
stretching vibrations of BO3 units that exist in the form of
various groups such as meta, pyro and ortho borates [45]. The
broadening of this peak indicates formation of pyroborates
at the expense of metaborates which in turn caused decrease
in NBOs. This behaviour was confirmed from the decrease
in density and molar volume values. The prominent kink
appearing at 1270 cm−1 has been attributed to the formation
of metaborate chains. The broad band ∼961 cm−1 may be
due to combination of stretching vibrations of B–O bonds
in tetrahedral BO4 units such as tri-, tetra-, and pentaborate
groups. The sharp absorption band ∼690 cm−1 indicates B–
O–B bending vibrations of borate network [45] and the
vibration of bridged oxygen, which connects the two trigonal
boron atoms [46].
The observed nonlinear variation in the properties such
as density, molar volume, refractive index, is attributed to
changes in the coordination state of boron due to the change
in modifier oxide content variation in the structural units
BO3 triangles, BO4 tetrahedra, nonbridging oxygen atoms,
and other structural groupings present in the glass network.
4. Conclusions
The double alkaline borate glasses, MgO-BaO-B2 O3 -CuO,
interestingly have shown similar decreasing trend in both
density and molar volume. A good correlation was observed
between the optical energy gaps calculated using absorption
spectrum fitting (asf) method for 𝑟 = 2 and from the
transmittance and reflection spectra.
The bond parameter 𝛼2 and 𝛽12 values of the spin
probe Cu2+ indicated in-plane 𝜎-bonding as well as inplane 𝜋-bonding as moderately ionic and out-of-plane 𝜋bonding (𝛽2 ) as mostly ionic. The observed variations in
spin-Hamiltonian parameters (𝑔‖ and 𝐴 ‖ ), number of spins
(𝑁), susceptibility (𝜒) have shown inflections with composition indicating a sort of mixed alkaline effect. Since the
variations are small, no significant structural changes might
have occurred in the glass network with the increasing MgO
content.
As the glass modifier with large ion size is decreased
(BaO content) in the glass network, 3D layer type BO4 units
decreased and 2D layer type BO3 units increased and as
a result number of NBOs lessened. In the present glasses,
10
it is concluded that both MgO and BaO acted as glass
network modifiers. The decrease in number of nonbridging
oxygen (NBOs) atoms in the glass was evident from the
broadening of infrared band around 1398 cm−1 which is in
turn manifested by the decrease in density, molar volume, and
decrease in refractive index values.
Acknowledgment
The authors would like to thank Head of Department of
Physics, Osmania University, for providing experimental
facilities.
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