# Physical, Optical, and Spectroscopic Studies on MgO-BaO-B2O3 Glasses

Authors: Samdani; Md. Shareefuddin; G. Ramadevudu; S. Laxmi Srinivasa Rao; M. Narasimha Chary
Journal: ISRN Ceramics
 (2013)

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## Abstract

The mixed alkaline effect in double alkaline borate glasses                        MgO-BaO-B2O3 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).


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## Body

## 1. Introduction

Binary alkali and alkaline borate glasses R2O-B2O3 (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 Na2O 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 B2O3-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-69B2O3-1CuO mixed alkaline glass systems.


## 2. Materials and Method

Mixed alkaline earth borate glassesxMgO-(30-x)BaO-69B2O3-1CuO 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 (H3BO3-99% 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.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
Composition in (mol %)
M (g/mole)
ρ
cal (g/cc) ± 0.001
ρ
th (g/cc) ± 0.001
V
M (cc/mol) ± 0.01
R
M
M
c
MgO
BaO
B2O3
CuO
MBBC-0
0.0
30.0
69
1
145.32
3.49
3.45
41.63
26.03
0.6252
MBBC-1
5.0
25.0
69
1
137.47
3.48
3.30
39.45
24.65
0.6248
MBBC-2
7.5
22.5
69
1
133.54
3.40
3.23
39.26
24.50
0.6240
MBBC-3
10.0
20.0
69
1
129.62
3.35
3.16
38.69
24.12
0.6234
MBBC-4
12.5
17.5
69
1
125.69
3.29
3.08
38.20
23.71
0.6206
MBBC-5
15.0
15.0
69
1
121.76
3.19
3.00
38.11
23.61
0.6195XRD 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 × 10−4cm−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.


## 3. Results and Discussion

### 3.1. XRD, Density, and Molar Volume

The X-ray diffraction spectra (Figure1) 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
(1)VM=MTρ,
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.Figure 1
X-ray diffractograms of the glass samples at room temperature.Figure 2
Variation of density and molar volume as a function of MgO content.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 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].


### 3.2. Optical Band Gap and Urbach Energy

The optical absorption spectra (Figure3) 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.Figure 3
Optical absorption spectra of Cu2+ ions of glass samples.Figure 4
Transmittance and reflectance spectra of some glass samples.The optical absorption coefficients (α) are evaluated from the optical transmittance (T), reflectance (R), and thickness “t” of the samples using the relation
(2)α(ν)=1tln[(1-R)T],
and the relation between α(ν) and photon energy (hν) of the incident radiation is given by [17, 18]
(3)α(ω)=constℏω(ℏω-Eopt)r,
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 (αhν)1/r as a function of photon energy hν (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 (αhν)1/r=0. Figure 5 shows Tauc’s plots between (αhν)1/2 and hν. 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.Table 2
Oxygen packing density (OPD), refractive index (n), molar electronic polarizability (αm), oxide ion polarizability (αo2-), Urbach energy (ΔE), energy gap (Eopt), theoretical basicity (Λth), experimental basisity (Λexp), and theoretical interaction parameter (Ath) of the glass samples.
Glass code
OPD (g·atm/L)
n
α
m (×10−24)
α
o
2
-
ΔE (eV)
E
opt
asf
E
opt(eV)
Λ
th
Λ
exp
A
th
(eV)
r = 2
r = 1/2
r = 2/3
MBBC-0
57
2.450
10.32
2.81
0.59
2.808
2.849
3.137
2.942
0.66
1.075
0.169
MBBC-1
60
2.449
9.78
2.67
0.74
2.814
2.846
3.060
2.938
0.64
1.044
0.177
MBBC-2
60
2.446
9.72
2.66
0.37
2.824
2.853
3.390
3.195
0.62
1.042
0.181
MBBC-3
61
2.443
9.57
2.62
0.46
2.833
2.856
3.180
2.999
0.61
1.032
0.184
MBBC-4
62
2.437
9.40
2.57
0.44
2.852
2.844
3.120
2.933
0.59
1.020
0.188
MBBC-5
62
2.419
9.36
2.48
0.61
2.916
2.918
3.190
2.946
0.58
0.996
0.192Figure 5
Tauc’s plot (αhν)1/2 versus (hν) for 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
(4)a(λ)=const(hc)r-1λ(1λ-1λg)r,
where λg, 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
(5)a(λ)=K1λ(1λ-1λg)+K2,
where K1=[const(hc)r-1t/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 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 (Eoptasf) in eV, is calculated from the parameter λg using the expression
(6)(Eoptasf)=1239.83λg.
The variation of (a/λ)1/r versus (1/λ) is shown in Figure 6. The values of optical band gaps (Eoptasf) 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 (Eoptasf) calculated from ASF method.Figure 6
(
a
λ
)
1
/
r versus (1/λ) (ASF) plots of some glass samples.For lower photon energies(ℏω) lying between 102 and 104 cm−1, absorption coefficient α(ω) follows Urbach law given as
(7)α(ω)=(const)×e(ℏω/ΔE),
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
(8)lnα(ω)=(ℏωΔE)-const.
The plots of natural logarithm of absorption coefficients ln(α) versus photon energy (ℏω) 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.Figure 7
Variation of(Eoptasf)  with MgO content in glass system.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 ofEopt and Urbach energy (ΔE) with MgO can be attributed to mixed alkaline effect [23, 24].


### 3.3. Refractive Index, Electronic Polarizability, and Molar Refraction

The refractive indices (n) of the samples are evaluated from the optical band gap values (Eoptasf) using the relation proposed by Dimitrov and Sakka [25]
(9)(n2-1)(n2+2)=1-Eoptasf20.The refractive index values calculated from (9) are given in Table 2. The refractive index values quoted correspond to the respective λg 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 (Eoptasf). 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
(10)Rm=(n2-1)(n2+2)Vm,
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
(11)αm=(34πNA)Rm,
where NA is Avogadro’s number. Dimitrov and Sakka [25] had derived the relationship between αo2- and (Eoptasf) using the relationship proposed by Duffy et al. [26]. This relationship has been modified by Banu et al. [27] and is given by
(12)αo2-((Eoptasf))=[(VM2.52)(1-((Eoptasf))1/2-0.981.23)-∑iPαi]q-1,
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-69B2O3-1CuO, 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 αo2-(Eoptasf) represents the electronic polarizability of oxide ion calculated using optical band gap values. Average oxide ion polarizability (αo2-) values B2O3 = 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 αo2- as expected. The values of molar refraction (Rm), molar polarizabilty (αm), and electronic polarizability of oxide ions αo2- are given in Table 1. The values Rm, αm, and αo2- have shown decreasing trend with increasing MgO content in the glass.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 criterionM=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.


### 3.4. Optical Basicity and Interaction Parameter

Theoretical optical basicity (Λth) 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 (Λth) values are determined by using the relation
(13)Λth=XMgOΛMgO+XBaOΛBaO+XB2O3ΛB2O3+XCuOΛCuO,
where XMgO, XBaO, XB2O3, 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 ΛMgO = 0.67, ΛBaO = 1.23, ΛB2O3 = 0.42, and ΛCuO = 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 (αo2-) and optical basicity:
(14)Λ(Eoptasf)=1.67[1-(1αo2-)].
The optical basicity values calculated using (13) and (14) using αo2-(Eoptasf) are designated as Λasf and are given in Table 2. The values of Λasf are higher than those of Λth.The polarizability state of an average oxide ion is described by the interaction parameter (Ath) 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 positive neighbors. The theoretical interaction parameter Ath is calculated using the following equation
(15)Ath=XMgOAMgO+XBaOABaO+XB2O3AB2O3+XCuOACuO.
The interaction parameter (Ath) 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 inαo2- 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 (αo2-) 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-69B2O3-1CuO (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 63Cu and 65Cu. Hence, (2I + 1), that is, four parallel and four perpendicular hyperfine (hf) components, are expected.Figure 8
EPR spectra of Cu2+ ions.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 for Cu2+ ions in other glass systems [31–33]. An axial spin-Hamiltonian is employed in the analysis of EPR spectra [34] which is given as
(16)H=β[g∥HzSz+g⊥(SXHX+SYHY)+A∥IzSz+A⊥(IXSX+IYSY)],
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:
(17)hν=g∥βH+mA∥+{154-m2}A⊥22g∥βH,hν=g⊥βH+mA⊥+{154-m2}A⊥2+A∥22g∥βH.
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 ν 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.Table 3
Spin-Hamiltonian parameters of Cu2+ ion in xMgO-(30−x)BaO-69B2O3-1CuO glass system.
Glass code
g
∣
∣
g
⊥
A
∣
∣  ×  104 (cm−1)
A
⊥  ×  104 (cm−1)
Δ
E
x
y(cm−1)
λ
p (nm)
N (×1020 kg−1)
MBBC-0
2.343
2.090
147
37
13263
754
2.440
MBBC-1
2.351
2.082
142
26
13184
759
0.815
MBBC-2
2.340
2.082
150
53
13038
767
0.845
MBBC-3
2.350
2.082
136
23
12970
771
3.465
MBBC-4
2.347
2.082
141
25
12853
778
6.407
MBBC-5
2.350
2.083
144
29
12853
778
2.354From 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 (B21g 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 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+.Figure 9
Variation ofg∥ and A∥ with MgO content.The ratio ofg∥/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) taking parting in the resonance is estimated by comparing the area under the absorption curve of present glass samples with that of CuSO4 : 5H2O (as standard)
(18)N=Ax(Scanx)2Gstd(Bm)std(gstd)2(Pstd)1/2[S(S+1)]stdAstd(Scanstd)2(gx)2Gx(Bm)x(Px)1/2[S(S+1)]x[std],
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.


### 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]:
(19)χ=Ng2β2J(J+1)3kBT,
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.Table 4
Optical absorption bands and bonding parameters of Cu2+ ions in the glass systems.
Glass code
α
2
β
2
β
1
2
Δ
E
x
y
,
x
z
τ
σ%
τ
π%
χ (×10−5 m3 kg−1)
MBBC-0
0.829
0.927
0.821
14408
37
36
0.790
MBBC-1
0.820
0.937
0.847
15958
39
31
0.263
MBBC-2
0.831
0.925
0.798
15939
37
40
0.272
MBBC-3
0.804
0.956
0.846
15939
43
31
1.190
MBBC-4
0.814
0.944
0.821
15919
40
36
2.067
MBBC-5
0.825
0.931
0.816
15800
38
37
0.760Figure10 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 nonlinear variations were observed in mixed alkali borate glasses [40].Figure 10
FTIR spectra of glass samples.


### 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 B21g→B22g 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 Figures11 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.Figure 11
Variation ofN and χ with MgO mole%.Figure 12
Variation of peak position of the optical absorption band with MgO content.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, B21g→A21g,B21g→B22g,andB21g→E2g, 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 B21g→B22g 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 B21g→B22g (ΔExy) transition.The calculated values (Table4) of α2 and β12 indicated in-plane 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 B2O3 glass network. The competition between the glass former cations and cupric ion in attracting neighboring alone pairs 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]:
(20)α2=[-(A∥P)+(g∥-2)+(37)(g⊥-2)+0.04],β2=[(g⊥ge-1)][ΔExy,yz828α2],β12=[(g∥ge-1)][ΔExy3312α2],
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 π-bonding 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]
(21)ΔExy,yz=1257.12ge-g⊥.
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:
(22)τσ=200(1-s)(1-α2)(1-2s)%,τπ=200(1-β12)%,
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.


### 3.10. FTIR Spectra

The FTIR absorption spectra of all the glass samples are illustrated in Figure10. 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.


## 3.1. XRD, Density, and Molar Volume

The X-ray diffraction spectra (Figure1) 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
(1)VM=MTρ,
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.Figure 1
X-ray diffractograms of the glass samples at room temperature.Figure 2
Variation of density and molar volume as a function of MgO content.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 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].


## 3.2. Optical Band Gap and Urbach Energy

The optical absorption spectra (Figure3) 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.Figure 3
Optical absorption spectra of Cu2+ ions of glass samples.Figure 4
Transmittance and reflectance spectra of some glass samples.The optical absorption coefficients (α) are evaluated from the optical transmittance (T), reflectance (R), and thickness “t” of the samples using the relation
(2)α(ν)=1tln[(1-R)T],
and the relation between α(ν) and photon energy (hν) of the incident radiation is given by [17, 18]
(3)α(ω)=constℏω(ℏω-Eopt)r,
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 (αhν)1/r as a function of photon energy hν (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 (αhν)1/r=0. Figure 5 shows Tauc’s plots between (αhν)1/2 and hν. 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.Table 2
Oxygen packing density (OPD), refractive index (n), molar electronic polarizability (αm), oxide ion polarizability (αo2-), Urbach energy (ΔE), energy gap (Eopt), theoretical basicity (Λth), experimental basisity (Λexp), and theoretical interaction parameter (Ath) of the glass samples.
Glass code
OPD (g·atm/L)
n
α
m (×10−24)
α
o
2
-
ΔE (eV)
E
opt
asf
E
opt(eV)
Λ
th
Λ
exp
A
th
(eV)
r = 2
r = 1/2
r = 2/3
MBBC-0
57
2.450
10.32
2.81
0.59
2.808
2.849
3.137
2.942
0.66
1.075
0.169
MBBC-1
60
2.449
9.78
2.67
0.74
2.814
2.846
3.060
2.938
0.64
1.044
0.177
MBBC-2
60
2.446
9.72
2.66
0.37
2.824
2.853
3.390
3.195
0.62
1.042
0.181
MBBC-3
61
2.443
9.57
2.62
0.46
2.833
2.856
3.180
2.999
0.61
1.032
0.184
MBBC-4
62
2.437
9.40
2.57
0.44
2.852
2.844
3.120
2.933
0.59
1.020
0.188
MBBC-5
62
2.419
9.36
2.48
0.61
2.916
2.918
3.190
2.946
0.58
0.996
0.192Figure 5
Tauc’s plot (αhν)1/2 versus (hν) for 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
(4)a(λ)=const(hc)r-1λ(1λ-1λg)r,
where λg, 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
(5)a(λ)=K1λ(1λ-1λg)+K2,
where K1=[const(hc)r-1t/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 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 (Eoptasf) in eV, is calculated from the parameter λg using the expression
(6)(Eoptasf)=1239.83λg.
The variation of (a/λ)1/r versus (1/λ) is shown in Figure 6. The values of optical band gaps (Eoptasf) 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 (Eoptasf) calculated from ASF method.Figure 6
(
a
λ
)
1
/
r versus (1/λ) (ASF) plots of some glass samples.For lower photon energies(ℏω) lying between 102 and 104 cm−1, absorption coefficient α(ω) follows Urbach law given as
(7)α(ω)=(const)×e(ℏω/ΔE),
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
(8)lnα(ω)=(ℏωΔE)-const.
The plots of natural logarithm of absorption coefficients ln(α) versus photon energy (ℏω) 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.Figure 7
Variation of(Eoptasf)  with MgO content in glass system.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 ofEopt and Urbach energy (ΔE) with MgO can be attributed to mixed alkaline effect [23, 24].


## 3.3. Refractive Index, Electronic Polarizability, and Molar Refraction

The refractive indices (n) of the samples are evaluated from the optical band gap values (Eoptasf) using the relation proposed by Dimitrov and Sakka [25]
(9)(n2-1)(n2+2)=1-Eoptasf20.The refractive index values calculated from (9) are given in Table 2. The refractive index values quoted correspond to the respective λg 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 (Eoptasf). 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
(10)Rm=(n2-1)(n2+2)Vm,
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
(11)αm=(34πNA)Rm,
where NA is Avogadro’s number. Dimitrov and Sakka [25] had derived the relationship between αo2- and (Eoptasf) using the relationship proposed by Duffy et al. [26]. This relationship has been modified by Banu et al. [27] and is given by
(12)αo2-((Eoptasf))=[(VM2.52)(1-((Eoptasf))1/2-0.981.23)-∑iPαi]q-1,
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-69B2O3-1CuO, 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 αo2-(Eoptasf) represents the electronic polarizability of oxide ion calculated using optical band gap values. Average oxide ion polarizability (αo2-) values B2O3 = 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 αo2- as expected. The values of molar refraction (Rm), molar polarizabilty (αm), and electronic polarizability of oxide ions αo2- are given in Table 1. The values Rm, αm, and αo2- have shown decreasing trend with increasing MgO content in the glass.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 criterionM=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.


## 3.4. Optical Basicity and Interaction Parameter

Theoretical optical basicity (Λth) 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 (Λth) values are determined by using the relation
(13)Λth=XMgOΛMgO+XBaOΛBaO+XB2O3ΛB2O3+XCuOΛCuO,
where XMgO, XBaO, XB2O3, 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 ΛMgO = 0.67, ΛBaO = 1.23, ΛB2O3 = 0.42, and ΛCuO = 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 (αo2-) and optical basicity:
(14)Λ(Eoptasf)=1.67[1-(1αo2-)].
The optical basicity values calculated using (13) and (14) using αo2-(Eoptasf) are designated as Λasf and are given in Table 2. The values of Λasf are higher than those of Λth.The polarizability state of an average oxide ion is described by the interaction parameter (Ath) 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 positive neighbors. The theoretical interaction parameter Ath is calculated using the following equation
(15)Ath=XMgOAMgO+XBaOABaO+XB2O3AB2O3+XCuOACuO.
The interaction parameter (Ath) 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 inαo2- 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 (αo2-) 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-69B2O3-1CuO (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 63Cu and 65Cu. Hence, (2I + 1), that is, four parallel and four perpendicular hyperfine (hf) components, are expected.Figure 8
EPR spectra of Cu2+ ions.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 for Cu2+ ions in other glass systems [31–33]. An axial spin-Hamiltonian is employed in the analysis of EPR spectra [34] which is given as
(16)H=β[g∥HzSz+g⊥(SXHX+SYHY)+A∥IzSz+A⊥(IXSX+IYSY)],
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:
(17)hν=g∥βH+mA∥+{154-m2}A⊥22g∥βH,hν=g⊥βH+mA⊥+{154-m2}A⊥2+A∥22g∥βH.
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 ν 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.Table 3
Spin-Hamiltonian parameters of Cu2+ ion in xMgO-(30−x)BaO-69B2O3-1CuO glass system.
Glass code
g
∣
∣
g
⊥
A
∣
∣  ×  104 (cm−1)
A
⊥  ×  104 (cm−1)
Δ
E
x
y(cm−1)
λ
p (nm)
N (×1020 kg−1)
MBBC-0
2.343
2.090
147
37
13263
754
2.440
MBBC-1
2.351
2.082
142
26
13184
759
0.815
MBBC-2
2.340
2.082
150
53
13038
767
0.845
MBBC-3
2.350
2.082
136
23
12970
771
3.465
MBBC-4
2.347
2.082
141
25
12853
778
6.407
MBBC-5
2.350
2.083
144
29
12853
778
2.354From 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 (B21g 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 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+.Figure 9
Variation ofg∥ and A∥ with MgO content.The ratio ofg∥/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) taking parting in the resonance is estimated by comparing the area under the absorption curve of present glass samples with that of CuSO4 : 5H2O (as standard)
(18)N=Ax(Scanx)2Gstd(Bm)std(gstd)2(Pstd)1/2[S(S+1)]stdAstd(Scanstd)2(gx)2Gx(Bm)x(Px)1/2[S(S+1)]x[std],
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.


## 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]:
(19)χ=Ng2β2J(J+1)3kBT,
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.Table 4
Optical absorption bands and bonding parameters of Cu2+ ions in the glass systems.
Glass code
α
2
β
2
β
1
2
Δ
E
x
y
,
x
z
τ
σ%
τ
π%
χ (×10−5 m3 kg−1)
MBBC-0
0.829
0.927
0.821
14408
37
36
0.790
MBBC-1
0.820
0.937
0.847
15958
39
31
0.263
MBBC-2
0.831
0.925
0.798
15939
37
40
0.272
MBBC-3
0.804
0.956
0.846
15939
43
31
1.190
MBBC-4
0.814
0.944
0.821
15919
40
36
2.067
MBBC-5
0.825
0.931
0.816
15800
38
37
0.760Figure10 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 nonlinear variations were observed in mixed alkali borate glasses [40].Figure 10
FTIR spectra of glass samples.


## 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 B21g→B22g 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 Figures11 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.Figure 11
Variation ofN and χ with MgO mole%.Figure 12
Variation of peak position of the optical absorption band with MgO content.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, B21g→A21g,B21g→B22g,andB21g→E2g, 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 B21g→B22g 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 B21g→B22g (ΔExy) transition.The calculated values (Table4) of α2 and β12 indicated in-plane 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 B2O3 glass network. The competition between the glass former cations and cupric ion in attracting neighboring alone pairs 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]:
(20)α2=[-(A∥P)+(g∥-2)+(37)(g⊥-2)+0.04],β2=[(g⊥ge-1)][ΔExy,yz828α2],β12=[(g∥ge-1)][ΔExy3312α2],
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 π-bonding 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]
(21)ΔExy,yz=1257.12ge-g⊥.
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:
(22)τσ=200(1-s)(1-α2)(1-2s)%,τπ=200(1-β12)%,
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.


## 3.10. FTIR Spectra

The FTIR absorption spectra of all the glass samples are illustrated in Figure10. 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-B2O3-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 parameterα2 and β12 values of the spin probe Cu2+ indicated in-plane σ-bonding as well as in-plane π-bonding as moderately ionic and out-of-plane π-bonding (β2) as mostly ionic. The observed variations in spin-Hamiltonian parameters (g∥andA∥), 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, 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.



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*Source: 419183-2013-12-24.xml*