Recently oxide glasses receive a considerable attention in view of their potential for use as laser hosts, in fiber and as nonlinear optical materials (Fuxi, 1992; Wang et al., 1995; Vogel et al., 1991). The studies on glasses of metal oxides are relatively meager due to difficulties in identifying and preparing such glasses although they show interesting electronic and nonlinear optical properties, (Sae et al., 1993; Shelpy, 1988; Miyaji et al., 1996). The present research pertains to optical and electrical properties glass systems. Dimitrov and Sakka (1996) have shown that for simple oxides, the average electronic oxide polarizability calculated on the basis of two different properties. Furthermore, they correlated between the linear refractive index and optical band-gap energy. In the present study we examine whether their observations can be extended to glasses formed from simple oxides. This is of a particular interest especially when the relevant quantities can be experimentally obtained for glass systems and polarizability values related to glasses are of value for developing glass systems with nonlinear optical properties. To our knowledge an attempt of this kind is being reported for the first time. We chose to B2O3-Na2O -TiO2 glass system for our study, as the oxide ion polarizability for TiO2 is relatively high. In addition we report dielectric constant, the loss factor and the dc electrical conductivity of this suggested glass system.
MATERIALS AND METHODS
The glass samples were prepared using appropriate amounts of grade reagents boron oxide, sodium oxide and titanium oxide, the weighted quantities of the starting materials for glass batch corresponding to the glass composition were mixed homogeneously. The mixture was placed in a ceramic crucible and heated slowly in an electric furnace to 1100°C. The temperature was raised gradually depending upon the glass composition. The crucible containing the melt was constantly agitated to ensure homogeneous mixing. Sufficient time was allowed for the melt to become visibly homogeneous and bubble free. The melt was rapidly quenched to room temperature between two stainless-steel plates. There was no noticeable reaction of the melt with crucible walls. The typical weight loss on melting under the experimental conditions can be neglected with respect to the values quoted for the components. The composition of the glass system was prepared in a series of 4 samples as shown in Table 1.
The samples were annealed at a temperature below glass transition temperature
and subsequently polished with commercial media and water free lubricant. The
glass samples were obtained with good transparency and uniform thickness of
4.0 mm. The dc electrical conductivity of prepared glasses, the polished glass
samples were carbon painted on both sides and kept in a cell for good contacts.
The value of applied voltage = 3.0 V and the voltage drop across the sample
and across a standard resistor were measured. Space-charge effects were minimized
by using a very low field, which was applied only briefly. The temperature of
the glass sample was controlled and measured by a chromel-alumel thermocouple
with an accuracy of ±1%. It was observed that the conductivity behavior
was always the same and the values of conductivity were within ±2% error
in different runs.
|| Compositions, densities, molar volumes, refractive indices,
molar refraction, polarizability, Urbach energy and optical energy of the
The densities of the samples were measured by Archimedes
method using toluene as the immersion liquid. The refractive index was measured by using the prism spectrometer. The absorption
spectra were measured using Shimadzu (3031) spectrophotometer.
Also an LCR bridge (Hioki model 3031, Japan) was used to carry out the dielectric measurements. The samples were coated with Carbon coatings for obtaining good contact. The accuracy in the measurements of dielectric constant ε- is ~ ±0.001 and that in dielectric loss tan δ is ~10-4.
The optical band-gap and Urbach energies of the glasses were obtained from the absorption spectra. the absorption coefficient α(ω) is given by Dayanand et al. (1994).
Where d is the thickness of the glass sample in cm, T and A are the spectral
transmittance and absorbance measured by the spectrophotometer as shown in fig.
1, for one sample of the glass series, as an example, α(ω) is
related to EP, the optical band-gap is given by;
Thus (αhω)1/2 in cm-1/2ev1/2 units
is plotted against ηω. The Urbach energies ΔΕ were obtained
from the slopes of the linear region of the plots of ln α(ω) against
Another optical parameter used as a measure of acidity of glass called the theoretical optical basicity of glass is given by Duffy and Ingram (1975)
The absorbance with different wavelength (nm) of the glass
with composition 77.5B2O3- 20Na2O- 2.5
TiO2 the sample thickness (4 mm) as an example
Where zi is the valence of ith, cation, ri is the ratio of the number of ith cations to that of oxide ions, γi is the basicity moderating parameter given by;
Where χi is Pauling,s electro negativity of the ith atom. The molar refractivity is calculated using the following relationship (Fanderlik, 1983);
Where n is the refractive index and Vm is the molar volume of the glass. The molar volume calculated from the density and the average molecular weight of the composition.
RESULTS AND DISCUSSION
The range of the glass formation in B2O3 - Na2O - TiO2 system extends up to (TiO2 = 5 mol%) and all the glasses samples prepared are transparent. The compositions in mol %, density (ρ), average molecular weight (M), refractive index and molar refractivity for the glasses under study were determined.
|| The variation of the relative dielectric, ε\
with TiO2 mol%
||The variation of dielectric constant versus the frequency
for the prepared glasses
Table 1 reports the density (ρ), molar volume (Vm), average molecular weight (M), refractive index (n) and molar refractivity (Rm), optical basicity (Λ), oxide ion polarizability (α02), optical band gap (Eopt) and Urbach energy (ΔΕ) for B2O3-Na2O-TiO2 glasses.
The dielectric constant ε\, of glasses samples depends on electronic,
ionic and dipole orientation contribution to the polarizability. The ionic polarizability
arises from the displacement of ions of opposite sign from their regular lattice
sites, resulting from the applied electric field, as well as from the deformation
of the electronic shells, resulting from the relative of the ions. The behavior
of ε\ our system described in Fig. 2 may be
attributed at low frequency to the polarizability arising from the contribution
of multi components in the glassy system.
||The variation of tanδ with frequency versus the temperature
of prepared glasses
As the frequency increases the ionic and orientation sources of polarizability
decreases and finally disappear due to the inertia of the molecules and ions.
The electronic polarizability αe is the only process which follows
the alternative fields at the visible spectrum. The ionic polarizability αi,
contributes to the polarizability at high frequency. The space charge αs
and αo contribute to the polarizability of the suggested glass
system at low frequency ( ~ 1000 Hz ), hence the dielectric constant ε\
increases as αs and αo increases by increasing
the ratio of TiO2 in the glass system as shown in Fig.
The relative dielectric constant εr/ for our glass system lie between the two values 3.5 to 11 at ~105 Hz, as shown in Fig. 3.
The Fig. 4 shows the change of tan δ with the applied frequency in Hz. The frequency variation of tan δ often displays peaks whose positions depend on the glass composition. A typical spectrum of tan δ values may be as little as 0.002 in the low loss region compared to as much as 0.03 in the high loss region. According to Jayaseelan et al., (2004), loss split into four components; firstly, conduction loss due to the mobility of network modifiers. With the increase in applied field frequency, the ions are increasingly unable to respond to the field. Hence this component decreases with frequency as shown in Fig. 4.
Likewise, when the mobility increases with temperature, the conduction loss
component increases with temperature too. Secondly the relaxation losses that
occur because of the relaxation process. These losses can be observed in the
low frequencies. Thirdly the resonance losses occur when the applied frequency
is the same as the characteristics vibration frequency of the atoms.
||The variation of the relative dielectric constant, ε\,
of the prepared glasses versus the temperature
And finally, the deformation losses occur when the atomic structure begins
to vibrate. Accordingly, the dielectric loss at low and moderate frequency takes
relatively high values due to the contribution of both ion jump and conduction
loss in addition to the electronic polarizability. At high frequency the ion
vibrations is the main source of dielectric loss, Jayaseelan et al.,
Also the relative dielectric constant εr/ for our glass system increases with increasing temperature as shown in Fig. 5.
The ac conductivity σ is calculated at different temperatures using the following relationship;
Where, ε0, is the vacuum dielectric constant for different frequencies.
Figure 6 shows the plot of log σ against 1/T for the prepared glasses system (B2O3 - Na2O - TiO2). From these plots the activation energy for conduction in the high temperature region was obtained over which a near linear dependence of log σ with 1/T.
Also the dc conductivity can be determined from the measured values of Rp (real part) i.e., the parallel resistance (the equivalent circuit of the glass sample ) as follows;
Since Z* = Z/ - jZ// is the complex impedance of equivalent
circuit for the sample of the glass system, so the real part of conductivity
where Gp = 1/Rp called the conductance, d is the thickness
sample, A is the area of contact of the sample and the electrode holder, in
or work (A = 0.5 cm2). The electrical conductivity of glasses may
be related to temperature by the Arrhenius equation;
Where, σ is the electrical conductivity of the sample, σo
is the pre- exponential factor around 102 -103 for glass.
Ea is the activation energy and K is the Boltzmann constant. The
plots of log σ against reciprocal of temperature for different glass samples
are reproduced in Fig. 6 and show a linear behavior in the
temperature range under study. The activation energy Ea obtained
from the slope are given in Table 1. Sodium borate oxide doped
with titanium glass show a wide range of conductivity behavior were reported
by Shelby (1988), furthermore the glasses such as fluroborates show relatively
high conductivity attributed to ionic conduction of fluoride anions. The present
glass shows also the latter behavior. For these glasses, the activation energies
(Ea) are relatively higher and are of the order of 1.28 eV, as shown
in Table 1. Temperature dependence of conductivity also shows
a similar behavior. These results show that TiO2 contributes to conductivity
significantly in this ternary glass. An increase in content would result in
an increase in covalent- linkages leading to a lowering of the band gap and
hence increase in isothermal conductivity.
Assuming that molar refractivity (Rm) and polarizability αm are additive quantities Dimitrov and Sakka obtained the relationship (1996).
Where, Ri, is ionic refraction of cation, RO2¯ is the refraction of oxide ion, respectively. P and q denote the number of cation and oxide ion in the chemical formula APOq,. This relationship leads to;
Duffy and Ingram (1995) put an experimental formula for obtaining the polarizability of oxide ion as a function of optical band gap as follows
Using the Lorenz -Lorenz, Eq. (5) for simple oxides, Dimitrov
and Sakka (1996) used the following linear relationship suggested by Duffy and
Substituting Eq. (11) in Eq. (8), these
authors obtained the required relationship between α02
(n) and Eopt. This formula was modified to the following relationship;
The values of α02¯for the glass system obtained from the experimentally measured refractive indices and optical bang-gap energies using the expressions (9) and (12), respectively are compared in Table 1. The result shows that there is close agreement in the polarizability values obtained from the two different experimental quantities. The agreement is particularly good in view of the possible errors in Eopt due to factors like thickness of the glass samples and the extrapolation method used for evaluating Eopt.
The values of α02- for the glass system obtained
from the experimentally measured refractive indices and optical bang-gap energies
using the expressions (9) and (12), respectively are compared in Table
1. The result shows that there is close agreement in the polarizability
values obtained from the two different experimental quantities. The agreement
is particularly good in view of the possible errors in Eopt due
to factors like thickness of the glass samples and the extrapolation method
used for evaluating Eopt. Our results further suggest that one should
not come to conclusion on the polarizability of oxide ions in glasses simply
from the values of the individual oxide components as other quantities such
as Rm and Vm characteristics of the glass also influence
the results. For instance, the oxide ion polarizability for the metal oxide
such as the TiO2 in order of ~ 2.368 x 10-24 cm3.
However, in glasses where this oxide is taken as the third component.
The widths (ΔΕ )of the tails of localized states within the optical
band gap obtained in term of Urbach energy for the present glass system lie
in the range reported earlier for other glasses. It is known that the broadening
of the excitation levels at the absorption edge is dominated by the random internal
electric fields due either to the lack of long-range order or presence of defects
Elkholy, (2003). For the glass system under study, the least Urbach energy (ΔΕ
= 0.79 eV ) and sharp absorption edge is observed for 5 mol%TiO2.
This suggests that defects in this glass are a minimum facilitating long range
order resulting in the least Urbach energy.
Present study reports some optical and electrical properties of B2O3 - Na2O - TiO2 glass system for different ratio of doping with TiO2 content. We calculated the oxide ion polarizabilities (αo2-) from two different quantities viz., refractive index and the optical band gap energy. The density, refractive index, polarizability, and optical basicity increase with increasing TiO2 content in the prepared glasses. On the other hand, the molar volume, molar refraction and optical energy gap decrease with increasing TiO2 content in the studied glasses. We concluded in the present study a large agreement between the summation of theoretical optical basicity of each component in the ternary prepared glass system and the optical basicity calculated as a function of the refractive index, n,.