CHAPTER 4

OPTICAL PROPERTIES

75

4.1 INTRODUCTION

The various optical parameters such as refractive index, optical band gap

energy, oxide ion polarizability, interaction parameter etc are determined from optical

absorption spectra. These parameters provides information about the electronic band

structure, band tail and localized states. Optically induced transitions, which gives

information about optical constants are studied from optical absorption spectroscopy.

These optical transitions in which electrons jump from valence band to conduction

band are classified as interband transitions, transition across the band gap edges,

impurity level excitation, excitation generated transition and intraband transition.

In amorphous materials, we have direct and indirect transitions. Both the

transitions involve the interaction of an electromagnetic wave with an electron in the

valence band, which is then raised across the fundamental gap to the conduction band.

In the case of direct optical transitions, the electron from the top of valence band is

removed into the bottom of the conduction band at the same wave vector for the

electron. But indirect transitions, the interaction with lattice vibrations (phonons)

takes place resulting the change of wave vector of the electron. This transition is also

known as photon assisted transition.

4.2 REVIEW OF EARLIER WORK

A brief review of the earlier work carried out on some optical properties of

glasses is presented.

Farouk et al [1] studied the effect of γ-radiation on the optical properties of the

glassy system [xMgF2–10Al2O3-(40-x) TeO2–50Li2B4O7], (x = 0, 15, 20 and

40 mol%). It was observed that γ-radiation enhances the formation of NBOs. This

76

leads to a decrease in the optical band gap energy. Radiation induced changes include

hole trapping by bridging oxygen causing the increase of B–O bond length.

Rajesh et al [2,3] investigated structural and optical properties using XRD,

DSC, FTIR, optical absorption and near infrared luminescence spectra of strontium

lithium bismuth borate glasses doped with various concentrations of Er3+ and also in

Nd3+ doped alkali and mixed alkali (Li, Na, K, Li–Na, Li–K and Na–K) heavy metal

(PbO and ZnO) borate glasses.

A series of un-doped borate glasses [4] with Li2B4O7, LiKB4O7, CaB4O7, and

LiCaBO3 compositions of high optical quality and chemical purity were obtained

from corresponding polycrystalline compounds using standard glass synthesis and

technological conditions developed by authors. The optically thermopoled second

harmonic generation (SHG) effect in the Li2B4O7, LiKB4O7, CaB4O7, and

LiCaBO3 glasses were investigated and analyzed.

Sailaja et al [5] reported the optical properties of cadmium bismuth borate

glasses doped with various concentrations of Sm3+ ions. FT-IR spectra of Sm3+ doped

glasses have been used to identify the functional groups present in the glasses. From

the absorption spectrum, the experimental oscillator strengths were determined and

have been used to calculate the Judd–Ofelt intensity parameters. By using the Jude–

Ofelt intensity parameters, various radioactive properties have been studied.

Gedam [6] reported Li2O-B2O3-Nd2O3 glasses prepared by conventional melt

quench technique. Optical characterizations of these glasses were carried out. The

density and refractive index of these glasses increased while optical band gap and

radiation length decreased due to structural changes.

77

Glasses in the system ZnF2–ZnO–As2O3–TeO2 [7] were prepared by normal

melt quenching method. The optical constants of these glasses are determined over a

spectral range, providing the complex dielectric constant to be calculated. The values

of the optical band gap Eg for all types of electronic transitions and refractive index

have been determined. The optical parameters such as, ε∞, ωp, Ed and E0 have been

estimated. The values of N/m* reflect an increase in the free carrier concentration

with increasing ZnF2 content. This leads to an increase in the reflectance, R which in

turn increases the refractive index.

Krishna Kumari et al [8] prepared and studied the structural changes of

Co2+ and Ni2+ ions doped ZnO−Li2O− K2O−B2O3 glasses investigated by UV–vis–

NIR and FT-IR spectroscopy. The optical band gap and Urbach energies exhibited

the mixed alkali effect. Various physical parameters such as refractive index, optical

dielectric constant, polaron radius, electronic polarizability and inter-ionic distance

were also determined. FT-IR measurements of the all glasses revealed that the

network structure of the glasses are mainly based on BO3 and BO4 units placed in

different structural groups in which the BO3 units being dominant. The optical

absorption spectra suggest the site symmetry of Co2+ and Ni2+ ions in the glasses are

near octahedral.

Samee et al [9] studied the mixed alkali effect in borate glasses containing

three types of alkali ions. From the absorption edge studies, the values of indirect

optical band gap, direct optical band gap and Urbach energy have been evaluated. The

values of Eopt and ΔE show non-linear behavior with compositional parameter

showing the mixed alkali effect. The average electronic polarizability of oxide ions

αo2-, optical basicity Λ, and Yamashita–Kurosawa's interaction parameter A have been

78

examined to check the correlations among them and bonding character. Based on

good correlation among electronic polarizability of oxide ions, optical basicity and

interaction parameter, the present Li2O–Na2O–K2O–B2O3 glasses were classified as

normal ionic (basic) oxides.

Baki and El-Diasty [10] prepared lithium tungsten borate glass (0.56−x)B2O3–

0.4Li2O–xZnO–0.04WO3 (0≤x≤0.1 mol%) by the melt quenching technique for

photonic applications. The spectroscopic properties of the glass such as glass molar

polarizability, oxide ion polarizability, optical basicity and Yamashita–Kurosawa's

interionic interaction parameter were determined in a wide spectrum range (200–

2500 nm) using a Fresnel-based spectrophotometric technique. Optical properties of

Ni2+ doped 20ZnO + xLi2O + (30 − x)Na2O + 50B2O3 (5 ≤ x ≤ 25) glasses [11] were

carried out at room temperature. The optical absorption spectra confirm the site

symmetry of the Ni2+ doped glasses are near octahedral. It was observed that the

optical band gap and Urbach energies exhibit the mixed alkali effect.

Vijaya Kumar et al [12] studied glasses with composition Bi2O3-B2O3-BaO.

The optical absorption spectra of the glasses revealed that the cutoff wavelength

increases and optical band gap energy decreased with increased in BaO content. The

Eopt values of these glasses were found to be in the range 2.72–3.15 eV where as the

value of ∆E lies in the range 0.45–0.27 eV. The polarizability of oxygen ions in these

glasses is determined using optical absorption data.

Saddeek et al [13] prepared glasses with compositions Na2B4O7–Bi2O3–MoO3,

The optical transmittance and reflectance spectrum of the glasses have been recorded

in the wavelength range 300–1100 nm. The values of the optical band gap Eopt for

indirect transition and refractive index have been determined. The average electronic

79

polarizability of the oxide ion αO2− and the optical basicity have been estimated from

the calculated values of the refractive indices. The variations in the different physical

parameters such as the optical band gap, the refractive index, the average electronic

polarizability of the oxide ion and the optical basicity with Bi2O3 and MoO3 content

have been analyzed and discussed in terms of the changes in the glass structure. The

results are interpreted in terms of the increase in the number of non-bridging oxygen

atoms, substitution of longer bond-lengths of Bi–O, and Mo–O in place of shorter B–

O bond and the change in Na+ ion concentration.

Optical absorption and emission spectra of Ho3+ doped alkali, mixed alkali and

calcium phosphate glasses [14] have been studied. Variation of Judd–Ofelt intensity

of parameters (Ωλ), peak wavelengths of the hypersensitive transitions (λp), radiative

transition probabilities (Arad) and peak emission cross-sections (σp) with the variation

of alkalis, mixed alkalis and calcium in the phosphate glass matrix has been studied.

The shift in peak wavelength of the hypersensitive transition and Judd–Ofelt intensity

parameter (Ω2) are correlated with the structural changes in the host matrix. From the

luminescence spectra, the emission cross-sections (σp) are evaluated for the two

emission transitions of Ho3+ ion.

The refractive index (n) and density (ρ) of Bi2O3–B2O3 glasses [15] were

measured in the temperature range of 30–150 °C in order to clarify the temperature

dependence of the electronic polarizability of oxide ions (αO2−) and optical basicity

(Λ). It was found that the values of n, αO2−, and Λ increase almost linearly with

increasing temperature. The value of the temperature dependence of refractive index,

dn/dT, increases with increasing Bi2O3 content. Contrary, the values of dαO2−/dT, and

dΛ/dT, tend to decrease with increasing Bi2O3 content. They suggested that the

80

temperature dependence of the electronic polarizability of oxide ions in these glasses

has a large contribution for the temperature dependence of the refractive index in

comparison with the contribution of the volume thermal expansion coefficient. The

features in the temperature dependence of αO2− and Λ in the present glass system

might be related to the extremely weak single bond strength of Bi2O3 compared with

the strong single bond strength of B2O3.

Elfayoumi et al [16] reported optical absorption and emission spectra of

Sm3+ and Eu3+ co-doped lithium borate glass in the spectral range from 350 to

2400 nm. The oscillator strength, Judd–Ofelt intensity parameters, branching ratios

and radiative transition probabilities were calculated. The obtained results are

discussed and compared with other literature data for Eu3+ in various compounds.

Padmaja and Kistaiah [17] and Subhadra and Kistaiah [18] carried out optical

absorption studies on mixed alkali borate glasses to understand the effect of

progressive doping of one type of alkali ion with another type of alkali ion. Optical

parameters such as optical band gap, Urbach energy, oxide ion polarizability, optical

basicity and interaction parameter were evaluated from the experimental data. The

observed optical band gap and Urbach energy exhibit mixed alkali effect (MAE).

Venkateswarlu et al [19] presents the optical absorption and emission

properties of Pr3+ and Nd3+ doped two different mixed alkali chloroborate glass

matrices of the type B2O3-LiCl-NaCl and B2O3-LiCl-KCl. The variation of Judd–

Ofelt parameters, total radiative transition probabilities, radiative lifetimes, emission

cross-sections and refractive index with alkali contents in the glass matrix have been

discussed.

81

Kesavulu et al [20] reported the results on mixed alkali effect in Li2O–Cs2O–

B2O3 glasses doped with Cr3+ ions studied by optical absorption, electron

paramagnetic resonance and luminescence techniques. The optical absorption

spectrum exhibits three bands characteristic of Cr3+ ions in octahedral symmetry.

From the optical absorption spectral data, the crystal field (Dq) and Racah parameters

have been evaluated. From ultraviolet absorption edges, the optical band gap and

Urbach energies have been calculated.

The optical parameters of Fe3+ and Mn2+ doped Li2O-K2O-ZnO-B2O3 mixed

alkali glasses [21] have been determined through optical absorption studies. The

glasses exhibit typical optical absorption spectra of Fe3+ and Mn2+ ions. Progressive

substitution of Li with K induces non-linear variations in various optical parameters,

such as optical band gap and Urbach energy with composition. Optical basicity, oxide

ion polarizability, and interaction parameter values have been evaluated for all the

glass specimens.

Hemantha Kumar et al [22] reported optical absorption and fluorescence

studies on sodium potassium phosphate glass doped with Nd2O3. From the absorption

spectra, Racah , spin-orbit and configuration interaction parameters were calculated.

Judd–Ofelt intensity parameters were used to study the covalency as a function of

Nd3+ concentration. Results show that covalency decreases with the increase of Nd3+

concentration. From the absorption spectra, the optical band gaps (Eopt) for both direct

and indirect transitions have been obtained. All these spectroscopic parameters are

compared for different Nd3+ concentrations. From these studies, a few transitions are

identified for laser excitation among various transitions.

82

Sreekanth Chakradhar et al [23,24] studied the optical absorption and EPR

spectra of MnO2 and V2O5 doped mixed alkali borate glasses. Optical band gap

energies (Eopt) and Urbach energies (ΔE) show the mixed alkali effect (MAE) with

composition. The present study gives an indication that the size of alkalis choosen, is

also an important contributing factor in showing the MAE. The theoretical values of

optical basicity (Λth) have also been evaluated.

Khafagy et al [25] employed optical absorption technique for measuring both

optical band gap and Urbach energy for Li2O-TeO2 - B2O3 -P2O5 glasses in the range

200–800 nm. The obtained results showed that a gradual shift in the fundamental

absorption edge toward longer wavelengths. It is observed that optical energy gap,

Eopt is decreased and Urbach energy, ΔE increased with the increase of Li2O in the

glass matrix up to 30 mol%. The compositional dependences of the above properties

are discussed.

Baki et al [26] studied the effect of MgO and BaO on the optical properties of

the ternary glass systems Na2O-B2O3-RO (R=Ba or Mg) doped with TiO2. The

dependence of the refractive index and extinction coefficient on glass composition

was carried out over a wavelength range of 0.3–2.5µm. The absorption coefficient,

both direct and indirect optical energy gaps, and Urbach energy were evaluated using

the absorption edge calculations. The different factors that play a role for controlling

the refractive indices such as coordination number, electronic polarizability, field

strength of cations, bridging and nonbridging oxygen, and optical basicity are

discussed in accordance with the obtained index data.

The optical absorption studies of Li2O–MgO–B2O3 glasses [27] containing

different concentrations of nickel oxide prepared by melt quenching technique

83

indicate that the nickel ions occupy both tetrahedral and octahedral positions in the

glass network. However, the octahedral positions seem to be dominant when the

concentration of nickel oxide is 0.4 mol% in the glass matrix.

Mahmoud [28] studied the room temperature optical absorption and reflection

spectra of lithium borobismuthate glasses, recorded in the wavelength range 190–

1100 nm. From the absorption edge studies, the values of the optical band gap ,

Urbach energy , refractive index and complex dielectric constant were determined.

The dispersion of the refractive index is discussed in terms of the single-oscillator

Wemple–DiDomenico model. Pisarska [29] evaluated the optical constants of lead

borate glasses containing Dy3+ ions using absorption and luminescence measurements.

El Batal [30] performed optical, infrared, EPR and Raman spectral studies of

some lithium borate glasses containing varying WO3 contents before and after gamma

ray irradiation. Optical properties of oxide glasses have been extensively investigated

in various host matrices. Many glasses have been developed for visible and infrared

optical devices. In them borate is a suitable optical material with high transparency,

low melting point, high thermal stability and good alkali and rare earth ion solubility

[31-33].

The optical gaps of B2O3, alkali borate and alkali fluoroborate glasses [34]

were determined. The gap of B2O3 glass was 8.0 eV and the value decreased

monotonically with decreasing the B2O3 content in both alkali fluoroborate and alkali

borate glasses. When compared at a constant B2O3 content, the gap is in the order

Li>Na>K> fluoroborate.

84

Optical absorption and emission studies [35] were carried out on neodymium

doped alkali fluoroborophosphate glasses with mixed alkali fluorides as network

modifiers. The refractive indices and Judd–Ofelt parameters of these glasses have

been measured. The refractive index and density of single and mixed alkali borate

glass systems [36] have been measured and used to calculate the molar volume, molar

refractivity and molar refractivity of oxygen ion in order to investigate the

configurational changes that might be induced in the glass structure as the constituent

alkali ion is gradually replaced by another. Kojima et al [37] determined sound

velocities, elastic constants and refractive indices of mixed alkali Cs2O-Li2O-

B2O3 glasses from Brillouin scattering spectra in the frequency range 0 to 30 GHz.

Optical absorption, fluorescence and laser characteristics of Ho3+ incorporated

glass systems of ZrF4-BaF2-A1F3-RF (RF = LiF-NaF or NaF-KF pair) were examined

[38]. Physical properties such as density, refractive index, molar refractivity and

dielectric constant were measured. The measured absorption intensities were matched

with the best fit Judd-Ofelt intensity parameters. The effects of the holmium glass

chemical compositions were examined for properties such as spontaneous emission

probabilities, branching ratios and radiative lifetimes of lasing transitions by the use

of the Judd-Ofelt model. Studies were also carried out to understand the mixed alkali

fluoride effects on the measured values of induced emission cross sections for the

observed luminescent transitions 5I7.6, 5F5 and 5S2 → 5I8 of holmium glasses.

Sdiri & H. Elhouichet [39] and Mahamuda, & Swapna [40] investigated

optical properties of Pr3+ ions in lithium borate and Tm3+ ions in MO-Li2O-

B2O3 (M=Mg, Ca, Sr and Ba) glasses. From the experimental values of oscillator

strengths and calculated matrix elements, the Judd–Ofelt parameters were obtained

85

and their compositional dependence was investigated systematically. The predicted

lifetime for fluorescent levels decreases with decreasing content of Li2O.

Refractive index, optical absorption, absorption and emission cross-sections of

Tm3+/Yb3+-doped alkali-barium-bismuth-tellurite glasses [41] were determined. Wide

infrared transmission window, high refractive index and strong blue three-photon up

conversion emission of Tm3+ indicate that Tm3+/Yb3+ co-doped glasses are promising

up conversion optical and laser materials.

Binary zinc borate glasses of varied composition were prepared by the melt

quenching technique to samples of good optical quality [42]. Absorption, fluorescence

and optical excitation spectra of the glass matrix have been investigated. It is shown

that the composition of the glass strongly affects the position of the emission and

excitation maximum. Both the emission and the excitation spectra were progressively

red shifted with increasing zinc content in the glass matrix.

Borates and silicate glasses [43] containing boron oxide have been widely

used for optical lenses with high refractive index and low dispersion characteristics.

Alkali borate glasses are of great technological interest especially lithium borates as

solid electrolytes because of their fast ionic conduction. The effect of the presence of

either aluminum or lead oxide, or the presence of one of the following transition

metal, Fe2O3, TiO2 or V2O5 in lithium borate glasses was investigated. Glass

containing lead oxide had the highest refractive index.

Rama Moorthy et al [44] investigated optical absorption and

photoluminescence properties of Dy3+-doped alkali borate and alkali fluoroborate

glasses. From the measured absorption spectra, the oscillator strengths were

86

determined from the area under the absorption bands. Judd-Ofelt and the intensity

parameters were used for the calculation of radiative transition rates, branching ratios,

radiative lifetimes and integrated absorption cross-sections. From the radiative

spectroscopic parameters, it is predicted that these Dy3+-doped glasses are found to be

more attractive for blue–green solid-state laser devices.

Agarwal et al [45] recorded room temperature optical absorption and

reflection spectra of Li2O–K2O–Bi2O3–B2O3 glasses in the wavelength range 400–800

nm. From the absorption edge studies, the values of optical band gap (Eopt) and

Urbach energy (ΔE) have been evaluated. The values of Eopt lie between 2.21 and 2.55

eV for indirect allowed transitions, and for indirect forbidden transitions, the values

vary from 1.86 to 2.31 eV. The refractive index (n) and optical dielectric constant (ε)

have been evaluated from the reflection spectra. n and ε and Eopt show nonlinear

variation in their values which supports the existence of MAE in the optical properties

of the present glass system.

Yasser Saleh Mustafa Alajerami and Sooraj Hussain et al [46,47] presents the

optical absorption and emission properties of Dy3+ and Sm3+ in mixed alkali borate

glasses The variation of the Judd–Ofelt intensity parameters, hypersensitive band

positions, radiative transition probabilities, branching ratios, emission cross-sections

and optical band gaps with glass composition have been discussed.

The optical properties of Li2O−K2O−Bi2O3−B2O3−V2O5 glass system were

studied [48] from the optical absorption spectra recorded in the wavelength range

200−800 nm. The fundamental absorption edge has been identified from the optical

absorption spectra. The values of optical band gap for indirect allowed transitions

87

have been determined. An attempt was made to correlate the EPR and optical results

and to find the effect of Bi2O3 content on these parameters.

Glasses with composition Li2O-Na2O-K2O-B2O3 were prepared by Samee et

al [49] using the melt quenching technique. Optical energy band gap for various

indirect and direct (allowed and forbidden) transitions were determined using Tauc

plots. Based on good correlation among refractive index based electronic

polarizability of oxide ions, optical basicity and the Yamashita–Kurosawa’s

interaction parameter, the present Li2O-Na2O-K2O-B2O3 glasses were classified as

semi covalent oxides.

4.3 AIM AND SCOPE OF THE PRESENT WORK

Mixed alkali effect (MAE) in borate glasses has been studied extensively. In

spite of numerous investigations, there appears to be no universally accepted

mechanism for various mixed alkali effects. Though the mixed alkali effect must be of

limited interest in technological applications, it is receiving due importance in

understanding the general problems pertaining to ion transport in glasses. Many

investigations have been reported on mixed alkali effect in phosphate, borate, tellurite,

bismuthate and silicate glasses which contain alkali and/or alkaline earth oxides [50-

57].

In this chapter the mixed alkali effect in xLi2O–(30-x)Na2O–10WO3–60B2O3

(0 ≤ x ≤ 30 mol%) glasses was investigated through optical absorption. Using the

optical data, various optical parameters such as cut-off wavelength, optical band gap

energy, Urbach energy, band gap based optical basicity and interaction parameter,

dispersion energy, oscillator energy, oscillator strength, high frequency dielectric

88

constant and refractive index, ratio of free carrier concentration to the free carrier

effective mass, plasma frequency, optical relaxation time etc, were determined.

4.4 RESULTS AND DISCUSSION

The room temperature optical absorption spectra of xLi2O–(30-x)Na2O–

10WO3–50B2O3 glass is shown in figure 4.1.The non-sharp absorption edges in figure

give a clear indication of the amorphous nature of the glasses. The UV absorption

edge or the cutoff wavelength of all glasses in the present study were determined and

are presented in table 4.1. The variation of cutoff wavelength as a

function of compositional parameter in both the glass systems is illustrated in figure

4.2. It is reported that the fundamental absorption edge shifts towards longer

wavelengths in single alkali borate glasses with an increase in alkali content [58, 59].

89

In the present mixed alkali glasses, from the above figure 4.2 it is clear that the cut-off

wavelength varies non-linearly when Li2O is replaced with Na2O. This non-linear

variation in cut-off wavelength is a consequence of mixed alkali effect.

Fig. 4.2 Cutoff wavelength as a function of compositional parameter RLi

in the present glasses.

The optical absorption co-efficient α(ν), near the fundamental absorption edge

was determined from the relation

α(ν) = (1/d) log(I0/It) = 2.303A/d (4.1)

where I0 and It are the intensities of the incident and transmitted beams, respectively,

and d is thickness of the glass sample. The factor log(I0/It) corresponds to absorbance.

Davis and Mott [60] and Tauc and Menth [61] relate this data to the optical band gap,

Eopt through the following general relation proposed for amorphous materials.

0.0 0.2 0.4 0.6 0.8 1.0280

290

300

310

320

330

340

λc = 313nm

λc = 338nmC

ut-o

ff w

avel

egth

(nm

)

Compositional parameter RLi

311

287

313

307304

0.0 0.2 0.4 0.6 0.8 1.0280

290

300

310

320

330

340

λc = 313nm

λc = 338nmC

ut-o

ff w

avel

egth

(nm

)

Compositional parameter RLi

311

287

313

307304

90

2.5 3.0 3.5 4.00

2000

4000

6000

8000

10000

x=30

(αhν

)2/3 (c

m-1eV

)2/3

hν (eV)

x=0x=5

x=25

n=2/3

α(ν) = B (hν− Eopt)n / hν (4.2)

where B is a constant related to the extent of the band tailing, hν is incident photon

energy and n is a number which characterizes the transition process. The exponent, n

takes the values 1/2, 2, 3/2 and 3 for direct allowed, indirect allowed, direct forbidden

and indirect forbidden transitions, respectively. By plotting (αhν)n as a function of

photon energy hν (Tauc plots), one can find the optical energy band gap for all

transitions. Figure 4.3 represents Tauc’s plots {(αhν)n vs hν} (n= 1/2, 2, 1/3, 2/3)

for x Li2O– (40−x)Na2O–10WO3–50B2O3 glass system. The values of optical band

gap energy Eopt can be obtained by extrapolating the absorption co-efficient to zero

transitions. The values of optical energy gap, Eopt, thus evaluated for the glass samples

at different values of n are listed in table 4.1.

Since the obtained values of the optical band gap (Eopt) are varying according

to the selected value of the exponent n, one cannot really decide which value of n is

better to be selected. Therefore, the Eq.4.2 may be rather used only for the

determination of the

91

1.0 1.5 2.0 2.5 3.0 3.5 4.00

10

20

30

40

50

60

70

80

90

x=0

x=25x=30

(αhν

)1/2 (c

m-1eV

)1/2

hν (eV)

x=5

n=1/2

2.5 3.0 3.5 4.00

5000

10000

15000

20000

25000

30000x=5

(αhν

)2 (cm

-1eV

)2

x=30

x=25

hν (eV)

x=0n=2

92

1.0 1.5 2.0 2.5 3.0 3.5 4.00

10

20

30

40

50

60

(αhν

)1/3 (c

m-1eV

)1/3

hν (eV)

x=0x=5

x=25 x=30

n=1/3

Fig. 4.3 (αhν)n versus hν, Tauc’s plots (n = 1/2, 2, 2/3 and 1/3) for the xLi2O-(30-x)Na2O-10WO3-60B2O3 glass system.

type of conduction mechanism, and Eopt itself should be determined using another

parameter the imaginary part of the dielectric constant, ε2 by which the exact value of

exponent can be selected.

The complex refractive index and dielectric function characterize the optical

properties of glass. The values of refractive index n and extinction coefficient k can

be determined from the theory of reflectivity of light. According to this theory, the

refractive index and extinction co-efficient can be expressed as [62]

n2 = (1+R1/2) / (1- R1/2) and k = αλ/4π (4.3)

where R is reflectivity of the sample in the transparent region of glasses studied and λ

is the wavelength. Figure. 4.4 and figure. 4.5 shows the variation of refractive index

and extinction coefficient as a function of wavelength for the xLi2O–(30−x)Na2O–

10WO3–60B2O3 glass system, respectively. It is clear that the refractive index

decreases with an increasing wavelength (low wavelength region) of the incident

photon energy until a constant value is reached at longer wavelengths. The extinction

93

300 400 500 600 700 800

0.00002

0.00004

0.00006

0.00008

0.00010

x= 10 mol%

x= 0 mol%

x= 15 mol%

Extin

ctio

n co

effic

ient (

k)

Wavelength (nm)

x= 25 mol%

300 400 500 600 700 800

1.5

2.0

2.5

3.0

3.5

4.0

4.5

x = 0 x = 5 x = 30

Refr

activ

e ind

ex (n

)

Wavelength (nm)

x = 25

coefficient is the imaginary part of the complex index of refraction, which also relates

to light absorption.

Fig. 4.4 The refractive index as a function of wavelength.

94

300 400 500 600 700 800

0.00002

0.00004

0.00006

0.00008

0.00010

x = 30 mol%

x = 20 mol%Ext

inct

ion

coef

ficie

nt (k

)

Wavelength (nm)

x = 5 mol%

Fig. 4.5 The extinction coefficient as a function of wavelength.

Real and imaginary parts of dielectric constant (ε1 and ε2) of a material are

related to the optical constants n and k values, using the formula

ε1= n2 - k2 and ε 2= 2nk (4.4)

Figure 4.6 shows the variation of real part of dielectric constant, ε 1, as a

function of photon energy hυ for the present glass samples. For all glass samples the

dielectric constant shows an exponential increase with photon energy.

95

1.5 2.0 2.5 3.0 3.5 4.01

2

3

4

x = 20 x = 15 x = 5

ε 1

Photo energy hν (eV)

x = 0

1.5 2.0 2.5 3.0 3.5 4.01

2

3

4

x= 10x= 25

ε 1

Photon energy (hν) (eV)

x= 30

Fig. 4.6 The real part of the dielectric constant as a function of photon energy.

96

2.0 2.5 3.0 3.5 4.0 4.50.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

3.812 eV

x = 0

x = 20

x = 10

ε 2

Photon energy (eV)

x = 15

2.0 2.5 3.0 3.5 4.0 4.50.00000

0.00005

0.00010

0.00015

0.00020

0.00025

0.00030

0.00035

x = 30

x = 25

ε 2

Photon energy (eV)

x = 5

3.767 eV

Fig. 4.7 Imaginary part of the dielectric constant as a function of photon energy.

97

0.0 0.2 0.4 0.6 0.8 1.03.5

3.6

3.7

3.8

3.9

4.0

Ban

d ga

p en

ergy

(eV

)

Compositional parameter RLi

Indirect allowed band gap direct allowed band gap Indirect forbidden band gap direct forbidden band gap

Figure 4.7 shows the imaginary part of the dielectric constant ε2, versus the

photon energy for the studied glass systems. The imaginary part of the complex

dielectric constant ε2 is related to extinction coefficient, which also relates to light

absorption. From the above figures, the optical band gap Eopt can be obtained by

extrapolating the imaginary part of the dielectric constant ε2 to zero as shown in the

figure 4.7. On a comparison of the optical energy gap values obtained from absorption

spectra in the case of indirect allowed transition are in good agreement with the values

estimated from the

Fig. 4.8 Optical band gap energy (for all transition) as a function of compositional

parameter RLi in present glasses.

dielectric measurements ε2. Thus, the type of electronic transition in the present glass

systems is indirect allowed. The values of optical band gap energy Eopt obtained from

the imaginary part of the dielectric constant ε2 are presented in table 4.1. In the

present glasses, the allowed indirect and direct band gap energy varies from 3.54 to

3.83 eV and 3.66 to 3.98 eV, respectively. Srinivasa Rao et al [63] and Huang et al

98

1.5 2.0 2.5 3.0 3.5 4.0

0

1

2

3

4

x = 30

x = 25x = 20

x = 15

x = 5

x = 10lnα

Photon energy (eV)

x = 0

[64] observed large band gap energies around 3.25 eV and 4.18 eV in PbO-Bi2O3-

As2O3-WO3 and Li2O-B2O3-WO3 glasses, respectively. The compositional

dependence of all optical band gap energy, Eopt for the present glass systems is

illustrated in figure 4.8. It is observed that the non-linear variation of band gap energy

with compositional parameter indicates the existence of mixed alkali effect.

Literature on optical properties of mixed alkali glasses support the notion of

defect formation in glass matrix caused by simultaneous movement of two unlike

mobile ions. Agarwal and co workers [45] have reported the existence of mixed alkali

effect in optical band gap in lithium-potassium borate glasses from the existence of a

minimum in optical band gap at equimolar concentrations of alkali cations. The

mixed alkali effect in indirect optical band gap energy is attributed to the formation of

large number of non-bridging oxygens (NBOs). The mixed alkali effect in optical

band gap energy was also reported by several other workers [14, 15, 6].

Fig. 4.9 Plots corresponding lnα vs hν for Li2O-Na2O-WO3-B2O3 glasses.

99

0.0 0.2 0.4 0.6 0.8 1.00.20

0.24

0.28

0.32

0.36

0.40

Urba

ch en

ergy (

eV)

compositional parameter RLi

The lack of crystalline long range order in amorphous or glassy materials is

associated with a tailing of density of states [65]. At lower values of absorption

coefficient, the extent of exponential tail of the absorption edge characterized by the

Urbach energy and it is given by

Fig.4.10. Compositional dependence of Urbach energy (ΔE) in the present

glasses.

α(ν) = C exp(hν/∆E) (4.5)

where C is a constant, ∆E is the urbach energy which indicates the width of the band

tails of the localized states. The optical absorption coefficient just below the

absorption edge shows exponential variation with photon energy indicating the

presence of Urbach’s tail. Figure 4.9 plots the variation of ln(α) against photon

energy, hν. The Urbach energy ∆E is calculated for the glasses taking the reciprocals

of slopes of these curves.

100

Table. 4.1: Cutoff wavelength (λc), Indirect allowed (αhυ)1/2, direct allowed (αhυ)2, indirect forbidden (αhυ)1/3, direct forbidden transitions (αhυ)2/3,

Eopt from ε2 and Urbach energy (ΔE) of the present glasses.

Glass composition λc (nm)

Optical band gap energies (Eo) (eV) ΔE (eV)

Eopt from ε2 (eV)

n = 2 n = 1/2 n = 2/3 n = 1/3

30Na2O-10WO3-60B2O3 338 3.660 3.538 3.602 3.552 0.285 3.534

5Li2O-25Na2O-10WO3-60B2O3 311 3.872 3.773 3.866 3.775 0.342 3.774

10Li2O-20Na2O-10WO3-60B2O3 287 3.977 3.835 4.023 3.808 0.394 3.832

15Li2O-15Na2O-10WO3-60B2O3 313 3.853 3.751 3.836 3.667 0.266 3.749

20Li2O-10Na2O-10WO3-60B2O3 307 3.931 3.818 3.895 3.759 0.288 3.812

25Li2O-5Na2O-10WO3-60B2O3 304 3.857 3.720 3.855 3.711 0.265 3.718

30Li2O-10WO3-60B2O3 313 3.900 3.770 3.893 3.852 0.235 3.767

The values of ∆E for different glass compositions are listed in table 4.1. The

exponential dependence of the optical absorption coefficient with photon energy may

arise from electronic transitions between the localized states. The density of these

states fall off exponentially with energy, which is consistent with the theory of Tauc

[66]. However, the exponential dependence of the optical absorption coefficient on

energy might arise from the random fluctuations of the internal fields associated with

the structural disorder in many materials. Figure 4.10 plots the variation of Urbach

energy ∆E as a function of compositional parameter in present glass systems. From

the above figure it is clear that the Urbach energy varies non-linearly, illustrating the

presence mixed alkali effect.

The dispersion of refractive index plays an important role in the research for

optical materials, because it is a significant factor for optical communication and in

designing devices for optical dispersion. An interesting model namely single

101

oscillator model describing the index dispersion behavior was proposed by Wemple

and Di- Domenico [67, 68].

This model is given to obtain a proper evaluation of the real part of the dielectric

constant ε1(ν). Hypotheses given to satisfy the model:

(1) the important interband transitions can be approximated by individual oscillators

νn,

(2) the summation over oscillators can be approximated, for ν <νn, by a summation

of the first strong oscillator and a proper combination of the higher order

contributions in which only the terms to order ν2 are retained providing a single

effective oscillator model of ε1(ν). It accounts for the dispersion curve according to

the relation:

(n2 – 1) = Ed E0/{(E0)2–(E)2} (4.6)

Table 4.2 Single oscillator energy (E0), dispersion energy (Ed), static refractive

index (n0), average oscillator wavelength (λ0) and oscillator strength (S0)

of present glasses.

Glass composition E0 (eV)

Ed (eV)

n0 λ0 (nm)

S0*106 (nm)-2

30Na2O-10WO3-60B2O3 3.825 0.324 1.041 338.7 1.031

5Li20-25Na2O-10WO3-60B2O3 3.966 0.430 1.053 326.4 1.152

10Li20-20Na2O-10WO3-60B2O3 3.811 0.541 1.069 343.2 1.125

15Li20-15Na2O-10WO3-60B2O3 3.939 0.703 1.086 354.4 1.273

20Li20-10Na2O-10WO3-60B2O3 3.847 0.613 1.077 335.3 1.193

25Li20-5Na2O-10WO3-60B2O3 3.855 0.663 1.079 365.2 1.096

30Li20-10WO3-60B2O3 3.905 0.721 1.088 342.6 0.964

102

10 12 14 16 180

1

2

3

4

(hν)2 (eV)2

x= 10x= 25

x= 30

x= 5

1/ (n

2 -1)

x= 20

where E=hν is the photon energy, E0 and Ed are two parameters connected to the

optical properties of the material and they are known as the single oscillator energy

and the oscillator strength (or dispersion energy) respectively. E0 defines the average

energy gap usually considered as the energy separation between the centers of both

the conduction and the valence bands. Ed is a measure of the average strength of the

interband optical transitions and is related to the coordination number of the atoms.

Plotting (n2-1)-1 against (hν)2 , and fitting it to the straight part of the curve in the

high-energy region allows to obtain E0 and Ed (the slope and the intercept values) of

the single oscillator parameters. Figures 4.11 plots the variation of 1/(n2-1) with (hν)2

in the present glass systems. A typical linear fit graph is shown in figure 4.12. The

average electronic energy gap E0 and the electronic oscillator strength Ed for the

present glasses were determined and were listed table 4.2. The values of E0 varies

between 3.811 eV and 3.966 eV and the values of Ed between 0.324 eV and 0.721 eV

in the present glasses.

Fig. 4.11 The relation between 1/(n2-1) and (hν)2 for the present glass system.

103

8 10 12 14 16 180.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

x = 15

1/ (n

2 -1)

(hν)2 (eV)2

x = 0

Fig. 4.12 A typical linear fit for x = 0 and 15 glass samples.

The static refractive index n0 is the refractive index at zero photon energy.

The static refractive index can be deduced from the dispersion relation as

n0 = {1+ Ed /E0}1/2 (4.7)

The static refractive index n0 can also be determined by extrapolation of the

linear part of 1/(n2-1) verses (hν)2 plots. The evaluated values of n0 for the present

glass systems are presented in table 4.2

The single-oscillator model enables us to calculate the refractive index at

infinite wavelength (static refractive index) n0, average oscillator wavelength λ0 and

oscillator strength S0 through the relation [69]

(n02 - 1) / (n2 - 1) = 1- (λ0

2 / λ2) (4.8)

104

0.000000 0.000003 0.000006 0.000009 0.000012 0.0000150.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

x = 0

1/ (n

2 -1)

1/λ2

x = 15

0.000006 0.000008 0.0000100

1

2

3

4 x= 25

x= 10

x= 20x= 5

1/(n

2 -1)

1/λ2 (nm)-2

x= 30

Fig. 4.13 The relation between 1/(n2-1) and 1/λ2 for the present glass system.

Fig. 4.14 A typical linear fit for x = 0 and 15 glass samples.

105

1/ (n2 - 1) = {1- (λ02

/ λ2)} / (n02 - 1)

1/ (n2 - 1) = 1/( n02 - 1) - {λ0

2 / (n02 - 1)}* 1/λ2

1/ (n2 - 1) = 1/( n02 - 1) - 1/ S0 * 1/ λ2

(4.9)

where S0 = (n02 -1) / λ0

2

The values of λ0, and S0 are derived from a linear plot of (n2 – 1)-1 verses 1/

λ2. Figures 4.13 plots the variation of (n2 – 1)-1 verses 1/ λ2 for xLi2O–(30−x)Na2O–

10WO3–60B2O3 glass system, respectively. A typical linear fit graph is shown in

figure 4.14. The oscillator strength S0 and average oscillator wavelength λ0 were

obtained from the slopes and intercepts of the above plots. The values of S0 and λ0 for

the present glasses are given in table 4.2.

The complex dielectric function describes the interaction of electromagnetic

waves with matter. The complex dielectric constant ε of the material in terms of the

optical constants n and k is given as:

(n+ik)2 = ε/ ε0 = (ε1+i ε2)/ ε0 (4.10)

where ε0 is the dielectric constant of free space. Separation of the real part and the

imaginary one leads to the real part, [70,71].

ε1= n2 - k2 = ε∞ - [e2/4π2c2 ε0 ] [Nc/ m*] λ2 (4.11)

and to the imaginary part,

ε2= 2nk = (ε∞ ωp2/8π3c3τ)λ3 (4.12)

Here ε0 is the free space dielectric constant, Nc/m* the ratio of free carrier

concentration, Nc, to the free carrier effective mass, m*, τ is the optical relaxation

time and ε∞ is the high frequency dielectric constant. The plasma frequency ωp for

the valence electrons is given by:

ωp= {e2 Nc / ε0 ε∞ m*}1/2 (4.13)

106

100000 200000 300000 400000 500000 6000001.5

2.0

2.5

3.0

3.5

4.0

4.5

ε∞

x = 20x = 10

Real

part

of di

electr

ic co

nsta

nt (ε

1)

λ2 (nm)2

x = 15

where e is the charge of the electron. The parameters ε∞ and Nc/m* can be obtained

from the ε1 verses λ2 plots. Figure 4.15 plots the variation of real part of the dielectric

constant ε1 as a function of λ2 for xLi2O–(30−x)Na2O–10WO3–60B2O3 glass

system. The evaluated values of ε∞ and Nc/m* of the present glasses were presented in

table 4.3.

Using the values Nc/m* and ε∞, the plasma frequency ωp for the present

glasses were determined and are presented in table 4.3. The optical relaxation time τ

was determined using the equation τ = 1/ ωp and the calculated wavelength λω=ωp that

corresponds to the plasma frequency ωp was evaluated from the relation λω=ωp =

2πc/ωp. Table 4.3 presents the values of τ and λω=ωp for the present glasses.

107

100000 200000 300000 400000 500000 600000

1.5

2.0

2.5

3.0

3.5

4.0

4.5

x = 30x = 25 x = 5

Real

part

of d

ielec

tric c

onsta

nt (ε

1)

λ2 (nm)2

x = 0

ε∞

Fig. 4.15 Dependence of ε1on λ2 in the present glasses.

Table 4.3 High frequency dielectric constant (ε ∞), the ratio of free carrier concentration

to the free carrier effective mass, (Nc/m*), plasma frequency (ωp), optical relaxation

time (τ) and plasma frequency wavelength (λω=ωp)

Glass composition ε∞ Nc/m*10

54

(kg-m3)

ωp*1013

(Hz)

τ*10-15

(Sec)

λ( ω=ωp)

*103Å

30Na2O-10WO3-60B2O3 1.615 73.13 40.10 2.49 47.0

5Li2O-25Na2O-10WO3-60B2O3 1.348 68.90 38.44 2.60 49.0

10Li2O-20Na2O-10WO3-60B2O3 1.400 118.28 49.44 2.02 38.1

15Li2O-15Na2O-10WO3-60B2O3 1.442 113.47 47.70 2.10 39.5

20Li2O-10Na2O-10WO3-60B2O3 1.473 101.51 44.65 2.24 42.0

25Li2O-5Na2O-10WO3-60B2O3 1.489 88.94 32.68 2.89 62.4

30Li2O-10WO3-60B2O3 1.396 97.21 49.59 2.10 46.2

108

0.0 0.2 0.4 0.6 0.8 1.0

1.644

1.646

1.648

1.650

1.652

Ref

ract

ive

inde

x

Compositional parameter RLi

4.4.1 Refractive index

Refractive indices of the present glasses are measured by Brewster’s angle

technique, by using the below equation

n = tan φB (4.14)

Figure.4.16 shows the compositional dependence of refractive index of the

present glasses at room temperature. The refractive index of the present glasses are

presented in Table.4.4, varies from 1.644 to 1.652 and it varies non-linearly,

indicating the presence of mixed alkali effect. Similar mixed alkali effect in refractive

index was observed in mixed alkali zinc borate glasses doped with cobalt [72]. Since

the refractive index of the present glasses are less than 1.7, they can be used as optical

glasses.

Fig. 4.16 Refractive index as a function of compositional parameter RLi in present glasses.

109

The refractive index (n) and the dielectric constant (ε) of the glass are related by [73]

ε = n2 (4.15)

The reflection loss from the glass surface was computed from the refractive index by

using the Fresnel’s formula [74].

R = [(n −1)/(n +1)]2 (4.16)

The molar refractivity Rm for each glass was evaluated using [75]

Rm = [(n2 −1)/(n2 +2)] Vm (4.17)

where Vm is the molar volume. By introducing Avogadro’s number NA, the molar

refraction Rm can be expressed as a function of polarizability αm [76].

Rm= (4 π αm NA) / 3 (4.18)

With αm in (Å3), this equation can be transformed to

Rm= 2.52 αm (4.19)

The evaluated values of no, ε, R, and Rm are presented in table 4.4.

Table 4.4 Refractive index (n), dielectric constant (ε), Reflection loss (R), molar refractivity (Rm) and polarizability (αm) of the present glass system.

Glass composition no ε R Rm (cm-3)

αm (ions/cc)

30Na2O-10WO3-60B2O3 1.6499 2.722 0.0601 10.800 4.286

5Li2O-25Na2O-10WO3-60B2O3 1.6509 2.725 0.0603 10.252 4.068

10Li2O-20Na2O-10WO3-60B2O3 1.6480 2.716 0.0599 10.261 4.072

15Li2O-15Na2O-10WO3-60B2O3 1.6500 2.723 0.0602 10.075 3.998

20Li2O-10Na2O-10WO3-60B2O3 1.6440 2.703 0.0593 9.786 3.883

25Li2O-5Na2O-10WO3-60B2O3 1.6470 2.713 0.0597 9.787 3.884

30Li2O-10WO3-60B2O3 1.6520 2.729 0.0604 9.921 3.937

110

4.4.2 ELECTRONIC POLARIZABILITY OF THE OXIDE ION ( −2Oα )

The electronic polarizability ( −2Oα ) is one of the most important properties or

parameters which govern the non-linear optical (NLO) responses of materials. Optical

non-linearity is caused by the electronic polarization of a material upon exposure to

intense light beams. Glasses are promising materials for NLO applications. The

electronic polarisability arises from oxygen being able to exist not only as bridging or

non-bridging but also with a degree of negative charge, which may be varied. This

negative charge should not be regarded as static but fluctuating depending on the

movement relative to other atoms to which it is linked. Oxygen has an extreme

versatile chemistry, forming oxides in which the chemical bond ranges from highly

covalent to highly electrovalent. Since glasses are composed of basic (ionic) and

acidic (covalent) oxides, it is the chemical composition that determines its ionic /

covalent state, i.e. the extent of negative charge borne by the oxygen atoms is

governed by the composition of the glass.

The electronic polarizability of oxide ions ( −2Oα ) as originally proposed by

Dimitrov & Sakka [77] can be calculated on the basis of energy gap and refractive

index data using the following equations

( ) ( ) 122 20

152.2

−−−

−

−

= ∑ Oi

omoO NEVE αα (4.20)

( ) ( ) 122 52.2

−−−

−

= ∑ Oi

mO NRn αα (4.21)

where Rm is the molar refraction related to refractive index n and molar volume Vm

and is expressed as

111

( )( ) mm VnnR

+−

=21

2

2

(4.22)

where ∑ iα in the above equations denote molar cation polarizability, Rm is the

molar refractivity, and 2ON − denotes the number of oxide ions in the chemical

formula. For a typical glass For a typical glass composition 10Li2O–20Na2O–

10WO3–60B2O3, the value of ∑ iα is given by 2[(0.10) αLi + (0.20) αNa] + [ (0.10)

αW] + 2[(0.60) αB]. The values of αLi = 0.029 Å3, αNa = 0.179 Å3, αW = 0.147 Å3

and ˛αB = 0.002 Å3 are used. The value of NO2− remains constant and is equal to 2.4

for all the glass samples. The calculated values of −2Oα for energy gap data,

designated as −2Oα (Eo) is presented in table 4.5.

4.4.3 OPTICAL BASICITY (Λ)

The optical basicity (Λ) of an oxide medium as proposed by Duffy and Ingram

[78,79] is a numerical expression of the average electron donor power of the oxide

species constituting the medium. It is used as a measure of the acid-base properties of

oxides, glasses, alloys, molten salts etc. The optical basicity can be determined

experimentally from optical absorption spectra of doped ions such as Tl+, Pb2+ or Bi3+

and also from x-ray photoelectron spectroscopy (XPS).

In most circumstances, the characteristic process of acid-base reactions in

oxide systems is "the transfer of an oxygen ion from a state of polarization to

another". In a chemically complex melt or glass the capability of transferring

fractional electronic charges from the ligands (mainly oxide ions) to the central cation

depends in a complex fashion on the melt structure, which affects the polarization

state of the ligand itself. The mean polarization state of the various ligands and their

112

ability to transfer fractional electronic charges to the central cation are nevertheless

represented by the "optical basicity" of the medium [79].

An intrinsic relationship proposed by Duffy [80] exists between electronic

polarizability of the oxide ions −2Oα and optical basicity of the oxide medium Λ and is

given by

−=Λ

−2

1167.1Oα

(4.23)

This relation presents a general trend towards an increase in the oxide ion

polarizability with increasing optical basicity. The optical basicity values obtained by

using −2Oα (Eo) data, from equation (4.23) and designated as Λ(Eo) and is presented in

table 4.5. The optical basicity Λ(Eo) values varies non linearly with increase in Li2O

content.

On the other hand the so-called theoretical optical basicity (Λth), for the

present glasses can be calculated using the following equation which is based on the

approach proposed by Duffy [80]

32323322 22 OBOBWOWOONaONaOLiOLith XXXX Λ+Λ+Λ+Λ=Λ (4.24)

where xLi2O, xNa2O , xWO3 and xB2O3 are the contents of individual oxides in mole%.

ΛLi2O, ΛNa2O, ΛWO3 and ΛB2O3 are the theoretical optical basicity values assigned to

oxides present in the glass. The values ΛLi2O=1,ΛNa2O =1.15, ΛWO3 =1.045 and ΛB2O3

=0.42 are used in the present study [81]. The theoretical optical basicity Λth values

calculated using above equation for the mixed alkali tungsten borate glasses are

presented in table 4.5. It is found that the theoretical optical basicity decreases slightly

with increasing Li2O content. A good agreement exists between the values of Λ(Eo)

and Λth.

113

4.4.4 INTERACTION PARAMETER (A)

The interaction parameter is a quantitative measure for the inter ionic

interaction of negative ions such as F- and O2- with the nearest neighbours. Dimitrov

and Komatsu [82,83] applied the interaction parameter A proposed by Yamashita and

Kurosawa [84] to describe the polarizability state of an average oxide ion in numerous

simple oxides and its ability to form an ionic covalent bond with the cation. The

optical cutoff based interaction parameter A(Eo) can be expressed as a sum from the

parts each cation with the given oxide ion contributes to the total interaction for an

averaged cation anion pair in the glass matrix

( )( )( )

( )( )( ) +

++

−+

++

−=

−++

−

−++

−

−

−

−

−

2

2

2

2

2 22 2ONafNa

OfONa

OLifLi

OfOLi XXA

αααααα

αααααα

( )

( )( )( )

( )( )−++

−

−++

−

++

−+

++

−−

−

−

−

233

2

32233

2

3 2 OBfB

OfOB

OWfW

OfWO XX

αααααα

αααααα

(4.25)

where −fα = 3.921 Å3

, the electronic polarizability of the free oxide ion is used, taking

into account the value of ionic refraction of O2- theoretically determined by Pauling

[85] and −2Oα corresponds to −2Oα (Eo) and −2Oα (n) . The energy gap based interaction

parameter A(Eo) and A(n) are determined from equation (4.25) and are presented in

table 4.5.It has been established that the Yamashita-Kurosawa interaction parameter A

is closely related to the oxide ion polarizability and optical basicity of oxide glasses.

That is, larger the oxide ion polarizability and optical basicity, the smaller is the

interaction parameter. The correlation between A and Λ for present glasses are shown

in figure 4.17and figure 4.18 indicating a linear distribution of the optical basicity

with respect to the interaction parameter and this can be used as the optical basicity

scale for oxide glasses. The interaction parameter decreases with increasing optical

114

1.00 1.02 1.04 1.06 1.080.05

0.06

0.07

0.08

Inter

actio

n par

amete

r A(E

o)

Optical basicity(Eo)

0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80

0.165

0.170

0.175

0.180

0.185

0.190

0.195

0.200

Inte

ract

ion

para

met

er A

(n)

Optical basicity Λ(n)

4.17 Relationship between optical basicity (E0) and interaction parameter A(Eo)

in the present glasses.

4.18 Relationship between optical basicity (E0) and interaction parameter A(Eo) in the present glasses.

115

basicity. It is observed in the present study, that the glasses containing large

intermediate values of Λ and A.

Based on good correlation among electronic polarizability of oxide ions

( −2Oα ), optical basicity (Λ) and interaction parameter (A), the various simple oxides

can be classified into three groups.

(1) Semicovalent acidic oxides, Eg. B2O3, P2O5, SiO2 etc. These have

low −2Oα ---- (1-2 Å3)

low Λ ---- ( < 1)

large A ---- (0.20 - 0.25 Å3)

Table 4.5: Energy gap and refractive index based oxide ion polarizability (αO2-),

and interaction parameter A, theoretical optical basicity Λ th and optical basicity Λ(E0 and n) of present glasses.

Glass composition (αO2-)

(Eo) A(Eo) Λth Λ(Eo) (αO2

-) (n)

A(n) Λ (n)

30Na2O-10WO3-60B2O3 2.785 0.052 0.702 1.070 1.734 0.167 0.707

5Li2O-25Na2O-10WO3-60B2O3 2.581 0.071 0.694 1.023 1.649 0.183 0.784

10Li2O-20Na2O-10WO3-60B2O3 2.582 0.070 0.687 1.023 1.657 0.182 0.662

15Li2O-15Na2O-10WO3-60B2O3 2.555 0.069 0.679 1.016 1.633 0.188 0.647

20Li2O-10Na2O-10WO3-60B2O3 2.489 0.066 0.672 0.999 1.591 0.197 0.620

25Li2O-5Na2O-10WO3-60B2O3 2.511 0.077 0.664 1.005 1.597 0.198 0.624

30Li2O-10WO3-60B2O3 2.524 0.076 0.657 1.008 1.626 0.193 0.642

116

(2) Normal ionic (basic) oxides, Eg. TeO2, In2O3 etc. These have

intermediate −2Oα ---- (2-3 Å3)

Λ ---- ( close to 1)

intermediate A ---- (0.02 - 0.08 Å3)

(3) Very ionic or very basic oxides, Eg. BaO, Bi2O3 etc. These have

high −2Oα ---- ( > 3Å3)

high Λ ---- ( > 1)

small A ---- (0.003 - 0.008 Å3)

From the obtained values of −2Oα , Λ and A, the present glasses fall in the group (2)

i.e. normal ionic (basic) oxides.

117

4.5 CONCLUSIONS

The following conclusions are drawn from the study of optical properties on

xLi2O–(30-x)Na2O–10WO3–60B2O3 glass.

• The non-sharp absorption edges in the present study give a clear indication of

the amorphous nature of the glasses. The cut-off wavelength varies non-

linearly when Li2O is replaced with Na2O. This non-linear variation in cut-off

wavelength is a consequence of mixed alkali effect.

• The refractive index decreases with an increasing wavelength (low

wavelength region) of the incident photon energy until a constant value is

reached at longer wavelengths.

• On a comparison of the optical energy gap values obtained from absorption

spectra in the case of indirect allowed transition are in good agreement with

the values estimated from the dielectric measurements. Thus, the type of

electronic transition in the present glass systems is indirect allowed.

• The observed non-linear variation of band gap energy with compositional

parameter indicates the existence of mixed alkali effect.

• The Urbach energy also varies non-linearly, illustrating the presence mixed

alkali effect.

• Using single oscillator model, the oscillator energy E0, the dispersion energy

Ed, the static refractive index n0, the oscillator strength S0 and average

oscillator wavelength λ0 were determined. The values of E0 varies between

3.811 eV and 3.966 eV and the values of Ed between 0.324 eV and 0.721 eV

in the present glass systems.

118

• The ratio of free carrier concentration to the free carrier effective mass Nc/m*,

the optical relaxation time τ and ε∞ the high frequency dielectric constant were

determined in the present glass systems.

• The real and imaginary parts of the optical conductivity dependence of energy

in xLi2O–(30−x)Na2O–10WO3–60B2O3 glasses increases non-linearly with

increasing photon energy. This suggests that the increase in optical

conductivity is due to electron excitation by photon energy. The non-linear

variation of optical conductivity with compositional parameter indicates the

existence of mixed alkali effect.

• Energy band gap based electronic polarizability of oxide ions −2Oα (E0),

optical basicity Λ(E0) and interaction parameter A(E0) were evaluated for the

present glass systems. From the obtained values of −2Oα , Λ and A, the present

glasses were classified as normal ionic (basic) oxides.

119

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