DIELECTRIC DISPERSION AND SPECTROSCOPIC

INVESTIGATIONS ON NA2SO4–B2O3–P2O5 GLASSES MIXED WITH LOW

CONCENTRATIONS OF TIO2

CHAPTER 3

In CHAPTER–III, a series of Na2SO4–B2O3–P2O5 glasses doped with different

concentrations of TiO2 (0 to 1.0 mol%) have been synthesized. Dielectric properties (over a

range of frequency and temperature) and a variety of spectroscopic (optical absorption,

IR, Raman and ESR) properties of these glasses have been investigated. The values of

dielectric parameters viz., dielectric constant, loss and ac conductivity at any frequency

and temperature are observed to increase with the concentration of TiO2. The optical

absorption and ESR spectral studies have pointed out that a part of titanium ions do exist

in Ti3+ state in addition to Ti4+ state especially in the samples containing higher

concentration of TiO2 The increase of dielectric constant with the concentration of TiO2 is

explained on the basis of space charge polarization due to increasing concentration of

various bonding defects in the glass network. The dielectric relaxation effects exhibited by

these glasses are quantitatively analyzed by pseudo Cole-Cole method and the spreading

of relaxation times is established. The ac conductivity is observed to increase with

increasing content of TiO2 , the mechanism responsible for such increase is well explained

based on the modifying action of Ti3+ ions.

Dielectric dispersion and spectroscopic investigations on Na2SO4–B2O3–P2O5 glasses mixed with low concentrations of TiO2

3.1 Introduction

Alkali sulphate mixed phosphate glasses are being used to immobilize

radioactive waste for long time safe storage [1]. These glasses are also proved

to be suitable for their application in micro batteries, smart card, medical

appliance [2, 3]. These materials exhibit high electrical conductivity (purely

ionic), compatible with the electrode materials and are thermally and

chemically stable. The SO42- ions largely dissolve in the phosphate glass matrix

and mostly remain as isolated units [4]. However, there are also reports

suggesting that sulphate ions and metaphosphate ions interact weakly and form

a small dynamic concentration of dithiophosphate (DTP) units in the glass

matrices [5]. Such weak and variable interaction between these two ions is

expected to influence the electrical properties to a large extent. A considerable

number of previous studies on a variety of physical properties of different

alkali sulfophosphate glasses are available in the literature [6-9]. The

introduction of B2O3 to alkali sulfophosphate glasses is expected to increase

the thermal stability of the glass network (since borate groups form M+[BO4]-

pairs) and also reported to increase the electrical conductivity [10-13].

The chemical inertness, thermal stability and also electrical properties of

alkali borosulfophosphate glasses can further be improved by mixing a small

quantity of TiO2 to the glass matrix. The addition of TiO2 further makes

75

borosulfophosphate glasses suitable for applications in non-linear optical

devices, integrated circuits and low loss optical waveguides [14]. Kityk and his

co-workers have reported extensive studies on non-linear optical (NLO)

properties of similar type of glass systems. Their studies have yielded valuable

information which will be useful for considering these types of glasses for

optically operated NLO devices [15, 16].

Normally, the ions of titanium exist in the glass in Ti4+ state and

participate in the glass network forming with TiO4, TiO6 and some times with

TiO5 (comprising of trigonal bipyramids) structural units [14, 17] . However,

there are also reports suggesting that these ions may also exist in Ti3+ valence

state in some of the glass matrices and acts as modifiers [17, 18]; such

variation in the coordination and valence of titanium ions are expected to cause

the structural modifications and local field variations in the glass network and

expected to influence the electrical properties to a large extent.

This part of the thesis is devoted to the studies on the influence of

titanium ions on dielectric and ac conductivity properties of Na2SO4–B2O3–

P2O5 glasses. To have some pre-assessment over the structural aspects of the

glasses which may help for clear understanding of the dielectric properties, we

have also undertaken the studies on optical absorption, ESR and IR studies.

The detailed compositions of the glasses used in the present study are as

follows:

76

T0: 40.0Na2SO4–30B2O3–30P2O5

T2: 39.8Na2SO4–30B2O3–30P2O5: 0.2TiO2

T4: 39.6Na2SO4–30B2O3–30P2O5: 0.4TiO2

T6: 39.4Na2SO4–30B2O3–30P2O5: 0.6TiO2

T8: 39.2Na2SO4–30B2O3–30P2O5: 0.8TiO2

T10: 39.0Na2SO4–30B2O3–30P2O5: 1.0TiO2

3.2 Brief Review of the previous work on TiO2 glass systems

Titanium is a common constituent of glasses and glass ceramics, and

silica with a few percent of TiO2 [19] is used for length standards and

astronomical mirror blanks because of its low–even negative–coefficient of

thermal expansion [20]. Recently, titania-doped silica played a crucial role in

the development of optical fibres [21]. At low concentrations, titanium

introduces new absorptions at the low-energy side of the principal silica

absorptions in both the IR and ultraviolet (UV). Smith et al have been reported

that, these are due to perturbed vibrational modes involving Ti–O–Si bonds

and to perturbed excitons arising from substitution of Ti4+ for Si4+[22].

TiO2–SiO2 mixed oxide glasses have received considerable attention

because of their interesting properties such as good chemical stability, low

thermal expansion coefficient, and high refractive index that lead to their

potential application in optoelectronic devices. [23-25]

Schultz reported that the SiO2–TiO2 glasses possess interesting

properties, i.e., up to about 10 mol% TiO2, titanium ions exists in fourfold

77

coordination and up to 16 mol% in a metastable state with titanium separated

in a second phase and octahedrally coordinated [26].

Conventional glass ionomer cements (GICs) was originally investigated

by Wilson & Kent [27] nearly 42 years ago. These materials are made of a

powder and liquid, which are mixed to generate a plastic mass, and afterward

changes to a rigid solid. A GI liquid is derived from an aqueous polyalkenoic

acid, for instance polyacrylic acid and the GI-powder is principally made of

fluoroaluminosilicate glass. When the powder and liquid are combined

together, an acid-base reaction happens [28]. GICs are beeing widely used as

an alternative of amalgam for restorative materials owing to their excellent

biocompatibility [29, 30]. These cements are translucent and adhesive to tooth

structure because of the similar coefficient of thermal expansion of glass

ionomer to tooth structure [31]. In previous study by Monmaturapoj, et al [32],

it was found that the glass contained ZrO2 had improved the strength of cement.

TiO2 is well known as the strong and tough material, and has similar structure

to ZrO2. Then, it was selected in this study to be doped in glass structure to

induce the strength. Therefore Not only TiO2 affected on the strength but also

shape of glass particles, powder to liquid ratios and concentration of acidic

copolymer. All these factors were studied for the purpose in improving the

compressive strength of GICs.

78

Chengbin Jing [33] has investigated on the SiO2–TiO2–GeO2 sol–gel

glass system and it was firstly ascertained to be the material to use in the

fabrication of a hollow waveguide for application in CO2 laser delivery.

Lee et al [34] reported that the TiO2 has been confirmed the

improvement in the mechanical properties of MgO–CaO–SiO2–P2O5 glass

systems and solved the problems of formation of cracks and showed that the

growth of crystalline layer is slowed down initial stage. These materials are

found to be very important in the biological and industrial field to elaborate

artificial bones and teeth.

Watanabe et al [35] studied and reported that the TiO2–BaO–ZnO–B2O3

glasses containing transition d-block metal oxides, such as TiO2, and proved

that these materials have potential application for nonlinear optics[36,37] and

as precursors for porous glass-ceramics[38-40]. In these systems, several

studies devoted to establish the role of TiO2 as a network-former and/or

network modifier as well as to determine if Ti4+ ions are fourfold or sixfold

coordinated [41, 42] These last aspects, and the high polarizability of titanium

ions, have been used to explain the increase of linear index and the nonlinear

characteristics for the high content titanium oxide glasses [36, 43, 44].

Inoue et al [45] reported that the TiO2-containiing glasses are expected

as alternatives of Pb-containing glasses and optical materials, and they have

been extensively studied in recent years. In oxide glasses, Ti4+ ions take

various coordinate structures as TiO4, TiO5 and TiO6, resulting in the specific

79

characteristics. Ti ions in tetrahedral TiO4 units are regarded as network former

(NWF), and those in octahedral TiO6 units are as network modifier (NWM). Ti

ions in TiO5 units play an intermediate role between NWF and NWM. TiO5

units are in a tetragonal pyramid structure with an extremely short Ti–O bond

in the axial direction. The oxygen atom in the axial Ti–O bond is regarded as

non-bridging oxygen (NBO), and the rest are attributed to bridging oxygen

(BO). A number of reports have been published concerning the coordination

structures of Ti ions in glass. Sakka et al. [46, 47] reported that Ti ions mostly

existed in TiO4 units in K2O–TiO2 and Cs2O–TiO2 glass systems. Kusabiraki et

al. [48] reported that coordination number of Ti ions in Na2O–TiO2–SiO2

glasses changed from 4 to 6 with increasing Na2O content.

Gulati et al [49] reported that the glass can be used in the ground and

space-based telescope industry for many years. More recently, Ti-doped silica

glass was chosen as a material for reflective mirrors in an extreme ultraviolet

lithography (EUVL) system [50]. In addition to its thermal expansion

properties, Ti-doped silica glass possess optical absorption characteristics that

are useful in making mirrors and other optical components, such as the high

index core of low loss fiber optical waveguides [51]

Hashimoto et al [52] have reported that TiO2–B2O3–P2O5 (TBP) based

glasses are promising materials as molding glasses with high transparency, low

Tg, and high nd. Ma et al [53] have studied the effect of TiO2 on phase

separation and crystallization of glass ceramics in CaO–MgO–Al2O3–SiO2–

80

Na2O system. From FESEM observation and EDS analysis, they concluded

that the more TiO2 content of glass, the more droplet separated phase and

crystal seeds are found after nucleation heat treatment. Tiefeng et al [54] have

studied the third-order optical nonlinear properties of Bi2O3–B2O3–TiO2

glasses using femto-second Z-scan method at 800 nm. The results have showed

that third-order optical nonlinearities are influenced by TiO2 concentration; the

largest value of nonlinear refraction γ obtained for these glasses is ~

8.85×10−14 cm2/W. Gorokhovsky et al [55] have investigated the vitrification

and crystallization behavior of melts produced at 1400 °C in the K2O–B2O3–

TiO2 ternary system. They have discussed that the obtained glass ceramic

materials as a source of fibrous TiO2, for composite reinforcement and as solid

lubricants. Hamzawy et al [56] have studied the effect of different

concentrations of titanium oxide (TiO2) on the crystallization behavior of

Li2O–Al2O3–SiO2 glasses prepared from local raw materials. Duhan et al [57]

have reported the frequency and temperature dependent conductivity

measurements on heat treated titanium bismuth silicate glasses by using

impedance spectroscopy in the frequency range from 20 Hz to 1 MHz. They

have observed an enhancement in conductivity of about 101-102 order is in heat

treated sample as compared to parent glass.

Chen et al [58] have investigated the third order optical nonlinear

properties in Bi2O3–B2O3–TiO2 transparent glass ceramics and they found that

large values of nonlinear refractive indices n2 in both as-quenched (1.983×10-13

81

cm2/W) and heat treated (2.645×10-13 cm2/W) transparent samples. The

influence of titanium ions on various physical properties including colour,

thermal expansion, compressibilities, elastic constants, sound velocities,

densities, viscosities, nucleation rates etc on a variety of inorganic glasses has

been reported by a number of researchers [59-68]. Kishioka et al [69] have

reported that the addition of TiO2 to phosphate glasses stabilizes the glass

structure. Lange and Navrotsky [70] have measured anomalously high

variations in heat capacities in some titanosilicate melts at temperatures just

above the glass transition temperatures. Information on the local structure

environment of Ti4+ ions in oxide glasses under ambient conditions has been

provided by a number of investigators by a variety of techniques like, Raman

spectroscopy [71-76], neutron scattering experiments [77], X-ray photo

electron spectroscopy [78], X-ray scattering experiment [79], X-ray absorption

fine spectroscopy [80-82] etc. Wu et al [83] have reported the dissolution of

TiO2 in calcium zirconoboro silicate glasses.

Lacerda et al [84] have investigated TiO2 - induced phase separation

and crystallization in SiO2–CaO–P2O5–MgO glasses. Laudisio et al [85] have

studied the devetrification behaviour of titanium in lithium germanate glasses.

Barbieri et al [86] have reported the effect of TiO2 on properties of alumino

silicate glasses and glass ceramics by thermal, microscopic and diffractometric

techniques. Fei Duan et al [87] have prepared BaO–SrO–TiO2–SiO2 glass

system and reported the piezoelectric properties of these glasses. Duan et al

82

[88] have studied the effect of changing TiO2 content on structure and

crystallization of CaO–Al2O3–SiO2 glass system. Abrahams and Hadzifejzovic

[89] have measured conductivity due to lithium ions in lithium alumino

phosphate glasses crystallized with TiO2. Grussaute et al [90] have reported

phosphate speciation in sodium phosphate silicate glasses containing TiO2.

Their studies revealed the formation of Ti–O–P covalent bonds, which they

have attributed to the electrostatic field strength of Ti4+ ions. Chowdari et al

[91] have recently reported XPS and ionic conductivity studies on lithium

alumino phosphate glass ceramics containing TiO2. Jivov et al [92] have

studied the crystalline nature of P2O5–CaO–ZnO glass system containing

titanium ions. Shaim et al [93] have reported the role of titanium in Na2O–

Bi2O3–P2O5 glasses on the structural properties. Aboukais et al [94] have

reported the EPR spectra of silica and fluoride glasses implanted with titanium.

Though, a considerable number of studies on some TiO2 glasses and glass

ceramics are available, still there is a lot of scope to investigate the role of

titanium ions on the structural aspects of Na2SO4–B2O3–P2O5 glasses and their

influence on physical properties.

3. 3. Results

3. 3.1. Physical parameters

The physical parameters such as titanium ion concentration Ni, mean titanium

ion separation Ri and polaron radius Rp were evaluated from the measured

83

values of density d and calculated average molecular weight M using the

conventional formulae [95] and were furnished in Table 3.1.

Table 3.1 Physical parameters of Na2SO4–B2O3–P2O5: TiO2 glasses

3. 3.2. DTA studies

In the Fig. 3.1, DTA scan for Na2SO4–B2O3–P2O5 glasses doped with

0.6 mol% of TiO2 is presented; the thermogram exhibited a typical glass

transition with the inflection point at about 415 oC following by an exothermic

peak due to crystallization at about 810 oC. With the increasing content of TiO2

in the glass matrix, the glass transition temperature is observed to decrease

(inset of Fig. 3.1). The value of (Tc–Tg), a parameter that represents thermal

stability of glass against devitrification, is found to decrease with the content

of TiO2 (inset of Fig. 3.1).

Glass → Physical parameter↓

T0 T2 T4 T6 T8 T10

Density d (g/cm3) 2.5556 2.5609 2.5678 2.5776 2.5844 2.5876

Dopant ion conc. Ni (x1020 ions/cm3)

--- 0.25 0.51 0.77 1.03 1.29

Interionic distance Ri (A

o) --- 33.98 26.94 23.49 21.32 19.77

Polaron radius Rp (Ao)

--- 13.69 10.89 9.47 8.59 7.97

Field Strength Fi (1015, cm-2)

--- 0.16 0.25 0.33 0.41 0.47

84

3.3.3 Optical absorption spectra

Fig. 3.2(a) presents optical absorption spectra of Na2SO4–B2O3–P2O5:

TiO2 glass samples recorded at room temperature in the wavelength region

300-1000 nm. The absorption edge for TiO2 free glass is identified at 288 nm,

whereas for the glass T2, it is observed at 312 nm. As the concentration of TiO2

is increased the edge exhibited red shift. Additionally, the spectrum of glass T2

exhibited two clearly resolved absorption bands at 516 and 691 nm.

Table 3.2 Data on optical absorption spectra Na2SO4–B2O3–P2O5: TiO2 glasses

As the concentration of TiO2 is continued to increase, the half width and

intensity of these two bands are observed to increase with the shifting of the

peak positions towards slightly longer wavelength (Table 3.2).

Band positions (nm) Glass

Cut-off wavelength (nm) 2B2g→ 2B1g

2B2g → 2A1g

Optical band gap (eV)

T0 292 - - 4.25

T2 318 509 678 3.90

T4 325 516 691 3.82

T6 329 524 698 3.77

T8 331 527 700 3.75

T10 354 532 706 3.50

85

Fig. 3.1 DTA trace of T6 glass. Inset shows the variation of Tg and Tc-Tg with the concentration of TiO2.

300 400 500 600 700 800 900 1000

Tg

Tc

390

430

0.2 0.4 0.6 0.8 1.0

380

420

Tc -T

g (o C

)

Tg (o C

)

Conc. TiO2 (mol%)

Temperature (oC)

End

oE

xo

86

Fig. 3.2(a) Optical absorption spectra of Na2O4–B2O3–P2O5: TiO2 glasses

2

6

10

14

18

22

26

30

250 350 450 550 650 750 850

2B2g → 2B1g

2B2g → 2A1g

Wavelength (nm)

Opt

ical

den

sity

(cm

-1)

T10

T2

T0

T4

T6

T8

87

Fig. 3.2(b) Tauc plots of Na2O4–B2O3–P2O5: TiO2 glasses. Inset shows the variation of optical band gap with the concentration of TiO2

88

From the observed absorption edges, we have evaluated the optical band

gaps (Eo) of these samples by drawing Tauc plots (Fig. 3.2 (b)) between

(α ωh )1/2 and ωh as per the equation [96]:

( ) ( )2oEc −= ωωωα hh (3.1)

A considerable part of each of these curves is observed to be linear indicating

that Eq. (3.1) is valid. The validity of this quadratic equation points out that the

optical band gap is caused by amorphous optical absorption edge. Some

deviations observed from this dependence may be due to trapping by

disordered states within the energy gap.

From the extrapolation of the linear portion of the curves of Fig. 3.2 (b),

the value of optical band gap (Eo) is determined and its variation with the

concentration of TiO2 is shown as the inset of the Fig. 3.2(b); the variation of

Eo with the content of TiO2 exhibited a decreasing trend

3.3.4 ESR spectra

ESR spectra of Na2SO4–B2O3–P2O5 glasses doped with different

concentrations of TiO2 recorded at room temperature are presented in Fig. 3.3.

The spectrum of glass T2 consists of an intense asymmetric spectral line

centered at about g = 1.970. The half width and the intensity of this signal

exhibited a gradual increase with the concentration of TiO2. The intensity (ℑ )

of the ESR signal, assumed to be proportional to the product of the peak-to-

peak height (I) and the square of its width (∆B)

89

ℑ ≈ I (∆B)2 (3.2)

is evaluated and its dependence with the concentration of TiO2 is shown as an

inset of Fig. 3.3. The figure shows that the intensity of the resonance signal

increases with increase in the concentration of TiO2.

3.3.5 IR spectra

The IR spectra (Fig. 3.4) of Na2SO4–B2O3–P2O5: TiO2 glasses exhibited

conventional vibrational bands due to phosphate groups in the regions 1277-

1295 cm−1 (anti−symmetrical vibrations of −2PO groups / P=O stretching

vibrations), 1085-1106 cm−1 (a normal vibrational mode of −34PO group arising

out of ν3 − symmetric stretching), 927-944 cm−1 (P−O−P asymmetric bending

vibrations/ this region may also consist of bands due to pyrophosphate groups

P2O74−) and another band in the region of 760 - 790 cm-1 due to P–O–P

symmetric stretching vibrations [97]. The spectra have also exhibited three

usual bands originated from borate groups in the regions 1381-1414 cm−1 due

to BO3 units, 944 - 964 cm−1 due to BO4 units and 709-724 cm−1 due to

bending vibrations of B–O–B linkages [98]. In the spectral regions 658-678

cm−1 and 1124-1148 cm−1 vibrational bands corresponding to bending and

asymmetric modes of SO42− groups, respectively are also observed [99, 100];

90

Fig. 3.3 ESR spectra of Na2O4–B2O3–P2O5: TiO2 glasses recorded at room temperature. Inset shows the variation of intensity of the signal with concentration of TiO2

200 250 300 350 400 450 500

T2

T4

T6

T8

T10

Fir

st d

eriv

ativ

e of

abs

orp

tion

(arb

. uni

ts)

Magnetic field (mT)

0.2 0.6 1.0Conc. TiO2 (mol%)

91

With the gradual introduction of TiO2 in the glass network, all the

asymmetrical bands are observed to grow at the expense of symmetrical bands.

The band due to Ti–O–Ti symmetric stretching vibrations of TiO4 units is also

expected in the region of P–O–P symmetric stretching vibrations (at about 760

cm-1). The pertinent data related to IR spectra are presented in Table 3.3.

Table 3.3 Data on infrared spectra Na2SO4–B2O3–P2O5: TiO2 glasses recorded at room temperature (Assignment of band positions in cm-1).

3.3.6 Dielectric Properties

The dielectric constant ε' and loss tan δ at room temperature ( ≈ 30 °C)

of TiO2 free Na2SO4–B2O3–P2O5 glasses at 1 kHz are measured to be 10.8 and

0.004, respectively. With increase in the concentration of TiO2 in the glass

matrix, these values are observed to increase considerably.

SO42- units Glass

sample BO3

units PO2- asym.

ν1 ν2

P-O-P asym. stretching

PO43-

groups/ BO4 units

P-O-P sym. stretch. &TiO 4 units

B-O-B linkages

TiO6 units

T2 1414 1295 1148 658 1085 944 762 709 620

T4 1405 1291 1146 664 1092 953 772 713 612

T6 1398 1286 1141 669 1094 958 779 717 601

T8 1390 1282 1135 671 1101 962 783 719 592

T10 1381 1277 1124 678 1106 964 797 724 581

92

Fig. 3.4 IR spectra of Na2O4–B2O3–P2O5: TiO2 glasses

400500600700800900100011001200130014001500Wave number (cm-1)

Tra

nsm

ittan

ce %

(1)

(1) BO3 units

(2) PO2- asymmetric

(3a) assymetric SO42- units

(3b) bending SO42- units

(4) P-O-P asymmetric

(5) PO43- groups/BO4 units

(6) P-O-P symmetric stretching and TiO4 units

(7) B-O-B linkages(8) TiO6 units

(6)

(5)(4)(3a)

(2)

(3b)(7)(8)

93

Fig. 3.5 represents the temperature dependence of ε' at 1 kHz of

Na2SO4–B2O3–P2O5 glasses doped with different concentrations of TiO2 and

the dependence of ε' with temperature at different frequencies for the glass T2 is

shown an inset of the same figure. The value of ε' exhibited a considerable

increase at higher temperatures especially at lower frequencies; the rate of

increase of ε' with temperature at any frequency is found to increase with

increase in the concentration of TiO2.

Fig. 3.6(a) represents a comparison plot of variation of tanδ with temperature,

measured at a frequency of 10 kHz for Na2SO4–B2O3–P2O5 glasses doped with

different concentrations of TiO2. Fig. 3.6(b) represents the temperature dependence of

tan δ of glass T6 at different frequencies. Variation of tanδ with temperature has

exhibited distinct maxima; with increase in frequency, the temperature maximum of

tanδ shifts towards higher temperatures and with increase in temperature, the

frequency maximum shifted towards higher frequencies, such variation indicates the

relaxation character of dielectric losses in these glasses [104]. The full width at half

maximum (FWHM) and the peak value (tan δ)max of the relaxation curve (that

represent the strength of the relaxation character) are observed to increase gradually

with the content of TiO2. Using the relation:

f = fo exp (_Wd/kBT), (3.3)

94

Fig. 3.5 A comparision plot of variation of dielectric constant with temperature at 1 kHz for Na2O4–B2O3–P2O5: TiO2 glasses. Inset gives the variation of dielectric constant with temperature at different frequencies of glass T2.

0

50

100

150

200

250

300

25 50 75 100 125 150 175 200 225 250Temperataure (oC)

εεεε'

T2

T8

T6

T4

T10

0

50

100

150

25 75 125 175 225Temperataure (oC)

εεεε'

0.1 kHz

100 kHz

10 kHz

1 kHz

95

Fig. 3.6 (a) A comparision plot of variation of Tan δ with temperature at

10 kHz for Na2O4–B2O3–P2O5: TiO2 glasses. (b) Variation of Tan δ with

temperature at different frequencies of glass T6

0.00

0.10

0.20

0.30

25 50 75 100 125 150 175 200 225 250Temperataure (oC)

Tan

δ

T2

T8

T6

T4

T10

0.00

0.10

0.20

25 50 75 100 125 150 175 200 225 250

0.1 kHz

100 kHz

10 kHz

1 kHz

Temperataure (oC)

Ta

n δ

(b)

(a)

96

Fig. 3.7 Variation of sac with 1/T at 100 kHz of Na2O4–B2O3–P2O5: TiO2 glasses. Inset (a) represents the variation of ac conductivity with activation energy, (b) variation of ac conductivity with different frequencies for the sample T6 and (c) Variation of exponent with the concentration of TiO2

1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

σ ac

( Ω-

cm)-1

1/T (10-3, K-1)

T2

T8

T6

T4

T10

0.65 0.85A.E. (eV)

σ ac

( Ω-

cm)-1

10-6

10-5

(a)

Frequency (Hz)

σ ac

( Ω-

cm)-

1

10-7

10-5

102104103

105

(b)

0.6

0.9

0.2 0.4 0.6 0.8 1.0

Conc. TiO2 (mol%)

Exp

on

en

t (s) (c)

10-4

10-5

10-6

10-7

97

Fig.3. 8 Variation of ε' and ε'' with 1/T at a frequency 10 kHz for the sample T10

10

30

50

70

90

110

3.3 2.9 2.6 2.4 2.2 2.0

0

1

2

3

4

1/T, 10-3 K-1

εεεε' εεεε''

ε ε

98

0.0

2.0

4.0

15 20 25 30εεεε'

εεεε''

πβ/2πβ/4

ωτo = 1

T

Fig. 3.9 A pseudo Cole–Cole plot at 10 kHz for the glass sample T8

the effective activation energy, Wd, for the dipoles is evaluated for the glasses doped

with different concentrations of TiO2. In Eq. (3.3), f is the relaxation frequency, kB is

the Boltzmann constant, T is absolute temperature and fo is a constant. The

activation energy Wd is found to decrease with increase in the concentration of TiO2

(Table 3.4).

99

Table 3.4 Summary of data on dielectric loss of Na2SO4–B2O3–P2O5: TiO2 glasses:

The a.c. conductivity σac is calculated at different temperatures using the

equation:

σac = ω ε'εo tan δ , (3.4)

(where εo is the vacuum dielectric constant and ω is the angular frequency) for

different frequencies and the plot of log σac against 1/T for all the glasses at

100 kHz is shown in Fig. 3.7; the conductivity is found to increase

considerably with increase in the concentration of TiO2 at any given frequency

and temperature. From these plots, the activation energy for the conduction in

Glass (tanδ)max.avg.

Temp. region of relaxation (oC)

AA. E. for dipoles (eV) (± 0. 01)

Spreading factor β

A. E. for conduction (eV) (± 0. 01)

Exponent s

T2 0.050 113-158 0.65 0.46 0.81 0.65

T4 0.061 97-147 0.62 0.48 0.79 0.70

T6 0.078 90-140 0.59 0.50 0.76 0.73

T8 0.126 79-128 0.56 0.53 0.70 0.77

T10 0.161 68-118 0.53 0.55 0.67 0.81

100

the high temperature region is evaluated and presented in Table 3.4 along with

other pertinent data.

3. 4. Discussion

The composition of Na2SO4–B2O3–P2O5: TiO2 glass system is an

admixture of glass formers, modifiers and intermediates. P2O5 is a strong glass

forming oxide, participates in the glass network with PO4 structural clusters.

The PO4 tetrahedra are linked together with covalent bonding in chains or rings

by bridging oxygens. Neighboring phosphate chains are linked together by

cross-bonding between the metal cation and two non-bridging oxygen atoms of

each PO4 tetrahedron [105]. The presence of such PO4 units in the titled glass

samples is evident from the IR spectral studies. B2O3 is also a strong glass

former, when it is mixed in the phosphate glasses, the tetrahedral boron entities

dominate in the phosphate-rich domain where as trigonal boron entities prevail

in the borate-rich side and form easily B–O–P bridges. The highest stability

occurs for fully polymerized glasses and can be related to the energetics of the

reaction B–O–B + P–O– P = 2(B–O–P); this relation also suggests that the B–

O–P linkage is more stable relatively than the mixture of B–O–B and P–O–P

linkages [106-109].

With the addition of Na2SO4 a gradual depolymerization of the

phosphate chains and formation of short phosphate units take place. During

this process the sulphate units remain as terminal groups without any chemical

101

interaction with the phosphate units [4]. As a consequence, variation in the

density is hardly expected with the variation in the content of Na2SO4; however,

due to the formation of dithiophosphate (DTP) units (due to the weak

interaction between pyrophosphates), a slight increase in the density is possible

(Table 3. 1). Normally the phosphate network contains [POO2/2O]- (phosphate

tetrahedra with one bridging oxygen) and [POO1/2O2]2- (phosphate tetrahedra

with two bridging oxygens) structural groups [110] as shown below:

O

P O P

O

O

OO

O + O2- → O P2

o

O-

o

+ O2- →

O

P O P

O

O-

OO

-O O P2O-

O

O-

Out of these two ions, it is the [POO2/2O]- ion that interacts with sulphate ion

and form SPO73- (dithiophosphate) species [98]. However there are some

affirmative reports (based on Raman and NMR investigations) on

sulfophosphate glasses suggesting that SO42- species do not contribute to

network formation and instead these groups participate in the

depolymerization of the phosphate network similar to Ti3+ and Na+ ions [111].

Titanium ions exist mainly in Ti4+ state in Na2SO4–B2O3–P2O5 glass

network. Nevertheless, the reduction of Ti4+ to Ti3+ is unavoidable during

melting at high temperatures and annealing processes of the glasses. Ti4+ ions

102

occupy both tetrahedral and substitutional octahedral sites as corner-sharing

[TiO6]2- units where as Ti3+ ions occupy only modifying positions and

depolymerize the glass network. TiO4 and TiO6 units of Ti4+ ions enter the

glass network and form linkages of the type P–O–Ti and B–O–Ti.

In detail the interaction of TiO2 with phosphate, borate and borophosphate

networks may be represented as follows:

(i) P2O5 ≡ 2 [POO3/2]; TiO2 ≡ [TiO4/2]; TiO2 + 2 [POO3/2] ⇒ [TiO6/2]2- + 2

[PO4/2]+

and diagrammatically as

O- O- O O O P O Ti O P O [TiO6/2]

2- + 2[PO4/2]

+ O O O- O-

(ii) B2O3 + 2TiO2 + 2O2 → 2[BO6/2]3 + [TiO4/2] + [TiO6/2]

(iii) B 2O3 + 3TiO2 + 2P2O5 + O2 → 2[BO6/2]3 + 4[PO4/2]

+ + 2[TiO4/2] + [TiO6/2]

These equations clearly suggest that incorporation of the Ti ions into the glass

network leads to some d-p charge transfer between the 3d Ti ions and the

surrounding ligands.

103

3. 4. 1 DTA

Tg and Tc–Tg values evaluated from DTA traces show a decreasing trend

with increase in the concentration of TiO2. Such trend indicates the decrease of

augmented cross–link density of various structural groups and closeness of

packing. This is possible only if there is a gradual increasing proportion of

Ti3+ ions that act as modifiers in the glass network.

3. 4. 2 Optical absorption Spectra

The electronic configuration of Ti3+ ion is 3d1. In octahedral field or

tetrahedral field, the ground state 2D of the 3d1 ion splits into 2E and 2T2 states.

In the tetragonally distorted octahedral field, the 2T2 state further splits into

three 2B2g (viz. xy , yz and zx ) states, whereas, the 2E excited state splits

into A1g223 rz − and B1g 22 yx − states. For d1 ions in tetragonally

compressed octahedron, the ground state is B2g xy . Hence, the bands

observed in the optical absorption spectra at about 540 nm and 690 nm of the

studied glass are assigned to 2B2g→2B1g and 2B2g→

2A1g transitions of the Ti3+

ions, respectively [112, 113]. With increase in concentration of TiO2, a gradual

growth of these two bands could clearly be seen; this observation indicates that

there is an increasing fraction of Ti3+ ions in the glass network.

The octahedrally coordinated Ti3+ ions, similar to Na+ ions, act as

modifiers and are expected to induce non-bridging oxygens (NBO’s) in the

glass network. The analysis of IR spectral results have also indicated that, in

104

the samples containing higher concentration of TiO2, the asymmetric

vibrational bands of phosphate groups dominate over symmetric bands. These

factors indicate an increase in the concentration of NBO’s in the glass network

with increase in the concentration of TiO2. Because of these reasons an

increase in the degree of localization of electrons there by an increase in the

donor centers in the glass network is possible. The presence of higher

concentration of these donor centers decreases the optical band gap and shifts

the absorption edge gradually towards higher wavelength side. The gradual

decrease in the proportion of network forming Ti4+ ions in the glass network

leads to an increase in the generation of donor centers; as a consequence, there

will be an increasing overlap between empty 3d states of Ti4+ sites and the

neighboring excited states of localized electrons originally trapped on Ti3+ ions.

Such overlap facilitates for the shrinkage of optical band gap and hence there is

a decrease of optical band gap with increase in the content of TiO2, as observed

(Table 3.3). In other words, the 3d levels of Ti ion within the effective energy

gap will be influenced by bonding-anti-bonding of 2p–O–2p B and s Na levels

to a large extent and contribute for the observed decrease of optical band gap.

The optical activation energy associated with the octahedral band of Ti3+

ions viz., 2B2g→2B1g is decreased from 2.44 eV to 2.32 eV with the increase

in the concentration of TiO2 from 0.2 to 1.0 mol% (Table 3.2); this is clearly a

characteristic signal of inter valence transfer or a polaronic type of absorption.

To be more specific, the associated electrons are trapped at shallow sites within

105

the main band gap. In terms of polaronic perception, this kind of situation is

only possible if the local potential fluctuation is small as compared to the

transfer integral, j. A small overlap between electronic wave-functions

(corresponding to adjacent sites) due to strong disorder is contributive to

polaron formation. So in terms of the polaron exchange the variation of optical

band gap can be explained as fallows: the electron delivered by the impurity

atom at the Ti4+ site converts this into a lower valence state Ti3+ and at the next

stage, the trapped electron at this Ti3+ site is transferred to the neighboring new

Ti4+ site by absorbing a photon energy. Thus the optical absorption in the glass

samples is dominated by polaronic transfer between the Ti3+ and Ti4+ species

[114, 115].

3. 4. 3 ESR Spectra

In the ESR spectra, the central line observed at g =1.987 is due to

tetragonally compressed octahedral excitations of Ti3+ ions from the ground

state xy [116, 117]. The observed increase of intensity and half-width of the

signal with the increase in the content of TiO2 suggests a gradual increase in

the concentration of Ti3+ ions in the glass network.

The other factors e.g., the jumping frequency of the charge carriers (from Ti3+

to Ti4+) which is proportional to exp (–W/kT) also accounts for such variations.

Here W=1/2 WD (mean energy difference between adjacent titanium ion sites)

+ WH (the activation energy for the hopping process of the polarons between

two identical sites). As the concentration of TiO2 is increased gradually, the

106

jumping rate of the polaron increases. This fact, together with the increasing

concentration of the Ti3+ accounts for the increasing intensity of the ESR signal.

3. 4. 4 IR Spectra

The IR spectral studies have revealed the intensity of the bands due to

asymmetric vibrations of phosphate groups and also BO3 groups grow at the

expense of symmetrical bands of phosphate and BO4 groups with increase in

the content of TiO2. Such variations suggest increasing modifying action of

titanium ions by creating larger number NBO’s in the glass network. As a

result, the phosphate coordination reduces from four fold to three fold, two fold

and even to one dimensional and the depolymerization of P–O–P, B–O–B, P–

O–B and also P–O–Ti chains takes place and the strength of the glass network

decreases. Thus the results of IR spectral studies point out that, there is

growing degree of disorder in the glass network with the increase in the

concentration of TiO2.

3. 4. 5 Dielectric properties

The dielectric parameters viz., ε', tan δ and σac are found to increase with

increase in temperature for all the studied glasses. Further, at any frequency

and temperature these parameters are found to increase with increase in the

content of TiO2 in the glass matrix. In general electronic, ionic, dipolar and

space charge polarizations contribute to the dielectric constant. Among these, it

is the space charge polarization (which depends up on concentration defects in

the glass network) that influences strongly the dielectric constant at lower

107

frequencies. As mentioned earlier, the Ti3+ ions similar to Na+ ions act as

modifiers and create dangling bonds and non bridging oxygen ions by

disrupting P−O−P, B−O−B, P−O−B, P−O−Ti and B−O−Ti linkages. In view

of this, the glass network consists of [SO4]2-, [POO1/2O2]

2–, [POO0/2O3]3–, Na+

and (NaSO4)- free ions (formed by the reaction, Na2SO4 ⇔ Na+ + (NaSO4)

− );

the defects thus produced create easy path ways for the migration of charges

that would build up space charge polarization and facilitate to an increase in

the dielectric parameters as observed [118-120]. Thus these results also support

the view point that there is an increasing degree of disorder in the glass

network due to the increasing fraction of Ti3+ ions that act as modifiers.

Conventionally, the dielectric relaxation effects are described with the

variable frequency at a fixed temperature. However, similar information can

also be obtained by analyzing these results at a fixed frequency at variable

temperature as suggested by Bottcher and Bordewijk [121].

Substituting Eq. (3.3) in standard Debye relations for dielectric relaxation, one

can obtain

[ ])ln(1)(),( 21' AkTWtghT ds ωεεεωε +−−+= ∞∞ (3.4)

)lncosh(

)(),( 2

1''

AkTWT

d

s

ωεεωε+

−= ∞ (3.5)

In Eqs. (3.4) and (3.5), ε∞ is temperature independent whereas, εs is largely

dependent on temperature. Keeping the fact in mind that the variation of

108

hyperbolic trigonometric functions in Eqs. (3.4) and (3.5) with temperature is

very minimal, these equations can be rewritten as

[ ]/))(11(1)(),( 21' kTTWtghT mds ωεεεωε −−−+= ∞∞ (3.6)

and [ ]kTTWT

md

s

/))(11(cosh

)(),( 2

1''

ωεεωε

−−= ∞ (3.7)

In Eqs. (3.6) and (3.7), Tm(ωωωω) is the temperature at where εεεε' exhibits

maximum value. Thus, as per the Eqs. (3.6) and (3.7), the plots of εεεε'(ωωωω, T) and εεεε''

(ωωωω, T) against 1/T should be centro symmetric and symmetric curves,

respectively in the dielectric relaxation region. As an example for one of the glass

samples (viz., T10) under investigation, the variations of εεεε'( ωωωω, T) and εεεε'' ( ωωωω, T)

with 1/T are shown in Fig.3. 8. The shape of these curves is well in accordance

with the Eqs. (3.6) and (3.7) and clearly confirms the relaxation character of

dielectric properties of these glasses.

With increase in the concentration of TiO2 an increase in the value of

(Tan δ)max and a shift region of dielectric relaxation towards lower temperature

have been noticed. Such variations indicate an increase in the concentration of

dipoles that contribute to the relaxation effects. The value of the effective

activation energy associated with the dipoles is observed to decrease with

increase in the content of TiO2 in the glass network (Table 3.4). This

observation points out that an increasing freedom for dipoles to orient in the

field direction. Earlier studies on the glasses containing variety of d1 ions (like

V4+, Mo5+, W5+, Cr5+, etc.,) indicated that the geometrical arrangement of these

109

ions with oxygens form complexes in such a way that they contribute to the

dielectric relaxation effects [122-125]; following these arguments , relaxation

effects exhibited by the present studied glasses can be attributed to Ti3+ (d1) ion

complexes.

Further, to know whether there is single relaxation time or spreading of

relaxation times for the dipoles, we have adopted a pseudo Cole-Cole plot

method (instead of conventional Cole-Cole plot between ε'(ω) and ε"(ω) at a

fixed temperature) suggested by Sixou [126] in which ε'(T) vs ε"(T) can be

plotted at a fixed frequency. The nature of variation of ε'(T) and tan δ with

temperature for these glasses indicates that the Cole-Davidson equation:

( )βωτ

εεεωεi

s

+−

+= ∞∞

1)(* . (3.8)

can safely be applied to these glasses. Separating real and imaginary terms of

Eq. (3.8), and rewriting with explicit temperature dependence of terms, one can

get

)(cos)]()[cos(),( TTT s βϕϕεεεωε β∞∞ −+=′ (3.9)

and )(sin)]()[cos(),( TTT s βϕϕεεωε β∞−=′′ . (3.10)

In Eqs. (3.9) and (3.10)

)(tan)(tan)( /11 KTWo

deAT ωωτϕ −− == . (3.11)

110

In Eq. (3.11) oA is a constant and Wd is the activation energy for dipoles.

The plot between ε'(T) and ε"(T) represented by the Eqs. (3.9) and (3.10) at a

fixed frequency is often called pseudo Cole-Cole plot, which cuts ε' axis at εs

and ε∞. Here, εs is known as high temperature dielectric constant (in contrast to

the low frequency dielectric constant in the conventional Cole-Cole plot) and

similarly ε∞ is the low temperature dielectric constant. The plot cuts ε' axis at

an angle of (π /2) β at low temperature side (as per Sixou [126]), here β is the

spreading factor for relaxation times. For Na2SO4–B2O3–P2O5 glass containing

0.8% of TiO2 (glass T8), a pseudo Cole–Cole plot at 10 kHz is shown in Fig.

3.9. The spreading factor β estimated from this plot is 0.61; such plots have

also been drawn for all the glasses and the value of β is estimated in a similar

way; the value of β is found to increase gradually with the increase in the

concentration of TiO2 (Table 3.3). The spreading of relaxation times in these

glasses may be understood as due to the experience of an approximately

random potential energy by the dipoles on diffusing through the distorted

structure of the glass [127, 128].

The activation energy associated with ac conductivity is found to

decrease with increasing TiO2 concentration. When log σac is plotted against

activation energy, Wac, a near linear relationship is found (inset (a) of Fig. 3.7).

This means that the conductivity enhancement is directly related to the

thermally stimulated mobility of the charge carriers in the high temperature

111

region. As mentioned earlier, the glasses under study exhibit mixed, ionic and

polaronic conductivity. Generally, electronic conduction is due to the polaron

hopping between Ti3+ and Ti4+ ions whereas, ionic conduction is due to

migration of Na+ ions. For these glasses, the ac conductivity increases with

increasing content of TiO2 (Fig. 3.7). One of the possible explanations for such

a behavior is that, the entry of Ti3+ ions into the glass network causes to

increase the concentration of dangling bonds in the glass network. This in turn

leads to decrease in the electrostatic binding energy and the strain energy for

the easy passage of conducting ions. Due to these reasons there will be a

substantial decrement in the jump distance of Na+ ions. Such behavior is in

good accordance with the observed decrease in activation energy for

conduction.

The frequency response of real part of ac conductivity is normally

described by power law dependence with ‘s’ as exponent:

10],)/(1[)( <≤+= sscdc ωωσωσ (3.12)

Indicating, σ (ω) is the sum of the dc conductivity and a fractional

power law dependent dispersive conductivity with exponent s. Here ωc is a

characteristic crossover frequency from dc to dispersive conductivity.

Within the framework of the linear–response theory, the frequency–dependent

conductivity can be related to

dtetrkTH

nq ti

R

c ωωωσ −∞

∫−=0

222

)(6

)( (3.13)

112

where q is the charge, nc is the mobile ion density, )(2 tr is the mean

square displacement of the mobile ions and HR is the Haven ratio (lies in

between 0.2 and 1.0) [129] which represents the degree of correlation between

successive hops.

More precisely, in Eq. (3.13) <r2> represents the mean squared

displacement particles performing random walks on a regular lattice. For

excursions shorter than the correlation length the mean squared displacement

r2 varies as a power law

t1-s . Under these conditions Eq. (3.12) modifies to

σ (ω) ∝ ωs (3.14)

with exponent s < 1. For the glass T2 , the value of ‘s’ (obtained by

plotting log σ (ω) vs ω, (inset (b) of Fig. 3.7)), is found to be 0.73. With

increase in the concentration of TiO2 the exponent is found to be increasing

gradually. In general‘s’ is a measure of the degree of interaction with the

environment. In fact this parameter depends on the glass composition and the

limit of measurement temperature. The low values of exponent ‘s’ (< 1) arises

from the distribution of the cluster sizes (determined by mutual correlations

between dipoles formed in the system) and the distribution of their relaxation

rates. Sidebottom while explaining the conduction mechanism in alkali

phosphate glasses, concluded that exponent‘s’ depends upon the

dimensionality of the local conduction space and it increases with increasing

113

dimensionality [130, 131]. Based on these studies the observed increase of ‘s’

( inset (c) of Fig. 3.7 ) with the concentration of TiO2. may be attributed to a

enhancement in the dimensionality of conducting space with increase in the

content of TiO2 [132].

The low temperature part of the conductivity (a near temperature

independent part as in the case of present glasses) up to nearly 70 oC can be

explained on the basis of quantum mechanical tunneling model [133] similar to

many other glass systems reported recently [134-136].

3.5 Conclusions

The glasses of the composition viz., (40-x)Na2SO4–30B2O3–30P2O5:

xTiO2 with 0 ≤ x ≤ 1.0 mol% in the steps of 0.2 were synthesized. Dielectric

and spectroscopic properties were investigated. The optical absorption and

ESR spectral studies revealed the existence of titanium ions in Ti3+ state in

addition to Ti4+ state in the glass network. The IR spectral results indicated the

degree of disorder in the glass network increases with the increase in the

concentration of TiO2. The values of dielectric parameters viz., dielectric

constant, loss and ac conductivity at any frequency and temperature are

observed to increase with the concentration of TiO2; the increasing space

charge polarization is found to be responsible for such an increase. The

dielectric relaxation effects exhibited by these glasses are quantitatively

analyzed by pseudo Cole-Cole method and the spreading of relaxation times is

established. The ac conductivity is observed to increases with increasing

114

content of TiO2; the mechanism responsible for such increase is well explained

based on the modifying action of Ti3+ ions.

115

References

[1] D. A. McKeown, I.S. Muller, H. Gan, I.L. Pegg, C.A. Kendziora, J. Non-Cryst. Solids 288 (2001) 191.

[2] X. Yu, J.B. Bates,G.E. Jellison Jr., F.X.Hart, J. Electrochem. Soc. 144

(1997) 524.

[3] F. Scholz, J. Solid State Electrochem. 15 (2011) 14.

[4] N. Da, O. Grassmé, K. H. Nielsen, G. Peters, L. Wondraczek, J. Non-Cryst. Solids 357 (2011) 2202.

[5] M. Ganguli, M.H. Bhat, K.J. Rao, Solid State Ionics 122 (1999) 23.

[6] I.A. Sokolov, I.V. Murin, V.E. Kriyt, A.A. Pronkin, Glass Phys. Chem. 37 (2011) 351.

[7] V. G. Vyatchina, L. A. Perelyaeva, M. G. Zuev and V. .L Mamoshin, Glass Phys. Chem. 29 (2003) 522.

[8] A.M. Pletnev, R.N. Lapina, O.B. Kozlova, S.G. Bamburov, Glass Phys. Chem. 28 (2002) 1.

[9] B.V.R. Chowdari, K.F. Mok, J.M. Xie, R. Gopalakrishnan, J. Non-Cryst. Solids 160 (1993) 73.

[10] G. Chiodelli, A. Magistris, Solid State Ionics 18 (1986) 356.

[11] R.V. Salokdar, V.K. Deshpande, K. Singh, J. Power Sources 25 (1989) 257.

[12] N.K. Karan, B. Natesa, R.S. Katiyar, Solids State Ionics 177 (2006) 1429.

[13] F. Muñoz, L. Montagne, L. Pascual, A. Durán, J. Non-Cryst. Solids 355 (2009) 2571.

[14] N. Shimoji, T. Hashimoto, H. Nasu, K. Kamiya, J. Non-Cryst. Solids 324 (2003)

50. [15] E. Golis, I.V.Kityk, J.Wasylak & J.Kasperczyk, Mater. Res. Bull. 31

(1996) 1057.

[16] I. V. Kityk and A. Majchrowski, Opt. Mater. 26 (2004) 33.

116

[17] A. Shaim, M. Et-tabirou, Mater. Chem. Phys. 80 (2003) 63.

[18] P. Nageswara Rao, C. Laxmi Kanth, D. Krishna Rao, N. Veeraiah, J.

Quant. Spectrom. Rad. Transfer 95 (2005) 37.

[19] M. E. Nordberg, U.S. Patent 2,326, 059 (3 Aug 1943); J. E. Nitsche, U.S. Patent 3,303,115 (5 Feb. 1967).

[20] P. C. Schultz and H. T. Smyth, in: Amorphous Materials, edited by R. W. Douglas and B. Ellis (Wiley-Interscience, London, 1972) 453

[21] J. Hecht, City of Light (Oxford University Press, London, 1999) 134.

[22] D. Y. Smith, C. E. Black, C. C. Homes, E. Shiles, Phys. Stat. Solidi. (c) 4 (2007) 838.

[23] D. Pickup, G. Mountjoy, G.W. Wallidge, R. Anderson, J.M. Cole, R.J. Newport, M.E. Smith, J. Mater. Chem. 9 (1999) 1299.

[24] C.F. Song, N.K. Li, P. Yang, D. Xu, D.R. Yuan, Thin Solid Films 413 (2002) 155.

[25] Hongpeng You and Masayuki Nogami, J. Phys. Chem. B 108 (2004) 12003.

[26] P. C. Schultz, J. Am. Ceram. Soc, 59 (1976) 214.

[27] A.D. Wilson, B.E. Kent, (1973). Surgical Cement. British Patent No.1316129.

[28] Nicholson, J.W. Chemistry of glass ionomer cements: A review of Biomaterials 19 (1998) 485.

[29] S Hübel, I. Mejàre, Int. J. Paediatr. Dent. 13 (2003) 2.

[30] J.Nourmohammadi, R. Salarian, M.Solati-Hashjin, F. Moztarzadeh Ceram. Int. 33 (2007) 557.

[31] A. Moshaverinia, S. Ansari, M.Moshaverinia, N.Roohpour, J.A. Darr, Rehman, Acta Biomater. 4 (2008) 432. [32] N. Monmaturapoj, S. Tanodekaew, W. Soodsawang, Ch.

Songklanakarin. J. Sci. Tech. 31 (2009) 337.

117

[33] C. Jing, X. Zhao, H. Tao, X.Wang and A. Liu, J. Mater. Chem. 13 (2003) 3066.

[34] Lee, J. shing, Hsu and C. King, Thermochim. Acta 333 (1999) 115.

[35] N. Watanabe , A.Y. Ramos, M.C.M. Alves ,H. Tolentino, L.C. Barbosa O.L. Alves, J. Mater. Res.15 (2000) 793.

[36] E.M. Vogel, J. Am. Ceram. Soc. 72 (1989) 719.

[37] E.M. Vogel, S.G. Kosinski, D.M. Krol, J.L. Jackel, S.R. Frieberg, M.K. Oliver, J.D. Powers, J. Non-Cryst. Solids 107 (1989) 244.

[38] H. Hosono, Z. Zhang, and Y. Abe, J. Am. Ceram. Soc. 72 (1989)1587.

[39] H. Hosono and Y. Abe, J. Non-Cryst. Solids 139 (1992) 86.

[40] H. Hosono, K. Imai, Y. Abe, J. Electrochem. Soc. 140 (1993) L7.

[41] S. Sakka, F. Miyaji, K. Fukumi, J. Non-Cryst. Solids 112 (1989) 64.

[42] J. Zarzycki, J. Mater. Sci. 6 (1971) 130.

[43] E.M. Vogel, M.J. Weber, and D.M. Krol, Phys. Chem. Glasses 32 (1991) 232.

[44] L. Canioni, L. Sarger, P. Segonds, A. Ducasse, C. Duchesne,E. Fargin, R. Olazcuaga, and G. le Flem, Solid State Commun. 84 (1992) 1065.

[45] K. Inoue1, S. Sakida2, T. Nanba1, Y. Miura1 Glass and Optical Materials Organized by S.W. Martin, A. Jha, and N.M. Ravindra Materials Science and Technology (MS&T) 2006: MATERIALS AND SYSTEMS – Vol.1

[46] S. Sakka, F. Miyaji, K. Fukumi, J. Non-Cryst. Solids, 112 (1989) 64.

[47] S. Sakka, F. Miyaji, K. Fukumi, J. Non-Cryst. Solids 107 (1989) 171

[48] K. Kusabiraki, J. Non-Cryst. Solids 95&96 (1987) 411.

[49] S.T. Gulati, M.J. Edwards, Proc. Adv. Mater. Opt. Precis. Struct. CR67 (1997) 107.

[50] K. Hrdina, SPIE 4889 (2002) 113.

[51] H. George, J.R. Sigel, in: M. Tomozawa, R. Doremus (Eds.), Treatise on Mater. Sci. Tech. 12 (1977) 5.

118

[52] T. Hashimoto, M. Murakami, H. Nasu, A. Ishihara, K. Kunii, J. Am. Ceram. Soc. 92 (2009) 1250.

[53] M. Ma, W. Ni, Y. Wang, Z. Wang, F. Liu, J. Non-Cryst. Solids 354 (2008) 5395.

[54] X. Tiefeng, C. Feifei, D. Shixun, N. Qiuhua, S. Xiang and W. Xunsi Physica B, 404 (2009) 2012.

[55] Gonzáles-Lozano, M.A., Gorokhovsky, A., Escalante-García, J. Ivan, J.

Non-Cryst. Solids 355 (2009) 114.

[56] O.A. Al-Harbi, E.M.A. Hamzawy, M. Mujtaba Khan, J. Appl. Sci. 9 (2009) 2981.

[57] S. Duhan, S. Sanghi, A. Agarwal, A. Sheoran, S. Rani, Physica B 404 (2009)1648.

[58] F.F. Chen, S.X. Dai, T.F. Xu, Q.H. Nie, X. Shen, X.S. Wang, Guangzi Xuebao/Acta Photonica Sinica 37 (2008) 215.

[59] F. Farges, J.R. Brown, J. John, Geochimica et Cosmochim. Acta 60 (1996) 3023.

[60] R.B. Greegor, F.W. Lyue, D.R.Sandstrom, P. Schultz, J. Non-Cryst. Solids 55 (1983) 27.

[61] A. Ramos, J. Petiau, J. Phys. C 846 (1985) 491.

[62] T. Dumas, J. Petiau, J. Non-Cryst. Solids 81 (1986) 201.

[63] A.A. Higazy, A.M. Hussein, M.I. Elhofy, Phys. Chem. Glasses 28 (1987) 164.

[64] A.R. Lange, I.S.E. Carmichael, Geochimica Cosmochimica Acta 57 (1987) 3001 .

[65] P.C. Hess, Physical Chem. of Magmas (1991) 152.

[66] D.B. Dingwell , Geochimica Cosmochimica Acta 56 (1992) 3404; Amer. Mineral. 77 (1992) 270.

[67] D.B. Dingwell, E. Paris, C. Romano, Phys. Chem. Mineral. 21 (1994) 501.

119

[68] H. Gan, “The speciation of solution properties of high field strength cations P5+, Ti4+, B3+ in aluminosilicate melts” Ph.D Dissertation, (Brown University, 1994).

[69] A. Kishioka, M. Haba, Bull. Chem. Soc. Jpn. 51 (1978) 2559.

[70] A.R. Langa, A. Navrotsky, Geochimica Cosmochimica Acta 51 (1993) 2931.

[71] T. Huebert, P. Reach, Phys. Chem. Glasses 32 (1991) 58.

[72] L.A. Farrow, E.M.Vogl, J. Non-Cryst. Solids 143 (1992) 59.

[73] S.A. Markgraf, A.S. Bhalla, J. Amer.Ceram Soc.75 (1992) 2630.

[74] H.V. Alberto, B.O. Mysen, Phys. Chem. Glasses 36 (1995) 114.

[75] G.S. Henderson, M.E. Fleet, Canadian Mineral. 33 (1995) 399.

[76] B. Mysen, D. Neuville, Geochimica Cosmochimica Acta 59 (1995) 325.

[77] A.A. Loshmanov, V.M. Sigaev and I.I. Yamzin, Fizika I Khimija Stekla 1 (1975) 35.

[78] T. Hanada, N. Soga, J. Non-Cryst. Solids 38 (1980) 105.

[79] F. Marumo, Y. Yabira and H. Morikawa, In Dynamic Process of Material Transport and Transformation in the Earth’s Interior, Terra Sci. Publ.Co; (1990) 53.

[80] F. Farges, A. Navrotsky and P. Richet, Abstr. Prog. IMA Meeting (Pisa), (1994) 114.

[81] E. Fargin, J. Non-Cryst. Solids 168 (1994) 132.

[82] E. Paris, D.B. Dingwell and C. Romano, Phys. Chem. Mineral. 21 (1994) 510.

[83] H.F. Wu, C.C. Lin, P. Shen, J. Non-Cryst. Solids 209 (1997) 76.

[84] S.R. Lacerda, R.N. Correia, M.H.V. Fernandes, J. Non-Cryst. Solids 221 (1997) 255.

[85] G. Laudisio, A. Aronne, P. Pernice, Thermochimica Acta 294 (1997) 173.

120

[86] L. Barbieri, L. Cristina, B. Anna, P. Gian Carlo, Mater. Res. Bull. 32 (1997) 637.

[87] F. Duan, C. Fang, H. Zhu, Mater. Lett. 34 (1998) 184.

[88] R.G. Duan, K.M. Liang, S.R. Gu, J. Eur. Cerm. Soc. 18 (1998) 1729.

[89] Abrahams, E. Hadzifejzovic, Solid State Ionics 134 (2000) 249.

[90] H. Grussaute, G. Palavit, J.L. Bernard, J. Non-Cryst. Solids 263 (2000) 312.

[91] B.V.R. Chowdari, G.V. Subba Rao, G.Y.H. Lee, Solid State Ionics 136 (2000) 1067.

[92] B. Jivov, Y. Dimitriev, E. Kashchieva, Int. J. Inorg. Mater. 3 (2001) 521.

[93] A. Shaim, L. Montagne, G. Palavit, Mater. Res. Bull. 37 (2002) 2459.

[94] A. Aboukais, V.A. Jachkin, O.A. Trul, E.A. Zhilinskaya, Opt. Mater. 19 (2002) 295.

[95] M. J. Weber, R. A. Saroyan and R. C. Ropp, J. Non-Cryst. Solids 44 (1981) 137.

[96] K. Morigaki, Physics of Amorphous Semiconductors, World Scientific, Singapore, 1999.

[97] G. Murali Krishna, Y. Gandhi, and N. Veeraiah, Phys. Stat. Solidi (a) 205 (2008) 177.

[98] K.J. Rao, Structural Chemistry of Glasses, Elsevier, Amsterdam, 2002..

[99] K. Nakamoto, Infrared Spectra of Inorganic and Coordination Compounds,

John Wiely & Sons, New York, 1962.

[100] A. Bhide, K. Hariharan, Mater.Chem.Phys.105 (2007) 213.

[101] Y. Dimitriev, V. Mihailova, V. Dimitrov and Y. Ivanova, J. Mater. Sci. Lett. 10 (1991) 1249.

[102] A. Shaim and M. Et-Tabirou, Mater. Res. Bull. 37 (2002) 2459.

121

[103] R. Balaji Rao, D. Krishna Rao and N. Veeraiah, Mater. Chem. Phys. 87 (2004) 357.

[104] B. Tareev, Physics of Dielectric Materials, Mir, Moscow, 1979.

[105] G. Little Flower, M. Srinivasa Reddy, M. V. Ramana Reddy, and N. Veeraiah, Z. Naturforsch 62 (2007) 315.

[106] R.K. Brow, D.R. Tallant, J. Non-Cryst. Solids 222 (1997) 396.

[107] E.T.Y. Lee, E.R.M. Taylor, J. Phys. Chem. Solids 66 (2005) 47.

[108] R.K. Brow, J. Non-Cryst. Solids 194 (1996) 267.

[109] J.J. Videau, J.F. Ducel, K. S Suh, J. Senegas, J. Alloys Compd. 188 (1992) 157.

[110] M. Ganguli, M.H. Bhat, K.J. Rao, Solid State Ionics 122 (1999) 23.

[111] N. Da, A.A. Enany, N. Granzow, M.A. Schmidt, P. St, J. Russell, L. Wondraczek, J. Non-Cryst. Solids 357 (2011) 1558.

[112] X A. Aboukais, L.D. Bogomolova, A.A. Deshkovskaya, V.A. Jachkin Krasil, N.A. Nikova, S.A. Prushinsky, O.A. Trul, S.V. Stefanovsky and E.A. Zhilinskaya, Opt. Mater. 19 (2002) 295.

[113] M.V. Ramachandra Rao, Y. Gandhi, L. Srinivasa Rao, G. Sahayabaskaran and N. Veeraiah, Mater. Chem. Phys. 126 (2011) 58.

[114] O. Cozar, D.A. Magdas, I. Ardelean, J. Non-Cryst. Solids 354 (2008) 1032.

[115] B.V.R. Chowdari, K. Radha Krishnan. J. Non-Cryst. Solids 224 (1998) 151.

[116] Isaac Abrahams and Emina Hadzifejzovic, Solid State Ionics 134 (2000) 249.

[117] B.V. Raghavaiah, C. Laxmikanth and N. Veeraiah, Optics Commun. 235 (2004) 341.

[118] N. Krishna Mohan, G. Sahaya Baskaran, N. Veeraiah, Phys. Stat. Sol. (a) 203 (2006) 2083.

[119] G. Naga Raju, N. Veeraiah, Physica B 373 (2006) 297.

122

[120] G. Murali Krishna, M. Srinivasa Reddy, N. Veeraiah, J. Solid State Chem. 180 (2007) 2747.

[121] C.J.F. Bottcher, P. Bordewijk, Thoery of Electric Polarization, Elsevier,

Oxford, 1978.

[122] L. Bih, El Omari, M. Haddad, J.M. Reau, D. Boudlich, A. Yacoubi, A. Nadiri, Solid State Ionics 132 (2000) 71.

[123] R.M. Abdelouhab, R. Braunstein and K. Baerner, J. Non-Cryst. Solids 108 (1989) 109.

[124] G. Srinivasarao and N. Veeraiah, J. Solid State Chem. 166 (2002) 104.

[125] Y. Gandhi, K.S.V. Sudhakar, M. Nagarjuna and N. Veeraiah, J. Alloys Compd. 485 (2009) 876.

[126] P. Sixou, P. Dansas, D. Gillot, J. Chem. Phys. 64 (1967) 834.

[127] C. Dyre, J. Non-Cryst.Solids 88 (1986) 271.

[128] S.R. Elliott, Physics of Amorphous Materials (Longman Science and Technology, Essex, 1990).

[129] H. Kahnt, J. Non-Cryst. Solids 203 (1996) 225.

[130] S. Lanfredi, P. S. Saia, R. Lebullenger, A.C. Hernandes, Solid State Ionics 146 (2002) 329.

[131] D. L. Sidebottom, Phys. Rev. Lett. 83 (1999) 983.

[132] S. Bhattacharya, A. Ghosh, Phys. Rev. B 70 (2004) 172203.

[133] I. G. Austin, N.F Mott, Adv. Phys.18 (1969) 657.

[134] G. Murali Krishna, N. Veeraiah, N. Venkatramaiah, R. Venkatesan, J. Alloys Compd. 450 (2008) 486.

[135] Ch. Srinivasa Rao, V. Ravi Kumar, T. Srikumar, Y. Gandhi, N. Veeraiah, J. Non-Cryst.Solids 357 (2011) 3094.

[136] K. Srilatha, L. Pavić, A. Moguš-Milanković, Ch. Srinivasa Rao, G.

Little Flower, V. Ravi Kumar, N. Veeraiah, J. Non-Cryst. Solids 357 (2011) 3538.