i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 4 9 7 1e1 4 9 7 6

Avai lab le a t www.sc iencedi rec t .com

journa l homepage : www.e lsev ier . com/ loca te /he

Thermal and crystallization kinetics of yttrium andlanthanum calcium silicate glass sealants for solidoxide fuel cells

Vishal Kumar, Rupali, O.P. Pandey, K. Singh*

School of Physics and Materials Science, Thapar University, Patiala, 147 004, India

a r t i c l e i n f o

Article history:

Received 2 April 2011

Accepted 21 May 2011

Available online 20 July 2011

Keywords:

Glass

Transition temperature

Differential thermal analysis

* Corresponding author. Tel.: þ91 1752393130E-mail address: kusingh@thapar.edu (K.

0360-3199/$ e see front matter Copyright ªdoi:10.1016/j.ijhydene.2011.05.124

a b s t r a c t

The crystallization kinetics of glass sealants is an essential parameter to check the suit-

ability of glass as a sealant. The crystallization kinetic behavior of calcium borosilicate

glasses were studied by Differential thermal analysis (DTA), X-ray diffraction (XRD) and

Fourier transform infrared spectroscopy (FTIR). These glasses were exposed for different

heat treatment durations in oxidizing atmosphere at 800 and 900 �C. XRD results indicate

the presence of La2SiO5 crystalline phase which increases the thermal expansion of the

glasses. However, yttria doped calcium borosilicate glass (CaY) sample could not form any

crystalline phase even after 10 h heat treatment at 900 �C. Moreover, the thermal expan-

sion coefficient (TEC), viscosity values and fragility index of the glasses indicate that

lanthanum doped calcium borosilicate glass (CaLa) might be a better glass sealant for solid

oxide fuel cell as compared to CaY glass.

Copyright ª 2011, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights

reserved.

1. Introduction viscosity and good adherence to all the components of SOFC to

Solid oxide fuel cell offers green energy with higher efficiency

which highlights the importance of this technology [1,2].

Based on design, solid oxide fuel cell (SOFC) can be categorized

into two main categories, namely tubular and planar design.

Planar design is better than tubular design due to its higher

current density with simple processing [2e7]. However, the

planar design of SOFC requires proper sealing at the edges of

the cells to prevent fuel leakage and air mixing during cell

operation [8,9]. Due to high temperature operation of SOFC

(800e1000 C) and different environments (oxidizing, reducing

and humid) in the stack, its sealing is a challengeable task. The

sealant material has to fulfill stringent requirements

including gas tightness, electrically insulating along with

stability of other cell components. It should have matching

thermal expansion coefficient with other components of

SOFC. The sealing glass should also possess a suitable

; fax: þ91 1752393005.Singh).2011, Hydrogen Energy P

encounter different TEC values of the components during

working of SOFC [10]. In order to satisfy above criteria the

sealant used in SOFC should have resistivity greater than

2 kU cm and also the viscosity value at joining temperature

should be 105 Pa s. The small thermal expansion mismatch

with respect to SOFC components (typically in the range of

10� 10�6 to 13� 10�6 K�1) and leak rate of the joining (less

than 10�7 mbar l s�1 cm�1 joined length) is the basic require-

ment of seal.

The glass and glass ceramics are considered as most suit-

able materials for sealant as compared to the conventional

sealing materials due to their compatibility with other

components of SOFC at high temperature (800e1000 �C) [11].The principal advantage of glass seals is that the glass

composition can be tailored to optimize physical properties

[12]. Apart from compatibility criteria, it should also have good

chemical stability in reducing, oxidizing and humid

ublications, LLC. Published by Elsevier Ltd. All rights reserved.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 4 9 7 1e1 4 9 7 614972

atmosphere. Additionally, sealant should be flexible to with-

stand compression and expansion which occur in different

part of the stacks during operation of the fuel cell.

Many studies have been performed on glass and glass

ceramics to achieve above mentioned properties which can

make them suitable as a sealant material for SOFC [13,14].

However, each category of glasses has its own limitations

such as mismatching of thermal expansion due to formation

of various crystalline phases during the operation of SOFC.

Additionally, interaction among the various components of

SOFC may also lead to formation of undesirable crystalline

phases. Some of these phases are very detrimental due to

their low thermal expansion as compared to other compo-

nents of SOFC. Therefore, based on earlier studies [15e17]

a glass composition CaOeSiO2eB2O3eA2O3 (A ¼ Y, La) was

selected for the present study. Effect of intermediate cations

and their field strength on the crystallization kinetics has been

studied. The structural and thermal properties of these

glasses have been characterized using X-ray diffraction,

Differential thermal analysis (DTA), Thermo gravimetric

analysis, and Fourier Transform Infrared Spectroscopy (FTIR).

2. Experimental

Glasses of composition 30CaOe40SiO2e20B2O3e10A2O3 (A¼Y,

La) (mol %) designated as CaY and CaLa for yttria and

lanthanum doping respectively were prepared by conven-

tional melting followed by splat quenching of the molten

glass. The purity of the constituent oxides were >99.9%.

Initially, these oxides were ball milled for 2 h in acetone

medium. The ball milled powders were kept in recrystallized

alumina crucible for melting in air. The melt was held at this

temperature for 1 h to ensure complete mixing and homoge-

nization of the melt. Finally, the melt was splat-quenched

using thick copper plates. The glassy nature of the samples

was confirmed by XRD analysis. The DTA/TGAmeasurements

were performed with Diamond Pyris TG/DTA (Perkin Elmer)

using Al2O3 powder as reference material in oxygen atmo-

sphere. The DTA curves of all the glasses were taken with

different heating rates of (10, 20, 30, 40 �C min�1) to calculate

the activation energy for transition. During DTA/TGA

measurements the temperature and weight loss detection

limit were �1 �C and 0.001 mg respectively. Furthermore, the

X-ray diffraction (XRD) study was also done on heat treated

samples for various durations to identify the formed crystal-

line phases. The XRD were performed using Rigaku model

Geiger diffractogramwith CuKa radiation (l ¼ 1.54 A) obtained

from copper target using an in built Ni filter. The scan speed

was 5� min�1. The dilatometer study was performed using

Netzsch DIL 402 PC in the temperature range 100e650 �C to

determine the thermal expansion coefficient (TEC) of glasses

and glass ceramics to study the effect of crystalline phase

formation on TEC. Fourier transform infrared (FTIR) spectra

were recorded in the range 2250 cm�1 to 400 cm�1 using

a Perkin Elmer- Spectrum BX with a spectral resolution of

1 cm�1 2mg of each test samplewasmixedwith 200mg of KBr

in an agate mortar and then pressed into 13 mm diameter

pellets. The FTIR spectrum was recorded for these pellets.

3. Results and discussion

3.1. Calculation of viscosity of glasses from dilatometerdata

Mott and Gurney [18] proposed a simple liquid theory which

established a relationship between pseudo-critical tempera-

ture (Tk) and the absolute melting point (Tm):

Tk

Tm¼ 2

3(1)

Later on Beaman [19] proposed that eqn (1) can also be used

for glasses and polymers. The modified equation can be

written as [20]:

Tg

Tl¼ 2

3(2)

The softening temperature (Ts) and glass transition

temperature (Tg) are obtained from the curve plotted between

thermal expansion and temperature during dilatometer

analysis. The value of Ts obtained from dilatometer curve is

725 �C and 740 �C for CaLa and CaY glass respectively when

thermal expansion reaches a maximum value. By fitting the

two linear parts of thermal expansion curve, the glass tran-

sition temperature (Tg) can be obtained, and its value is 710 �C

and 725 �C for CaLa and CaY glass respectively. The viscosity

values of glasses are fixed and independent of materials [21].

These values are given in equation (3).

Tg/hg¼1013:6dPas;Ts/hs¼1011:3dPas;Tm/hm¼106dPas (3)

AccordingtotheVogeleFulchereTamman(VFT)equation [22]:

logh ¼ Aþ BT� To

(4)

where A, B and T0 are constants. Using Eq. (3), these constants

can be obtained by resolving coupled equations for the

investigated glasses. The values of thermal expansion coeffi-

cient (TEC), transition temperature (Tg), softening temperature

(Ts) and viscosity (h) are obtained from dilatometer data.

These values are used to calculate the viscosity of CaLa and

CaY glasses using VFT equation.

logh ¼ 4:18þ 1020:11T� 935

(5)

logh ¼ 4:42þ 1015T� 832:29

(6)

Fig. 1 shows viscosity versus temperature curves of CaLa

and CaY glass using Eq. (5) and (6) respectively. The calculated

viscosity values of CaLa and CaY glasses are 107.9 dPa s and

109.6 dPa s respectively. The viscosity value of CaLa glass is

well within the required viscosity value of sealing material

[21,22].

The thermal expansion coefficients (TEC) of the glasses and

glass ceramics obtained from dilatometer data in the

temperature range 200e650 �C is given in Table 1. From the

slope of the linear part of thermal expansion curve (i.e.

200e650 �C), the thermal expansion coefficient (TEC) for CaY

and CaLa glasses are around (8 � 10�6 K�1).

Fig. 1 e Variation of viscosity with temperature for CaLa

and CaY gla.

a

b

y = 35.003x - 24.935y = 74.812x - 63.156

9.810

10.210.410.610.8

1111.211.411.611.8

0.976 0.986 0.996 1.006 1.016 1.026 1.036

ln(T

g2 /)

1000/Tg

Fig. 2 e (a) DTA plot of CaY and CaLa glasses. (b) Kissinger

plot of CaY and CaLa glasses.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 4 9 7 1e1 4 9 7 6 14973

3.2. Differential thermal analysis

Fig. 2(a) showstheDTAcurve forCaYandCaLaglassesatheating

rate of 10C min�1. The transition, crystallization and melting

temperature of all the glasses are given in Table 2. The crystal-

lizationpeakswere observed to shift towardhigher temperature

with respect to the increasing heating rate in both the glasses

which is because of delay in attaining thermal equilibrium [16].

The activation energy of all the glasses were calculated

using Kissinger equation [23,24]

ln�T2p=b

�¼ �

Ep=RTp

�þ constant (7)

where b is heating rate and R is gas constant. From the

experimental data a graph between ln (Tp2/b) versus (1000/Tp)

was plotted as shown in Fig. 2 (b). The slope of this graph gives

the activation energy (A.E) of transition. The A.E of transition

for CaY glass is very high as compared to CaLa glass (Table 1).

Rayet.al [25]. have reported that Tg is related to the density of

covalent cross linking, number and strength of co-ordinate

links formed between oxygen atoms and the cations and the

oxygen density of network. Higher values of these factors

correspond to higher Tg. In case of CaY glass, Y3þ might be

acting as the network former where it may have higher

number of covalent cross linking. The non-bridging oxygen

due to modification of glass network by Ca2þ might be bonded

by Y3þ cations which lead to higher Tg of this particular glass

as compared to CaLa glass. Thermal data obtained from DTA

measurement of these glasses was used to calculate the

fragility index and activation energy for transition.

Table 1 e TEC for linear part of the curve (200e650 �C).

SampleName

TEC(10�6/K) Glass

TEC(10�6/K) Glass

ceramic 800 �C 10 h

T(10�6/K

ceramic 80

CaY 7.94 8.22 8.

CaLa 8.06 8.43 8.

3.3. Fragility index (F)

Generally, strong glass formers show Arrhenius type behavior

in viscosity versus temperature curve. On the other hand non

Arrhenius behavior is manifestation of fragile glass former

[25]. Moreover, fragile glass exhibits weak interatomic/inter-

molecular bonding. For the present glasses, the fragility index

value is calculated using the following relation [26,27]

F ¼ Et

RTgln10(8)

Where Et is the activation energy for glass transition.

It is reported that fragility index for strong and fragile glass

former varies from F ¼ 16 to F ¼ 20 respectively [28,29]. On the

basis of calculations CaLa and CaY are strong glass forming

liquids. However, CaLa (F ¼ 19.1) is stronger glass former than

CaY (F ¼ 32) glass.

EC) Glass0 �C 100 h

TEC(10�6/K) Glass

ceramic 900 �C 1 h

TEC(10�6/K) Glass ceramic

900 �C 10 h

21 8.06 8.05

42 8.39 8.11

Table 2 e Transition, crystallization, melting temperature, T G A, activation energy and fragility index of glasses.

SampleName

Composition Tg (�C)Dilatometer

Tg (�C)(DTA)

Tc

(�C)Tm

(�C)% Wt. loss

50e1000 (�C)A.E

(kJmol�1)FragilityIndex

CaY 30CaOe40SiO2e20B2O3e10Y203 724 738 e 902 2.7 621 19.1

CaLa 30CaOe40SiO2e20B2O3e10La203 710 718 760 882 0.2 291 33.2

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 4 9 7 1e1 4 9 7 614974

3.4. Thermal expansion coefficient (TEC)

The thermal expansion coefficient of the splat-quenched and

annealed glass is given in Table 1. The transition point (Tg) and

the softening point (Ts) of the investigated glass was calcu-

lated from the dilatometric curve. From the slope of the linear

part of thermal expansion curve (i.e. 200e650 �C) as shown in

Fig. 3, the thermal expansion coefficients (TEC) of the glass

and glass ceramics (GCs) was calculated. The thermal

expansion of parent glasses and glass ceramics lies in the

range (7.9e8.4 � 10�6 K�1).

The CaLa glass exhibited higher TEC value than CaY glass.

The higher TEC in this glass as compared to other glasses can

be associated with the higher ionic radii of La3þ. After heat

treatment when it turns into glass ceramic the TEC value

increases. This is due to the formation of crystalline phases

which improve the TEC of this glass. The CaLa glass and glass

ceramics have higher TEC value compared to CaY samples. It

is important to note that highest TEC value is observed in case

of glass ceramics which were heat treated at 800 �C for 10 and

100 h as shown in Table 1. Thismeans thatmaximum value of

TEC lies in the crystallization range i.e. z800 �C where glass

matrix undergoes maximum structural rearrangement. For

the glass ceramics heat treated at 900 �C (near melting point)

for 1 and 10 h the value of TEC decreases.

3.5. X-ray diffraction for crystallization study

Glass ceramics, as-prepared by controlled crystallization of

glasses, exhibit superior mechanical properties than glasses

0 100 200 300 400 500 600 700

0.0

0.1

0.2

0.3

0.4

0.5

0.6

dL/L

o (%

)

Temperature (oC)

CaY-1hCaY-10h

Fig. 3 e Thermal expansion curve of CaY glass ceramic

heat treated for 1 and 10 h at 900 �C.

which depend upon nature of nucleated phases. These exhibit

variations in TEC values depending on the type of nucleated

crystalline phases and their volume fraction in the glass

matrix. Glass ceramics also show higher chemical stability

than glasses, especially, under SOFC operating conditions.

The present glasses were subjected to different heat treat-

ment, namely 10e100 h at 800 �C and 1e10 h at 900 �C. The as-

prepared glasses were found to be amorphous and exhibited

two broad halos in the X-ray diffractogram. It is possible that

Y2O3 is associated with B2O3 and SiO2 network simulta-

neously. The two humps as shown in Fig. 4 are due to silicate

and borate network which are trying to grow simultaneously

in the matrix. The CaY glass has the higher glass transition

temperature because of higher cross link density and higher

field strength of Y3þcation. The intentional addition of inter-

mediate oxide might lead to phase separation in glass

network. Phase separation is common phenomenon in alka-

line borosilicate glasses [30]. This glass could not form any

crystalline phase even after heat treatment at 900 �C for 10 h.

As shown in Table 2, this glass exhibits very high activation

energy (605 KJmol�1). In our earlier reports [15e17] it is

observed that the addition of Y2O3 in any glass composition

increases the stability of the glasses without forming any

detrimental crystalline phase during heat treatment.

Conclusively the addition of Y2O3 prevents crystallization.

The CaY glass has the higher glass transition temperature

because of higher cross link density and higher field strength

Fig. 4 e XRD pattern of CaY heat treated at (a) 800 �C for 10 h

(b) 800 �C 100 h (c) 900 �C for 1 h (d) 900 �C 10 h.

2000 1500 1000 50098

100

102

104

106

108

Tra

nsm

issi

on(a

rb. u

nits

)

1/cm

CaLa CaLa-1h CaLa-10h

Fig. 6 e FTIR transmission spectra of CaL glass and glass

ceramic heat treated for 1 h and 10 h at 900 �C.

i n t e r n a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 4 9 7 1e1 4 9 7 6 14975

of Y3þcation. It is possible that Y2O3 is associated with B2O3

and SiO2 network simultaneously, the two humps as shown in

Fig. 4 are due to silicate and borate networkwhich are trying to

grow simultaneously in the matrix. The high field strength of

Y3þ compared to B2O3 and SiO4 pulls the borate and silicate

network thus producing a strain in thematrix. However, when

heat treatment is given to glasses it provides sufficient energy

(which further depends on duration of heat treatment) to

cations for movement in the glass matrix. As the time dura-

tion of heat treatment increases the stress relaxation in the

matrix takes place.

The XRD patterns of CaLa glass are shown in Fig. 5. Most

likely La2O3 is modifying the silicate network which leads to

formation of monoclinic La2SiO5 crystalline phase after heat

treatment. Even after 100 h heat treatment at 800 �C (Fig. 5(b))

no new phase has formed. However, the full width at half

maxima (FWHM) of peaks decreased with increase in time

duration of heat treatment. Fig. 5(a) and (c) show small humps

in XRD pattern which indicate that the amorphous content in

glass is still present. This amorphous content is consumed by

crystalline phase La2SiO5 as shown in Fig. 5(b) and (c) due to

increase in time duration of heat treatment.

3.6. FTIR investigation

FTIR transmittance spectra of heat treated glass ceramics

show the structural rearrangement as compared to glasses as

shown in Figs. 6 and 7. All the spectra exhibit three broad

transmittance bands at 300e600 cm�1, 600e800 cm�1 and

1300e1500 cm�1.

Fig. 5 e XRD pattern of CaL heat treated at (a) 800 �C for 10 h

(b) 800 �C for 100 h (c) 900 �C for 1 h (d) 900 �C for 10 h.

These diffused bands are indicative of the general disorder

in the silicate network which is mainly due to a wide distri-

bution of Qn units (polymerization in the glass structure,

where n denotes the number of bridging oxygen) occurring in

these glasses. The bands in the 300e600 cm�1 region are due

to bending vibrations of SieOeSi linkages. The transmittance

band in the 650e800 cm�1 region in the glasses is attributed to

the bending vibrations of bridging oxygen between trigonal

boron atoms and is also related to the stretching vibrations of

the AeO bonds with A3þ ions in four-fold coordination (A ¼ Y,

La) [31]. The band in the region 1350e1500 cm�1 corresponds

to BeO vibrations in BO3 triangle. Borate glasses show two

characteristic bands derived from the BeO bonds in the BO3

triangles which appears at 1300e1500 cm�1 and the BO4

tetrahedra at 1000 cm�1 [32]. The broad band in the

800e1300 cm_1 is assigned to the stretching vibrations of the

2000 1500 1000 50094

96

98

100

102

104

106

108

110

112

114

Tran

smis

sion

(arb

. uni

ts)

1/cm

CaY CaY-1h CaY-10h

Fig. 7 e FTIR transmission spectra of CaY glass and glass

ceramic heat treated for 1 h and 10 h at 900 �C.

i n t e rn a t i o n a l j o u r n a l o f h y d r o g e n en e r g y 3 6 ( 2 0 1 1 ) 1 4 9 7 1e1 4 9 7 614976

SiO4 tetrahedron with different number of bridging oxygen

atoms [33,34]. These bands get shifted under the influence of

surrounding cations, the extent and the direction of this shift

depends on the type of cation present in the glass matrix.

The bands become little broader in glass ceramic sample

which indicate some rearrangement in glass matrix. Apart

from some common bands in FTIR spectra of CaLa glass as

shown in Fig. 6 a special band centered at 1120e1320 cm�1

appears which is due to boroxol rings and borate stretching

[35]. This band might be attributed to BO4 stretching which

shifts to lower wave number and the intensity decreases as

time duration for heat treatment increases. Similarly a trans-

mission band observed at 1450e1500 cm�1 correspond to BeO

vibrations of various borate groups and intensity of this peak

decreases as the time duration of heat treatment increases.

No additional transmission band formation takes place after

increasing time duration of heat treatment. However, after

10 h heat treatment the transmission peaks shift toward lower

wave number.

The transmission spectra of CaY (Fig. 7) glass shows band

in the frequency range of 638e726 cm�1 due to the vibrations

of oxygen bridge between trigonal boron atoms. Another band

is observed at 814e982 cm�1. It is due to SieO� stretching with

two non-bridging oxygens [35]. The transmission band at

1150e1240 cm�1 and the peak at 1328 cm�1 are due to the

presence of borate groups (tri, tetra, pentaborate groups).

Furthermore, a transmission band at 1450e1500 cm�1 is

ascribed to BeO vibrations of various borate groups.

CaY could not show any appreciable change in the FTIR

spectra of glass (amorphous) and heat treated (1hr & 10 h)

glass ceramic. On the other hand CaLa sample shows

remarkable difference in glass and glass ceramic due to

regrouping in SieOeSi and BO4 structure. Additionally, the

shift of the bands at lower wave number in glass ceramic also

indicates that these systems have more stability than their

glass counterpart. The peaks centered at 1300 cm�1 and

1500 cm�1 are more intense for amorphous glass showing

coexistence of borate and silicate network in glass matrix

which has also been indicated in XRD. However, after heat

treatment for 1 and 10 h these bands get diffused.

4. Conclusions

CaLa glass ismore stable than CaY glasses. Addition of Y2O3 as

an intermediate prevents the crystallization and enhances the

thermal properties of the glasses. No detrimental phase was

formed after heat treatment of the glasses. FT-IR spectra could

not show any appreciable change in amorphous glass and

heat treated glass except little change in band intensity and

shift in peak position. The TEC value of CaY, CaLa heat treated

glass was observed to be higher than their glass counterparts.

Apart from this, the heat treated glasses show maximum

values of TEC near crystallization region which is also the

working temperature of SOFC. The viscosity, fragility index

and TEC values indicate that CaLa can be a better glass sealant

for SOFC at operating temperature of 800 �C.

Acknowledgment

The financial support provided by Department of Science and

Technology (DST), Govt of India, under the scheme SR/S2/

CMP-48/2004 is greatly acknowledged. One of the authors

(Vishal Kumar) would also like to acknowledge CSIR for their

financial assistance.

r e f e r e n c e s

[1] Yang Zhenguo, Xia Guanguang, Meinhardt Kerry D,ScottWell K, Stevenson Jeff W. J Mater Eng Perform 2004;13(3):327e34.

[2] Minh NQ. Solid State Ionics 2004;174:271e7.[3] Singhal SC. Solid State Ionics 2003;152e153:405e10.[4] Minh NQ. J Am Ceram Soc 1993;76(3):563e88.[5] Steele BCH, Heinzel A. Nature 2001;414(6861):345e52.[6] Badwal SPS. Solid State Ionics 2001;143(1):39e46.[7] Gauckler LJ, Beckel D, Buergler BE, Jud E, Muecke UP,

Prestat M, et al. Syst Mater Chimia 2004;58(12):837e50.[8] LaraC,PascualMJ,DuranA. JNon-CrystSolids2004;348:149e55.[9] Lara C, Pascual MJ, .Keding R, Duran A. J Power Sources 2006;

157:377e84.[10] Wang R, Lu Z, Liu C, Zhu R, Huang X, Wei Bo, et al. J Alloys

Compounds 2007;432(1e2):189e93.[11] Lahl N, Singh K, Singheiser L, Hilpert K. J Mater Sci 2000;35:

3089e96.[12] Simner SP, Stevenson JW. J Power Sources 2001;102:310e6.[13] Sohn Sung-Bum, Choi-Ho Se-Young, Kirr-Sup Gyeung,

Song Hue, Kim Goo-Dae. J Am Ceram Soc 2004;87(2):254e60.[14] Fergus Jeffrey W. J Power Sources 2005;147:46e7.[15] Singh K, Gupta N, Pandey OP. J Mater Sci 2007;42:6426.[16] Arora A, Shaaban ER, Singh K, Pandey OP. J Non-Cryst Solids

2008;354(33):3994.[17] Kumar Vishal, Arora Anu, Pandey OP, Singh Kulvir. Int J

Hydrogen Energy 2008;33(1):434.[18] Mott NF, Gurney RW. Rep Prog Phys 1938;5:46.[19] Beaman RG. J Polym Sci 1952;9:470.[20] Sakka S, Mackenzie JD. J Non-Cryst Solids 1971;6:145.[21] Ghosh Saswati, Kundu P, Das Sharma A, Basu RN, Maiti HS.

J Eur Ceram Soc 2008;28:69e76.[22] Fulcher GS. J Am Ceram Soc 1925;8:39.[23] Kissenger HE. Ann Chem 1957;29(11):1702.[24] Chen HS. J Non-Cryst Solids 1978;27:257.[25] Ray NH. J Non-Cryst Solids 1977;23:261.[26] Chebli K, Saiter JM, Grenet J, Hamou A, Saffarini G. Physica B

2001;304:228.[27] Wakkad MM, Shok EK, Mohamed SH. J Non-Cryst Solids 2000;

265:157.[28] Viglis TA. Phys Rev B 1993;47:2882.[29] Bohmer R, Nagi KL, Angell CA, Plazek DJ. J Chem Phys 1993;

99:4201.[30]. Arora A, Goel A, Shaaban ER, Singh K, Pandey OP, Ferreira

Physica JMF. B Condensed Matter 2008;403(10e11):1738e46.[31] Goel A, Tulyaganov Dilshat U, Kharton V. Acta Materialia

2008;56(13):3065.[32] Stoch L, Sroda M. J Mol Struct 1999;511e512:77e84.[33] Lin S-L, Hwang CS. J Non-Cryst Solids 1996;202:61e7.[34] Kohli JT, Shelby JE, Frye JS. Phys Chem Glasses 1992;33:73e8.[35] Elbatal Fatma HA, Khalil Magda MI. Mater Chem Phy 2003;

82(2):375.