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Ultrasonic relaxation of some CdO boro-tellurate glasses

Journal: Canadian Journal of Physics

Manuscript ID cjp-2016-0363.R1

Manuscript Type: Article

Date Submitted by the Author: 21-Jul-2016

Complete List of Authors: Gaafar, M.; National Institute for Standards, Ultrasonic Mahmoud, I.; Physics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt, Physics

Keyword: Boro-tellurate glasses, Ultrasonic velocity, Activation energy, Deformation potential, Thermal expansion coefficient

https://mc06.manuscriptcentral.com/cjp-pubs

Canadian Journal of Physics

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Ultrasonic relaxation of some CdO boro-tellurate

glasses

M. S. Gaafar 1,3,*

, I. S. Mahmoud 2,3

1 Ultrasonic Laboratory, National Institute for Standards, Tersa Str., P. O. Box

136, El-Haram, El-Giza 12211, Egypt.

2 Physics Department, Faculty of Science, Suez Canal University, Ismailia, Egypt.

3 Physics Department, College of Science, Zulfi, Majmaah University, KSA.

ABSTRACT:

50 B2O3 – (50-x) TeO2 – x CdO glass system, with x = 0, 10, 20, 30, 40 and 50

mol % have been prepared, to measure the longitudinal ultrasonic attenuation at

frequencies of 2, 4, 6 and 14 MHz in the temperature range from 120 to 300 K. Well-

defined broad peaks of the absorption curves were observed at different temperatures

depending on the glass composition and the operating frequency. The maximum

peaks shifted to higher temperatures with the increase of the operating frequency

implying the presence of some kind of relaxation process. This process suggested as

due to the thermally activated relaxation process. The variation of the average

activation energy of the process is mainly depending on CdO mol % content. Such

dependence, was analyzed in terms of the loss of standard linear solid type, with low

dispersion and a broad distribution of Arrhenius type relaxation with temperature

independent relaxation strength. The obtained acoustic activation energy values were

quantitatively, interpreted in terms of the number of loss centers (number of oxygen

atoms that vibrate in the double well potential).

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Keywords: Boro-tellurate glasses; Ultrasonic velocity; Activation energy;

Deformation potential; Thermal expansion coefficient.

*email address: [email protected]

1. Introduction

Tellurite, borate and borotellurite glasses have been widely investigated for their

scientific interest and practical applications [1-5]. Borate glasses are known for

having high thermal stability, high chemical durability, good solubility of rare-earth

ion and also for their ease of synthesis [4],[6] and [7]. Tellurite glasses have lower

phonon energy if compared to phosphates and silicates glasses, large infrared

transparency, good thermal and mechanical stability, good chemical durability, low

melting temperature, high refractive index, high dielectric constant and suitability as a

host matrix to dopant action [2-17]. These features make tellurite glasses promising

candidates for photonic applications, such as fiber in optical communication, window

materials and up-conversion laser. The addition of tellurium oxide to another glass

former, such as B2O3, can lead to the production of interesting structural units that

affect the physical properties of the glass network [2] and [18].

Gaafar et al. [19] had employed the elastic properties, X-ray and FT-IR

spectroscopy to study the role of CdO on the structure of the 50 B2O3 - (50-x) TeO2 -

x CdO glass system, with different CdO contents (0, 10, 20, 30, 40 and 50 mol%).

Elastic properties and Debye temperature have been investigated using sound wave

velocity measurements at 4 MHz at room temperature. The authors reported that the

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density increases and the molar volume decreases while both sound velocities

decrease with increase in x. They also showed that, the Cd2+

ions are incorporated into

the network structure of these glasses in the form of CdO6, decreasing the molar

volume and compensate for the decrease in the average coordination number of

tellurium atoms which was the reason for the increase in elastic moduli.

The longitudinal ultrasonic attenuation in 20Li2O – (80-x) B2O3 – xWO3

(0≤x≤12.5) glass system, was measured by Gaafar & Mahmoud [20] using pulse echo

technique at ultrasonic frequencies 2, 4, 6 and 14 MHz in the temperature range from

150 to 300 K. They reported that, the longitudinal ultrasonic absorption at low

temperatures showed the presence of well-defined peaks whose heights increase as

the applied frequency increases. Those peaks were attributed to a thermally activated

relaxation governed by Arrhenius relationship. Also, the peak temperature was found

to decreases as the WO3 content increases. The values of activation energy and the

attempt frequency were found to increase at two different rates with increasing the

WO3 content in the glass system investigated, which means the glass network

modification/forming role of WO3.

The aim of this search work is to study the variation of ultrasonic attenuation in

three different glass series 50 B2O3 – (50-x) TeO2 – x CdO with different CdO

contents, in the temperature range 120 - 300 K and at four different ultrasonic

frequencies. The variations of glass composition in the ultrasonic relaxation process

will throw more light on the strength and binding of these glasses network structures

with replacement of TeO2 by CdO.

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2. Experimental details

2.1. Preparation of glasses

The glass samples having the general chemical formula 50 B2O3 - (50-x) TeO2 -

x CdO glass system with different CdO contents (0, 10, 20, 30, 40 and 50 mol%) have

been prepared by the melt quenching technique. Required quantities of Analar grade

TeO2, CdO and H3BO3, were mixed together by grinding the mixture repeatedly to

obtain a fine powder. The mixture was melted in a porcelain crucible in an electrically

heated furnace under ordinary atmospheric conditions at a temperature of about 1200

K for 2 hrs to homogenize the melt. The obtained glass samples from the melt

quenching were poured into preheated stainless-steel mould, were heat treated at a

temperature of about 20 K below their calorimetric glass transition temperature for 2

hrs to remove any internal stresses. In order to measure the ultrasonic attenuation

accurately, each glass sample was first ground on a glass plate using SiC abrasives by

setting it in a holder to maintain the two opposite faces parallel. Then the two opposite

faces were polished in order to be suitable for use in the ultrasonic attenuation

measurements. The deviation in the parallelism of the two opposite side faces was

about ±8 µm.

2.2. Density measurements

The density values (ρ) of all glass compositions were determined employing

Archimedes principle using toluene. The experiment was repeated three times and the

error in density measurements for all glass samples is ±0.005 g/cm3.

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2.3. Ultrasonic attenuation measurements

A cryostatic setup with liquid air as cryogen was used to set the sample at the

desired temperature between that of liquid air and room temperature. The glass

sample together with the bonded transducer (nonak – stopcock grease which proved to

be satisfactory couplant) were placed in a suitable holder and placed inside the cooled

chamber. A thermocouple was placed in direct contact with the sample in order for

the temperature of the sample to be measured.

Measurements of ultrasonic attenuation were performed using an ultrasonic flaw

detector USIP 20 (Krautkramer – Germany). The method used in this study was the

pulse echo technique where only one transducer acted as transmitter and receiver

simultaneously. All experiments were carried out in the temperature range from 150

to 300 K and at four ultrasonic frequencies namely; 2, 4, 6 and 14 MHz. heights of

two successive echoes were measured and then the attenuation coefficient was

calculated using the following equation;

=

2

1log2

20

A

A

dα (1)

where d is the thickness of the sample, A1 and A2 are the heights of the first and

second echo, respectively, which represent the amplitudes of the two echoes.

3. Results and discussion

3.1. Glass transition temperature

The glass transition temperature (Tg) values with mol % content of CdO

concentration are shown in Fig. 1 and Table 2. With the increase in CdO content from

0 to 50 mol %, the Tg values decreased from 769 to 726 K. Gaafar et al. [19]

analyzed the FTIR spectra of the glass system 50 B2O3 – (50-x) TeO2 – x CdO and

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reported that, the presence of CdO at the expense of TeO2 in the glass system from 0

to 50 mol %, caused the transformation of TeO4 trigonal bi-pyramids units into TeO3

trigonal pyramids units. This is may be related to the decrease in Tg values. Also, the

bond strength plays a competitive role in decreasing the Tg values. The bond

strengths of Cd–O, B–O and Te–O are 235.6, 808.8 and 376.1 (kJ/mol), respectively

[21], so the decrease in Tg values is most likely due to the replacement of of Te–O

linkage by the weaker Cd–O linkage.

The calculated values of thermal expansion coefficient α of the glasses under study

(according to Makishima and Mackenzie [22]) were found to increase from 51.3×10−7

to 157.5×10−7

1/◦C with the increase in CdO content from 0 to 50 mol %, as shown in

Fig. 1 and Table 2. Srivastava and Srinivasan [23] have stated that the thermal

expansion coefficient of materials depends on the strength of bonds. Therefore, the

decrease in the values of thermal expansion coefficient explains the decrease in Tg

values. Moreover, the decrease in the values of stretching force constant F (which

were calculated according to bond compression model [24]) and average bond

dissociation energy per unit volume Gi (calculated according to Makishima and

Mackenzie [22]), confirms the decrease in Tg values, as represented in Fig. 2.

3.2. Ultrasonic studies

Results of Ul and Ke with CdO contents are shown in Table 1. As shown in

Table 1 and Fig. 3, the longitudinal wave velocity values were found to decrease with

addition of CdO mol % contents at the expense of TeO2. While the variation of bulk

modulus (Ke) increased with CdO mol % content [19].

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The dependence of ultrasonic attenuation coefficient at four operating

frequencies 2, 4, 6, and 14 MHz, are shown in Figs. 4 & 5, of glass compositions 50

B2O3 –50 TeO2 – 0 CdO and 50 B2O3 –10 TeO2 – 40 CdO as an examples. All other

glass compositions showed the same behaviour as those shown in Figs. 4 & 5. Well-

defined broad peaks are observed at temperatures range from 120 to 300 K with

change in CdO content. These figures showed that, with increasing operating

frequency, the peak shifts to the higher temperatures and the height of this peak

increases linearly.

In addition, it clearly seen from the figures that, the temperature peak position

shifts to lower temperature with the increase in CdO content. Moreover, the tails of

the loss curves overlap with each other's, which is mainly due to the thermal

broadening as the operating frequency, is increased.

The plots of the inverse of the temperature peaks and ln the operating

frequencies are shown in Fig. 6, for all glass compositions. All plots showed straight

lines confirming that for a given glass composition, the peaks fit an equation of the

form;

p

p

oKT

Eff −= exp (2)

where fo and Ep are the classical vibration frequency (attempt frequency) and

activation energy respectively. They were, obtained from the intercept and the slope

of the lines. Figs. 4 & 5 together with Fig. 6, suggest that some sort of relaxation

process is operative. Results of the ultrasonic attenuation, peak temperature, classical

attempt frequency and activation energy of the relaxation process are given in Table 1.

The values of Ep increased with the increase in CdO content as shown in Fig. 7. Such

increase in activation energy indicates that the structure becomes open and the bonds

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are less stable with addition CdO with lower bond strength than TeO2 as the stretching

force constant and the average bond dissociation energy are decreased as shown in

Fig. 2.

It has been reported [20 & 25], that the peaks in the temperature dependence of

acoustic wave absorption in inorganic oxide and halogenide glasses occurring in the

range 4 to 300 K, have been attributed to loss mechanisms of the standard linear solid

type, with low dispersion (SLSLD) and Arrhenius-type relaxation times. Such loss

mechanism attributed to the presence of atoms moving in double-well potentials

corresponding to two equilibrium configurations (see Fig. 8). Experimental values of

activation energy and attempt frequency suggest wells. In such absorption loss peaks,

the atoms will vibrate in the double well potentials trying to overcome the barrier

height when ultrasonic wave (with certain resonant frequency) is applied and the

temperature is increased. Applying ultrasonic waves with higher frequency results in

the activation of larger number of atoms to vibrate in the double well potentials at

higher temperatures (as the absorption loss peaks are frequency and temperature

dependent). Thus, the absorption loss peak heights are increased with increasing

frequency.

Thus, the absorption loss peaks observed in our investigation were suggested as

due to the thermally activated particles, and the relaxation processes then can be

attributed due to a particles moving in asymmetric double-well potentials of atomic

dimension. This particle motion can be described as an oscillation around either of

two-well potential minima. Passage of ultrasonic waves through the material will

disturb the equilibrium, and resulted in a relative energy shift between the two minima

of the double wells by an amount ∆E = Dε, where D is the deformation potential

which shows the energy shift of the relaxing states in a strain field of unit strength and

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(ε) is the magnitude of the strain field. The particle relaxes to the equilibrium

configuration again by overcoming the barrier between the two wells via the

thermally activated process. The relaxation time depends on the temperature and

barrier height (activation energy). Such behaviours of absorption loss peaks were

found to be similar to those observed else were; TeO2 - V2O5 [14], TeO2 - V2O5 –

ZnO and TeO2 - V2O5 - CeO [16], Li2O – B2O3 – WO3 [20], Nb2O5 – TeO2 and PbO -

Nb2O5 – TeO2 [26], and Na2O − Al2O3 − B2O3 − ZnO [27].

According to Gaafar & Mahmoud [20], Bridge & Patel [25], Gaafar et al. [27]

and Abd El-Moneim [28], they reported the compositional dependent of activation

energy (Ep) with the experimental bulk modulus, average stretching force constant (F)

and average atomic ring diameter (l). Therefore, applying linear regression between

Ep and F(F/K)0.576

, yields a relationship;

( ) 16606.0104576.05

)( +−= − KFFxE thP (3)

with a correlation coefficient of 99.9 %.

In addition, applying regression between the experimentally determined number of

loss centers per oxygen atoms and the average stretching force constant with bulk

modulus, the number of loss centers per oxygen atoms can be calculated using

exponential decay method, yielding the following relationship;

)/(002.0

)( 194.11711.0 KFF

th eN −∗+= (4)

with a correlation coefficient of 99.9 %.

The values of the experimental bulk modulus and average stretching force

constant were reported earlier in Ref. [19]. Also, the values of the theoretically

obtained average activation energy and number of loss centers per oxygen atoms

(Ep(th) & N(th)) were given in Tables 1 & 2.

The deformation potential is given by Gaafar and Sidkey [29] in the form;

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325.1 pED = (5)

The values of deformation potential (D) of the glass compositions investigated

are given in Table 1. It can be seen that the deformation potential increases with the

increase of CdO mol % content.

Thus, the ultrasonic waves resulted in a thermal inequilibrium, and the

relaxation process will restore the equilibrium again. The particle can surmount the

barrier between the double-wells in a thermally activated process. Moreover, the

width of the temperature peaks, indicates that a single relaxation process with

( )ppo KTEexpττ = makes this relation is unsuitable for description. Furthermore,

the activation energies, Ep, obtained in this study (Table 1) are spread of values

around a fixed value obtained in crystalline 50 B2O3 – (50-x) TeO2 – x CdO

compositions, i.e. some kind of average over a broad distribution of activation

energies. Thus, the loss peaks have to be described in terms of the distribution of

relaxation times with each relaxing particle moving in the double-well potential [30].

Also, for a system of (n) particles per unit volume moving in identical double well

potentials of barrier height (see Fig. 8), the internal friction is given by the equation;

ωαV

Q21 =−

222

2

11

1

τωωτ

ρ +

+∆=

∆KTed

d

V

nD (6)

( ) ( ) dEdEnnXed

d

V

D

kT

∆∆+

+∆= ∫ ∫

∞

∆

∞

22

0 0

2

2

11

1

τωωτ

ρ

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where

+=

∆−KTKT

E

o ee 1ττ , where K is Boltzmann’s constant, T is the absolute

temperature, α is the ultrasonic absorption coefficient in Nepers per unit length, ω is

the angular frequency, V is the phase velocity, τ is the relaxation time, τo-1 is the

attempt frequency for the particle in either well, ∆ is the free-energy difference

between corresponding particle states in the two wells, i.e. the separation of the well

minima, n is the number of loss centers and D is the deformation potential which

represents the energy shift of the two well states in a strain field of unit strength

averaged over all possible well orientation. Thus, for the asymmetric distribution,

where ∆ ≥ 2KT and taking n(∆) = no, equation (6) can be rewritten with a constant

independent of both ∆ and E in the simple form;

( )∫∞

−

+=

0

222

21

1

2

τωωτ

ρdEEn

V

DnQ o (7)

where n(E)dE is the number of two-well systems (number of loss centers), with

barrier height in the range from E to (E + dE) which is expressed as a function of

vibrating particles.

The borate glasses are regarded as three-dimensional networks A–O–A (A=

cation, O = anion) bonds, there will be also a distribution of both the thermally

averaged cation – anion – cation spacing about an equilibrium value and a

corresponding distribution of (A–O–A) angles. In addition, there will be always a

distribution of A–A separations (bond lengths) with values either greater or less than

the equilibrium (crystalline) value. Therefore, the total number of the two – well

systems per unit volume is proportional to the oxygen density [25].

Considering a distribution of double-well systems of vibrating particles, that

will arise from the spread of cation-anion spacing with a distribution of barrier heights,

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which are proportional to the bond strength, for both longitudinal and transverse

motions of oxygen or boron atoms as the most lighter vibrating particles (since

tellurium, and cadmium atoms have relatively larger masses), then for any one of the

double-well system A-O-A, further oxygen atoms situated to the left and the right of

cation A will be situated at sites slightly at different distances from the later [20]. It

follows that the variability of B–O–B, B–O–Cd, B–O–Te, Cd–O–Te, Te–O–Te and

Cd–O–Cd bond angles means that there is a spread of the atomic ring size in the glass

system under investigation. The distribution of asymmetries ∆ will appear as a second

order effect. At peak temperature Tp, the oxygen atoms consisted in the double-well

system will change the configuration by thermal activation energy, with hopping over

the barrier.

Therefore, the total number of double – well potential systems (loss centers, i.e.

number of oxygen atoms which will absorb ultrasonic wave) per unit volume (n), is

given by,

( )∫∞

=0

dEEnn (8)

( )∫∞

=0

2

2

2dEEc

Dn

V

o

ρ (9)

where the integral ( )∫∞

0

dEEc is the area under the curve relating α and T in Figs. 4 & 5.

Gilroy and Phillips [30] have assumed that for asymmetric double – well

potential n(E) takes the form;

( ) ( ) ( )pp EEEEn −= exp1 (10)

Assuming that po En 1= , where Ep is the activation energy, then equation (9)

can take the form;

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( )∫∞

=0

2

2

2dEEc

D

EVn

pρ (11)

As reported before [20], it is hard to justify this assumption for the form of n(E),

it has the advantage that n is expressed in terms of the experimental parameters Ep

and ( )∫∞

0

dEEc of the acoustic loss process alone. The purpose of choosing a specific

form for n(E), is to make possible a discussion of the compositional dependence of

the two well systems and no more.

Therefore, the total number of two – well systems per unit volume was

calculated for the absorption loss peaks observed to all investigated glass

compositions at applied ultrasonic frequency of 2 MHz, which has been selected as an

example (in order to discuss the compositional dependence of the number of two well

systems per unit volume), and showed in Table 2 and Fig. 9.

The Oxygen density [O] was also calculated for the three glass systems under

investigation according to an equation [31] in the form;

[ ]G

CNO A

16= (12)

where C is the total amount of oxygen in 100 gm of the glass, G is the volume of 100

gm of glass, and NA is Avogadro’s number. Table 2 showed the values of the number

of loss centers per unit volume, number of loss centers per oxygen atoms N and

oxygen density. The relaxation strength A indicates the height of the internal friction

peak, which in turn is a measure of the number of relaxation units exists in the glass

composition and the quantity of unrelaxed strain contributed by each unit. The

relaxation strength A for the different glass series studied was calculated from the

equation given by Carini et al [32] as;

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f

VA

πα2

= (13)

where α is the ultrasonic attenuation coefficient in dB/cm (maximum relaxation loss

at Tp), V is the longitudinal ultrasonic velocity and f is the operating frequency. Table

1 showed the values of relaxation strength which are an indication of the defect

concentrations. It shows that, at the same operating frequency, the relaxation strength

increases with increasing CdO modifier content. Moreover, the relaxation strength

decreases with increasing the operating frequency for the same modifier content.

The variation of the number of loss centers per oxygen atom N with CdO

content, have been shown in Fig. 10. It is clearly seen that, the increase in CdO

modifier content resulted in an increase for all; the number of two-well systems per

oxygen atom (number of vibrating atoms), the relaxation strength and the deformation

potential due to the replacement of TeO2 (with coordination numbers between 3 & 4)

by CdO (with octahedral coordination number), thus the activation energy of the

relaxation process is increased with the increase in cross-link density which can be

explained by taking into account two factors. First, the increase in the distribution of

cadmium ions among the B–O chains as a network modifier, which causes the

increase in the cross-link density of the glass, network structure. The second is the

decrease in the relative strength of bonds [33-34], which consequently means the

increase in the number of two-well systems per oxygen atom (number of vibrating

atoms).

Thus, addition of CdO modifier content (with larger bond length and lower

bond strength) at the expense of TeO2, resulted in the following;

a) Decrease in the average bond strength of the glass network structure (see

Table 2), that led to the increase in the number of two well systems (i.e. the

increase in the number of atoms which are free to vibrate), and consequently

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the increase in the average activation energy (the barrier height of the two

well systems).

b) Increase in the time of the relaxation process as it directly depends on the

classical attempt frequency of vibration, deformation potential and the

relaxation strength.

3.3. Theoretical treatment of longitudinal vibrations

The central force model was proposed according to Bridge & Patel [25], the

deformation potential was calculated theoretically using the following equation,

x

y

Nn

MqD

Ab

th δδ

ρ

=

2 (14)

where q is longitudinal modulus equals to (K+(4/3)G), K and G are the bulk and shear

moduli respectively, M is the mass of one kilo mole, NA is Avogadro’s number, ρ is

the density, nb is the number of A-O-A units per formula unit (3 or 4 for B2O3, 3 or 4

for TeO2 and 6 for CdO), δx is the bond length times 2 and δy is the separation of

minima in the two-well potential as shown in Fig. 8. δx was taken according to [35-

36]. The values of δy were calculated according to the theoretical treatment of

longitudinal two-well systems, which are shown in Fig. 11. Values of the longitudinal

modulus are given in Table 2.

The mutual potential energies of linear arrangement of the three atoms,

consisting of an anion in the middle of two cations (or vice versa), separated by a

distance Ro with position r of the oxygen atom O in the glass compositions; 50 B2O3 –

50 TeO2 – 0 CdO, 50 B2O3 – 30 TeO2 – 20 CdO, 50 B2O3 – 10 TeO2 – 40 CdO and 50

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B2O3 – 0 TeO2 – 50 CdO, are shown in Fig. 11. They were calculated for various

values of elongation, according to the equation given by Bridge & Patel [25] as;

( ) ( )

−++

−+−=

m

o

m

o rerrb

rerraU

2

11

2

11 (13)

where 6<m>12. In glass system under investigation, the types of bonds present are;

(B–O–B), (B–O–Cd), (B–O–Te), (Te–O–Cd), and (Te–O–Te). The constant a for a

given molecular type is given by;

−=mr

aU

o

o

11 (14)

the constant b is given by; ( ) marb m

o

1−= ,where ro is the bond length, Uo is the cation-

anion bond energy, and e is the elongation which equals e = (R/2ro), i.e. A-A

separation divided by the equilibrium separation 2ro. Taking m equals to 9, values of

the constants a, b, Uo, longitudinal and transverse separations of minima in the two

well potential and theoretical deformation potentials are given in Table 2 for each

glass composition.

It clearly seen that the single minimum potential occurs for the elongation less

than (e<1) for all glass systems. For elongation values above 30 %, the two-well

potential starts to develop. For elongations between 57.9 – 99.4 %, the potential

barrier increases from 0.345 eV to 0.685 eV when CdO content between 0 to 50

mol %. In addition, with the increase of CdO content from 0 to 50 mol %, the mutual

potential energy (see Table 2) will decrease as a direct effect of decreasing the

average bond strength and the average stretching force constant.

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The theoretically calculated deformation potential values corresponding to the

elongations listed in Table 2, were found to be in good agreement with those

experimentally determined. They showed that the incorporation of CdO between 0

and 50 mol % content, caused the linear elongation of B-O bonds from 57.9 to reach

99.4%.

4. Conclusions

The longitudinal ultrasonic absorption at low temperatures showed the presence

of well-defined peaks whose heights increase with increasing the applied frequency.

Those peaks ascribed to the thermally activated relaxation governed by Arrhenius

relationship. In addition, the peak temperature values decreased with the increase in

CdO content. The activation energy, the attempt frequency, deformation potential and

relaxation strength values were found to increase with increasing the CdO content.

Moreover, the values of the number of loss centers increased with the increase in

activation energy, due to the replacement of CdO content with higher bond length,

higher coordination number and lower bond strength at the expense of TeO2 with

lower bond length and higher bond strength, which will cause the decrease in the

average bond strength and linear increase in the elongation of B-O bonds. Such

parameters are dependent on the experimental bulk modulus, average stretching force

constant and average atomic ring diameter, which have been discussed earlier in Ref.

[19].

Acknowledgement

The authors would like to express their sincere thanks to the Deanship of

scientific research at Majmaah University, KSA, for supporting this search work in

the project No. 18.

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[9] E.S. Yousef, J. Alloys Compd. 561 (2013) 234-240.

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[11] K. Hirao, S. Kishimoto, K. Tanaka, S. Tanabe, N. Soga, J. Non. Cryst. Solids

139 (1992) 151-156.

[12] K. Shioya, T. Komatsu, H.G. Kim, R. Sato, K. Matusita, J. Non. Cryst. Solids

189 (1995) 16-24.

[13] R. El-Mallawany, J. Mater. Research 7 (1992) 224-228.

Page 18 of 34



For Review O

nly

19

[14] M. A. Sidkey, R. El-Mallawany, R. I. Nakhla, A. Abd El-Moneim, Physica

Status Solidi (a) 159 (1997) 397-404.

[15] M. A. Sidkey, R. A. El-Mallawany, A. A. Abousehly, Y. B. Saddeek, Mater.

Chem. Phys. 74 (2002) 222-229.

[16] R El-Mallawany, M Sidky, H Afifi, J. Appl. Phys. 107 (2010) 053523.

[17] R El-Mallawany, M Sidkey, A Khafagy, H Afifi, Mater. Chem. Phys. 37 (1994)

197-200.

[18] S.P.H.S. Hashim, H.A.A. Sidek, M.K. Halimah, K.A. Matori, W.M.D.W. Yusof,

M.H.M. Zaid, Int. J. Mol. Sci. 14 (2013) 1022-1030.

[19] M. S. Gaafar, I. Shaarany, T. Alharbi, J. Alloys Compd. 616 (2014) 625-632.

[20] M. S. Gaafar, I. S. Mahmoud, J. Alloys Compd. 657 (2016) 506-514.

[21] D. R. Lid, CRC Handbook of Chemistry and Physics, 8th

edition, CRC Press,

London (2000).

[22] A. Makishima, J.D. Mackenzie, J. Non-Cryst. Solids 22 (1976) 305-313.

[23] C.M. Srivastava, C. Srinivasan, Science of Engineering Materials, 2nd ed., New

Age International (P) Ltd., New Delhi (1997).

[24] A. A. Hegazy, B. Bridge, J. Non-Cryst. Solids 72 (1985) 81-108.

[25] B. Bridge, N. D. Patel, J. Mater. Sci. 21 (1986) 3783-3800.

[26] M. S. Gaafar, A. Y. Azzam, Bull. Mater. Sci. 38(1) (2015) 119-128.

[27] G. E. El-Falaky, M. S. Gaafar, N. S. Abd El-Aal, Curr. Appl. Phys. 12 (2012)

589-596.

[28] A. Abd El-Moneim, Physica B. 334 (2003) 234-243.

[29] M. S. Gaafar and M. A. Sidkey, Phys. Chem. Glasses 45 (2004) 7-14.

[30] K. S. Gilroy, W. A. Phillips, Phil. Mag. B 43 (5) (1981) 735-746.

[31] R. EL Mallawany, Mat. Chem. Phys. 39 (1994) 161-165.

Page 19 of 34



For Review O

nly

20

[32] G. Carini, M. Cutroni, M. Federico, G, Galli, Solid State Commun. 44 (1982)

1427-1430.

[33] M. S. Gaafar, A. M. Abdeen Mostafa, S. Y. Marzouk, J. Alloys Compd. 509

(2011) 3566-3575.

[34] M. S. Gaafar, S. Y. Marzouk, H. Mady, Phil. Mag. 89(26) (2009) 2213-2224.

[35] R. E. Lambson, G. Saunders, B. Bridge, R. El Mallawany, J. Non-Cryst. Solids,

69 (1984) 117-133.

[36] A. Berthereau, Mater. Res. Bull., 29 (9) (1994) 933-941.

Page 20 of 34



For Review O

nly

0.0 0.1 0.2 0.3 0.4 0.5

720

730

740

750

760

770

Tg

αααα

CdO mol. %

Tg [

K]

40

60

80

100

120

140

160

Th

erm

al

ex

pan

sio

n c

oe

ffic

ien

t, αα αα

[1

/°C

]

Fig. 1. Plot of the glass transition temperature (Tg) and thermal

expansion coefficient (α) of the investigated glass system with CdO mol

% content.

Page 21 of 34



For Review O

nly

0 10 20 30 40 50

260

270

280

290

300

310

320

330

340

350

F

Gi

CdO mol %

Str

etc

hin

g f

orc

e c

on

sta

nt

[N/m

]

50

52

54

56

58

60

62

Dis

so

cia

tio

n e

nerg

y, G

i [k

J/m

ol]

Fig. 2. Behaviours of stretching force constant (F) and dissociation

energy (Gi) of the investigated glass system with CdO mol % content.

Page 22 of 34



For Review O

nly

0 10 20 30 40 50

4780

4800

4820

4840

4860

4880

4900

4920

4940

Lo

ng

itu

din

al

ult

raso

nic

wa

ve

velo

cit

y,

Ul [

m/s

]

CdO mol %

Fig. 3. Dependence of longitudinal ultrasonic wave velocity (Ul) of the

investigated glass system with CdO mol % content.

Page 23 of 34



For Review O

nly

140 160 180 200 220 240 260 280 300

1.5

2.0

2.5

3.0

3.5

4.0

Ult

ras

on

ic a

tte

nu

ati

on

co

eff

icie

nt

[dB

/cm

]

Temperature [K]

2 MHz

4 MHz

6 MHz

14 MHz

Fig. 4. Ultrasonic attenuation coefficient curves of glass composition 50

B2O3 –50 TeO2 – 0 CdO.

Page 24 of 34



For Review O

nly

120 140 160 180 200 220 240 260 280 300

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Ult

ras

on

ic a

tte

nu

ati

on

co

eff

icie

nt

[dB

/cm

]

Temperature [K]

2 MHz

4 MHz

6 MHz

14 MHz

Fig. 5. Ultrasonic attenuation coefficient curves of glass composition 50

B2O3 –10 TeO2 – 40 CdO.

Page 25 of 34



For Review O

nly

0.0040 0.0045 0.0050 0.0055 0.0060

14.5

15.0

15.5

16.0

16.5 Cd0

Cd10

Cd20

Cd30

Cd40

Cd50

Ln

F [

MH

z]

1/T [K-1]

Fig. 6. Plot of the logarithm of operating frequency and inverse of

temperature peak for the investigated glass system.

Page 26 of 34



For Review O

nly

0 10 20 30 40 50

0.126

0.128

0.130

0.132

0.134

0.136

0.138

0.140

0.142

Ac

tiv

ati

on

en

erg

y, E

P [

eV

]

CdO mol %

Fig. 7. Behaviour of the activation energy of the investigated glass

system.

Page 27 of 34



For Review O

nly

Fig. (8). Double well potential.

∆

E

Page 28 of 34



For Review O

nly

0 10 20 30 40 50

0.8

1.0

1.2

1.4

1.6

1.8

2.0N

um

ber

of

los

s c

en

ters

, n

x1

027 [

m3]

CdO mol %

Fig. 9. Plot of the number of loss centers per unit volume (n).

Page 29 of 34



For Review O

nly

0 10 20 30 40 50

5.0

5.2

5.4

5.6

5.8

6.0

6.2

Nu

mb

er

of

loss

cen

ters

per

ox

yg

en

ato

m, N

CdO mol %

Fig. 10. Plot of the loss centers per oxygen atom (N).

Page 30 of 34



For Review O

nly

-0.2 -0.1 0.0 0.1 0.2

-6.5

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

50B2O

3 - 50TeO

2 - 0CdO

0 %

40 %

60 %

100 %

U/2

(e

V)

r (nm)

-0.2 -0.1 0.0 0.1 0.2

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

50B2O

3 - 30TeO

2 - 20CdO

0 %

40 %

60 %

100 %

U/2

(e

V)

r (nm)

-0.2 -0.1 0.0 0.1 0.2

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

50B2O

3 - 10TeO

2 - 40CdO

0 %

40 %

60 %

100 %

U/2

(eV

)

r (nm)

-0.2 -0.1 0.0 0.1 0.2

-6.0

-5.5

-5.0

-4.5

-4.0

-3.5

-3.0

-2.5

-2.0

50B2O

3 - 0TeO

2 - 50CdO

0 %

40 %

60 %

100 %

U/2

(e

V)

r (nm)

Fig. 11. Plots of the potential wells for the longitudinal motion of the two

well systems at different elongations of 0, 40, 60 and 100%, as examples

in order guide the viewer.

Page 31 of 34



For Review Only

A D

[eV]

Ep(th)

[eV]

Ep

[eV]

fo x1011

[s-1

]

Tp

[K]

α

[dB/cm]

F

[MHz]

Ke

[GPa]

Ul

[m/s]

Vm

x10-6

[m3/ mol]

ρ

[g/cm3]

Glass composition mol %

CdO TeO2 B2O3

0.374

0.205

0.165

0.088

0.380 0.127 0.127 0.040 196

216

238

255

2.623

2.845

3.479

3.923

2

4

6

14

54.1 4925 29.42 3.895 0 50 50

0.383

0.209

0.167

0.092

0.386 0.131 0.131 0.054 193

213

233

248

2.699

2.910

3.535

4.106

2

4

6

14

56.6 4904 26.99 4.130 10 40 50

0.398

0.220

0.170

0.094

0.390 0.134 0.132 0.076 188

205

226

237

2.814

3.078

3.610

4.215

2

4

6

14

59.1 4881 24.83 4.365 20 30 50

0.404

0.261

0.175

0.095

0.396 0.137 0.136 0.121 182

198

214

229

2.883

3.679

3.732

4.308

2

4

6

14

61.2 4846 22.88 4.600 30 20 50

0.417

0.276

0.189

0.100

0.403 0.139 0.139 0.194 178

190

208

219

2.992

3.907

4.068

4.573

2

4

6

14

63.3 4816 21.12 4.835 40 10 50

0.442

0.294

0.228

0.120

0.408 0.141 0.142 0.301 172

186

198

212

3.196

4.204

4.405

4.910

2

4

6

14

65.1 4782 19.53 5.070 50 0 50

Page 32 of 34



For Review Only

Table 1. Variation of density (ρ), molar volume (Vm), longitudinal ultrasonic wave velocity (Ul), experimental bulk modulus (Ke), frequency (F),

longitudinal ultrasonic attenuation coefficient (α), peak temperature (Tp), attempt frequency (fo), activation energy (Ep), theoretically calculated

activation energy (Ep(th) according to eq. (3), deformation potential (D) and relaxation strength (A) for glass system 50 B2O3 – (50-x) TeO2 – x

CdO.

Page 33 of 34



For Review Only

Table 2. Representation of the glass transition temperature (Tg), thermal expansion coefficient (α), number of loss centers per unit volume (n),

Oxygen density [O], number of loss centers per oxygen atom (N), theoretically determined number of loss centers per oxygen atom (Nth)

according to eq. (4), average bond length (R), Longitudinal modulus (q), elongation (e), theoretically determined deformation potential (Dth) and

mutual potential energy (Uo).

Uo

[eV]

Dth

[eV]

e

%

q

[GPa]

R

[nm]

Nth

%

N

%

[O]

x1028

[m3]

n

x1027

[m-3

]

α

1/°C

Tg

[K]

Glass composition mol %

CdO TeO2 B2O3

6.111 0.376 57.9 94.48 0.1709 0.187 0.185 5.117 0.947 51.3 769 0 50 50

5.966 0.387 63.3 99.32 0.1706 0.200 0.209 5.355 1.118 67.8 762 10 40 50

5.822 0.389 68.8 103.99 0.1730 0.217 0.225 5.580 1.256 86.6 755 20 30 50

5.677 0.400 79.1 108.03 0.1777 0.238 0.237 5.791 1.372 107.9 744 30 20 50

5.532 0.404 89.2 112.14 0.1783 0.262 0.268 5.988 1.608 131.6 735 40 10 50

5.387 0.405 99.4 115.94 0.1792 0.289 0.299 6.168 1.845 157.5 726 50 0 50

Page 34 of 34



for review only - university of toronto t-spacefor review only 7 the dependence of ultrasonic...

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