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1. IntroductionAl2O3–PbO–B2O3 glasses might have a complex structure. This is because all the component oxides have various structural units that depend on the glass composition. B2O3 forms, with modifier oxides, glassy networks consisting of symmetric BO3 trian-gles, BO4 tetrahedra and asymmetric BO3 units. The concentration and the form of these units depend on the modifier oxide content in glass. These units may arise either as separated units or in the form of groupings such as boroxol, penta-, tri-, di-, meta-, pyro- and orthoborate.(1,2)

NMR investigations on PbO–B2O3 glasses(3,4) indi-cated that lead enters the network only as modifier at low PbO contents (<15 mol%). In this case Pb2+ ions are used to form BO4 tetrahedra in the borate network at a rate of two BO4 units for each Pb2+ ion. Above 15–20 mol% PbO lead starts to act partially as network former in the form of PbO4 units. It is assumed that PbO4 units associate preferentially to BO3 units rather than BO4 ones.(3) The fraction of the network former PbO increases in a nearly monotonic manner.(5) In contrast the fraction of the modifier PbO, and thus the fraction N4 of four-coordinated boron atoms, increase to a maximum around 50 mol% PbO. Up to that PbO concentration nonbridging oxygen ions (NBOs) do not form in the borate network. Bray et al(3) excluded formation of NBOs also for PbO>50

mol%. On the other hand Raman spectroscopy has been used by Meera et al(2) to investigate the structure of PbO–B2O3 glasses. They indicated that above 50 mol% PbO the concentration of chain and ring type metaborate units (NBOs) increases at the expense of BO4 ones.

The role of Al2O3 in the structure depends greatly on the type and composition of glass. Al2O3 is as-sumed to enter R2O–Al2O3–SiO2 glasses (R2O being an alkali oxide) as AlO4 tetrahedra and/or AlO6 octahedra, depending on the glass composition. AlO4 is a network building unit whereas AlO6 is a network modifier. Only AlO4 units would form for Al2O3/R2O≤1.(6,7) AlO6 units are formed for Al2O3/R2O>1, i.e. in case of alkali oxide deficiency with respect to Al2O3. In R2O–Al2O3–SiO2 glasses Al2O3 has priority to associate itself with an equivalent quan-tity of alkali oxide.(8) The same rules are applicable for Na2O–Al2O3–B2O3–SiO2 glasses.(9) NMR results of Gresch & Müller-Warmuth(10) revealed another behaviour in Na2O–Al2O3–B2O3 glasses. It has been indicated that there is a competition between Al2O3 and B2O3 to form AlO4 and BO4 tetrahedra. BO4 units were detected even in glasses having Al2O3/Na2O>1. Bishop & Bray(11) came earlier to similar conclusions for the formation of AlO4 and BO4 tetrahedra in CaO–Al2O3–B2O3 glasses. Naruse et al(12) assumed that in BaO–Al2O3–B2O3 glasses aluminium ions enter the network as triclusters (AlB3O7 units) regardless the ratio of BaO/Al2O3. Such an assumption was not in agreement with the results of Osaka et al(13) * Corresponding author. Email hdoweidar@mans.edu.eg

Sites distribution and properties of Al2O3–PbO–B2O3 glassesH. Doweidar,* K. El-Egili, G. El-Damrawi & R. M. RamadanGlass Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura 35516, POB 83, Egypt

Manuscript received 23 March 2007Revised version received 19 October 2007Accepted 29 October 2007

Infrared spectra, density and electric conduction have been investigated for xAl2O3.(50−x)PbO.50B2O3 glasses (0≤x≤20 mol%). The fraction of four-coordinated boron atoms has been calculated from the area under the component bands of the IR spectra. It decreases with increasing Al2O3 content which assumes association of modifier PbO with AlO4 tetra-hedra at the expense of BO4 ones. Analysis of density data suggests that Al2O3 enters the structure in a single form as network forming AlO4 tetrahedra. Both the electric conductivity and activation energy decrease with increasing Al2O3 content. The effects are attributed to the presence of two types of Pb ions as charge carriers; the ions linked to BO4 units and those linked to AlO4 tetrahedra.

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who argued that the idea of triclusters is not neces-sary to explain the properties of CaO–Al2O3–B2O3 and BaO–Al2O3–B2O3 glasses. Recently Doweidar et al(14) indicated that in (30−x)Na2O.xAl2O3.70B2O3 glasses Na2O associates preferentially with Al2O3, up to Al2O3/Na2O=1, to form AlO4 tetrahedra. They attributed changes in physical properties for Al2O3/Na2O>1 to formation of triclusters. From the above discussion it can be assumed that, in general, Al2O3 has priority to associate with modifier oxide to form AlO4 tetrahedra. Formation of triclusters is a matter of composition (Al2O3/R2O>1) or the type of glass.

It appears therefore that there is a variety of prob-able structural forms of the oxides, especially Al2O3, in PbO–Al2O3–B2O3 glasses. The aim of the present work is to explore the structure of these glasses and to correlate it with the physical properties.

2. Experimental

Glasses having the formula xAl2O3.(50−x)PbO.50B2O3 (Table 1) were prepared by melting reagent grade Al2O3, PbO and H3BO3. The well mixed mixtures were melted in alumina crucibles in an electric furnace at a temperature ranged between 1000°C and 1450°C, depending on the glass composition. The melt was left between 30 min and 1 h under the atmospheric condition in the furnace during which the melt was occasionally swirled. The melt was quenched to room temperature by pressing it between two iron plates. The obtained samples were homogeneous and transparent.

The density (D) of the glasses (Table 1) was de-termined at room temperature using Archimedes method with xylene as an immersion liquid. Three samples of each glass were used to determine the density. A random error in the density measurements was found as ±0·03 g/cm3.

For the dc conductivity measurements, samples were ground to obtain parallel surfaces of 12–15 mm diameter and a thickness ranging between 1–2 mm. The two parallel surfaces of the sample were coated with graphite as electrodes. The radius of the coated area is 5 mm. The resistance was measured using an insulation tester type TM14 (Level Electronics LTD, England) with a range of 103 to 1013 Ω. As a rule

three samples of each glass were used to measure the resistance over a temperature range 30–400°C. The experimental error in determining the activation energies for conduction is estimated to be less than 0·02 eV, whereas a relative error in the conductivity is expected to be ±5%.

The infrared spectra of the glasses were recorded at room temperature, immediately after glass prepara-tion, using the KBr disc technique. A Mattson 5000 FTIR spectrometer was used to obtain the spectra in the wavenumber range of 200–2000 cm−1, with a resolution of 2 cm−1. At least two samples of each glass were investigated. Infrared spectra were corrected for the dark current noises and background using the two-point baseline correction. Then the spectra were normalised by making the absorption of each spectrum varies between 0 and 1 arbitrary units. In addition such normalisation is necessary to eliminate the concentration effect of the powder sample in the KBr disc.

3. Results

Figure 1 shows the infrared spectra of the glasses investigated. There are various features in the range of 200–1800 cm−1. A mild peak is observed around 710 cm−1. Its centre seems to be independent of the Al2O3 content of glass. Furthermore there are two strong peaks around 960 and 1333 cm−1. The centre of the peak at 960 cm−1 does not depend on the glass com-position whereas that of the 1333 cm−1 band shifts to higher wavenumbers as the Al2O3 content increases. In addition, there are two shoulders at nearly 1050 and 1240 cm−1. The centres of these shoulders change slightly with the composition of glass.

Figure 2 represents the change with composition of both density D and molar volume Vm. There is a linear decrease in D and a linear increase in Vm when increasing the Al2O3 content.

Figure 3 shows the dependence of the logarithm

H. DoweiDar et al: SiteS DiStribution anD propertieS of al2o3–pbo–b2o3 glaSSeS

Table 1. Composition, experimental density Dm, calcu-lated density Dc and calculated N4 values of the studied glassesAl2O3 PbO B2O3 Dm Dc N4

(mol%) (mol%) (mol%) (g cm−3) (g cm−3)0 50 50 5·58 5·56 0·5052 48 50 5·30 5·32 0·4235 45 50 5·15 5·16 0·40510 40 50 4·72 4·76 0·29815 35 50 4·45 4·43 0·22120 30 50 4·11 4·11 0·138

Figure 1. Infrared spectra of xAl2O3.(50−x)PbO.50B2O3 glasses. Values of x are given (in mol%) at the plots

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of conductivity (log σ) on the reciprocal of absolute temperature for the glasses investigated. The linear change of log σ suggests that the conduction process follows the Arrhenius relation

σ=σ0 exp(−E/kT) (1)

In this relation σ0 is a constant that depends on the glass composition and its thermal history, E the activation energy for the conduction process, k Boltz-mann’s constant and T the absolute temperature.

4. Discussion

The peaks in infrared spectra of oxide glasses are related to certain vibrational modes of specific struc-tural groups. Quantitative analysis of IR spectra can be done by deconvoluting the absorption peaks into component bands. The concentration of a structural group in glass is related to the relative area of the bands related to that group. Deconvolution technique has been successfully used to analyse IR spectra of various types of glass.(14–16) In Figure 4 is shown, as an example, deconvolution of the IR spectrum of 10Al2O3.40PbO.50B2O3 glass. Table 2 summarises the deconvolution data of the component bands (band centre and relative area) of the studied glasses.

The low frequency bands (≤450 cm−1) are generally

attributed to vibrations of metal ions against their network sites.(17–19) In the present study such bands can be referred to vibrations of Pb2+ and Al3+ ions. On the other hand bands related to vibrations of borate groups are reported in the region >550 cm−1,(17) which would be considered here. The fraction N4 of four-co-ordinated boron atoms can be calculated depending on the assignment of the component bands in the IR spectra. In general the bands in the region 690–1100 cm−1 are attributed to borate arrangements containing

H. DoweiDar et al: SiteS DiStribution anD propertieS of al2o3–pbo–b2o3 glaSSeS

Figure 2. Dependence of density () and molar volume ( ) on Al2O3 content of the studied glasses. Filled symbols represent calculated data. Calculated densities have been obtained from Equation (10) and the given parameters

Figure 3. Conductivity–temperature dependence of the glasses investigated

Figure 4. Deconvolution of infrared spectrum of the glass 10Al2O3–40PbO–50B2O3. For the meaning of the assign-ment please see the text

Table 2. Deconvolution parameters of the infrared spectra of the studied glasses. C is the component band centre (cm−1) and A is the relative area of the component band (%)0% C 266 419 609 699 847 959 1069 1222 1317 1412 A 1·38 2·18 0·58 0·76 8·14 31·97 8·48 6·53 31·39 8·602% C 294 435 694 827 940 1048 1102 1219 1342 1463 A 1·10 5·38 4·94 5·22 24·16 8·54 3·31 9·66 30·85 6·835% C 314 394 698 833 943 1071 1194 1280 1388 1459 A 1·34 4·26 4·84 4·28 24·06 8·92 5·07 27·78 15·02 4·4310% C 339 444 699 922 1031 1088 1215 1353 1485 A 2·12 4·18 3·21 16·18 8·13 2·90 4·53 56·48 2·13 15% C 333 444 702 923 1059 1198 1330 1478 A 0·70 6·98 6·30 13·06 6·12 4·69 55·92 6·25 20% C 348 456 704 957 1064 1192 1279 1416 A 0·47 1·19 4·82 5·56 7·08 13·40 18·11 49·35

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BO4 groups whereas those in the region 1200–1500 cm−1 are related to borate groups containing BO3 units with nonbridging oxygen ions (NBOs).(20–25) The band at about 610 cm−1 arises from in-plane bending vibration of BO3 units.(26) The bands around 700 and 1095 cm−1 are attributed to pentaborate groups.(17,21) Each of these groups contains one BO4 unit and four symmetric BO3 units. The bands at about 840, 940 and 957 cm−1 are attributed to vibrations of BO4 units.(17) Bands around 1040 cm−1 are considered to be due to BO4 units(17) and this is taken as a basis to refer the bands in the region 1030–1070 cm−1 to these groups.

On the basis of the above presentation, the main peak centered around 1333 cm−1 in the spectrum of 50PbO.50B2O3 (Figure 1) might be due to vibrations of BO3 groupings that contain NBOs (meta, ortho and pyroborates). This assumption is however in contradiction with the results of NMR(3,4) and Ra-man(2) spectroscopies that exclude formation of NBOs for PbO<50 mol%. In the present study, all glasses containing Al2O3 have PbO<50 mol%. Figure 5 shows that the relative area under the IR curves in the region 650–1160 cm−1 (the region containing BO4 tetrahedra) decreases linearly with increasing the Al2O3 content. Conversely, there is a linear increase in the relative area of the component bands in the region 1160–1520 cm−1 (the region that might contain NBOs). Such behaviour doesn’t match with the idea that the bands in the last region are related to structural units containing NBOs. These thoughts are based on the fact that in the studied glasses Al2O3 increases at the expense of PbO and Al2O3 would consume modifier PbO to enter the structure as AlO4 units. The above conclusion leads to another one that the assignment of the bands in the region 1160–1520 cm−1 might be revised. As it would appear from the present study the bands in this region would be related to struc-tural units containing only symmetric BO3 units. In this respect, it is noteworthy that a strong band

arises around 1370 cm−1 in the IR spectra of Li2O–B2O3 glasses up to 33 mol% Li2O.(22) Again, formation of NBOs in such glasses is far from being expected as revealed from NMR results.(27)

By using the above assignment of the component bands it would be possible to calculate N4 for the studied glasses. Details about calculations are given elsewhere.(15) Table 1 shows the obtained N4 values. In Figure 6 is shown that N4 decreases steadily upon increasing Al2O3 content. Owing to the constant B2O3 content the decrease in N4 would be a result of two factors. The first one is the decrease of PbO content, which in turn decreases the fraction of modifier lead (PbOm).(5) Secondly, the increase in Al2O3 con-tent would increase, at least partially, the quantity of modifier lead needed to form AlO4 tetrahedra PbOm(Al). The overall effect is a reduction in the quan-tity of PbOm that would associate with B2O3 (PbOm(B)) to form BO4 units.

The quantity (in mol%) of B2O3 in the form of both BO4 and BO3 units can be calculated from the relations

BO4=N4(B2O3) (2)

and

BO3=(B2O3)–BO4 (3)

Figure 6 shows a steady decrease in the quantity of BO4 and an increase in that of BO3 when increasing Al2O3 content. Concerning the structural form of Al2O3 in the structure we would at first assume that it would associate with an equivalent quantity of modifier PbO (PbOm(Al)) to form AlO4 tetrahedra. Then the quantity of PbOm(Al) should be taken as that of Al2O3 in glass, i.e.

PbOm(Al)=Al2O3 (4)

The quantity of PbO (PbOm(B)) that associates with

H. DoweiDar et al: SiteS DiStribution anD propertieS of al2o3–pbo–b2o3 glaSSeS

Figure 5. Variation with composition of the relative area under the IR spectra in the regions 700–1160 cm−1 and 1160–1520 cm−1

Figure 6. Fraction N4 of four-coordinated boron atoms as a function of the Al2O3 content. N4 values are used to cal-culate the quantities (in mol%) of B2O3 present in glass as BO4 units (Equation (2)) and BO3 units (Equation (3))

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B2O3 to form BO4 tetrahedra would be

PbOm(B)=BO4 (5)

The total modifier lead (PbOm) is then

PbOm=PbOm(Al)+PbOm(B) (6)

The quantity of PbO that enters the structure as network former PbO4 units (PbOf) would be

PbOf=PbO–PbOm (7)

The number of AlO4 units per mole of glass would be

nAl4=2[Al2O3 (mol%)]NA/100 (8)

where NA is Avogadro’s number. In a similar manner the number per mole of glass of BO4 units (nB4) and BO3 units (nB4) can be calculated. The number of PbO4 units (nPb4) is given as

nPb4=[PbOf (mol%)]NA/100 (9)

This is because each Pb atom of that type would produce only one PbO4 unit.

Figure 7 shows the dependence of PbOm(Al), PbOm(B) and PbOf on the Al2O3 content. An increase in Al2O3 causes a linear decrease in both PbOm(B) and PbOf and a linear increase in PbOm(Al). Such changes are predictable from Equations (4), (5) and (7). It is ob-served that PbOm(Al), PbOm(B) change oppositely with nearly equals rates. This reveals that PbOm doesn’t change when changing Al2O3 and PbO contents. This is clearly shown in Figure 8. This figure shows also a comparison between the data of PbO–B2O3 glasses and the studied PbO–Al2O3–B2O3 glasses. The data for PbO–B2O3 glasses are based on N4 data taken from references.(3,4) It appears that the structural units formed from PbO have mostly the same concentra-

tion in both types of glass. This means that Al2O3 behaves as if it were completing the B2O3 content in binary PbO–B2O3 glass system. In other words, formation of AlO4 units (within 20 mol%) proceeds like that of BO4 units in case of presence of a modifier oxide, i.e. at a rate of two AlO4 tetrahedra per Al2O3 molecule. This conclusion reveals that formation of aluminum triclusters is not to be considered in the glasses investigated.

The validity of the above assumptions can be tested by trying to calculate the density of the studied glasses. By considering the structural units present in glass the density can be given as

D=(nAl4MAl4+nB3MB3+nB4MB4+nPb4MPb4)/ (nAl4VAl4+nB3VB3+nB4VB4+nPb4VPb4) (10)

H. DoweiDar et al: SiteS DiStribution anD propertieS of al2o3–pbo–b2o3 glaSSeS

Figure 7. Dependence of the content of various compo-nents on the concentration of Al2O3. PbOm(Al) represents the quantity of modifier PbO which associates with AlO4 tetrahedra, whereas PbOm(B) is that associating with BO4 tetrahedra. PbOf is the quantity of PbO that acts as net-work former

Figure 8. Concentration of the total modifier (PbOm) and network former lead oxide (PbOf) as a function of PbO content in the studied glasses (open symbols) and in PbO–B2O3 glasses (filled symbols)

Figure 9. VAl4 as a function of r2/q (the reciprocal of the field strength of the modifier ion). Open symbol () rep-resents data for Na2O–Al2O3–SiO2,(8) Li2O–Al2O3–SiO2, K2O–Al2O3–SiO2, CaO–Al2O3–SiO2.(31) Filled symbol ( ) shows the data for PbO–Al2O3–B2O3 glasses (the present study)

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Figure 10. Logarithm of electric conductivity (at 300°C) and the activation energy for conduction in dependence of the Al2O3 content

Here nAl4, nB3, nB4 and nPb4 are, respectively, the number per mole of glass of AlO4, BO3, BO4 and PbO4 units, respectively. MAl4, MB3, MB4 and MPb4 and VAl4, VB3, VB4 and VPb4 are respectively the masses and volumes of the corresponding structural units. Due to the ionic nature of the Pb–O bonding for the modifier PbO(28) MAl4 is taken as the mass of (Al+2·5O+0·5Pb) and MB4 as the mass of (Al+2·5O+0·5Pb). From analysing the density data of PbO–B2O3 glasses(5) mean values of the volumes were obtained (for 14<PbO≤48·3 mol%) as VB3=3·12×10−23 cm3, VB4=3·80×10−23 cm3 and VPb4=4·4×10−23 cm3. Previous studies(29,30) indicated that the volumes of structural units in binary glasses are the same in multicomponent glasses having the same units. Trials were carried out to use these values in Equation (10) to calculate VAl4. A reasonable agree-ment between the experimental and the calculated density (Dc), Figure 2, could be attained by taking VAl4=4·35×10−23 cm3, VB3=3·15×10−23 cm3, VB4=3·85×10−23 cm3 and VPb4=4·45×10−23 cm3. The agreement between densities by using these values suggests that Al2O3 enters the structure of the studied glasses in a single form that is AlO4 tetrahedra. It is worth mentioning that the predicted value of VAl4 found here is com-parable with values obtained for various glasses; Na2O–Al2O3–SiO2 (5·1×10−23 cm3),(8) Li2O–Al2O3–SiO2 (4·04×10−23 cm3), K2O–Al2O3–SiO2 (6·14×10−23 cm3) and CaO–Al2O3–SiO2 (4·135×10−23 cm3).(31) Although these are silicate glasses, it is found that the volume of AlO4 tetrahedra is mostly the same in borate or silicate matrices.(14) Figure 9 shows a linear dependence of VAl4 on r2/q. The latter is the reciprocal of field strength of the modifier ion linked to AlO4 tetrahedron, where r is the radius of modifier ion and q is its electric charge. As found previously,(31) this linear dependence sug-gests ionic nature for the bond between the modifier ion and the negative charge on AlO4 unit.

In Figure 10 is shown the dependence of the activation energy and log σ300 (logarithm of con-ductivity at 300°C) on the Al2O3 content. There is a

limited decrease in both quantities with increasing the concentration of Al2O3. In the region of 0–20 mol% Al2O3 the decrease in E is about 0·13 eV. The decrease in log σ300 is about one and a half order that practically occurs in the region of 0–10 mol% Al2O3. From a specific point of view, the decrease in both quantities is an odd behaviour. In normal cases, as shown from Equation (1), an increase in the activation energy is accompanied with a decrease in conductiv-ity and vice versa. At a constant temperature the conductivity is determined with two parameters; σ0 and E. The change of conductivity with composition would then depend on the rate with which each of these parameter changes. The pre-exponential factor is given(32) as

σ0=Nq2a2f/2KT (11)

Here N denotes the concentration of mobile ions, q is the ionic charge, a is the separation distance between sites and f is the vibration frequency of the ion.

Equations (1) and (11) are specified for glasses having a single-type charge carrier. In case of differ-ent types of charge carriers the conductivity might be described by

σ=∑Niqiµi (12)

where µi refers to the mobility of charge carrier of i-type. In the studied glasses there are two types of charge carrier. These are Pb ions linked to both BO4 and AlO4 tetrahedra. Equation (12) can then rewrit-ten as

σ=σB+σAl (13)

where σB and σAl are conductivities due to the above types of Pb ions. In turn this relation can be expressed as

σ=σ0(B)exp(−ΕB/KT)+σ0(Al)exp(−ΕAl/KT) (13a)

It appears that the change in conductivity of the studied glasses would depend on the rate of change of σ0(B), σ0(Al), ΕB and ΕAl. As shown in Figure 7 PbOm(B) decreases whereas PbOm(Al) increases when increasing the Al2O3 content. Such changes might cause opposite effects on both σ0 and Ε. The features in Figure 9 are certainly related to the concentration of mobile ions and their distribution in the glass network, thus their effect on σ0 and Ε. Unfortunately, it is not possible to determine the fraction of mobile ions in PbOm(B) and PbOm(Al) and their rates of change with composition.

Conclusion

The present study is a trial to elucidate the complex structure of xAl2O3.(50−x)PbO.50B2O3 glasses. The IR spectra have been analysed to calculate N4 values of the studied glasses. The obtained values are used

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to get the concentration of various components in the glasses. The results reveal formation of AlO4 tetrahedra at the expense of BO4 tetrahedra when increasing Al2O3 content. The correlation of density with the structure has been employed to trace the role of Al2O3 in the structure. It is deduced that Al2O3 might serve only as network former in the form of AlO4 tetrahedra. The presence of two types of mobile Pb ions is considered as the reason for abnormal correlation between the electric conductivity and activation energy.

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