Analysis and prediction for elastic properties of quaternary tellurite Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glasses

Journal of Non-Crystalline Solids 522 (2019) 119580

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Analysis and prediction for elastic properties of quaternary tellurite Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glasses

T

⁎

Amin Abd El-Moneima, , R. El-Mallawanyb a b

Physics Department, Faculty of Science, Zagazig University, Zagazig, Egypt Physics Department, Faculty of Science, Menoufia University, Shebin El-Koam, Egypt

A R T I C LE I N FO

A B S T R A C T

Keywords: Glass Tellurite Elastic moduli

Analysis and prediction have been carried out for elastic properties of quaternary tellurite xAg2O–(35–x) (0.5V2O5–0.5MoO3)–65TeO2 and xWO3–(75–x)B2O3–10MgO–15TeO2 glass systems. This has been achieved on the basis of Makishima–Mackenzie's theory, Rocherulle et al. model and Abd El-Moneim and Alfifi's approaches. It has been found that, both Makishima–Mackenzie's theory and Abd El-Moneim and Alfifi's approaches can be applied successfully to predict the compositional changes in elastic moduli of WO3–B2O3–MgO–TeO2 glasses. In case of Ag2O–V2O5–MoO3–TeO2 glasses, the best correlation between theoretical and experimental elastic moduli can be achieved if the effect of the basic structural units TeO4, TeO3, VO4, VO5, MoO4 and MoO6 is taken into account. In compared to Makishima-Mackenzie's theory, Rocherulle et al. model appears to be more applicable for predicting Poisson's ratio. Moreover, the compositional changes in bulk modulus are predictable from the molar volume.

1. Introduction As the world's reliance on glass increases, functionalized glasses have a huge demand. Tellurite glasses have an interesting physical properties when compared to borate, germanate, silicate or phosphate glasses [1–9]. The study of elastic / mechanical properties of tellurite glasses as a function of composition is very informative about the microstructure and behavior of network formers and modifiers. Vitreous TeO2 is composed of TeO4 trigonal bipyramids, which are connected to each other through the covalent TeeOeTe linkages [10–13]. Due to the technological applications of tellurite glasses, the elastic and physical properties of pure TeO2 glass [10–13], binary ZnO-TeO2 [14], B2O3TeO2 [15], BaO-TeO2 [16], WO3-TeO2 [17], V2O5-TeO2 [18], La2O3TeO2 [19], MoO3-TeO2 [20] and CuO-TeO2 [21] glasses, ternary AlF3ZnO-TeO2 [13], TiO2-V2O5-TeO2 [22], Bi2O3-V2O5-TeO2 [23], Li2OB2O3-TeO2 [24], Ag2O-B2O3-TeO2 [25], Na2O-B2O3-TeO2 [26], K2OWO3-TeO2 [27], La2O3-WO3-TeO2 [17], WO3-PbO-TeO2 [28–30],WO3–Ag2O–TeO2 [31], V2O5-PbO-TeO2 [32], ZnO-Nb2O5TeO2 [33] and Ag2O–V2O5–TeO2 [34] glasses and quaternary TeO2B2O3-P2O5-Li2O [35], Ag2O–V2O5–MoO3–TeO2 [36], WO3–B2O3–MgO–TeO2 [37], NiO–B2O3–MgO–TeO2 [37] and MxOyNb2O5-WO3-TeO2 [38] glasses have been studied using ultrasonic techniques. The composition dependence of density, molar volume, elastic moduli and Poisson's ratio yielded valuable information about ⁎

the structural changes in the tellurite network. The addition of modifiers to the tellurite network causes the structural modification of tellurium, which transforms TeO4 trigonal bipyramids (tbp) into TeO3+1 polyhedra and then to TeO3 trigonal pyramid (tp). The estimation of elastic moduli based on glass composition is also very useful for the development of glassy materials. The most widely used model is the one proposed by Makishima and Mackenzie [39,40], which expressed the elastic moduli as a function of chemical composition, dissociation energy per unit volume and packing density of the glass. Thereafter, Rocherulle et al. [41] have extended MakishimaMackenzie's model [39,40] to oxynitride glasses. A thermodynamic factor, which results from the substitution of oxygen by nitrogen within the vitreous network, is introduced in the expression of packing density. Results showed that, for majority of the investigated glasses, the theoretical and observed elastic properties are in excellent agreement. A review of literature reveals that a considerable number of studies [39–53] on the correlation between the experimental and theoretical elastic moduli of borate, phosphate, silicate and oxynitride glasses have been carried out on the basis of Makishima-Mackenzie's model [39,40] and/or Rocherulle et al. model [41]. Before 1999, there were no articles have been reported deal with the estimation of elastic moduli and Poisson's ratio of tellurite glasses from their chemical composition on the basis of Makishima-Mackenzie's model [39,40] and/or Rocherulle et al. model [41]. On 1999, Inaba

Corresponding author. E-mail address: [email protected] (A.A. El-Moneim).

https://doi.org/10.1016/j.jnoncrysol.2019.119580 Received 27 April 2019; Received in revised form 29 June 2019; Accepted 15 July 2019 0022-3093/ © 2019 Elsevier B.V. All rights reserved.

Journal of Non-Crystalline Solids 522 (2019) 119580

A.A. El-Moneim and R. El-Mallawany

where ρ and Ψ are the respective glass density and total number of atoms in glass formula unit, whereas Mi and xi are the respective molecular weight and molar fraction of the ith component.

et al. [42] have determined empirically the dissociation energy per unit volume of TeO2 oxide, for the first time. The same authors [42] have used the determined dissociation energy per unit volume of TeO2 oxide and evaluated the theoretical Young's modulus for number of simple and complex tellurite glass systems from Makishima-Mackenzie's model [39,40]. The results revealed a reasonable agreement between the theoretical and experimental values. Besides Makishima-Mackenzie's theory [39,40] and Rocherulle et al. model [41], many efforts have been made during the last few years to predict changes in the elastic properties of glasses. For example, Abd ElMoneim and Alfifi [51] have proposed a semi-empirical formula, which predicts changes in the bulk modulus in term of the ratio between packing density and mean atomic volume. The proposed semi-empirical formula was verified for the phosphate-based PbO–P2O5, V2O5–P2O5, CuO–P2O5 and Cr2O3–doped Na2O–ZnO–P2O5 glasses [51], telluritebased BaF–TeO2 [54], AlF3-ZnO-TeO2 [55] and Ag2O–V2O5–TeO2 [51] glasses, borate-based Li2O–B2O3–V2O5 [52] and PbF2-PbO-B2O3 [55] glasses as well as fluoride NaF-LiF-ZrF4-BaF2-AlF3 glasses [55]. In the last few years, Abd El-Moneim and his co-authors [45,47–50,53,56,57] have reported a number of studies deal with the prediction of changes in elastic moduli and ultrasonic attenuation coefficient for the V2O5contained tellurite, borate and phosphate glasses on the basis of the above mentioned models [39–41] and approaches [51]. They observed a disagreement between the theoretically calculated and experimentally measured values of elastic moduli. This disagreement has been attributed to the anomalous behavior between the calculated dissociation energy per unit volume of the glass and experimental elastic moduli [48–50]. Thereafter, Abd El-Moneim [48–50] has corrected this anomalous behavior by estimating the dissociation energy of V2O5 oxide from the average single bond strength of VeO bonds that are present in the VO4 and VO5 structural units. An excellent agreement between theoretical and experimental elastic moduli was achieved. The main objectives of the present work are to analyze the elastic properties and predict their changes in the quaternary tellurite xAg2O–(35–x)(0.5V2O5–0.5MoO3)–65TeO2 (0 ≤ x ≥ 25 mol%) and xWO3–(75–x)B2O3–10MgO–15TeO2 (0.2 ≤ x ≥ 1 mol%) glass systems. The correlation between elastic and compositional parameters has been carried out on the basis of the well known models and approaches in the field such as, Makishima-Mackenzie's model [39,40], Rocherulle et al. model [41] and Abd El-Moneim and Alfifi's approaches [51]. The structural role of WO3, B2O3, MgO, Ag2O, V2O5 and MoO3 oxides in the tellurite network has also been declared. In addition to this, the agreement between the theoretical and experimental values of elastic moduli and Poisson's ratio has been investigated.

2.2. Makishima-Mackenzie's theory [39,40] for elastic moduli and Poisson's ratio Makishima and Mackenzie [39,40] have reported a theoretical model for calculating the packing density (defined as the ratio between the minimum theoretical volume occupied by the ions and the corresponding ionic volume of the glass), dissociation energy per unit volume (defined as the volume density of binding energy), elastic moduli and Poisson's ratio of the glass. The same authors [39,40] have expressed these parameters for multi-component glasses in terms of the packing factor and dissociation energy per unit volume of the oxide constituent as follows:

Packing density:Vt =

∑ xi Gi

(5)

Young′s modulus: Eth = 8.36 Vt Gt

(6)

Bulk modulus: Kth = 10.0 Vt2 Gt

(7)

Shear modulus: Sth = 3 Kth/(10.2 Vt − 1)

(8)

Longitudinal modulus:Lth = Kth + 4Sth/3

(9)

Poisson′s ratio: μth = 0.5 − (1/7.2 Vt )

(10)

where Gi and Vi are the respective dissociation energy per unit volume and packing factor of the ith component. For ith component oxide in the form AnOm, the values of Gi and Vi can be estimated from the respective Eqs. (11) and (12);

Gi =

ρi Ui Mi

(11)

Vi =

4 π Na (n RA3 + m RO3 ) 3

(12)

where RA and RO are the respective ionic radius of metal and oxygen, Na is Avogadro's number and Ui is the dissociation energy per mole (molar dissociation energy) of the ith component. 2.3. Abd El-Moneim and Alfifi's approaches [51] for bulk modulus Abd El-Moneim and Alfifi [51] suggested that the experimental bulk modulus of glasses can be predicted in terms of the ratio between packing density and mean atomic volume according to the following semi-empirical formula;

K = Q (Vt / V )γ

(13)

where γ & Q are two new constants. Values of γ & Q depend strongly upon the type of the glass network and its constitution. 3. Results

2.1. Molar volume and mean atomic volume

Table 1 summarizes the composition, density, molar volume, mean atomic volume and experimental elastic properties of the investigated xAg2O–(35–x)(0.5V2O5–0.5MoO3)–65TeO2 (0 ≤ x ≥ 25 mol%) and xWO3–(75–x)B2O3–10MgO–15TeO2 (0.2 ≤ x ≥ 1 mol%) glass systems. The experimental data were taken from Ref. [36] for xAg2O–(35–x) (0.5V2O5–0.5MoO3)–65TeO2 glass system and taken from Ref. [37] for xWO3–(75–x)B2O3–10MgO–15TeO2 glass system. On the other hand, the values of molar volume and mean atomic volume were calculated from the respective Eqs. (1) and (2). It is seen from this table that, all the parameters depend strongly upon composition of the glass.

The molar volume and mean atomic volume of multi-component oxide glasses can be obtained from the molecular weights of the constituent components and measured density as follows;

Molar volume:VM = M / ρ

(1)

Mean atomic volume:V = VM /Ψ

(2)

i

(4)

i

i

Generally, various elastic properties of glassy material depend upon its composition and to a considerable extent upon its structure. Multicomponent oxide glasses can be regarded as solution of oxides, in which each oxide exerts its own influence so that any physical or structural property may reasonably be considered as the sum of the influences of all individual oxides.

∑ xi Mi

∑ xi Vi

Dissociation energy per unit volume: Gt =

2. Theory

Molecular weight:M =

ρ M

(3) 2

Journal of Non-Crystalline Solids 522 (2019) 119580

A.A. El-Moneim and R. El-Mallawany

Table 1 Physical and elastic properties of quaternary Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glasses. x (mol %)

ρ ( ± 0.0283 g/cm3)

Kexp ( ± 0.6 GPa)

xAg2O–(35 − x)(0.5V2O5–0.5MoO3)–65TeO2 glass systema 0 4.492 26.2 5 4.684 30.9 10 4.82 33.5 15 5.12 34.3 20 5.513 34.7 25 5.97 35.5 xWO3– (75–x)B2O3–10MgO–15TeO2 glass systema 0.2 2.4256 45.254 0.4 2.4032 41.664 0.6 2.1981 38.296 0.8 2.165 37.526 1 1.8279 31.351 a

Sexp ( ± 0.2 GPa)

Lexp ( ± 0.4GPa)

Eexp ( ± 2 GPa)

μexp ( ± 0.01)

VM (cm3/mol)

V (cm3/mol)

16.5 17.8 18.9 16.6 15.2 14.4

48.1 54.5 58.8 56.3 55 54.6

40.8 44.8 47.8 42.8 39.8 38

0.24 0.26 0.26 0.29 0.31 0.32

35.79 35.06 34.78 33.42 31.66 29.81

9.24 9.34 9.59 9.55 9.38 9.17

32.936 22.869 19.882 18.456 15.432

77.168 72.155 64.805 62.133 51.926

61.046 57.996 50.846 47.569 39.771

0.2752 0.268 0.2787 0.2887 0.2886

33.19 33.64 36.92 37.64 44.76

7.55 7.65 8.4 8.57 10.2

The data of Ag2O–V2O5–MoO3–TeO2 glasses were taken from Ref. [36] and those of WO3–B2O3–MgO–TeO2 glasses were taken from Ref. [37].

60

Bulk modulus (GPa)

Generally, it is expected that behavior of molar volume with composition is completely opposite that of density. Table 1 shows that this is true for both xAg2O–(35–x) (0.5V2O5–0.5MoO3)–65TeO2 and xWO3–(75–x)B2O3–10MgO–15TeO2 glass systems. The compositional changes in the density of xAg2O–(35–x)(0.5V2O5–0.5MoO3)–65TeO2 glass system can be understand from the variation in molecular weights of the constituent components, which increase in the Ag2O > TeO2 > B2O3 > MoO3 order. In case of xWO3–(75–x) B2O3–10MgO–15TeO2 glass system, the substitution of the lighter B2O3 mole by mole by the heavier WO3 decreases the density of the prepared glasses. This means that the observed changes in the density and molar volume of these glasses are related to the type of structural units that form due to the substitution of B2O3 by WO3 rather than the constitution of the glass. Generally, the structural changes in the network of glasses are closely related to changes in their physical and elastic properties. The results of elastic moduli and Poisson's ratio show a weakening in the structure and decrease in the rigidity of the glass with the substitution of WO3 by B2O3 in xWO3–(75–x)B2O3–10MgO–15TeO2 glass system or the substitution of Ag2O by (0.5V2O5 + 0.5MoO3) in xAg2O–(35–x)(0.5V2O5–0.5MoO3)–65TeO2 glass system. The decrease in the rigidity can be attributed to the creation of non-bridging oxygen atoms (NBOs) in the glass, which need low energy for breaking the bond in the network.

40

Ag-V-Mo-Te glasses 20 20

30

40

50

Molar volume (cm3 /mol) Fig. 1. Dependence of bulk modulus on molar volume in WO3–B2O3–MgO–TeO2 and Ag2O–V2O5–MoO3–TeO2 glasses. The solid lines represent the least-square fitting of the data.

the semi-empirical Eq. (14) to xAlF3–01ZnO-(99-x)TeO2 glass system was achieved when b = 0.52 and C = 178.9 [55], (10-x)AlF3-xZnO90TeO2 glass system when b = 0.53 and C = 186.9 [55], xBaF2-(1x)TeO2 glass system when b = 1.05 and C = 1125 [60], xNaF-(20-x) LiF-48ZrF4-24BaF2-8AlF3 glass system when b = 2.49 and C = 26535 [55], xNaF-(30-x)LiF-42ZrF4-21BaF2-7AlF3 glass system whenb = 2.22 and C = 85398 [55], V2O5-P2O5 glasses when b = 2.31 and C = 41400 [47], PbO-P2O5 glasses when b = 1.22 and C = 2700 [51], V2O5-Li2OB2O3 glasses when b = 3.00 and C = 6.38 × 105 [45], RO-Al2O3-B2O3 (R = Mg, Ca or Sr) glasses when b = 1.92 and C = 3.7 × 104 [61] and TiO2–CaO–Al2O3–B2O3 glasses when b = 4.38 and C = 8.8 × 107 [62]. The dependence of b and C values on type of the glass and its composition is in consistent with Eq. (14) and suggests that the molar volume is an important factor in predicting the elastic moduli of the present WO3–B2O3–MgO–TeO2 and Ag2O–V2O5–MoO3–TeO2 glasses, likewise other oxide glasses.

According to Gopal et al. [58] and Rajendran et al. [59] approaches, the bulk modulus of the glass can be correlated to the molar volume as follows; (14)

where b and C are two constants, their values depend on the type of the glass and its composition. Fig. 1 shows the dependence of bulk modulus on molar volume in the two present WO3–B2O3–MgO–TeO2 and Ag2O–V2O5–MoO3–TeO2 glasses. The observed rapid decrease in the bulk modulus with increasing molar volume supports the validity of the semi-empirical Eq. (14) for these glasses. The least-square linear regression performed on log(K) and log(VM) yields the semi-empirical Eq. (15) for WO3–B2O3–MgO–TeO2 glasses and the semi-empirical Eq. (16) for Ag2O–V2O5–MoO3–TeO2 glasses; 1.12 K VM = 2243

W-B-Mg-Te glasses

30

3.1. Bulk modulus - molar volume correlation

b K VM =C

50

3.2. Bulk modulus - ratio between packing density and mean atomic volume correlation

(15)

with correlation coefficient of 0.97, b = 1.12 and C = 2243; 1.20 K VM = 2240

The semi-empirical formula (13) suggested that, a plot of K versus (Vt / V ) ratio would give a forward proportionality. The data of K versus (Vt / V ) have been presented in Fig. 2. As can be seen from this figure, the semi-empirical formula (13) is valid for WO3–B2O3–MgO–TeO2 glasses only. The least-square linear regression performed on log(K) and

(16)

with correlation coefficient of 0.553, b = 1.20 and C = 2240. One interesting observation is that Eqs. (15) and (16) have approximately the same values of C andb. Previous studies revealed that the best fitting of 3

Journal of Non-Crystalline Solids 522 (2019) 119580

A.A. El-Moneim and R. El-Mallawany

Bulk modulus (Gpa)

50

3.3. Agreement between theoretical and experimental elastic moduli and Poisson's ratio

W-B-Mg-Te glasses

According to Makishima-Mackenzie's theory [39,40], the elastic properties of glasses depend strongly on the two significant compositional parameters Vt and Gt. However, in case of the borate-based and B2O3-contained glasses, the modifier atoms cause changes in the coordination number of boron atoms from three to four and vice versa. Thus, boron atoms in borate-based glasses are both three-or four-fold coordinated. The change of boron coordination results in changes in the physical and elastic properties of the glasses. Consequently, the dissociation energy per unit volume and packing density of xWO3–(75-x) B2O3–10MgO–15TeO2 glass system can be expressed by the respective relationships (18) and (19):

40

30

Ag-V-Mo-Te glasses

20 0.0205

0.0405

0.0605

0.0805

Ratio between packing density and mean atomic volume (mol /cm3)

(18)

VB2 O3 = N4 V4 + (1 − N4 ) V3

(19)

where N4 and N3 = (1 − N4) are the respective concentrations of BO4 and BO3 groups, whereas G4 and G3 are their respective dissociation energy per unit volume. On the other hand, V4 and V3 are the packing factors of B2O3 oxide, which corresponding the 4-and 3-coordinated boron, respectively. The calculated values of Vt and Gt for the present Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glass samples are given in Table 2. The theoretical values of elastic moduli and Poisson's ratio, which have been calculated in terms of Vt and Gt are given the same table. The applied values of ρi, Mi, Gi and Vi for the oxide components Ag2O, V2O5, MoO3, TeO2, WO3, B2O3 and MgO are listed in Table 3. In the calculation, it has been suggested that boron atoms are equally distributed between BO4 and BO3 structural units. This is due to the fact that the concentrations of these structural units in the investigated WO3–B2O3–MgO–TeO2 glass samples are not unknown so far. Likewise the experimentally measured parameters, all the theoretical parameters are strongly dependent upon the constitution of the glass. The relationship between the experimental and theoretical values is demonstrated in Fig. 3 for elastic moduli of WO3–B2O3–MgO–TeO2 glasses, Fig. 4 for elastic moduli of Ag2O–V2O5–MoO3–TeO2 glasses and Fig. 5 for Poisson's ratio of both Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glasses. However, the following conclusions can be obtained from these figures:

Fig. 2. Variation of bulk modulus with the ratio between packing density and mean atomic volume in WO3–B2O3–MgO–TeO2 and Ag2O–V2O5–MoO3–TeO2 glasses. The solid line represents the least-square fitting of the data.

log(Vt / V ) yields the semi-empirical (17) equation for these glasses; K = 200.3 (Vt / V )0.561

G B2 O3 = N4 G4 + N3 G3

(17)

with correlation coefficient of 0.97, Q = 200.3 and γ = 0.561. These results reveal that WO3–B2O3–MgO–TeO2 glasses have values of Q and γ completely different from those reported previously when demonstrating the same semi-empirical formula (13) for tellurite-based (1x)TeO2-xBaF2 (Q = 108.1 and γ = 0.40) [54], 01ZnO-xAlF3-(99-x)TeO2 (Q = 80.75 and γ = 0.325) [55] and xZnO-(10-x)AlF3-90TeO2 (Q = 95 and γ = 0.375) [55] glass systems, borate-based PbF2-PbO-B2O3 (Q = 16495 and γ = 3.699) [55] and Li2O-B2O3-V2O5 (Q = 164.3 and γ = 0.663) [52] glasses or phosphate–based PbO-P2O5 (Q = 1272 and γ = 1.44) [51], V2O5-P2O5 (Q = 884 and γ = 1.25) [51] and Cr2O3doped Na2O-ZnO-P2O5 (Q = 4752 and γ = 4.77) glasses [51]. Changing the values of Q and γ with changing the type of glass and its constitution confirms the success of the semi-empirical formula (13) for predicting the compositional dependence of elastic moduli in WO3–B2O3–MgO–TeO2 glasses. In case of Ag2O–V2O5–MoO3–TeO2 glasses, the data of the ratio (Vt / V ) are quite dispersed and do not shows a clear correlation with K. This behavior is against the semi-empirical formula (13) and suggests that the elastic moduli of these glasses are not predictable from the ratio (Vt / V ) .

i- The theoretical and experimental elastic moduli of WO3–B2O3–MgO–TeO2 glasses are in excellent agreement for majority of the samples. The correlation ratio between the theoretical and observed values changes from 78.4% to 59.1% for bulk modulus, from 93.5% to75% for shear modulus, from 90.5% to 86% for Young's modulus and from 99.8% to 92.3% for longitudinal modulus;

Table 2 Theoretically calculated compositional and elastic properties of quaternary Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glasses on the basis of MakishimaMackenzie's theory [39,40]. x (mol %)

Vt

Gt (kcal/cm3)

xAg2O–(35 − x)(0.5V2O5–0.5MoO3)–65TeO2 glass system 0 0.5452 14.23 5 0.5361 13.73 10 0.5206 13.22 15 0.5212 12.71 20 0.5285 12.25 25 0.5382 11.69 xWO3– (75–x)B2O3–10MgO–15TeO2 glass system 0.2 0.4973 13.56 0.4 0.4909 13.56 0.6 0.4474 13.57 0.8 0.4391 13.58 1 0.3694 13.58

Kth (GPa)

Sth (GPa)

Lth (GPa)

Eth (GPa)

μth

Vt / V

d

42.3 39.46 35.83 34.53 34.22 33.86

27.82 26.49 24.94 24 23.38 22.63

79.3 74.7 69 66.45 65.31 63.95

64.86 61.54 57.54 55.38 54.12 52.6

0.245 0.241 0.233 0.234 0.237 0.242

0.059 0.0574 0.0543 0.0546 0.0563 0.0587

2.52 2.3 2.26 1.94 1.75 1.62

33.53 32.68 27.16 26.18 18.53

24.7 24.46 22.87 22.58 20.08

66.39 65.22 57.57 56.21 45.24

56.37 55.65 50.76 49.85 41.94

0.221 0.217 0.19 0.184 0.124

0.0659 0.0642 0.0533 0.0512 0.0362

2.91 2.2 2.08 1.97 1.97

4

Journal of Non-Crystalline Solids 522 (2019) 119580

A.A. El-Moneim and R. El-Mallawany

0.5

Mi (g mol)

ρi (g/cm3)

Vi [63] (cm3/mol)

Gi [63] (kcal/cm3)

Ci

Ag2O V2O5 MoO3

231.74 181.88 143.94

7.143 3.357 4.692

14.6 35.4 21.3

0.4500 0.6534 0.6943

TeO2 WO3 B2O3

159.60 231.85 69.62

5.670 7.160 2.460

MgO

40.31

3.580

14.7 (TeO4 units) 21.3 20.8 (BO4 units) 15.2 (BO3 units) 7.9

6.51 16.63 16.70 – 12.92 (TeO4 units) 16.22 19.81 (BO4 units) 5.41 (BO3 units) 21.53

Experimental elastic modulus (GPa)

Oxide

Experimental Poisson's ratio

Table 3 Different factors for the simple oxides Ag2O, V2O5, MoO3, TeO2, WO3, B2O3 and MgO.

0.5222 0.6578 0.7350 0.5371 0.7016

W-B-Mg-Te

0.4

0.3

0.2

0.1

0

105

Bulk modulus Shear modulus Longitudinal modulus Young's modulus

90

0

0.1

0.2

0.3

0.4

0.5

Theoretical Poisson's ratio

75 Fig. 5. Agreement between theoretical and experimental Poisson's ratios in both WO3–B2O3–MgO–TeO2 and Ag2O–V2O5–MoO3–TeO2 glasses on the basis of Makishima-Mackenzie's theory [39,40]. The solid line is the1:1 correlation line.

60 45 30

iii- Although the agreement between theoretical and experimental Poisson's ratios is satisfactory for majority of Ag2O–V2O5–MoO3–TeO2 glasses, it is unsatisfactory for WO3–B2O3–MgO–TeO2 glasses. The correlation ratio changes from 98% to75.6% in Ag2O–V2O5–MoO3–TeO2 glasses and from 81% to 43% in WO3–B2O3–MgO–TeO2 glasses.

15 0 0

15

30

45

60

75

90 105

Theoretical elastic modulus (GPa)

The above results reveal that the calculated values of Vt and Gt are not suitable for predicting the elastic properties of some of WO3–B2O3–MgO–TeO2 glass samples and majority of Ag2O–V2O5–MoO3–TeO2 glass samples. These results are quite similar to those reported previously by us for other V2O5-contained glasses [45,47–50,53,56,57].

Fig. 3. Agreement between theoretical and experimental elastic moduli in WO3–B2O3–MgO–TeO2 glasses on the basis of Makishima-Mackenzie's theory [39,40]. The solid line is the1:1 correlation line.

Experimental elastic modulus (GPa)

Ag-V-Mo-Te

100

Bulk modulus Shear modulus Longitudinal modulus Young's modulus

80

4. Discussion 4.1. WO3–B2O3–MgO–TeO2 glasses

60

It is a well-known fact that B2O3 and TeO2 oxides are good glass formers [10,13,64]. On the other hand, WO3 is a conditional glass former, whereas MgO oxide is a glass modifier. The network of vitreous B2O3 is considered to be composed of planar BO3 tps and B–O–B linkages [64]. This glass has ρ = 1.83 gcm−3, K = 13.2 GPa, S = 6.1 GPa, L = 21.3 GPa and E = 15.9 GPa [64]. On the other hand, the network of vitreous TeO2 is composed of TeO4 trigonal bipyramids (tbp), which are connected to each other through the covalent Te–O–Te linkages [10]. It has been found that pure TeO2 glass has ρ = 5.105 gcm−3, K = 31.7GPa, S = 20.6GPa, L = 59.1GPa, E = 50.7GPa and σ = 0.233 [10]. Recently, Sidek et al. [13] have been reported ρ = 4.806 gcm−3, K = 28.04 GPa, S = 21.5 GPa, L = 56.71 GPa, E = 51.37 GPa and σ = 0.19 for pure TeO2 glass. The elastic moduli data for the base 75B2O3–10MgO–15TeO2 glass sample can be obtained by extrapolating the composition dependence of elastic moduli for the xWO3–(75-x)B2O3–10MgO–15TeO2 glass system through the composition range from 0.2 to 1 mol% down to the zero WO3 content (see Fig. 6). It was found that the base 75B2O3–10MgO–15TeO2 glass sample has L = 83.78 GPa, E = 67.33 GPa, K = 48.40 GPa and S = 33.74 GPa. These values of elastic moduli are greater than those of pure TeO2 [10,13] and B2O3 [64] glass as well as binary xTeO2-(100-x)B2O3 (60 ≤ x ≥ 80 mol%) glass system [65]. These results suggest that, the 10 mol% of MgO oxide

40 20 0 0

20

40

60

80

100

Theoretical elastic modulus (GPa) Fig. 4. Agreement between theoretical and experimental elastic moduli in Ag2O–V2O5–MoO3–TeO2 glasses on the basis of Makishima-Mackenzie's theory [39,40]. The solid line is the1:1 correlation line.

ii- In case of Ag2O–V2O5–MoO3–TeO2 glasses, the agreement between theoretical and experimental data of bulk modulusis satisfactory for majority of the samples (correlation ratio ranges between 99.3% and 62%). On the other hand, all the theoretical values of shear, Young's and longitudinal moduli are much greater than the corresponding experimental values and the agreement is unsatisfactory. The correlation ratios are < 75.8%, 85.4% and 83.1% for shear, Young's and longitudinal moduli, respectively 5

Journal of Non-Crystalline Solids 522 (2019) 119580

105

0.36

Bulk modulus Shear modulus Longitudinal modulus Young's modulus

90

0.32

75

Poisson's ratio

Experimental elastic modulus (GPa)

A.A. El-Moneim and R. El-Mallawany

60 45 30

0.28

0.24

15 0 0

0.2

0.4

0.6

0.8

1

0.2

1.2

1

WO3 (mol %)

1.5

2

2.5

3

Fractal bond connectivity

Fig. 6. Dependence of experimental elastic moduli on WO3 content in WO3– B2O3–MgO–TeO2 glasses. The solid lines represent the least-square fitting of the data.

Fig. 7. Poisson's ratio of WO3–B2O3–MgO–TeO2 glasses as a function of fractal bond connectivity. The solid line represents the least-square fitting of the data.

ZnO-TeO2, oxyfluoride borate PbO-PbF2-B2O3 and fluoride ZrF4-NaFLiF-BaF2-AlF3 glasses [55]. These results confirm the validity of Abd ElMoneim's semi-empirical relationship μ = A − zd [56] not only for the present WO3–B2O3–MgO–TeO2 glasses, but also for oxyfluoride and alkali fluoride glasses. The divergence between the theoretical and experimental elastic parameters (elastic moduli and Poisson's ratio) of WO3–B2O3–MgO–TeO2 glasses can be attributed to the follow reasons:

in the base 75B2O3–10MgO–15TeO2 glass is consumed in the transformation of BO3 triangles into BO4 tetrahedra through creation of extra bridging oxygen atoms (BO). At the same time Mg2+ ions take the interstitial positions in the glass network. Accordingly, this glass sample is considered to be composed of BO3, BO4 and TeO4 groups, which are connected to each other through the B–O–Te linkages. The rapid decrease in the elastic moduli of the quaternary xWO3–(75-x) B2O3–10MgO–15TeO2 glass system with the progressive increase in WO3 concentration and expense of B2O3 suggest that WO3 enters these glasses as a network modifier. This may results in the breaking the B–O–Te linkages and creation of non-bridging oxygen atoms (NBOs). This reaction can be takes place either by the transformation of BO4 tetrahedra into BO3 triangles (BO4→BO3 reconversion) or by the conversion of TeO4 tbp into TeO3+1 polyhedral and then to TeO3 tp. The increase of WO3 concentration is expected to create more NBOs, which in turns reduces the network connectivity and makes the glass structure soft and weak in its resistance to mechanical deformation. This is consistent with the data of density, molar volume, mean atomic volume, packing density and Poisson's ratio,. The inverse proportionality between K and VM in Fig. 1 supports this discussion. The above discussion can be further supported as follows: (i) Fractal bond connectivity (d = 4Sexp/Kexp) is an important parameter used to deduce changes in the network dimensionality and elastic properties of material. It has been suggested that the value of d equals 3 for threedimensional networks, 2 for two-dimensional layer structures and 1 for one-dimensional chain [66]. The rapid decrease in d from 2.91 to 1.97 with the increase of WO3 content from 0.2 to 1 mol% in WO3–B2O3–MgO–TeO2 glasses suggests the network of these glasses changes gradually from three-dimensional structure to three-dimensional structure. This confirms the modifier role of WO3 and agrees well with the forward proportionality between K and the ratio (Vt / V ) in Fig. 2; and (ii) Recently, Abd El-Moneim [56] found that the dependence of Poisson's ratio on d was fitted by an inverse linear relation μ = A − zd, where A and z are two constants, their values depend on the type of the glass and its constitution. The data of μ versus d have been presented in Fig. 7 for WO3–B2O3–MgO–TeO2 glasses. The fitted curve in the figure can be represented by relationship μ = 0.466 − 0.09d with correlation coefficient of 0.997, A = 0.466 and z = 0.09. Previously, it has been found that the dependence of μ on d was fitted into the empirical linear relation μ = 0.5 − 0.09d for other tellurite-based glasses [56], μ = 0.447 − 0.082d for borate-based Li2OB2O3-V2O5 glasses [52], μ = 0.45 − 0.083d for oxyfluoro-zinc-tellurite glasses [67] and μ = 0.5458 − 0.085d for oxyfluoride tellurite AlF3-

i- According to Eqs. (6)–(9), a plotting of elastic moduli against Vt or Gt would yield a forward proportionality. In case of the present WO3–B2O3–MgO–TeO2 glasses, the compositional dependence of Vt is quite similar to that of elastic moduli. On the other hand, the dissociation energy per unit volume remains almost constant as shown in Table 2; ii- In the calculation, we have considered that boron atoms are equally distributed between BO4 and BO3 groups. This is due to lack of information about the concentrations of these groups. In fact, BO4 and BO3 concentrations depend on composition of the glass; and iii- According to the above discussion, the dissociation energy per unit volume of TeO2 oxide can be expressed as:

GTeO2 = NTeO4 GTeO4 + NTeO3 GTeO3

(20)

where GTeO4 and GTeO3 are the dissociation energy per unit volume of TeO4 and TeO3 units, respectively, whereas NTeO4 and NTeO3 are their respective concentrations. Also, the packing factor of the same oxide can be expressed as

VTeO2 = NTeO4 VTeO4 + NTeO3 VTeO3

(21)

where VTeO3 and VTeO4 are the respective packing factors of TeO2, which corresponding 3-and 4-coordinated tellurium, respectively. In the present calculation, we have ignored the effect of TeO3 groups and NBOs on the packing density and dissociation energy per unit volume of the glass. This is due to the lack of information about the values of NTeO3, GTeO3 and VTeO4. In addition to this, we have applied the dissociation energy per unit volume of 12.92 kcal/cm3for TeO2 oxide [42]. This value has been determined empirically by Inaba et al. [42] from Young's modulus of vitreous TeO2. 4.2. Ag2O–V2O5–MoO3–TeO2 glasses Table 1 and Fig. 8 reveals that the compositional dependence of experimental elastic properties in quaternary xAg2O–(35 − x) (0.5V2O5–0.5MoO3)–65TeO2 glass system show a maximum at 6

Journal of Non-Crystalline Solids 522 (2019) 119580

A.A. El-Moneim and R. El-Mallawany

Young's modulus (GPa)

80

Table 4 Packing factor and dissociation energy per unit volume for simple oxides V2O5, MoO3, TeO2 and B2O3.

70

Theoretical

Oxide

Basic structural unit

Vi [63] (cm3/mol)

Gi [63] (kcal/cm3)

V2O5

VO4 VO5 MoO4 MoO6 TeO4 TeO3 BO4 BO3

35.4 – 20.9 21.3 14.7 – 20.8 15.2

6.89 8.27 – 16.70 12.92 – 19.81 5.41

60 50

MoO3

40

TeO2

Experimental

B2O3

30 20 -10

-5

0

5

10

15

20

25

VV2 O5 = NVO4 VVO4 + NVO5 VVO5

(24)

VMoO3 = NMoO4 VMoO4 + NMoO6 VMoO6

(25)

30

Ag2O (mol %)

where VVO4 and VVO5 are the respective packing factors, which corresponding the 4-and 5-coordinated vanadium atoms in V2O5, whereas VMoO4 and VMoO6 are those of MoO3 oxide, which corresponding the 4and 6-coordinated molybdenum atoms, respectively. The available data for the dissociation energy per unit volume and packing factor of TeO2, V2O5 and MoO3 oxides, which corresponding to the different basic structural units are given in Table 4. Unfortunately, the values of VVO5, GMoO4, GTeO3 and VTeO3 are unreported at present. The newly calculated values for the dissociation energy per unit volume (denoted by Gt′) and packing density (denoted by Vt′) of the quaternary xAg2O–(35 − x)(0.5V2O5–0.5MoO3)–65TeO2 glass system under investigation are listed in Table 5. The values of theoretical elastic moduli (denoted by Kth′, Sth′, Lth′ and Eth′) and Poisson's ratio (denoted by μth′) are also given in the same table. In calculating of GV2O5 , vanadium atoms are considered to be equally distributed between the two structural units VO4 and VO5. Also, in calculating of VMoO3 , molybdenum atoms are considered to be distributed between MoO4 and MoO6 groups. This is due the lack of information about the values of NVO4, NVO5, NMoO4 and NMoO6. One interesting observation is that, all values of Gt′ are smaller than those of Gt.At the same time, the value of Vt′ and Vt are in the same range. Fig. 9 illustrates the relation between theoretical and experimental elastic moduli of xAg2O–(35 − x) (0.5V2O5–0.5MoO3)–65TeO2 glass system. In compared to Fig. 4, the agreement between the theoretical and experimental values is much better for majority of the samples. The correlation ratio changes from 97.8% to 69.7% in case of bulk modulus, from 82.9% to 66.2% in case of shear modulus, from 93.2% to 68.2% in case of Young's modulus and from 90.8% to % 70.8 in case of longitudinal modulus. These results suggests the dissociation energies per unit volume VO4 and VO5 groups, besides the packing factors of MoO4 and MoO6 groups play an important role in improving the agreement between the theoretical and experimental elastic moduli of Ag2O–V2O5–MoO3–TeO2 glasses. Considering the effect of all the structural units, it is first necessary to identify all the types of bonds present in the prepared glass and then to ascribe appropriate values of Gi, Vi, Gt and Vt for each type of bonds by using neutron diffraction, Raman EXAFS and FTIR data. Thus, taking into account the effect of all structural units that present in the network, besides the uncertainty inherent in experimental measurements, we believe that the Makishima-Mackenzie's theory [39,40] as well as Abd El-Moneim and Alfifi's approaches [51] are suitable for predicting the compositional dependence of elastic moduli not only in Ag2O–V2O5–MoO3–TeO2 glasses but also in WO3–B2O3–MgO–TeO2 glasses.

Fig. 8. Dependence of experimental and theoretical Young's moduli on Ag2O content in Ag2O–V2O5–MoO3–TeO2 glasses. The solid lines are drawn as guides to the eyes.

x = 10 mol%. On the other hand, the packing density and dissociation energy per unit volume show a progressive decrease with Ag2O addition. As a result, a divergence between the theoretical and experimental elastic moduli is noticed and the correlation ratio between theoretical and experimental values changes markedly with composition as shown in Fig. 8 for Young's modulus as an example. However, a review of literature reveals that V2O5 can enter the same network either as a network-modifier or as a network-former, depending upon its concentration [18,68,69]. As a network-former, vanadium ions can exist either in the valence state V5+ by formation of VO5 groups or in the valence state V4+ by formation of VO4 groups. Also, MoO3 is a conditional glass former [36] and Ag2O is a glass modifier. Accordingly, Ag+ ions are participated interstitially in the glass structure. The recent FTIR result of Ismail et al. [36] on the same present xAg2O–(35 − x) (0.5V2O5–0.5MoO3)–65TeO2 glass system showed that: i- The network of these glasses are composed of VO4, VO5, MoO4, MoO6, TeO3 and TeO4 groups, which are connected to each other through the of Te–O–Te, V–O–V, Mo–O–Mo, V–O–Te, Mo–O–Te and Mo–O–V linkages; ii- The ratio of intensity and area of the TeO4 tbp to TeO3 tp increases for glass samples having x ≤ 10 mol% and decreases for glass samples having x > 10 mol%; iii- For x ≤ 10 mol%, TeO2 is incorporated into the network as a glass former by formation of TeO4 tbps; and iv- During the composition range x ≤ 10 mol%, MoO3 behaves as a glass former by forming MoO6 groups, whereas for x > 10 mol%, it behaves as a glass modifier by forming MoO4 groups. The effect of the basic structural units on the packing density and dissociation energy per unit volume of xAg2O–(35 − x) (0.5V2O5–0.5MoO3)–65TeO2 glass system can be taken into account as follows. For V2O5 and MoO3 oxides, the dissociation energy per unit volume can be written as;

GV2 O5 = NVO4 GVO4 + NVO5 GVO5

(22)

G MoO3 = NMoO4 G MoO4 + NMoO6 G MoO6

(23)

where NVO4, NVO5, NMoO4 and NMoO6 are respective concentrations of the structural units VO4, VO5, MoO4 and MoO6 groups, whereas GVO4, GVO5, GMoO4 and GMoO6 are their respective dissociation energies per unit volume. In the same meaner, the packing factor can be expressed for V2O5 and MoO3 oxides as:

4.3. Theoretical - experimental Poisson's ratios correlation on the basis of Rocherulle et al. model [41] As mentioned above in the introduction, Rocherulle and his co7

Journal of Non-Crystalline Solids 522 (2019) 119580

A.A. El-Moneim and R. El-Mallawany

Table 5 Theoretically calculated compositional and elastic properties of quaternary xAg2O–(35 − x)(0.5V2O5–0.5MoO3)–65TeO2 glass system on the basis of MakishimaMackenzie's theory [39,40]. Vt′

Gt′ (kcal/cm3)

Kth′ (GPa)

Sth′ (GPa)

Lth′ (GPa)

Eth′ (GPa)

μth′

0 5 10 15 20 25

0.5452 0.5361 0.5206 0.5212 0.5285 0.5382

12.65 12.37 12.09 11.80 11.52 11.24

37.60 35.55 32.77 32.05 32.18 32.56

24.73 23.87 22.81 22.28 21.99 21.76

70.49 67.30 63.10 61.68 61.42 61.49

57.66 55.44 52.62 51.42 50.90 50.57

0.245 0.241 0.233 0.234 0.237 0.242

Experimental elastic modulus (GPa)

x (mol %)

100

Table 6 Theoretically calculated packing density and Poisson's ratio of Ag2O–V2O5–MoO3)–TeO2and WO3–B2O3–MgO–TeO2 glasses on the basis of Rocherulle et al. model [41].

Bulk modulus Shear modulus Longitudinal modulus Young's modulus

80

x (mol %)

60

xAg2O–(35 − x)(0.5V2O5–0.5MoO3)–65TeO2 glass system 0 0.5753 5 0.5641 10 0.5529 15 0.5417 20 0.5305 25 0.5193 xWO3–(75–x)B2O3–10MgO–15TeO2 glass system 0.2 0.6256 0.4 0.6257 0.6 0.6257 0.8 0.6257 1.0 0.6258

40 20 0 0

20

40

60

80

100

Theoretical elastic modulus (GPa) Fig. 9. Agreement between theoretical and experimental elastic moduli of Ag2O–V2O5–MoO3–TeO2 glasses on the basis of Makishima-Mackenzie's theory [39, 40]. The theoretical values were calculated after taking into account the effect of the basic structural units on the dissociation energy per unit volume and packing density of the glass. The solid line is the1:1correlation line.

Experimental Poisson's ratio

∑ xi Ci i

μth∗ = 0.5 − (1/7.2 Ct )

0.259 0.254 0.249 0.244 0.238 0.233 0.278 0.278 0.278 0.278 0.278

0.5

workers [41] have extended Makishima –Mackenzie's [39,40] to oxynitride glasses. They made a modification on the expression of packing density by introducing a thermodynamic factor, which results from the substitution of oxygen by nitrogen within the vitreous network. According to Rocherulle et al. model [40], the packing density and Poisson's ratio of multi-component oxide glasses can be calculate from the following two equations;

Ct =

μth∗

Ct

Ag-V-Mo-Te W-B-Mg-Te

0.4

0.3

0.2

0.1

(26)

0 0

(27)

where Ci = ρiVi/Mi is the packing density for component oxide i. The calculated values of Ct from Eq. (26) and those of μth∗ from Eq. (27) are listed in Table 6 for the same present Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glasses. The applied values of Ci for the component oxides Ag2O, V2O5, MoO3,TeO2, WO3, B2O3 and MgO are given in Table 3. It was found that, all the investigated glass samples have Ct values greater than Vt values. This is reflected in the theoretical values of Poisson's ratio μth∗ and improves significantly its agreement with the experimentally measured values as shown in Fig. 10. The correlation ratio changes from 97.7% to 72.8% in Ag2O–V2O5–MoO3–TeO2 glasses and from 99.7% to 96.3% in WO3–B2O3–MgO–TeO2 glasses. This suggests that Eq. (27) is more applicable than Eq. (10) in predicting Poisson's ratios of Ag2O–V2O5–MoO3–TeO2 and WO3–B2O3–MgO–TeO2 glasses.

0.1

0.2

0.3

0.4

0.5

Theoretical Poisson's ratio Fig. 10. Relation between theoretical and experimental Poisson's ratios in WO3–B2O3–MgO–TeO2 and Ag2O–V2O5–MoO3–TeO2 glasses. The theoretical values were calculated on the basis of Rocherulle et al. model [41]. The solid line is the1:1correlation line.

B2O3–10MgO–15TeO2 (0.2 ≤ x ≥ 1 mol%) glass systems have been analyzed and predicted. Prediction has been carried out by correlating the elastic moduli and Poisson's ratio with the most significant compositional parameters on the basis of (i) Makishima-Mackenzie's theory [39,40], (ii) Rocherulle et al. model [41], and (iii) Abd El-Moneim and Alfifi's approaches [51]. The following conclusions were achieved: i- Elastic moduli of WO3–B2O3–MgO–TeO2 glasses are predictable from both Makishima-Mackenzie's theory [38,39] and Abd ElMoneim and Alfifi's approaches [51]. An excellent agreement between the theoretical and experimental elastic moduli was achieved for majority of the samples;

5. Conclusions The elastic properties of the quaternary tellurite xAg2O–(35–x) (0.5V2O5–0.5MoO3)–65TeO2 (0 ≤ x ≥ 25 mol%) and xWO3–(75–x) 8

Journal of Non-Crystalline Solids 522 (2019) 119580

A.A. El-Moneim and R. El-Mallawany

ii- The basic structural units VO4, VO5, MoO4 and MoO6 play an important role in improving the agreement between theoretical and experimental elastic moduli of Ag2O–V2O5–MoO3–TeO2 glasses; and iii- The correlation between theoretical and experimental Poisson's ratios on the basis of Rocherulle et al. model [41] is much better than that based on Makishima-Mackenzie's theory [39,40].

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