1. Introduction

Metal oxides display physical properties ranging from piezoelectricity to superconductivity, from negative thermal expansion to ionic conductivity and transparent conductors. They are used in computers, Li-ion batteries, fluorescent lights, cellular phones, and fuel cells. Many well-designed properties of the glass are determined by the elements with mixed valences (in which an element has two or more different valences while forming a compound) in the structure unit [1]. High-temperature superconductor [2] was a milestone in the study of metal-oxides and is an effective example for the mixed valence chemistry. Mixed valence effect is required for glasses to stimulate electronic, structural, and chemical progress leading to specific functionality. The valence states of metal cations in glass can be governed chemically using orbital hybridization.

Borate glasses are composed of structural groupings as boroxol, tetraborate, diborate, which are linked by bridging oxygens, where the glass consists of microdomains of boroxol rings [3]. Near the glass-transition temperature the boroxol rings break up leading to a more open structure which affects strongly the glass behavior as a host material. In lead borate glass the extreme difference between the masses of the lead and the boron atom are favorable for spectroscopic investigations. This is because increasing the heavy metal oxide content causes an increase in the glass thermal stability. Furthermore, glasses containing cations (such as Pb²⁺, As³⁺, or Bi³⁺) with an outer electron shell of 18 + 2 electrons should have higher polarizabilities and lower melting temperatures [4]. In the same context, lead monoxide possesses interesting semiconducting and photo conducting properties with potential applications in imaging devices, electro photography and laser technology.

Selenium has empty d-orbitals which can form four or six bonds by unpairing electrons. Overlap of a p-orbital on the oxygen with a d-orbital on Se gives a pπ-dπ interaction [5]. To obtain effective pπ-dπ overlap, the size of the d-orbital must be similar the size of the p-orbital. Since Se has a covalent radius of 1.14 Åwhile for Cr it is 1.17 Å, therefore, an overlap between them might be highly credible. Upon the glass structure, a strong overlap possibly arise providing 2p-3d orbital hybridization. Such orbital hybridization manifests itself as an increase in glass optical polarizability throughout spin-orbit coupling mechanism [6]. Selenium oxide possesses two kinds of structures as selenite and selenate around Se atom. Selenite (SeO₃^2-) acts as a modifier in the glass network with three coordinated oxygen and one lone pair of electrons, whereas the selenate (SeO₄^2-) with four coordinated oxygen occupies tetrahedral sites in the glass network and acts as a network former [7, 8].

The role of an ion in glass environment is largely determined by its ionic radius a, and its effective electrostatic field strength eZ/a² where eZ is the ionic charge. According to stereochemical reasoning, coordination number four is suggested for small ions to be incorporated in interatomic space between four closed-packed oxygens. Octahedron of close-packed oxygens-coordination number 6-or even more is required for larger ions. Transition metals with valences of +3 or +4 such as Cr, which having a lower electronegativity, with oxides have a higher electronegativity such as SeO₂ are required to design the glass optoelectronic structure such as the glass band gap [9-11].

Existing of chalcogenide elements in glass network provides a number of amorphous semiconductor-like properties [12, 13]. For instance, increasing the relative atomic mass of the chalcogen or its proportion in the glass reduces its average bond strength [14]. Elements such as Se have electronic structure s²p⁴ tend to gain two electrons forming M^2- ions, or to share two electrons and thus forming two covalent bonds. Many well-designed properties of the glass are obtained by using elements with mixed valences in the structure network [1]. In the present work, 3d-4p orbital replacement of B₂O₃ by a combination of Cr₂O₃ andSeO₂ is used to engineer the molar volume of a heavy metal borate glass. The chemical bond approach is used to analyze and to explain the role of mixed valence effect on the glass molar volume to enhance the expected glass ionic conductivity.

2. Experimental Details

2.1. Glass Preparation

Three series of lead borate glasses of composition xCr₂O₃-(0.25-x) B₂O₃–0.75PbO, xSeO₂-(0.25-x)B₂O₃– 0.75PbOand x(Cr₂O₃-SeO₂)-(0.25-x)B₂O₃–0.75PbO are prepared, Table 1, where x is the oxide molar fraction. The used materials were of chemically pure grade, in the form of H₃BO₃, Cr₂O₃, SeO₂ and Pb₃O₄. The amount of the glass batch was 50 g melt^-1. The glass was prepared by melt quenching technique using porcelain crucibles in an electric furnace. The temperature of melting was 1100C, whereas the duration of melting was one hour after the last traces of batches were disappeared. To avoid the presence of bubbles in the glass melt, the melt was continuing stirred during the glass preparation. Then the melt was poured onto stainless steel mould and annealed at around 350^oC to remove the thermal strains. Optical slabs were prepared by grinding and polishing of the prepared samples with paraffin oil and minimum amount of water. The thickness of the glass slabs was about 3 mm. Polishing was completed with stannic oxide and paraffin to reach a minimum surface roughness which was tested by an interferometric method. The homogeneity of the glasses was examined using two crossed polarizers.

2.2. Measurement of Glass Density

The hydrostatic density of the glasses, ρ, at room temperature was measured by the Archimedes principle using a sensitive microbalance. The error in measuring the glass density was 0.001 g/cm³.

3. Results and Discussion

3.1. Density and Molar Volume

The molar volume, V_m, of the glass was calculated using the expression:

(1)

where ρ is the glass density, x_i is the molar fraction and M_i is the molecular weight of the ith component, respectively. Table 1 illustrates the measured variation in the heavy metal borate glassdensity and molar volume due to incorporation of small equal molar fractions of SeO₂ and Cr₂O₃ on the expense of B₂O₃ content. This means that the bond length or interatomic spacing between the atoms may be attributed to the variation in the stretching force constants of the bonds inside the glass network.

Table 1. Glass compositions, density and molar volume

3.2. Intermolecular Separation and Bond Density

Replacement of Cr₂O₃ or/and SeO₂ into the glass network instead of B₂O₃ makes effective changes for the density and molar volume of the base glass sample (i.e., sample 1). Since the molar masses of Cr₂O₃ and SeO₂ are 99.99 and 110.96 g/mol, respectively, while for B₂O₃ is 69.622 g/mol, so the replacement of SeO₂ by B₂O₃ explains such increase in the glass density of the base sample with increasing SeO₂ content as in samples 5, 6 and 7 (second series). The density and molar volume show opposite behavior (sample 4), where with the same SeO₂ amount (x = 0.006) the glass density increased by 1.06% and the molar volume decreased by 1.01%. The behavior of glass density reveals that, with the increase in SeO₂ contenta partial reversible transformation occurs for a part of selenite groups (SeO₃^2-) into the more densselenate (SeO₄^2-) with its four coordinated oxygen occupying tetrahedral sites in the glass network.

In the same context, the fluctuation in the glass density which is seen with samples1, 2, 3, and 4 (first series) due to replacement of Cr₂O₃ by B₂O₃ may beat tributed to the conversion of chromium ions from Cr⁶⁺ state to Cr³⁺ state and vise verse. Sample 7 with Cr₂O₃ molar fraction 0.006 has the lowest density, second series. It means the conversion of chromium ions from Cr⁶⁺ state into Cr³⁺ state which has the longest ionic radius (0.65 Å) in compare with Cr⁶⁺ that has ionic radius 0.36Å. Also the existing of Cr³⁺ ions acts as modifier which may create an inconsistency in the number of nonbridging oxygen bonds NBO relative to bridging oxygen bonds (BO). Glass samples 8, 9, and 10 (third series), which containa variable equal share of mole fraction, x, for bothCr₂O₃and SeO₂, show a profound decrease in the glass density compared to the base glass sample. Such unexpected density and molar volume behaviors may be attributed to the creation of an excess of nonbridging oxygen bonds which open up the structure of the glass networks.

Analyzing the glass molar volume is more informative by correlate it with the role of SeO₂ and Cr₂O₃ hybridization on the number of bonds per unit volume (n_b). The number of bonds per unit volume of the glass is calculated using the relationship [15, 16]:

(2)

where n_c is the coordination number of the cation. The used coordination number of B³⁺, Pb²⁺, Cr³⁺ and Se⁴⁺ are 4, 8, 6, and 4, respectively. Thus, the molar volume is found to increase with the decrease in number of bonds per unit volume of the present glass. Molar volume decreases also with increasing the SeO₂ and/or Cr₂O₃ content, as shown in Fig. 1. In comparison between sample 1 (base) and sample 10, the molar volume, V_m, is increased from 34.544 to 35.151cm³/mol, respectively, accompanying with a decrease in number of bonds per unit volume, n_b, from 12.2010²⁸ m^-3 to 12.0010²⁸ m^-3. So the increase in glass molar volume could be ascribed to some structural changes such as the increase in nonbridging oxygen bond density and in addition the associated decrease in the number of bonds per unit volume of the glass which is recognized with the equal share increase in molar fraction for both SeO₂ and Cr₂O₃ up to x = 0.006.

Figure 1. Number of bonds per unit volume versus oxide molar fractions

3.3. Oxygen Molar and Packing Densities

According to chemical bond approach and for further explanation the obtained glass molar volume and density behavior, many additional parameters would also be calculated which are; the volume of glass in which 1 mole of oxygen is contained (the molar volume of oxygen, V_o) and oxygen packing density (OPD). The molar volume of oxygen is given by [17]:

(3)

where n_i is the number of oxygen atoms in each oxide. The oxygen packing density is calculated from the density and composition using the formula:

(4)

where C is the number of oxygens per formula unit. The determined oxygen molar density and oxygen packing density of the glass samples are shown in Figs. 2, 3. Regarding to samples 1 and 10, the obtained increase in oxygen molar volume from 28.20 to 28.74 cm³/mol, respectively, is associated with an increase in oxygen packing density from 115.79 to 256.04 mol/l. It confirms the formation of nonbridging oxygen bonds with the replacement of B₂O₃ by equal share of both SeO₂ and Cr₂O₃ contents up to a molar fraction of 0.006 (sample 10). This finding may be associated with a formation of more negatively charged tetrahedral units, which leads to a variation in the ratio between triagonal units and the anionic tetrahedral units of the glass network [18, 19].

Figure 2. Oxygen molar volume versus oxide molar fractions

Figure 3. Oxygen packing density versus oxide molar fractions

In addition, conversion of chromium ions from CrO₄²⁻ structural units to predominantly Cr³⁺ state in octahedral environment may occur, taking part in network modifier positions. This situation is also responsible for the increase in nonbridging oxygens due to which an increase in the molar volume is obtained. Absence of CrO₄²⁻ structural units causes an increase in the degree of depolymerization of the glass network. For a chromium and selenium addition, as the case of samples 8, 9 and 10, a gradual conversion of chromium ions from Cr⁶⁺ state to Cr³⁺ state exists and the Cr³⁺ ion in such case acts as modifiers breaking up local symmetry and introduces coordinated bond defects in these glasses.

3.4. Boron Molar Volume and Glass Network Free Space

The average boron-boron separation d_B-B is calculated to give more insight on the modification of the glass network due to the presence of SeO₂ and Cr₂O₃. The boron atoms are the central atoms with negatively charged tetrahedral units. Thus the boronmolar volume which corresponds to the volume that contains one mole of boron atoms within the specific glass structure is fined as [20]:

(5)

where x_B is the molar fraction of B₂O₃ oxide. The average boron-boron separation d_B-B is calculated using the expression:

(6)

where N_A is Avogadro’s number (6.022810²³ g/mol). Since depends on cation species, therefore, the calculated values of average boron-boron separationd_B-B are increased with the increase in the SeO₂ and Cr₂O₃ contents from 0.337 nm (sample 1) to 0.344 nm for sample 10. Thus, the incorporation of SeO₂ and Cr₂O₃ on expense of B₂O₃ leads to a substantial expansion of the glass structural network which confirms the obtained density and molar volume values. Furthermore, the calculated values of boronmolar volume illustrate that with increasing both SeO₂ and Cr₂O₃ contents together on the expense of boron oxide, the is increased from 23.029 (sample 1) to 23.248 cm³/mol, respectively, as in case of sample 10. Since depends on cation species, therefore, with the increase in the SeO₂ and Cr₂O₃ contents, an increase in the average boron-boron separation may be obtained. Thus, the incorporation of SeO₂ and Cr₂O₃ on expense of B₂O₃ leads to a substantial non densification of the glass structural network which approves the obtained density and molar volume values. The increase in the bond length or inter-atomic spacing between the atoms may be also attributed to a decrease in the stretching force constants of the bonds inside the glass network.

Additionally, the decrease in the number of bonds per unit volume, n_b, can be investigated by the determination of interatomic distance between Se and Cr atoms. For a glass has an oxide component, i, of x_iA_bO_c, where b and c are the valence of both the anion O and cation A, respectively, then the concentrations of the ions A and O are given by [20]:

(7)

(8)

The minimum separation distance, d, between identical ions is given by:

(9)

In comparison of the base sample with sample 10, the interatomic separation between oxygen atoms d_o-o of lead oxide increases from 0.425 nm to 0.428 nm with increasing of the combination of SeO₂ and Cr₂O₃ contents on the expenses of boron oxide content. This confirms once again the obtained increase in the glass molar volume. The ions without any spacing between them occupy only a volume equal to V_i which is given by where r_i is the radius of the ion i and the summation is taken over all the ions present in one mole of the glass. Then the free space, V_f, in one mole of the glass [20] which is not occupied by the ions is equal to . As shown in Fig. 4, increasing the mole fraction contents of SeO₂ and Cr₂O₃ together up to 0.006 (sample 10) increases the free space per mole from 21.14 (sample 1) to 21.75 cm³/mole, respectively. So the conjunct introduction of SeO₂ and Cr₂O₃ enhances the 2p electron density of the unshared oxygen ion which in turn increases the ionicity of chemical bonds of glass. Hence it increases the intermolecular free space which leads to increase the glass molar volume [21].

Figure 4. Free space per mole versus oxide molar fractions

3.5. Molar Volumeand the Bond Ionicity

Boron has ionic cation radius 0.20 Å while Se and Cr have relative large ionic cation radii 1.84 and 0.65 Å, respectively. Therefore, it is expected that, with the insertion of Se and Cra transformation of a part of BO₃ groups into BO₄ groups is taking place. It produces an assured increase in the number of nonbridging oxygen bonds (NBO) relative to the bridging bonds (BO), which manifests itself by the increase in molar volume. Furthermore, the ionicity of oxides decreases with increasing polarization power of cations [22]. Accordingly, ionic character or bond ionicity (I_b) could describe the bonding nature of the investigated glass [23]. Therefore, the change in the molar volume of the present glass system could be discussed on the basis of a number of parameters such as electronegativity difference and Pauling’s ionicity. The glass electronegativity difference, Δχ_i, is calculated using the formula:

(10)

The electronegativity difference of the glass constituent oxide which is given by [24]:

(11)

where and are the Pauling electronegativity of the anion (oxygen) and that of the cation, respectively. Applying Pauling’s empirical definition of bond ionicity, I_b, where

(12)

gives a value for I_b of the glass. The electronegativity differences of the glass constituent oxide bonds B-O, Cr-O, Se-O and Pb-O are 1.4, 1.89, 0.89 and 1.44, respectively. The calculated bond ionicity, I_b, of the different glass samples exhibits a decrease in its value from 0.4002 with the base sample to 0.398 with 0.006 SeO₂ mole fraction (sample 4). In case of Cr₂O₃ with 0.006 mole fraction (sample 7) the bond ionicity is increased to be 0.402 due to the high electronegativity difference of Cr₂O₃.

With continues replacement of SeO₂ and Cr₂O₃ instead of B₂O₃, the bond ionicity showed almost no variation in its value which was 0.4002. This result could be understood through the change of some amount of Cr³⁺ with ionic radius 0.65 Å to Cr⁶⁺ which has less ionic radius of 0.36 Å. In general, it illustrates that there is a relationship between molar volumes of the glass and ametric atomic scale such as electronegativity differences of the glass constituent oxide bonds [25]. According to the classification for morphology of non-crystalline solids based on bond ionicity [26], the present glass system is considered as modified continuous random networks with increased interstitial spaces.

3.6. Nearest-neighbor Coordination

Because of its large glass forming region, nearest-neighbor coordination in a quaternary glass system is mostly appropriate to explain the obtained glass molar volume values. The average coordination number, m, in the present glass system is defined by

(13)

where n_i is coordination number of the cation. The used coordination number of B³⁺, Pb²⁺, Cr³⁺ and Se²⁺ions are 4, 8, 6, and 4, respectively. The calculated values of average coordination number of the investigated glasses show an increase upon the partial introducing for both SeO₂ and Cr₂O₃ into the glassnetwork instead of boric acid. The increase in glass average coordination number from 7.00 to 7.006 exhibits the same trend of glass molar volume which is increased from 34.544 to be 35.151 cm³/mol, respectively. This behavior confirms that the average coordination number and molar volume are strongly correlated. Therefore, the induced structural change by SeO₂ and Cr₂O₃ in the glass partially converts BO₃ unit to BO₄ structural unit and the glass network begins to break up producing nonbridging oxygen bonds (NBOs). Such an expansion of the network due to NBOs with weaker BO₄units (that is less tightly bounded with more polarized excited electrons) explains the obtained increase in the molar volume of sample 10.

Thus the increase in the glass molar volume due to mixed valence effect may result from the competition between three types of negative site with different binding energy. The first type is due to the units where the negative charge is distributed around the boron site. The second is due to the conversion from bridging to nonbridging oxygen bonds which increases the negative charge localized on the B-O bond with a deeper potential well. The third is due to conversion of chromium ions from Cr⁶⁺ state to Cr³⁺ state. Thus through the mixed valence effect, with 3d-4p orbital replacement of B₂O₃ by a combination of small conjoint molar fractions of Cr₂O₃ and SeO₂, the molar volume of a heavy metal glass could be tuned. Thus it is possible to make comparatively cheap junctions with important implications for the economics of solar cells. No doubt, this anionic conduction would motivate the research on chalcogen-oxide glasses for Li-ion batteries, fluorescent lights, cellular phones, and fuel cells. So, increasing the glass molar volume might contribute directly in the production of promising glasses for ionic conduction domain [18, 27-29].

4. Conclusions

Conduction band mainly consists of atomic orbitals of cationic atoms, since anionic atoms are more electronegative than cationic atoms. Upon the structure of investigated glass, the p- and d- orbitals strongly interact so that the d-states of the transition metal atoms Cr hybridize with the chalcogen Se p-bands. Such orbital hybridizationis basically corresponding to nonbonding states with more optical polarization. Depending on the nature of valence orbitals, the substitution of p- and d-block elements results as increase in the glass molar volume through creation of nonbridging oxygen bonds. The looked-for mixed valence effect (through a very small replacement of boron oxide content by an equal share of molar fractions of SeO₂ and Cr₂O₃) is to replace strong oxygen linkages of triagonal units by weaker anionic tetrahedral unit linkages and the more polarizable Cr³⁺ state. The projected result would be glass network weakening with a decrease in both the melting temperature and the viscosity of the melt. Due to the weaker bonding, the molar volume increases and the glass network becomes more open. It provides wide pathways get ways for ions such as Li⁺ to be more easily mobile in the glass matrix. The orbital hybridization is proven itself as an active technique to control the glass molar volume and thus to regulate effectively the glass ionic conduction. The gained results would encourage and may drive to further prospective researches on the fields of interest related to the present study.

ACKNOWLEDGEMENTS

This work is supported by the National Research Centre, Egypt project no. 10070402.