Silicate glasses mean silica, soda lime silica glass, and borosilicate glass. Silica is the dioxide form of silica, SiO₂, and occurs mostly as quartz sand, flint, and agate. It is formed when silicon is exposed to oxygen. The commercially supplied SiO₂ glasses (microscope slides) employed in this study have mass density as 2.65 g/cm³ and molecular weight as 60.08 g/mol. The other silicate glasses (soda lime and borosilicate microscope slides) are also commercially supplied. A typical composition of soda lime silicate glass is 73% SiO₂ + 15% Na₂O + 7% CaO + 4% MgO + 1% Al₂O₃, and its mass density is 2.5 g/cm³. Since the molecular weights of all these compositions are known in the literature and so they can be printed as 60.08 g/mol, 61.98 g/mol, 56.0774 g/mol, 40.3044 g/mol, and 101.96 g/mol, respectively. We have measured the molecular weight of soda lime as the average of sums of the % molecular weights of all constituents and measuring the molecular weight of soda lime using the mole % of all participating cations in the composition. As a result, the average molecular weight of soda lime silicate is measured as 59.34 g/mol.

The typical chemical composition of borosilicate 7059 glass is 80% SiO₂ + 13% B₂O₃ + 4% Na₂O + 3% Al₂O₃, and its mass density is 2.76 g/cm³. The molecular weights of all compositions relating to 7059 glass (as found in the literature) can be printed respectively as 60.08 g/mol, 69.62 g/mol, 61.98 g/mol and 101.96. Following the method as we did for soda lime glass, the average molecular weight of 7059 silicate glass is determined as 62.69 g/mol.

Next, molecular volume (V_m) of any solid = Molecular weight/Mass density = M/ρ = cc/mol. So, for silica glass, V_m = 60.08/2.65 = 22.672 cc/mol; for soda lime, V_m = 60.08/2.65 = 23.74 cc/mol; and for 7059 silicate glass, V_m = 60.08/2.65 = 22.714 cc/mol.

These silicate glasses are available in many forms and sizes such as rod, tube, or microscopic slide. In this work, silicate flat glasses were obtained commercially as microscopic slides. Microscope slides of these glasses measure about 75 mm by 25 mm and are about 1 mm thick.

Silica and other glass slides were washed with “Micro” cleaning fluids (purchased from International Products Corporation) and rinsed in tap water and distilled water. Having been left to soak in freshly distilled water for several hrs, the substrates were flushed with both acetone and iso-propyl alcohol (IPA). The substrates were then subjected to ultrasonic distillation unit containing distilled water for 3 min, and finally were cycled for more than 20 min in a vapour degreasing unit (Sholet unit) in which iso-propyl alcohol was reflexed continuously, and at this stage the cleaning run was complete.

The refractive indices were measured using both Abbe refractometer with a sodium vapour lamp as the light source emitting the light at a wavelength, λ, of 589.3 nm (D line) and ellipsometry using a laser with a wavelength at 632.8 nm.

In the first stage, the data on molar refraction (R_m), molar electron polarizability (α_me), and optical band gap (E_g) of silicate glasses (silica, soda lime, borosilicate 7059) were generated from Tables 2-4 using the following course of action.

Molar refraction (R_m) is related to molar volume (V_m) by the relation [58] [59]

R m = ( n 2 − 1 n 2 + 2 ) V m (5)

where

V m = M ρ = molecularweight massdensity (6)

Molar electronic polarizability (α_me) can be related with the molar refractive index by an expression [60] [61]

α m e = R m 2.52 (7)

According to Duffy, there also exists a good correlation between molar refraction and the band gap energy (E_g) of the materials (or glasses) and that is given as [60] [61]

R m = V m [ 1 − E g 20 ] (8)

The required data on the above optical parameters was obtained using Equations (5)-(8).

In the second stage, the following models were used to obtain other properties. The electronic oxide ion polarizabilities based on refractice index and optical band gap α_o2- (n) and α_o2- (E_g) for the silicate glasses were determined using their reported refractive indices (n) and the obtained optical band gaps (E_g). The oxide ion polarizability based on refractive index was calculated using relation as reported by Meen and Bhatia [62] [63]

α 0 2- ( n ) = [ ( V m 2.52 ) ( n 2 − 1 n 2 + 2 ) − ∑ α i ] q − 1 . (9)

where V_m is molar volume; n, the refractive index; E_g expresses the optical band gap of the glass; ∑ α i denotes the sum of molar cation polarizabilities of all constituents, and q⁻¹ is the inverse of total number of oxide ions in the chemical formula of the oxide.

In the case of silica glass, the physical parameters like V_m, ∑ α i , and q⁻¹ involved in the Equation (9) are given and/or measured as follows.

V m = Molecularweight Massdensity = 60.08 2.65 = 22.672   mol − 1 / cm − 3 ; V m 2.52 = 8.997 ;

the cation polarizability for SiO₂, ∑ α i = 0.033   Å 3 {A41, A42}; the inverse of number of oxide ions in SiO₂, q − 1 = 0.504 × 10 − 24 cm 3 / ions . It should be noted that the value of “q” is the number of moles of oxide ions in SiO₂ multiplied by Avogado numbers. Substituting all these values into Equation (9), the Equation (9) is reshaped as

α 0 2- ( n ) = [ 8.997 × ( n 2 − 1 n 2 + 2 ) − 0.033 ] × 0.504 × 10 − 24 . (10)

The values of n and α_o2- (n) for a silica glass [using Equation (10)] were measured from 1.5119 to 1.5111 and 1.3438 to 1.3420, respectively over the temperature range 295 - 373 K using ellipsometer at λ = 633.8 nm. The values of n and α_o2- (n) relating to silica glass were respectively measured from 1.5276 to 1.5274 and 1.3786 to1.3782, respectively over the temperature range 297 - 322 K using Abbe refractometer at λ = 589.3 nm.

In the case of soda lime silicate glass, we have V m = Molecularweight Massdensity = 59.34 2.50 = 23.74   mol − 1 / cm − 3 ; V m 2.52 = 9.42 ;

∑ α i = 0.1153   Å 3 ; q − 1 = 0.593 × 10 − 24 cm 3 / ions . Substituting all these values into Equation (9), we obtain new relation as:

α 0 2- ( n ) = [ 9.42 × ( n 2 − 1 n 2 + 2 ) − 0.1153 ] × 0.593 × 10 − 24 (11)

The values of n and α_o2- (n) for a soda lime glass [using Equation (11)] were measured from 1.5086 to 1.5065 and 1.6012 to 1.5954, respectively over the temperature range 295 - 373 K using ellipsometer at λ = 633.8 nm. The values of n and α_o2- (n) relating to silica glass were respectively measured from 1.5074 to 1.5070 and 1.5983 to1.5969 over the temperature range 298 - 322 K using Abbe refractometer at λ = 589.3 nm.

In the case of borosilicate 7059 glass, we have V m = Molecularweight Massdensity = 62.27 2.76 = 22.562   mol − 1 / cm − 3 ; V m 2.52 = 8.953 ;

∑ α i = 0.0448   Å 3 ; q − 1 = 0.524 × 10 − 24 cm 3 / ions . After substituting all these values into Equation (9), we have new equation as

α 0 2- ( n ) = [ 8.953 × ( n 2 − 1 n 2 + 2 ) − 0.0448 ] × 0.524 × 10 − 24 (12)

The values of n and (α_02- (n)) for a borosilicate 7059 glass [using Equation (12)] were measured from 1.5296 to 1.5281 and 1.4329 to 1.4288, respectively over the temperature range 295 - 473 K using ellipsometer at λ = 633.8 nm. The values of n and (α_02- (n)) relating to borosilicate 7059 glass were respectively measured from 1.5283 to 1.5281 and 1.4297 to1.4287 over the temperature range 297 - 322 K using Abbe refractometer at λ = 589.3 nm.

Similarly, optical band gap based oxide ion polarizability of any silicate glass can be calculated using the following relation [63] [64]

α 0 2- ( E g ) = [ ( V m 2.52 ) ( 1 − E g 20 ) − ∑ α i ] q − 1 (13)

Using all the values of the optical parameters as mentioned above, the respective relations regarding silica, soda lime, and borosilicate 7059 glasses are printed as:

α 0 2- ( E g ) = [ 8.997 × ( 1 − E g 20 ) − 0.033 ] × 0.504 × 10 − 24 (14)

α 0 2- ( E g ) = [ 9.42 × ( 1 − E g 20 ) − 0.1153 ] × 0.593 × 10 − 24 (15)

α 0 2- ( E g ) = [ 8.953 × ( 1 − E g 20 ) − 0.0448 ] × 0.524 × 10 − 24 (16)

In the case of silica glass, the optical band gap (E_g) using Equation (14) was measured as 9.8 eV at room temperature and it increased to 9.81 at 373 K. The oxide ion polarizability of silica glass α_o2- (E_g) using Equation (14) was measured from 1.3427 to 1.3408 over the temperature range 295 - 373 K using ellipsometer at λ = 633.8 nm. The values of optical band gap relating to silica glass were measured from 9.59 to 9.592 eV over the temperature range 297 - 322 K using Abbe refractometer at λ = 589.3 nm, and the values of α_o2- (E_g) relating to silica glass were measured from 1.3766 to 1.3764 using Abbe refractometer over the same temperature range and at the same wavelength range.

For soda glass, E_g was measured from 9.845 to 9.88 eV over the temperature range 295 - 427 K using ellipsometer at λ = 633.8 nm, and the oxide ion polarizability of soda lime silicate glass using Equation (15) was measured from 1.6014 to 1.5941 using ellipsometer over the same temperature range and at the same wavelength. The values of optical band gap and α_o2- (E_g) relating to soda lime silicate glass were measured respectively from 9.862 to 9.870 eV and from 1.5991 to 1.5972 over the temperature range 298 - 322 K using Abbe refractometer at λ = 589.3 nm. Similarly, the values of optical band gap and α_o2- (E_g) relating to borosilicate 7059 glass [using Equations (8) and (16)] were measured respectively from 9.56 to 9.58 eV and from 1.4223 to 1.4193 over the temperature range 295 - 473 K using elipsometer at λ = 633.8 nm. The values of optical band gap (E_g) and α_o2- (E_g) relating to 7059 glass were measured respectively from 9.574 to 9.58 eV and from 1.4195 to 1.4191 over the temperature range 297 - 322 K using Abbe refractometer at λ = 589.3 nm. The complete generated temperature dependent data on the oxide ion polarizability regarding investigated silicate glasses are included in Tables 5-7, and are plotted in Figure 3, Figure 5 and Figure 7. It

should be noted that the values of n and (α_02- (n)) measured from both optical techniques (Ellipsometry and Abbe 60 refractometer) showed agreeable consistency. The interpretation of this data along with the data on optical basicity is given in the next section.

The theoretical optical basicity (A_th) for the materials under study can be measured using the relation [62] [63]

A t h = ∑ x i A i , (17)

where A_i is the individual optical basicity of each of the constituting oxides, and x_i is the molar concentration of the respective constituent oxide.

The optical basicity can be alternatively calculated from the relationship of basicity and molar refractivity. Duffy [65] explained that there is an intrinsic relationship between oxide ion polarizability α_O2- and optical basicity of the glass medium by the following correlation.

This equation indicates that the optical basicity increases with increasing oxide ion polarizability. The newly generated data of optical basicity using Equation (18) is shown in Tables 5-7 and plotted in Figure 4, Figure 6 and Figure 8. The values of optical basicity can also be calculated by the data of oxide ion polarizability α_O2- (E_g) [generated by optical band gap (E_g) values] using the relation suggested by Duffy [65]

A ( E g ) = 1.67 [ 1 − 1 α O 2 - ( E g ) ] . (19)

In the first step, the values of optical basicity (refractive index based) of all investigated silicate glasses are calculated theoretically and are printed as 0.48, 0.5825, and 0.5085 for the silica glass, soda lime glass, and borosilicate 7059 silicate glass, respectively. The values of optical basicity of all constituting oxides

have been taken from the references [62] [64]. In the second step, by the help of temperature dependent refractive index data (both ellipsometric and Abbe: Tables 2-4), we have measured the optical basicity values {A (n)} and {A (E_g)} of investigated silicate glasses using the Equations (18) and (19), and the obtained results are included in Tables 5-7 and are plotted in Figure 4, Figure 6 and Figure 8. The measured optical basicity values of investigated glasses at room temperature are given as A (n) = 0.4272, 0.6271, 0.5045 for the silica, soda lime silicate, and borosilicate 7059 glasses, respectively (using ellipsometry), and A (n) = 0.4586, 0.6251, 0.5018 for the silica, soda lime silicate, and borosilicate 7059 glasses, respectively using Abbe refractometer. It should be noticed that the experimental values of optical basicity A(n) are very close to the theoretically calculated optical basicity (A_th) values regarding silica, soda lime, and borosilicate 7059 glasses.

As shown in Tables 5-7, refractive index (n) is decreased from 1.5119 to 1.5111 and optical band gap (E_g) of silica glass is increased from 9.8 to 9.81 eV over the temperature range 295 to 373 K using ellipsometer; and the n-value is decreased from 1.5276 to 1.5274 and E_g is increased from 9.59 to 9.592 eV over the temperature range 297 to 322 K using Abbe refractometer. In the case of soda lime silicate glass, refractive index (n) is decreased from 1.5086 to 1.5065 and optical band gap (E_g) of soda lime glass is increased from 9.845 to 9.88 eV over the temperature range 295 to 427 K using ellipsometer; and then-value is decreased from 1.5074 to 1.5070 and E_g is increased from 9.862 to 9.870 eV over the temperature range 298 to 322 K using Abbe refractometer. The refractive index (n) associated with borosilicate 7059 glass is decreased from 1.5296 to 1.5281 and optical band gap (E_g) is increased from 9.56 to 9.88 eV over the temperature range 295 to 473 K using ellipsometer; and the n-value is decreased from 1.5283 to 1.5281 and E_g is increased from 9.574 to 9.58 eV over the temperature range 297 to 322 K using Abbe refractometer.

Figure 4, Figure 6 and Figure 8 also show that refractive index based optical basicity is decreased from 0.4272 to 0.4255 and A (E_g) is decreased from 0.4262 to 0.4245 (silica glass) over the temperature range 295 - 373 K using ellipsometer; A (n) is decreased from 0.4586 to 0.4582 and A (E_g) is decreased from 0.4569 to 0.4567 over the temperature range 297 - 322 K using Abbe refractometer. In the case of soda lime silicate, A(n) is decreased from 0.6271 to 0.6232 and A (E_g) is decreased from 0.6269 to 0.6224 over the temperature range 295 - 427 K using ellipsometer; A (n) is decreased from 0.6251 to 0.6242 and A (E_g) is decreased from 0.6256 to 0.6243 over the temperature range 298 - 322 K using Abbe refractometer. The value of A (n) associated with borosilicate 7059 glass is decreased from 0.5045 to 0.5012 and A (E_g) is decreased from 0.4958 to 0.4933 over the temperature range 295 - 473 K using ellipsometer; A (n) is decreased from 0.5018 to 0.5010 and A (E_g) is decreased from 0.4935 to 0.4930 over the temperature range 297 - 322 K using Abbe refractometer.

Here, let me interpret the reported data on oxide ion polarizability and optical basicity regarding silicate glasses briefly as follows.

Figures 3-8 show that the optical band gap (E_g) value of silicate glasses is increased as temperature is increased. Such an increase can be explained by suggesting that the non-bridging oxygen (NBO) ions content decreases and leading to an increase in the value of E_g. Generally, the less polarizable cations in the glass matrix does not cause effective retardation of the light propagation through the vitreous network to lead to an increase in the refractive index (n). It is also very clear from Figure 3, Figure 5 and Figure 7 that both of refractive index and energy band gap based oxide ion polarizability have the same decreasing trend as the temperature increases. The decreasing trend occurs due to decreasing amount of non-bridging oxygen (NBO), and that trend is due to small single bond strength and small polarizability associated with the silicate glass system.

Next, the disagreement between A_th and experimental basicity value might occur as a result of significant structural changes such as change in coordination number. It can be clearly seen from the obtained values of optical basicity (Figure 4, Figure 6 and Figure 8) that the optical basicity on the basis of n and E_g is decreased as temperature is increased. The decreasing trend in both optical basicity values indicates that the glasses prepared are acidic in nature and have very small amount of polarizability. The decrease in the optical basicity values (due to increase in temperature) is due to decreasing negative charge on the oxygen atoms that lead to decreasing covalency in the cation-oxygen bonding associated with the silicate glasses [66].

So low values of optical basicity and of oxide ion polarizability [67] [68] [69] suggest that the silicate glasses are not novel glasses (optical functional glasses) for non-linear optical (NLO) devices or for three dimensional displays [70] [71] [72] [73] and biological systems [74]. However, any change of oxygen bonding in the glass network, for instance, the formation of non-bridging oxygen, can change the characteristic absorption edge leading to an increase in both the electronic and oxide ion polarizability in the network for NLO applications.

Since any methodology such as atomic force microscopy for the purpose to evaluate the electronegativity of any material (or any chemical compound) cannot take into account the real crystal structure of the material, i.e., it does not estimate the real distances of the chemical bonds in the structure under consideration. In contrast oxide ion polarizability and optical basicity are based on the experimentally obtained materials constants such as refractive index or energy gap which closely are related to the real electronic structure of the oxides. So, we have measured the values of electronegativity of silicate glasses by using the experimental data on oxide ion polarizability and optical basicity being generated by the reported data on ellipsometer and Abbe refractometer over the temperature range 295 - 473 K.

There are many empirical models in the literature [75] [76] [77] [78] [79] which relate electronegativity to oxide ion polarizability or to optical basicity of a material, but the values of electronegativity, or of oxide ion polarizability [α_O2- (n)] or of optical basicity of silicate glasses calculated by most of the models seem to be too large. So, we have followed the following approach for this problem.

According to Reddy et al. [76], the following empirical relation between oxide ion polarizability and average electronegativity is as follows:

α O 2 - ( n ) = 4 . 624 − 0. 7569 ζ a v , (20)

where, ζ_av is the average electronegativity of the material (or glass).

It is with great regret that this equation is not accurate to calculate electronegativity of a glass and so it needs some amendment. Accordingly a modified formula with a minor change in Equation (20) can be rewritten as the following:

α O 2 - ( n ) = 4 . 624 − 0. 6430 ζ a v (21)

This new Equation (21) measures the values of electronegativity of silicate glasses under study which are in agreement with the values of electronegativity as measured by other researchers. We have also developed our own model known as Zahid model correlating oxide ion polarizability and electronegativity and that model now exists as

0.92 ζ a v = 6.039 − α O 2 - ( n ) (22)

The values of electronegativity of silicate glasses as measured by Equation (21) are in good agreement with the values measured using Equation (22). All the values of electronegativity measured using Equations (21) and (22) are included in Tables 8-10, and are plotted in Figures 9-14.

Similarly, in the case of optical basicity and electronegativity, we have only followed the model by Reddy [76] [77] who have derived the following empirical relationship for the refractive index based optical basicity, A (n) associated with the electronegativity of a material:

A ( n ) = 1.59 − 0.2279 ζ 1 a v , (23)

where ζ 1 a v is the average electronegativity of the material. This formulation is very suitable for the silicate glasses. Here, we have also established the empirical relation between optical basicity and average electronegativity known as Zahid model and that exists as:

2 A ( n ) = ζ a v − 0.85 (24)

The values of electronegativity using Zahid model [Equation (24)] are also in good agreement with the values measured using other models [Equation (23)]. All the values of electronegativity measured using Equation (23) and Equation (24) are tabulated in Tables 8-10, and are plotted in Figures 9-17.

Figures 9-17 show that for a silica glass, both the refractive index based optical basicity.

α_O2- (n) and A (n) are decreased from 1.3438 to 1.3420 and from 0.4272 to 0.4255, respectively; while the values of (ζ_1av) calculated) using Zahid model and other models on the base of α_O2- (n) are increased from 5.1035 to 5.1054 and from 5.1014 to 5.1042, respectively; and are increased from 5.5317 to 5.5504 and from 5.1022 to 5.1097 on the base of A (n), respectively over the temperature range 295 - 373 K using ellipsometer. Both the refractive index based optical basicity α_O2- (n) and A (n) relating to silica glass are decreased from 1.3786 to 1.3782 and from 0.4586 to 0.4582, respectively; while the values of (ζ_1av) calculated) using Zahid model and other models on the base of α_O2- (n) are increased from 5.0657 to 5.0661 and from 5.0473 to 5.0479, respectively; and are increased from 5.2111 to 5.2149 and from 4.9645 to 4.9662 on the base of A (n), respectively over the temperature range 297 - 322 K using Abbe refractometer.

The values of α_O2- (n) and A (n) relating to soda lime glass are decreased from 1.6012 to 1.5954 and from 0.6271 to 0.6232, respectively, while the calculated values of (ζ_1av) using Zahid model and other models on the base of α_O2- (n) are increased from 4.8237 to 4.830 and from 4.7011 to 4.7101, respectively; and are increased from 4.0393 to 4.0592 and from 4.2251 to 4.2422 on the base of A (n), respectively over the temperature range 297 - 427 K using ellipsometer. Both the refractive index based optical basicity α_O2- (n) and A (n) relating to soda lime glass are decreased from 1.3786 to 1.3782 and from 0.4586 to 0.4582, respectively; while the calculated values of (ζ_1av) using Zahid model and Reddy model on the base of α_O2- (n) are increased from 5.0657 to 5.0661 and from 5.0473 to 5.0479, respectively; and are increased from 5.2111 to 5.2149 and from 4.9645 to 4.9662 on the base of A (n), respectively over the temperature range 297 - 322 K using Abbe refractometer.

In the case of borosilicate 7059 glass, both α_O2- (n) and A (n) are decreased from 1.4329 to 1.4288 and from 0.5045 to 0.5012, respectively; while the values of electronegativity (ζ_1av) calculated on the base of α_O2-(n) using Zahid model and other models, are increased from 5.0066 to 5.0111 and from 4.9628 to 4.9692, respectively; and are increased from 4.8143 to 4.8404 and from 4.7631 to 4.7775, respectively, measured on the base of A (n) over the temperature range 295 - 473 K using ellipsometer. Both the refractive index based optical basicity α_O2-(n) and A (n) relating to borosilicate 7059 glass are decreased from 1.4297 to 1.4288 and from 0.5018 to 0.5017, respectively; while the calculated values of (ζ_1av) using Zahid model and Reddy model on the base of α_O2-(n), are increased from 5.0101 to 5.0111 and from 4.9678 to 4.9692, respectively, and are increased from 4.8357 to 4.8420 and from 4.7749 to 4.7784 on the base of A (n), respectively over the temperature range 297 - 322 K using Abbe refractometer.

Generally, as the difference in electronegativity between any two elements within a chemical compound approaches zero, the bond becomes less ionic and more covalent. As a difference of electronegativity exceeds zero and approaches 1.7, the bond becomes more polar covalent, and if the difference gets increasingly larger than 1.7, a bond between any two elements is more likely to be ionic [80] [81].

Since the calculated values of electronegativity are found in the range 4.0393 - 5.5504 for the silicate glasses (silica, soda lime, and borosilicate 7059), so from the above analysis all these glasses have an ionic character.