ANOVA was performed to determine which parameters were significantly affecting glass durability. Table 3 indicated that the longitudinal velocity square affected all the longitudinal modulus (p ≤ 0.05). The finding also illustrated that the shear velocity square affected the shear modulus 2 (p = 0.039) and shear modulus 3 (p = 0.004). Hence, it could be concluded that all the longitudinal modulus, shear modulus 2 and shear modulus 3 were the parameters that produced quality glass durability. Duncan's post hoc tests revealed that there was a significant difference between some pairs of means of glass properties (Tables 3, 4 and 5). For longitudinal velocity square factor, the values of longitudinal modulus 1 have been observed to have ranged from (61.17 ± 1.42) to (66.97 ± 2.52) between erbium concentrations (Table 2). The highest mean value of longitudinal modulus 1 was found at 0.05 erbium concentration and the lowest at 0.02. The longitudinal modulus 1 was significantly different between concentrations of (0.02, 0.03, 0.01); (0.01, 0.04) and 0.05 (Tables 3, 4 and 5). Longitudinal modulus 2 showed a statistically significant increase in erbium concentrations from (60.90 ± 1.41) to (65.99 ± 2.48) (p≤0.05) (Table 2). The longitudinal modulus 2 was significantly different between (0.01, 0.02); (0.02, 0.03, 0.04) and (0.03, 0.04, 0.05 (Tables 3, 4 and 5). The same trend can be seen for longitudinal modulus 3. The erbium concentrations increased from (62.46 ± 1.45) to (68.09 ± 2.56) (p≤0.05) (Table 2). The highest mean erbium concentration for longitudinal modulus 3 was recorded at 0.05. The value of 0.05 concentration (subset 3) was not in the same subset as subsets 1 and 2. Therefore, 0.05 concentration was significantly different from 0.01, 0.02, 0.03 and 0.04 concentrations (Tables 3, 4 and 5). The mean values between erbium concentrations for longitudinal modulus 4 and 5, from (60.73 ± 1.41) to (55.62 ± 2.09) and from (58.86 ± 1.36) to (59.73 ± 2.24) respectively (P≤0.05) (Table 2). The lowest mean value was recorded at 0.05 concentration (subset 1) for longitudinal modulus 4 and 0.05 concentration was significant different from 0.01, 0.02, 0.03 and 0.04 concentrations as in subsets 2 and 3 (Tables 3, 4 and 5). For Longitudinal modulus 5, the erbium concentrations were significantly different between (0.02, 0.01, and 0.05); (0.05, 0.04) and (0.04, 0.03) (Tables 3, 4 and 5). For shear velocity square factors, the mean values for shear modulus 2 and 3 were observed to be fluctuated between erbium concentrations from (20.41 ± 0.47) to (20.42 ± 0.77) and from (20.17 ± 0.47) to (20.39 ± 0.77) respectively (P≤0.05) (Table 2). The 0.02 concentration value for shear modulus 2 was significantly different from 0.01, 0.03, 0.04 and 0.05 concentrations. Therefore, it was placed in one subset (subset 1) while other concentrations in another subset (subset 2) (Tables 3, 4 and 5). For shear modulus 3, the erbium concentrations were significantly different between (0.03, 0.02); (0.02, 0.04, 0.01) and (0.04, 0.01, 0.05) (Tables 3, 4 and 5). Therefore, there were 3 subsets produced (Tables 3, 4 and 5).
The analysis extended to the means plot in determining the optimum or the best condition for produced a quality glass durability. Figure 2 depicted that the average Longitudinal Modulus 1 was maximized when the Longitudinal Velocity Square 1 was 12.202 and the erbium concentration was 0.05. Figure 3, on the other hand showed that the optimum level of average Longitudinal Modulus 2 was reached at Longitudinal Velocity Square 2 of 12.025 and erbium concentration of 0.05. It was also found that the best condition that could maximize the average of Longitudinal Modulus 3 was when the Longitudinal Velocity Square 3 was 12.406 and the erbium concentration was 0.05 (Figure 4). Meanwhile, in Figure 5, it could be seen that the Longitudinal Velocity Square 4 of 11.586 (erbium concentration – 0.03) could maximize the average of Longitudinal Modulus 4. Based on Figure 6, the best condition that could maximize the average of Longitudinal Modulus 5 was Longitudinal Velocity Square 5 of 11.637 with erbium concentration of 0.03. In additional, the finding presented that the best condition that could maximize the average of Shear Modulus 2 was Shear Velocity Square 5 of 3.805 with erbium concentration of 0.03 (Figure 7). Figure 8 revealed that the best condition that could maximize the average of Shear Modulus 3 was when the Shear Velocity Square 5 was 3.715 at erbium concentration of 0.05 .
As has been discussed, (p≤0.05) in statistics sight provide the most significant data to be applied. Effective prediction made for all longitudinal modulus, shear modulus 2 and shear modulus 3 can be strongly related to the respect of longitudinal and shear velocities, originally. Before longitudinal velocities been ruled by two, the original longitudinal modulus has acted as initial data to produce good values for longitudinal modulus. All the values of longitudinal velocities in the materials perspective based on data statistic provided are the values to produce glass that can withstand pressure longitudinally or called as longitudinal modulus. Meanwhile, shear modulus 2 is predicted having the most significant value when amount of shear velocity 2 has been applied to the glass samples. Therefore, glass samples are able to withstand the pressure in a shear and longitudinal directions as compared and depicted in Figure 9 among all the elastic moduli. Figures 9 and 10 depict the image of the exerted force of elastic moduli and Poisson’s ratio act on the glass samples.
The longitudinal and shear velocities are the other name of ultrasonic velocities. It is strongly related to the creation of non-bridging and bridging oxygen within the glass system. Kannapan et al., (2009)  has determined that the small values of ultrasonic velocity are attributed to the small amount of electronegativity of element that causes the network to form a weak bond within the glass structure and allow easy creation of non-bridging oxygen. In this case, erbium oxide with the smallest electronegativity, 1.24 has less capability for the attraction of the atoms as compared to zinc (1.65) and tellurium (2.1). This occurrence will eventually create weaker bond, and this is predicted to happen during execution of shear wave throughout the experiment when erbium concentration is 0.01, 0.03, 0.04 and 0.05. Consequently, the glass network will loosen up and create more free spaces between the atoms which will cause the ultrasonic wave to be transmitted slower and decrease its velocity.
Besides that, the presence of erbium oxide in the glass series proves the ability of the elements to act as a glass modifier that modify the glass structure in the glass system. This condition will cause a decrease in shear velocity. Saddeek (2004)  had mentioned that the inclusion of erbium oxide would modify the glass structure by splitting the Te-O-Te bond and promote the conversion of bridging oxygen into non-bridging oxygen by forming a trigonal bipyramid into a trigonal pyramid . Furthermore, the addition of erbium oxide into the glass interstices enables more ions to be opened up which will weaken the glass structure. These explain the reason for the insignificant values of all shear modulus except for shear modulus 2.
In the meantime, the replacement of lighter molecular weight of tellurium dioxide and zinc oxide by heavier molecular weight of erbium oxide will cause changes in the overall weight of the glass and promotes stronger connection between the bonds in the glass. This indirectly will be a strong indicator to conclude that all values of longitudinal modulus are significant as listed in Table 3 . They have also reported that the formation of glass network with large concentration of dopants in the interstices space would increase the molar mass of the glass sample and improve the compactness as well .
Furthermore, the increasing compactness of the glass can also cause by the close distance between the molecules where it allows the transmission of the ultrasonic wave to pass through the glass sample easier. Closer distance between the molecules will result in formation of bridging oxygen in the glass system and contributes to the improvement of the connectivity within the glass network. This is relevant and can be inferred to follow all the significant values of longitudinal modulus that can be used for the fabrication of fiber optic. Other than that, large values of ultrasonic velocities can also be supported by large packing density as mentioned by Elokr and AbouDeif, (2016) .
Parameters such as density, molar volume, longitudinal velocity, shear velocity, shear modulus 1, shear modulus 3, shear modulus 4 and shear modulus 5 were not statistically significant at 0.05 level of significant (P≥0.05) as tabulated in Table 3. The insignificant difference of means between groups can be explained by several reasons. Factor of erbium oxide, initially have affected the significance of the parameters including density, molar volume and longitudinal and shear velocities. Density and molar volume are interrelated to each other in this work where both parameters are theoretically related. Nevertheless, in this work, erbium concentration has played a role in the glass sample. The insignificance of the parameters can first be attributed to the presence of erbium oxide the glass samples. The bond length, inter-atomic spacing within the atoms, the presence of non-bridging oxygen atoms and the rearrangement of the lattice [19–21] might affect the vicinity of the glass structure. The bond length of Er atoms which is 2.26 Å is longer than the bond length of Te atoms (1.6 Å) and Zn atoms (1.42 Å). The increase in the bond length of the dopants will enhance the inter-atomic spacing between the atoms which can influence the escalation of the molar volume in the glass sample  that produce numbers of non-bridging oxygen that causes the bond to break. Therefore, the spaces between the glasses are growing exponentially and more excess free volume are formed . Numbers of bridging oxygen can be formed by the formation of more tellurite networks of trigonal pyramid compared to trigonal bipyramid . In addition, the increment of the molar volume can also be predicted by large d-spacing obtained by XRD spectra.
Proper thickness with flat parallel surface of the glass sample is another crucial factor to be discussed. For elastic measurement, the thickness is required to be thicker and both surface of the glass sample must be as parallel as possible. This is to ensure the transmission of ultrasonic wave can propagate smoothly in the glass in order to obtain the smooth wave form. Due to the thinning of the glass sample and less parallel surface of the glass which actually should be equal or more than 5 mm, the ultrasonic wave was most probably can transmit in the glass sample unevenly making the obtained outcome not significant to be used.
Therefore, based on the statistical data been compared with physical data, some values of the parameters were highlighted and predicted to be used as indicator for the application. Table 6 list parameter estimates for the significant factors that will produce an efficient fiber optic durability.
Values of significant parameters in materials perspective based on statistics sight
Longitudinal velocity square (m2/s2)
Longitudinal modulus (GPa)
Shear velocity square (m2/s2)
Shear modulus (GPa)
10130.0 – 12410.0
50.45 – 76.16
3480.0 – 3840.0
17.50 – 24.05