## 3 Results and Discussion  
### Density and Malar Volume  
Density of glass is a property of interest where it reflects any structural variations in a glass network, and the measured density of a glass is usually used to calculate molar volume. Density was measured for different M(PO\({}_{3}\))\({}_{n}\) contents in (70-x)V\({}_{2}\)O\({}_{5}\)-5 ZnO-22 BaO-3B\({}_{2}\)O\({}_{3}\)-xM(PO\({}_{3}\))\({}_{n}\) (mol%) (where M = Al, Mg mol%, n = 3, 2, respectively) a glass system. Figure 2a shows that the density of (70-x)V\({}_{2}\)O\({}_{5}\)-5 ZnO-22 BaO-3B\({}_{2}\)O\({}_{3}\)-xM(PO\({}_{3}\))\({}_{n}\) glass system (mol%) decreased from 3.53 g/cm\({}^{3}\) to 3.43 g/cm\({}^{3}\) and 3.25 g/cm\({}^{3}\) with an increase in Mg(PO\({}_{3}\))\({}_{2}\) and Al(PO\({}_{3}\))\({}_{3}\) contents up to 15 mol%, respectively. In other word, a reduction of density for substituting 15 mol% Mg(PO\({}_{3}\))\({}_{2}\) and 15 mol% Al(PO\({}_{3}\))\({}_{3}\) instead of V\({}_{2}\)O\({}_{5}\) was found to be 3.36% and 8.49%, respectively. Generally, variation of density can be easily explained by molecular weight and atomic density, i.e., as the elements of the lower molecular weight and atomic density were replaced with the elements with a heavier molecular weight and atomic density, the density of the glass system would be increased. Several studies reported these trends, i.e., the increase of the density in the P\({}_{2}\)O\({}_{5}\)-Al\({}_{2}\)O\({}_{3}\)-BaO-La\({}_{2}\)O\({}_{3}\) and ZnO-B\({}_{2}\)O\({}_{3}\)-P\({}_{2}\)O\({}_{5}\)-TeO\({}_{2}\) glass system by replacing elements with those of a heavier molecular weight [13; 14]. Our current results on density are in opposition to this trend. To analyze the variation of the density in terms of atomic density in the current glass system, we compared the atomic density among the three elements, i.e., V\({}_{2}\)O\({}_{5}\), Al(PO\({}_{3}\))\({}_{3}\), Mg(PO\({}_{3}\))\({}_{2}\) (atomic density: 3.36, 2.78, 2.74, respectively). Replacement with a relatively lighter atomic density coincided with the decreasing trend of density. However, although the atomic densities of Mg(PO\({}_{3}\))\({}_{2}\) and Al(PO\({}_{3}\))\({}_{3}\) are very similar, the reduction widths of the two values of density could not be explained. In other words, discussion of density based on molecular weight and atomic density could not be completely applied to all glass systems. The molar volume (\(V_{m}\)) was calculated using Equation (1) as shown below [15]:  
\[V_{m}=\frac{M}{d}\Big{(}in\ \mathrm{cm^{3}mol^{-1}}\Big{)} \tag{1}\]  
where \(M\) is the molar mass and \(d\) is the density of the glass. As shown in Figure 2b, the molar volume was plotted as a function of xM(PO\({}_{3}\))\({}_{n}\) (where M = Al, Mg mol%, n = 3, 2, respectively) in the (70-x)V\({}_{2}\)O\({}_{5}\)-5 ZnO-22 BaO-3B\({}_{2}\)O\({}_{3}\)-xM(PO\({}_{3}\))\({}_{n}\) (mol%) glass system. It was founded that molar volume increased from 47.39 cm\({}^{3}\)/mol to 49.05 cm\({}^{3}\)/mol and 55.60 cm\({}^{3}\)/mol, with an increase in Mg(PO\({}_{3}\))\({}_{2}\) and Al(PO\({}_{3}\))\({}_{3}\) contents up to 15 mol%, respectively. The basic building units of a phosphate glass system are the PO\({}_{4}\) tetrahedra. These tetrahedrons are connected through bridging oxygen to form different phosphate structures. The chains and rings are linked through terminal oxygen bonded with the modifying cations [15]. It can be seen that the volume of M(PO\({}_{3}\))\({}_{n}\) (where M = Al, Mg, n = 3,  
Figure 2: Variation of (**a**) Density and (**b**) Molar volume with respect to M(PO\({}_{3}\))\({}_{n}\) concentration in (70-x)V\({}_{2}\)O\({}_{5}\)-5 ZnO-22 BaO-3B\({}_{2}\)O\({}_{3}\)-xM(PO\({}_{3}\))\({}_{n}\) (where M = Al, Mg, n = 3, 2, respectively, mol%) glass system. 2, respectively, mol%) is larger than that of V\({}_{2}\)O\({}_{5}\). The number of tetrahedrons in the current system is proportional to the ionic status of cation, i.e., divalent (M = Mg) and trivalent (M = Al) metal ions. A similar study by [PERSON] et al.