Glass samples have been synthesized in quaternary system based on TeO₂–oxide within composition, 85TeO₂–5Nb₂O₅–5ZnO–5Ag₂O, 68TeO₂–5Nb₂O₅–20ZnO–7Na₂O and [(75−𝑥)TeO₂–5Nb₂O₅–20ZnO–𝑥PbO, 𝑥 = 7, 18 mol%]. Structural characterization of the glasses was studied with respect to their thermal stability, refractive indices, third order nonlinear optical susceptibility, IR spectra and Vickers hardness. For four different prepared glasses, density in the range from 5.3744 to 6.0731 g.cm^-1, the glass transition temperature (𝑇_g) in the range from 326 to 350 °C and refractive indices, 𝑛, in the range from 2.1273 to 2.2123 at 435 nm and Vickers hardness, 𝐻_v, in the range from 2.91 to 3.44 GPa were determined. The value of third order nonlinear optical susceptibilities |𝜒⁽³⁾| ≈ 17.9 .10^-13 esu of glass within composition, 68TeO₂–5Nb₂O₅–20ZnO–7PbO, was measured by using degenerate four-wave mixing (DFWM).

Quaternary tellurite glasses with composition 75TeO$_2$–5WO$_3$–15Nb$_2$O$_5$–5M$_x$O$_y$ in mol%, where M$_x$O$_y$ =(Na$_2$O, Ag$_2$O, ZnO, MgO, CuO, NiO, TiO$_2$, MnO$_2$), were prepared by the normal melt-quenching method. The ultrasonic velocities (longitudinal and shear) were measured in these glasses using the pulse-echo technique at room temperature. Their elastic moduli, microhardness and Debye temperature were calculated and discussed in terms of the modifier’s ionicity and quantitatively in terms of number of bonds per unit volume and the cross-link density. In this study, the values of ultrasonic velocities, elastic moduli, Debye temperature and microhardness were found to be strongly dependent on three factors, namely: (i) modifier’s ionicity; (ii) trigonal pyramid (TeO$_3$)/trigonal bipyramid (TeO$_4$) ratio; and (iii) glass transition temperature $T_g$. We used the Makishima and Mackenzie’s model to calculate the theoretical elastic moduli and to indicatethat the experimental values were in good agreement with the theoretical values.