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Quaternary glass series of nano and micro-particles europium oxide (III), i.e. Eu2O3, of composition [{(TeO2)0.7 (B2O3)0.3}0.7 (ZnO)0.3](1-y) (EnOm)y, where EnOm is nano or micro Eu2O3 particles coded as TBZEu-NPs and TBZEu-MPs with y = 1.0–5.0 mol% was prepared by melt-quenching technique. Using the pulse-echo technique, the ultrasonic velocities of the glasses were examined. The experimental value of TBZEu-NPs longitudinal, shear, bulk, and Young's modulus ranges between 53.469 and 85.259 GPa, 21.801–24.086 GPa, 24.401–54.790 GPa, and 50.394–61.419 GPa, respectively. For the TBZEu-MPs glasses, they ranged from 46.335 to 87.365 GPa, 21.645–24.649 GPa, 17.475–54.499 GPa, and 45.959–64.260 GPa, respectively. Density and elastic properties were predicted and simulated using an artificial neural network (ANN) model. The correlation coefficients for density, elastic moduli, and Poison's ratio obtained using the ANN model range from 0.9881 to 0.9997. The fitted R-squared value is greater than 95%, and the percentage error calculated is less than 7%. The obtained results were compared to those obtained using the Makishima-Mackenzie elastic model. The prepared glass sample's physical properties and elastic constants indicate that they are sufficiently strong for laser applications.

Quaternary glass series of nano and micro-particles europium oxide (III), i.e. Eu2O3, of composition [{(TeO2)0.7 (B2O3)0.3}0.7 (ZnO)0.3](1-y) (EnOm)y, where EnOm is nano or micro Eu2O3 particles coded as TBZEu-NPs and TBZEu-MPs with y = 1.0–5.0 mol% was prepared by melt-quenching technique. Using the pulse-echo technique, the ultrasonic velocities of the glasses were examined. The experimental value of TBZEu-NPs longitudinal, shear, bulk, and Young's modulus ranges between 53.469 and 85.259 GPa, 21.801–24.086 GPa, 24.401–54.790 GPa, and 50.394–61.419 GPa, respectively. For the TBZEu-MPs glasses, they ranged from 46.335 to 87.365 GPa, 21.645–24.649 GPa, 17.475–54.499 GPa, and 45.959–64.260 GPa, respectively. Density and elastic properties were predicted and simulated using an artificial neural network (ANN) model. The correlation coefficients for density, elastic moduli, and Poison's ratio obtained using the ANN model range from 0.9881 to 0.9997. The fitted R-squared value is greater than 95%, and the percentage error calculated is less than 7%. The obtained results were compared to those obtained using the Makishima-Mackenzie elastic model. The prepared glass sample's physical properties and elastic constants indicate that they are sufficiently strong for laser applications.