Correlation between the dimensionality and the constants of elasticity of rare-earth doped borate glasses

This work was devoted to explore the correlation between the dimensionality and the computed theoretically constants of elasticity of borate based glasses doped with rare-earth oxides. The dimensionality of the glassy network has been calculated in terms of the d ratio which is equal to 4 C ₄₄/K _e and discussed in terms of the cross-link density and number of network bonds per unit volume of these glasses. Constants of elasticity were calculated in terms of the bond compression model and the Makishima-Mackenzie model. The average cross-link density, the number of network bonds per unit volume, the average stretching-force constant, and the ratio of the estimated bulk modulus (K _bc) to the experimentally determined (K _e) have been calculated and discussed in terms of the bond-compression model. Young??s modulus, the packing density, and the dissociation energy have been calculated and analyzed in terms of the Makishima-Mackenzie model. The results showed that the computed elastic moduli and the dimensionality of the borate glasses containing La₂O₃ or Gd₂O₃ are strongly dependent on the concentration of the structural units of the constituent oxides and types of bonds between these units.