Investigations of the Elastic Moduli of Er2O3 NPs Doped TeO2 – B2O3 – SiO2 Glasses using Theoretical Models


  • U. S. Aliyu Department of Physics, Faculty of Science, Federal University Lafia, Nasarawa Sate, Nigeria
  • I. G. Geidam Department of Physics, Faculty of Sciences, Yobe State University Damaturu, Nigeria
  • M. S. Otto Department of Physics, Faculty of Science, Federal University Lafia, Nasarawa Sate, Nigeria
  • M. Hussaini Department of Physics, Faculty of Sciences, Umar Suleiman College of Education Gashua, Yobe State, Nigeria


Erbium oxide, Tellurite Glass, Elastic Moduli, Poisson Ratio, Theoretical Models


Elastic moduli of {[(TeO2)0.7 (B2O3)0.3]0.8 (SiO2)0.2}1-y (Er2O3 NPs)y glasses  with y = 0.01, 0.02, 0.03, 0.04, 0.05 were studied in this work using the theoretical elastic models. The Makishima & Mackenzie, Rocherulle and bond compression models were employed for the study. In the Makishima and Mackenzie model, the packing density was calculated from the bulk glass molar weight and the bulk glass density whereas in Rocherulle model it is determined as the individual oxides. Young, shear and bulk moduli as well as the Poisson ratio were calculated for the glasses in the Makishima and Rocherulle models, while longitudinal, was calculated in addition to young, bulk and shear moduli using the bond compression model. Bond per unit volume number (nb), bulk modulus, bulk modulus ratio (Kbc/Ke), atomic ring size (?) and stretching force constant were also calculated and presented. The values of the Young, bulk and shear moduli obtained from Makishima model increased from 52.854 to 55.335 GPa, 35.754 to 39.862 GPa and 21.080 to 21.809 GPa respectively with Er2O3 NPs composition increase from 1% to 5%.. The Rocherulle model presented increasing values for Young, bulk and shear moduli as 56.910 to 58.432 GPa, 41.452 to 44.450 GPa and 22.385 to 22.809 GPa respectively with Er2O3 NPs composition increase from 1% to 5%. The bond compression model presented much higher values of the elastic moduli compared to the experimentally obtained values and showed an increasing trend as the Er2O3 NPs concentration increases. In the glass network, the atomic ring size value decreased from 0.5698 to 0.5091 nm indicating an increase in the close packing of atoms. Based on the elastic moduli values presented by all the models, Makishima and Mackenzie model presented a more reliable data and hence represents the best model for the studied glass system.  


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How to Cite

Aliyu, U. S., Geidam, I. G., Otto, M. S., & Hussaini, M. (2022). Investigations of the Elastic Moduli of Er2O3 NPs Doped TeO2 – B2O3 – SiO2 Glasses using Theoretical Models. Journal of the Nigerian Society of Physical Sciences, 4(1), 9–15.



Original Research