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Theoretical analysis of constants of elasticity of lead calcium alumino-borosilicate glass system

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Abstract

This paper reports on the constants of elasticity of xPbO-RNa2B4O7-(100 − R − x) CAS with 0 ≤ x ≤ 50, and 50 ≤ R ≤ 75 mol % glass system (CAS is calcium alumino silicate glasses). The constants of elasticity were calculated in terms of the bond compression model and 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 to analyze the role of PbO. Young’s modulus, the packing density and dissociation energy have been calculated and analyzed according to the Makishima-Mackenzie model. The dimensionality of the glassy network has been calculated in terms of the d ratio (4C 44/C 12) and discussed in terms of the cross-link density of these glasses. C 12 = C 11−2C 44, C 11 and C 44 are the longitudinal and shear elastic constant. The results show good agreement between the experimental and theoretical data for the representation of the constants of elasticity of borosilicate glasses.

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Authors and Affiliations

  1. Physics Department, Faculty of Science, Al-Azhar University, P.O. 71452, Assiut, Egypt

    Yasser B. Saddeek

  2. Physics Department, Faculty of Engineering, the German University in Cairo (GUC), New Cairo, P.O. 11835, Egypt

    Safaa A. Bashier

  3. Civil Engineering Department, Industrial Education College, University of Beni Sweif, Beni Sweif, Egypt

    Saddek Amr Bakr

  4. Civil Engineering Department, College of Engineering and Islamic Archi., Umm Al-Qura University, Mecca, Kingdom of Saudi Arabia

    Saddek Amr Bakr

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  1. Yasser B. Saddeek
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  2. Safaa A. Bashier
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  3. Saddek Amr Bakr
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Correspondence to Yasser B. Saddeek.

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Saddeek, Y.B., Bashier, S.A. & Bakr, S.A. Theoretical analysis of constants of elasticity of lead calcium alumino-borosilicate glass system. Glass Phys Chem 38, 437–443 (2012). https://doi.org/10.1134/S1087659612050069

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