Glass Physics and Chemistry

, Volume 38, Issue 4, pp 373–378 | Cite as

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.


borate glasses elastic properties packing density rare-earth 


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  1. 1.
    Agnesi, A., Dallocchio, P., Pirzio, F., and Reali, G., Compact Sub-100-fs Nd: Silicate Laser, Opt. Commun., 2009, vol. 282, no. 10, pp. 2070–2073.CrossRefGoogle Scholar
  2. 2.
    Kalaycioglu, H., Cankaya, H., Ozen, G., Ovecoglu, L., and Sennaroglu, A., Lasing at 1065 nm in Bulk Nd3+-Doped Telluride-Tungstate Glass, Opt. Commun., 2008, vol. 281, no. 24, pp. 6056–6060.CrossRefGoogle Scholar
  3. 3.
    Iparraguirre, I., Azkargorta, J., Fernández-Navarro, J.M., Al-Saleh, M., Fernández, R., and Balda, J., Laser Action and Upconversion of Nd3+ in Tellurite Bulk Glass, J. Non-Cryst. Solids, 2007, vol. 353, nos. 8–10, pp. 990–992.CrossRefGoogle Scholar
  4. 4.
    Shanmuga Sundari, S., Marimuthu, K., Sivraman, M., and Surendra Babu, S., Composition-Dependent Structural and Optical Properties of Sm3+-Doped Sodium Borate and Sodium Fluoroborate Glasses, J. Lumin., 2010, vol. 130, no. 7, pp. 1313–1319.CrossRefGoogle Scholar
  5. 5.
    Pisarska, J., Pisarski, W., and Ryba-Romanowski, W., Laser Spectroscopy of Nd3+ and Dy3+ Ions in Lead Borate Glasses, Opt. Laser Technol., 2010, vol. 42, no. 5, pp. 805–809.CrossRefGoogle Scholar
  6. 6.
    Ishii, M., Kuwano, Y., Asai, T., Asaba, S., Kawamura, M., Senguttuvan, N., Hayashi, T., Kobayashi, M., Nikl, M., Hosoya, S., Sakai, K., Adachi, T., Oku, T., and Shimizu, H.M., Boron-Based Oxide Scintillation Glass for Neutron Detection, Nucl. Instrum. Methods Phys. Res., Sect. A, 2005, vol. 537, nos. 1–2 (special issues), pp. 282–285.CrossRefGoogle Scholar
  7. 7.
    Saddeek, Y., Structural and Acoustical Studies of Lead Sodium Borate Glasses, J. Alloys Compd., 2009, vol. 467, nos. 1–2, pp. 14–21.CrossRefGoogle Scholar
  8. 8.
    Doweidar, H. and Saddeek, Y., FTIR and Ultrasonic Investigations on Modified Bismuth Borate Glasses, J. Non-Cryst. Solids, 2009, vol. 355, no. 6, pp. 348–354.CrossRefGoogle Scholar
  9. 9.
    Saddeek, Y., Synthesis and Properties of MoO3-V2O5-PbO Glasses, Philos. Mag., 2009, vol. 89, no. 26, pp. 2305–2320.CrossRefGoogle Scholar
  10. 10.
    Saddeek, Y.B., Aly, K.A., Dahshan, A., El Kashef, I.M., Optical Properties of the Na2O-B2O3-Bi2O23-MoO3 Glasses, J. Alloys Compd., 2010, vol. 494, nos. 1–2, pp. 210–213.CrossRefGoogle Scholar
  11. 11.
    Lavin, V., Babu, P., Jayasankar, C., Martin, I., and Rodriguez, V., On the Local Structure of Eu3+ Ions in Oxyfluoride Glasses: Comparison with Fluoride and Oxide Glasses, J. Chem. Phys., 2001, vol. 115, no. 23, pp. 10935–10944.CrossRefGoogle Scholar
  12. 12.
    Saddeek, Y., Gaafar, M., and Bashier, S., Structural Influence of PbO by Means of FTIR and Acoustics on Calcium Alumino-Borosilicate Glass System, J. Non-Cryst. Solids, 2010, vol. 356, nos. 20–22, pp. 1089–1095.CrossRefGoogle Scholar
  13. 13.
    Saddeek, Y., Aly, K., and Bashier, S., Optical Study of Lead Borosilicate Glasses, Phys. B (Amsterdam, Neth.), 2010, vol. 405, no. 10, pp. 2407–2412.Google Scholar
  14. 14.
    Saddeek, Y., Abousehly, A., and Hussien, S., Synthesis and Several Features of the Na2O-B2O3-Bi2O3-MoO3 Glasses, J. Phys. D: Appl. Phys., 2007, vol. 40, no. 15, pp. 4674–4681.CrossRefGoogle Scholar
  15. 15.
    Bridge, B., Patel, N., and Waters, D., On the Elastic Constants and Structure of the Inorganic Oxide Glasses, Phys. Status Solidi A, 1983, vol. 77, no. 2, pp. 655–668.CrossRefGoogle Scholar
  16. 16.
    Bridge, B. and Higazy, A., Model of the Compositional Dependence of the Constants of Elasticity of Polycomponent Oxide Glasses, Phys. Chem. Glasses, 1986, vol. 27, no. 1, pp. 1–14.Google Scholar
  17. 17.
    Makishima, A. and Mackenzie, J., Direct Calculation of the Young’s Moidulus of Glass, J. Non-Cryst. Solids, 1973, vol. 12, no. 1, pp. 35–45.CrossRefGoogle Scholar
  18. 18.
    Makishima, A. and Mackenzie, J., Calculation of Bulk Modulus, Shear Modulus, and Poisson’s Ratio of Glass, J. Non-Cryst. Solids, 1975, vol. 17, no. 2, pp. 147–157.CrossRefGoogle Scholar
  19. 19.
    Makishima, A., Tamura, Y., and Sakaino, T., Constants of Elasticity and Refractive Indices of Aluminosilicate Glasses Containing Y2O3, La2O3, and TiO2, J. Am. Ceram. Soc., 1978, vol. 61, nos. 5–6, pp. 247–249.CrossRefGoogle Scholar
  20. 20.
    Rocherulle, J., Ecolivet, C., Poulain, M., Verdier, P., and Laurent, Y., Elastic Moduli of Oxynitride Glasses: Extension of Makishima and Mackenzie’s Theory, J. Non-Cryst. Solids, 1989, vol. 108, no. 2, pp. 187–193.CrossRefGoogle Scholar
  21. 21.
    Inaba, S., Fujino, S., and Morinaga, K., Young’s Modulus and Compositional Parameters of Oxide Glasses, J. Am. Ceram. Soc., 1999, vol. 82, no. 12, pp. 3501–3507.CrossRefGoogle Scholar
  22. 22.
    Hwa, L., Hsieh, K., and Liu, L., Constants of Elasticity of Low-Silica Calcium Alumino—Silicate Glasses, Mater. Chem. Phys., 2003, vol. 78, no. 1, pp. 105–110.CrossRefGoogle Scholar
  23. 23.
    Chen, C., Wu, Y., and Hwa, G., Temperature Dependence of Elastic Properties of ZBLAN Glasses, Mater. Chem. Phys., 2000, vol. 65, no. 3, pp. 306–309.CrossRefGoogle Scholar
  24. 24.
    Doweidar, H. and Saddeek, Y., Effect of La2O3 on the Structure of Lead Borate Glasses, J. Non-Cryst. Solids, 2010, vol. 356, nos. 28–30, pp. 1452–1457.CrossRefGoogle Scholar
  25. 25.
    Saddeek, Y., Yahia, I., Aly, K., and Dobrowolski, W., Spectroscopic, Mechanical, and Magnetic Characterization of Some Bismuth Borate Glasses Containing Gadolinium Ions, Solid State Sci., 2010, vol. 12, no. 8, pp. 1426–1434.CrossRefGoogle Scholar
  26. 26.
    Saddeek, Y., Structural Analysis of Alkali Borate Glasses, Phys. B (Amsterdam, Neth.), 2004, vol. 344, nos. 1–4, pp. 163–175.Google Scholar
  27. 27.
    Saddeek, Y., Structural Interpretations of Aluminosilicate Glasses, Phys. B (Amsterdam, Neth.), 2005, vol. 363, nos. 1–4, pp. 19–24.Google Scholar
  28. 28.
    Saddeek, Y., Gaafar, M., Abd El-Aal, N., and Abd ElLatif, L., Structural Analysis of Some Alkali Diborate Glasses, Acta Phys. Pol., A, 2009, vol. 116, no. 2, pp. 211–216.Google Scholar
  29. 29.
    El-Adawy, A. and Moustafa, Y., Elastic Properties of Bismuth Borate Glasses, J. Phys. D: Appl. Phys., 1999, vol. 32, no. 21, pp. 2791–2796.CrossRefGoogle Scholar
  30. 30.
    Shaaban, E., Shapaan, M., and Saddeek, Y., Structural and Thermal Stability Criteria of Bi2O3-B2O3 Glasses, J. Phys.: Condens. Matter 2008, vol. 20, no. 15, pp. 155108–155116.CrossRefGoogle Scholar
  31. 31.
    Tilocca, A., de Leeuw, N.H., and Cormack, A.N., Phys. Rev. B, 2006, vol. 73, no. 10, article 104209 (14 pages).Google Scholar
  32. 32.
    Saddeek, Y. and Abd El-Latif, L., Effect of TeO2 on the Constants of Elasticity of Sodium Borate Glasses, Phys. B (Amsterdam, Neth.), 2004, vol. 348, nos. 1–4, pp. 475–484.Google Scholar
  33. 33.
    Saddeek, Y., Elastic Properties of Gd3+-Doped Tellurovanadate Glasses Using Pulse-Echo Technique, Mater. Chem. Phys., 2005, vol. 91, no. 1, pp. 146–153.CrossRefGoogle Scholar
  34. 34.
    El-Mallawany, R.A.H., Tellurite Glasses Handbook: Physical Properties and Data, New York: CRC Press, 2002.Google Scholar
  35. 35.
    Wells, A.F., Structural Inorganic Chemistry, Oxford (United Kingdom): Oxford University Press, 1975, 4th ed.Google Scholar
  36. 36.
    Varshneya, A.K., Fundamentals of Inorganic Glasses, New York: Academic Press, 1994.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.Physics Department, Faculty of ScienceAl-Azhar UniversityAssiutEgypt

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