Skip to main content
SpringerLink
Log in

Maxwell equation for conductivity of dielectrics as the basis of direct relationship of ionic electrical conductivity and mechanical losses in glasses. New problems of physical chemistry of glass

  • Published:
Glass Physics and Chemistry Aims and scope Submit manuscript

Abstract

Use of the Maxwell equation for the conductivity of dielectrics and the theory of mechanical losses in glasses caused by ionic shifts has made it possible to calculate directly the temperature of the “ionic” maximum of mechanical losses using data on direct current conductivity. The Maxwell equation was used without changes, in the view accepted in electromagnetic theory. An intuitive physicochemical interpretation of the nature of ionic conductivity measured at constant voltage as a relaxation process was suggested. Verification of the suggestion equation’s validity was performed for one-alkali glasses in silicate, borosilicate, phosphate, borate, and germanate systems. The ratio of calculated and experimental values of the temperature of the “ionic” internal-friction maximum corresponds to 0.995 ± 0.034 and does not depend on the frequency of measurements of internal friction (it changed by four orders) or the parameters characterizing conductivity. These results also confirm the validity of the Maxwell equation for the conductivity of dielectrics. The possibility of describing the direct current ionic conductivity of glasses as a Debye relaxation transition proved in this work is a consequence of the constant voltage condition. The design of a theory for the condition of natural decay of a given potential, when the Kohlrausch relaxation regularity becomes valid, represents a principally important problem of physics and physical chemistry of disordered systems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Nemilov, S.V., Thermodynamic and Kinetic Aspects of the Vitreous State, Boca Raton, Florida, United States: CRC Press, 1995.

    Google Scholar 

  2. Greaves, G.N. and Sen, S., Inorganic Glasses, Glass-Forming Liquids, and Amorphous Solids, Adv. Phys., 2007, vol. 56, no. 1, pp. 1–166.

    Article  CAS  Google Scholar 

  3. Nemilov, S.V., Structural Relaxation in Oxide Glasses at Room Temperature, Phys. Chem. Glasses, 2007, vol. 48, no. 4, pp. 291–295.

    CAS  Google Scholar 

  4. Nemilov, S.V., Relaxation Processes in Inorganic Melts and Glasses: An Elastic Continuum Model as a Promising Basis for the Description of the Viscosity and Electrical Conductivity, Glass Phys. Chem., 2010, vol. 36, no. 3, pp. 253–285.

    Article  CAS  Google Scholar 

  5. Nemilov, S.V., Structural Aspect of Possible Interrelation between Fragility (Length) of Glass-Forming Melts and Poisson’s Ratio of Glasses, J. Non-Cryst. Solids, 2007, vol. 353, nos. 52–54, pp. 4613–4632.

    Article  CAS  Google Scholar 

  6. Nemilov, S.V., The Review of Possible Interrelations between Ionic Conductivity, Internal Friction, and the Viscosity of Glasses and Glass-Forming Melts within the Framework of Maxwell Equations, J. Non-Cryst. Solids, 2011, vol. 357, no. 4, pp. 1243–1263.

    Article  CAS  Google Scholar 

  7. Nemilov, S.V., Interrelation between the Shear Modulus and the Molecular Parameters of Viscous Flow for Glass-Forming Liquids, J. Non-Cryst. Solids, 2006, vol. 352, nos. 26–27, pp. 2715–2725.

    Article  CAS  Google Scholar 

  8. Maxwell, J.C., A Treatise on Electricity and Magnetism, Oxford: Clarendon, 1891, 3rd ed., vol. 1.

    Google Scholar 

  9. Maxwell, J.C., A Treatise on Electricity and Magnetism, Oxford: Clarendon, 1891. Translated under the title Traktat ob elektrichestve i magnetizme, Moscow: Nauka, 1989, vol. 1.

    Google Scholar 

  10. Stratton, J.A., Electromagnetic Theory, New York: McGraw-Hill, 1941.

    Google Scholar 

  11. Maxwell, J.C., On the Dynamical Theory of Gases, Philos. Trans., 1867, vol. 157, pp. 49–88.

    Article  Google Scholar 

  12. Becker, R., Theorie der Elektrizität: Band I. Einführung in die Maxwellsche Theorie der Elektrizität, Leipzig: Elfte Auflage, 1941.

    Google Scholar 

  13. Feynman, R., Leighton, R., and Sands, M, The Feynman Lectures on Physics: Volume 2: Mainly Electromagnetism and Matter, Reading: Addison-Wesley, 1964. Translated under the title Feinmanovskie lektsii po fizike: Vypusk 6. Elektrodinamika, Moscow: Editorial URSS, 2004.

    Google Scholar 

  14. Frenkel’, Ya.I., Elektrodinamika (Obshchaya teoriya), Sobranie izbrannykh trudov (Electrodynamics (The General Theory of Electricity): A Collection of Selected Works), Moscow: Academy of Sciences of the Soviet Union, 1956, vol. 1 [in Russian].

    Google Scholar 

  15. Landau, L.D. and Lifshitz, E.M., Elektrodinamika sploshnykh sred. Tom 8. Teoreticheskaya fizika, Moscow: Nauka, 1992. Translated under the title Course of Theoretical Physics: Volume 8. Electrodynamics of Continuous Media, Oxford: Butterworth-Heinemann, 1993.

    Google Scholar 

  16. Moynihan, C.T., Balitactac, N., Boone, L., and Litovitz, T.A., Comparison of Shear and Conductivity Relaxation Times for Concentrated Lithium Chloride Solutions, J. Chem. Phys., 1971, vol. 55, no. 6, pp. 3013–3019.

    Article  CAS  Google Scholar 

  17. Angell, C.A., Mobile Ions in Amorphous Solids, Annu. Rev. Phys. Chem., 1992, vol. 43, pp. 693–718.

    Article  CAS  Google Scholar 

  18. Vedishcheva, N.M., Shakhmatkin, B.A., and Wright, A.C., The Structure-Property Relationship in Oxide Glasses: A Thermodynamic Approach, Adv. Mater. Res., 2008, vols. 39–40, no. 1, pp. 103–110.

    Article  Google Scholar 

  19. Myuller, R.L., Electrical Conductivity of Solid Ion-Atom Valence Compounds. II: Experimental and Theoretical Expressions for the Molar Conductivity of Borosilicate, Zh. Tekh. Fiz., 1955, vol. 25, no. 2, pp. 246–255.

    CAS  Google Scholar 

  20. Skanavi, G.I., Fizika dielektrikov (Oblast’ slabykh polei) (The Physics of Dielectrics: The Region of Weak Fields), Moscow: Gostekhteorizdat, 1949 [in Russian].

    Google Scholar 

  21. Mazurin, O.V., Glass in a Direct Electric Field, in The Structure of Glass: Volume 4. Electrical Properties and Structure of Glass, Mazurin, O.V., Ed., New York: Consultant Bureau, 1965, pp. 5–55.

    Google Scholar 

  22. Glasstone, S., Laidler, K., and Eyring, H., The Theory of Rate Processes, New York: McGraw-Hill, 1941.

    Google Scholar 

  23. Nemilov, S.V., Kinetics of Elementary Processes in the Condensed State: I. Relationship of the Statistical and Quantum Models of Electrical Conduction with the Kinetic Dushman Equation, Zh. Fiz. Khim., 1967, vol. 41, no. 8, pp. 1934–1941.

    CAS  Google Scholar 

  24. Nemilov, S.V., On the Relationship between the Statistical and Quantum Models of Electrical Conduction in Solids, in Stekloobraznoe sostoyanie. Elektricheskie svoistva stekla. Trudy Vsesoyuznogo simpoziuma (Proceedings of the All-Union Symposium on the Vitreous state: Electrical Properties of Glass), Yerevan: AN ArmSSR, 1969, vol. 5,issue 1, pp. 61–68.

    Google Scholar 

  25. Nemilov, S.V., Entropy of Activation and the Nature of Ionic and Atomic Displacements in the Glass, Tr. Gos. Opt. Inst., 1972, vol. 39, no. 170, pp. 107–124.

    CAS  Google Scholar 

  26. Polanyi, M. and Wigner, E., Uber die Interferenz von Eigenschwingungen als Ursache von Energieschwankungen und chemischer Umsetzungen, Z. Phys. Chem., Abt. A, 1928, vol. 139, pp. 439–452.

    CAS  Google Scholar 

  27. Hanggi, P., Talkner, P., and Borkovec, M., Reaction-Rate Theory: Fifty Years after Kramers, Rev. Mod. Phys., 1990, vol. 62, no. 2, pp. 251–341.

    Article  Google Scholar 

  28. Nemilov, S.V., Theoretical and Experimental Justification of the Method for Measurement of the Viscosity of Glasses on the Basis of the Indentation of Solid Indenters into a Plate, Fiz. Khim. Stekla, 1977, vol. 3, no. 2, pp. 148–157.

    CAS  Google Scholar 

  29. Zdaniewsky, W.A., Rindone, G.E., and Day, D.E., The Internal Friction of Glasses, J. Mater. Sci., 1979, vol. 14, pp. 763–775.

    Google Scholar 

  30. Shelby, J.E. and Day, D.E., Mechanical Relaxation in Mixed-Alkali Silicate Glasses: Results, J. Am. Ceram. Soc., 1969, vol. 52, no. 4, pp. 169–177.

    Article  CAS  Google Scholar 

  31. Roling, B. and Ingram, M.D., Analysis of Mechanical Losses Due to Ion-Transport Processes in Silicate Glasses, Phys. Rev. B: Condens. Matter, 1998, vol. 57, no. 22, pp. 14192–14199.

    Article  CAS  Google Scholar 

  32. Postnikov, V.S., Fizika i khimiya tverdogo sostoyaniya (The Physics and Chemistry of the Solid State), Moscow: Metallurgiya, 1978 [in Russian].

    Google Scholar 

  33. Knödler, D., Stiller, O., and Dietrich, W., Dynamic Structure Factor and Acoustic Attenuation in Disordered Solid Electrolytes, Philos. Mag. B, 1995, vol. 71, no. 4, pp. 661–667.

    Article  Google Scholar 

  34. Roling, B., Happe, A., Ingram, M.D., and Funke, K., Interrelation between Different Mixed Cation Effects in the Electrical Conductivity and Mechanical Loss Spectra of Ion Conducting Glasses, J. Phys. Chem. B, 1999, vol. 103, no. 20, pp. 4122–4127.

    Article  CAS  Google Scholar 

  35. Khar’yuzov, V.A. and Zorin, A.P., On the Calculation of the Dielectric Permittivity of Glass Composition, in Elektronnaya tekhnika. Seriya 14. Materialy (Neorganicheskie dielektriki) (Electronic Engineering: Series 14. Materials (Inorganic Dielectrics)), 1967, no. 3, pp. 65–69.

  36. Mazurin, O.V., Electrical Properties of Glasses, in Steklo. Spravochnik (A Reference Book on Glasses), Pavlushkin, N.M., Ed., Moscow: Stroiizdat, 1973, pp. 46–59 [in Russian].

    Google Scholar 

  37. SciGlass-7.0: Database, Shrewsbury, Massachusetts, United States: Institute of Theoretical Chemistry, 2005.

  38. Roling, B. and Ingram, M.D., Mixed Alkaline-Earth Effect in Ionic Conducting Glasses, J. Non-Cryst. Solids, 2000, vol. 265, nos. 1–2, pp. 113–119.

    Article  CAS  Google Scholar 

  39. Dyre, J.C., Maass, P., Roling, B., and Sidebottom, D.L., Fundamental Questions Relating to Ion Conduction in Disordered Solids, Rep. Prog. Phys., 2009, vol. 72, no. 1, pp. 1–15.

    Google Scholar 

  40. Rötger, H., Neuere Erkenntnisse über das Relaxationsverhalten der Glaser, Silikattechnik, 1959, vol. 10, no. 2, pp. 57–62.

    Google Scholar 

  41. De Waal, H., Internal Friction of Sodium Disilicate Glass after Ion Exchange, Phys. Chem. Glasses, 1969, vol. 10, no. 3, pp. 108–116.

    Google Scholar 

  42. Sokolov, I.A., Tarlakov, Yu.P., Ustinov, N.Yu., Valova, N.A., and Pronkin, A.A., Influence of the Nature of an Alkali Cation on the Electrical Conductivity of Vitreous MePO3 (Me = Li, Na, or K), Glass Phys. Chem., 2003, vol. 29, no. 3, pp. 305–309.

    Article  CAS  Google Scholar 

  43. Ngai, K.L., A Review of Critical Experimental Facts in Electrical Relaxation and Ionic Diffusion in Ionically Conducting Glasses and Melts, J. Non-Cryst. Solids, 1996, vol. 203, pp. 232–245.

    Article  CAS  Google Scholar 

  44. Volchek, A.O., Gusarov, A.I., and Dotsenko, A.V., Mechanisms of Nonexponential Relaxation in the Glass Transition Region, Glass Phys. Chem., 1996, vol. 22, no. 4, pp. 301–306.

    CAS  Google Scholar 

  45. Silescu, H., Heterogeneity at the Glass Transition: AReview, J. Non-Cryst. Solids, 1999, vol. 243, nos. 2–3, pp. 81–108.

    Article  Google Scholar 

  46. Williams, G., Molecular Motion in Glass-Forming Liquids, J. Non-Cryst. Solids, 1991, vol. 131–132, pp. 1–12.

    Article  Google Scholar 

  47. Nemilov, S.V., Physical Ageing of Silicate Glasses, Glass Sci. Technol., 2003, vol. 76, no. 1, pp. 33–42.

    CAS  Google Scholar 

  48. Ngai, K.L., Universality of Low-Frequency Fluctuation, Dissipation, and Relaxation Properties of Condensed Matter: Part 1, Commun. Solid State Phys., 1979, vol. 9, no. 4, pp. 127–140.

    CAS  Google Scholar 

  49. Ngai, K.L., Universality of Low-Frequency Fluctuation, Dissipation, and Relaxation Properties of Condensed Matter: Part 2, Commun. Solid State Phys., 1979, vol. 9, no. 5, pp. 141–155.

    Google Scholar 

  50. Ngai, K.L., Rajagopal, A.K., and Teitler, S., Slowing Down of Relaxation in a Complex System by Constrained Dynamics, J. Chem. Phys., 1988, vol. 88, no. 8, pp. 5086–5094.

    Article  CAS  Google Scholar 

  51. Palmer, R.G., Stein, D.L., Abrahams, E., and Anderson, P.W., Models of Hierarchically Constrained Dynamics for Glassy Relaxation, Phys. Rev. Lett., 1984, vol. 53, no. 10, pp. 958–961.

    Article  Google Scholar 

  52. Van Kampen, N.G., Stochastic Processes in Physics and Chemistry, Amsterdam: North-Holland, 1995.

    Google Scholar 

  53. Chamberlin, R.A. and Kingsbury, D.W.J., Non-Debye and Non-Arrhenius Primary Response of Liquids, Glasses, Polymers, and Crystals, J. Non-Cryst. Solids, 1994, vols. 172/174, pp. 318–326.

    Article  Google Scholar 

  54. Chamberlin, R.A., Böhmer, R., Sanchez, E., and Angell, C.A., Signature of Ergodicity in the Dynamic Response of Amorphous Systems, Phys. Rev. B: Condens. Matter., 1992, vol. 46, no. 9, pp. 5787–5790.

    Article  Google Scholar 

  55. Chamberlin, R.A., Non-Arrhenius Response of Glass-Forming Liquids, Phys. Rev. B: Condens. Matter, 1993, vol. 48, no. 21, pp. 15638–15643.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg State University of Information Technologies, Mechanics, and Optics, Birzhevaya liniya, 4, St. Petersburg, 199034, Russia

    S. V. Nemilov

Authors
  1. S. V. Nemilov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. V. Nemilov.

Additional information

Original Russian Text © S.V. Nemilov, 2012, published in Fizika i Khimiya Stekla.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nemilov, S.V. Maxwell equation for conductivity of dielectrics as the basis of direct relationship of ionic electrical conductivity and mechanical losses in glasses. New problems of physical chemistry of glass. Glass Phys Chem 38, 27–40 (2012). https://doi.org/10.1134/S1087659612010105

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1087659612010105

Keywords

Search

Navigation