The Polycluster Theory for the Structure of Glasses: Evidence from Low Temperature Physics

Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 197)

Abstract

The problems of the intermediate-range atomic structure of glasses and of the mechanism for the glass transition are approached from the low-temperature end in terms of a scenario for the atomic organization that justifies the use of an extended tunneling model. The latter is crucial for the explanation of the magnetic and compositional effects discovered in non-metallic glasses in the Kelvin and milli-Kelvin temperature range. The model relies on the existence of multi-welled local potentials for the effective tunneling particles that are a manifestation of a non-homogeneous atomic structure deriving from the established dynamical heterogeneities that characterize the supercooled liquid state. It is shown that the extended tunneling model can successfully explain a range of experiments at low temperatures, but the proposed non-homogeneous atomic structure scenario is then tested in the light of available high resolution electron microscopy imaging of the structure of some glasses and of the behaviour near the glass transition.

Notes

Acknowledgements

The Author is very grateful to Maksym Paliienko and Silvia Bonfanti for their help with data fitting. He gratefully acknowledges stimulating discussions with A.S. Bakai. Part of this work was carried out whilst visiting the Physics Department of McGill University in Montreal (CA). The Author is grateful to Hong Guo for support and to him, to Martin Grant and Mark Sutton for useful discussions. On-going support from INFN-Pavia through Iniziativa Specifica GEOSYM-QFT is gratefully acknowledged.

References

  1. 1.
    G. Jug, Theory of the thermal magnetocapacitance of multi-component silicate glasses at low temperature. Phil. Mag. 84(33), 3599–3615 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    W.A. Phillips (ed.), Amorphous Solids: Low Temperature Properties (Springer Verlag, Berlin, 1981)Google Scholar
  3. 3.
    P. Esquinazi (ed.), Tunneling Systems in Amorphous and Crystalline Solids (Springer, Berlin, 1998)Google Scholar
  4. 4.
    W.H. Zachariasen, The atomic arrangement in glass. J. Am. Chem. Soc. 54, 3841–3851 (1932); ibid.: The vitreous state. J. Chem. Phys. 3, 162–163 (1935)Google Scholar
  5. 5.
    B.E. Warren, The diffraction of X-rays in glass. Phys. Rev. 45, 657–661 (1934)ADSCrossRefGoogle Scholar
  6. 6.
    W.M. MacDonald, A.C. Anderson, J. Schröder, Low-temperature behavior of potassium and sodium silicate glasses. Phys. Rev. B 31, 1090–1101 (1985)ADSCrossRefGoogle Scholar
  7. 7.
    G. Jug, M. Paliienko, Evidence for a two-component tunnelling mechanism in the multicomponent glasses at low temperatures. Europhys. Lett. 90, 36002 (2010)ADSCrossRefGoogle Scholar
  8. 8.
    C. Enss, Anomalous behavior of insulating glasses at ultra-low temperatures. Adv. Solid State Phys. 42, 335–346 (2002)CrossRefGoogle Scholar
  9. 9.
    P. Strehlow, M. Wohlfahrt, A.G.M. Jansen, R. Haueisen, G. Weiss, C. Enss, S. Hunklinger, Magnetic field dependent tunneling in glasses. Phys. Rev. Lett. 84, 1938–1941 (2000)ADSCrossRefGoogle Scholar
  10. 10.
    M. Wohlfahrt, P. Strehlow, C. Enss, S. Hunklinger, Magnetic-field effects in non-magnetic glasses. Europhys. Lett. 56, 690–694 (2001); M. Wohlfahrt, Ph.D. Thesis (Heidelberg 2001), www.ub.uni-heidelberg.de/archiv/1587
  11. 11.
    P. Nagel, A. Fleischmann, S. Hunklinger, C. Enss, Novel isotope effects observed in polarization echo experiments. Phys. Rev. Lett. 92, 245511 (2004)Google Scholar
  12. 12.
    A.A. Lebedev, O Polimorfizme i Otzhige Stekla. Trud’i Gos. Opt. Inst. 2, 1–20 (1921) (in Russian); ibid., Izv. Akad. Nauk SSSR, Otd. Mat. Estestv. Nauk, Ser. Fiz. 3, 381 (1937)Google Scholar
  13. 13.
    J.T. Randall, H.P. Rooksby, B.S. Cooper, The diffraction of X-rays by vitreous solids and its bearing on their constitution. Nature 125, 438 (1930); ibid: X-ray diffraction and the structure of vitreous solids. I. Z. Kristallogr. 75, 196–214 (1930)Google Scholar
  14. 14.
    E.A. Porai-Koshits, Genesis of concepts on structure of inorganic glasses. J. Non-cryst. Sol. 123, 1–13 (1990)ADSCrossRefGoogle Scholar
  15. 15.
    A.C. Wright, Crystalline-like ordering in melt-quenched network glasses? J. Non-cryst. Solids 401, 4–26 (2014); ibid.: The great crystallite versus random network controversy: a personal perspective. Int. J. Appl. Glass Sci. 5, 31–56 (2014)Google Scholar
  16. 16.
    A.S. Bakai, The polycluster concept of amorphous solids, in Glassy Metals III, H. Beck and H. -I. Günterodt (eds.), Topics in Applied Physics, vol. 72, 209–255 (Springer, Berlin, 1994)Google Scholar
  17. 17.
    A.S. Bakai, Poliklastern’ie Amorfn’ie Tela, Khar’kov “Synteks” (Khar’kov, Ukraine, 2013). (in Russian)Google Scholar
  18. 18.
    G. Adam, J.H. Gibbs, On the temperature dependence of cooperative relaxation properties in glass-forming liquids. J. Chem. Phys. 43, 139–146 (1965)ADSCrossRefGoogle Scholar
  19. 19.
    L. Berthier, G. Biroli, Theoretical perspective on the glass transition and amorphous materials. Rev. Mod. Phys. 83, 587–645 (2011)ADSCrossRefGoogle Scholar
  20. 20.
    C.A. Angell, Perspective on the glass transition. J. Phys. Cem. Solids 49, 863–871 (1988)ADSCrossRefGoogle Scholar
  21. 21.
    V. Lubchenko, P.G. Wolynes, Theory of structural glasses and supercooled liquids. Annu. Rev. Phys. Chem. 58, 235–266 (2007)ADSCrossRefGoogle Scholar
  22. 22.
    S.L. Simon, G.B. McKenna, Experimental evidence against the existence of an ideal glass transition. J. Non-Cryst. Solids 355, 672–675 (2009)ADSCrossRefGoogle Scholar
  23. 23.
    G. Hägg, The vitreous state. J. Chem. Phys. 3, 284–349 (2016)Google Scholar
  24. 24.
    U. Satoshi, H. Koibuchi, Finsler geometry modeling of phase separation in multi-component membranes. Polymers 8, 284 (2016)CrossRefGoogle Scholar
  25. 25.
    J. Hwang, Z.H. Melgarejo, Y.E. Kalay, I. Kalay, M.J. Kramer, D.S. Stone, P.M. Voyles, Nanoscale structure and structural relaxation in \(\text{ Zr }_50\text{ Cu }_45\text{ Al }_5\) bulk metallic glass. Phys. Rev. Lett. 108, 195505 (2012)ADSCrossRefGoogle Scholar
  26. 26.
    M.M.J. Treacy, K.B. Borisenko, The local structure of amorphous silicon. Science 335, 950–953 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    J.C. Phillips, Realization of a Zachariasen glass. Solid State Comm. 47, 203–206 (1983)ADSCrossRefGoogle Scholar
  28. 28.
    M.M. Hurley, P. Harrowell, Kinetic structure of a two-dimensional liquid. Phys. Rev. E 52, 1694–1698 (1995)ADSCrossRefGoogle Scholar
  29. 29.
    H. Sillescu, Heterogeneity at the glass transition: a review. J. Non-Cryst. Solids 243, 81–108 (1999)ADSCrossRefGoogle Scholar
  30. 30.
    M.D. Ediger, Spatially heterogeneous dynamics in supercooled liquids. Annu. Rev. Phys. Chem. 51, 99–128 (2000)ADSCrossRefGoogle Scholar
  31. 31.
    K. Vollmayr-Lee, A. Zippelius, Heterogeneities in the glassy state. Phys. Rev. B 72, 041507 (2005); K. Vollmayr-Lee, W. Kob, K. Binder, A. Zippelius, Dynamical heterogeneities below the glass transition. J. Chem. Phys. 116, 5158–5166 (2002)Google Scholar
  32. 32.
    C. Donati, S.C. Glotzer, P.H. Poole, W. Kob, S. Plimpton, Spatial correlations of mobility and immobility in a glass-forming Lennard-Jones liquid. Phys. Rev. E 60, 3107–3119 (1999)ADSCrossRefGoogle Scholar
  33. 33.
    P.-G. de Gennes, A simple picture for structural glasses. C. R. Phys. 3, 1263–1268 (2002)ADSCrossRefGoogle Scholar
  34. 34.
    H.P. Baltes, A cellular model for the specific heat of amorphous solids at low temperatures. Solid State Commun. 13, 225–228 (1973)ADSCrossRefGoogle Scholar
  35. 35.
    W.A. Phillips, Two-level states in glasses. Rep. Prog. Phys. 50, 1657–1708 (1987)ADSCrossRefGoogle Scholar
  36. 36.
    J.A. Sussmann, Electric dipoles due to trapped electrons. Proc. Phys. Soc. 79, 758–774 (1962). (London)ADSCrossRefMATHGoogle Scholar
  37. 37.
    G. Jug, M. Paliienko, Multilevel tunneling systems and fractal clusters in the low-temperature mixed alkali-silicate glasses. Sci. World J. 2013, 1–20 (2013)CrossRefGoogle Scholar
  38. 38.
    G. Jug, Multiple-well tunneling model for the magnetic-field effect in ultracold glasses. Phys. Rev. B 79, 180201 (2009)ADSCrossRefGoogle Scholar
  39. 39.
    G. Jug, M. Paliienko, S. Bonfanti, The glassy state magnetically viewed from the frozen end. J. Non-Crys. Solids 401, 66–72 (2014)ADSCrossRefGoogle Scholar
  40. 40.
    C.C. Yu, A.J. Leggett, Low temperature properties of amorphous materials: through a glass darkly. Comm. Cond. Mat. Phys. 14, 231–251 (1988)Google Scholar
  41. 41.
    G. Jug, S. Bonfanti, W. Kob, Realistic tunneling systems for the magnetic effects in non-metallic real glasses. Phil. Mag. 96, 648–703 (2016)ADSCrossRefGoogle Scholar
  42. 42.
    S. Bonfanti, G. Jug, On the paramagnetic impurity concentration of silicate glasses from low-temperature physics. J. Low Temp. Phys. 180, 214–237 (2015)ADSCrossRefGoogle Scholar
  43. 43.
    L. Siebert, Ph.D. Thesis (Heidelberg University, 2001), www.ub.uni-heidelberg.de/archiv/1601
  44. 44.
    H.M. Carruzzo, E.R. Grannan, C.C. Yu, Non-equilibrium dielectric behavior in glasses at low temperatures: evidence for interacting defects. Phys. Rev. B 50, 6685–6695 (1994)ADSCrossRefGoogle Scholar
  45. 45.
    M. Paliienko, Multiple-welled tunnelling systems in glasses at low temperatures. Ph.D. Thesis (Università degli Studi dell’Insubria, 2011), http://insubriaspace.cineca.it/handle/10277/420
  46. 46.
    F. LeCochec, F. Ladieu, P. Pari, Magnetic field effect on the dielectric constant of glasses: evidence of disorder within tunneling barriers. Phys. Rev. B 66, 064203 (2002)ADSCrossRefGoogle Scholar
  47. 47.
    B.P. Smolyakov, E.P. Khaimovich, Pis’ma Zh. Eksp. Teor. Fiz. 29, 464 (1979) (in Russian); ibid.: Dynamic processes in dielectric glasses at low temperatures. Sov. Phys. Uspekhi, 25, 102–115 (courtesy A. Borisenko) (1982)Google Scholar
  48. 48.
    S. Ludwig, P. Nagel, S. Hunklinger, C. Enss, Magnetic field dependent coherent polarization echoes in glasses. J. Low Temp. Phys. 131, 89–111 (2003)ADSCrossRefGoogle Scholar
  49. 49.
    S. Ludwig, P. Nagel, S. Hunklinger, C. Enss, Direct coupling of magnetic fields to tunneling systems in glasses. Phys. Rev. Lett. 88, 075501 (2002)ADSCrossRefGoogle Scholar
  50. 50.
    A. Würger, A. Fleischmann, C. Enss, Dephasing of atomic tunneling by nuclear quadrupoles. Phys. Rev. Lett. 89, 237601 (2002)ADSCrossRefGoogle Scholar
  51. 51.
    J.L. Black, B.I. Halperin, Spectral diffusion, phonon echoes and saturation recovery in glasses at low temperatures. Phys. Rev. B 16, 2879–2895 (1977)ADSCrossRefGoogle Scholar
  52. 52.
    V.L. Gurevich, M.I. Muradov, D.A. Parshin, Electric dipole echo in glasses. Sov. Phys. JETP 70, 928 (1990)Google Scholar
  53. 53.
    Y.M. Galperin, V.L. Gurevich, D.A. Parshin, Nonlinear resonant attenuation in glasses and spectral diffusion. Phys. Rev. B 37, 10339–10349 (1988)Google Scholar
  54. 54.
    C. Enss, S. Ludwig, R. Weis, S. Hunklinger, Decay of spontaneous echoes in glasses. Czechoslovak J. Phys. 46, 2247–2248 (1996)ADSCrossRefGoogle Scholar
  55. 55.
    D. Simatos, G. Blond, R. Roudaut, D. Champion, J. Perez, A.L. Faivre, Influence of heating and cooling rates on the glass transition temperature and the fragility parameter of sorbitol and fructose as measured by DSC. J. Thermal Anal. 47, 1419–1436 (1996)CrossRefGoogle Scholar
  56. 56.
    J. Buchholz, W. Paul, F. Varnik, K. Binder, Cooling rate dependence of the glass transition temperature of polymer melts: molecular dynamics study. J. Chem. Phys. 117, 7364–7372 (2002)ADSCrossRefGoogle Scholar
  57. 57.
    A. Smerzi, S. Fantoni, S. Giovanazzi, S.R. Shenoy, Quantum coherent atomic tunneling between two trapped Bose-Einstein condensates. Phys. Rev. Lett. 79, 4950 (1997)ADSCrossRefGoogle Scholar
  58. 58.
    M. Albiez, R. Gati, J. Fölling, S. Hunsmann, M. Cristiani, M.K. Oberthaler, Direct observation of tunneling and nonlinear self-trapping in a single Bosonic Josephson junction. Phys. Rev. Lett. 95, 010402 (2005)ADSCrossRefGoogle Scholar
  59. 59.
    J. Zarzycki, Proceedings of X International Congress on Glass, No. 12 (Kyoto, Japan, 1974), p. 28Google Scholar
  60. 60.
    J. Zarzycki, Glasses and the Vitreous State (Cambridge University Press, Cambridge, 1991), p. 172Google Scholar
  61. 61.
    W. Vogel, Glass Chemistry, 2nd edn. (Springer, Berlin, 1992), p. 74Google Scholar
  62. 62.
    A. Borisenko, Hole-compensated \(\text{ Fe }^{3+}\) impurities in quartz glasses: a contribution to Subkelvin thermodynamics. J. Phys.: Condens. Matter 19, 416102 (2007)Google Scholar
  63. 63.
    A. Borisenko, G. Jug, Paramagnetic tunneling systems and their contribution to the polarization echo in glasses. Phys. Rev. Lett. 107, 075501 (2011)ADSCrossRefGoogle Scholar
  64. 64.
    E. Proutorov, H. Koibuchi, Orientation asymmetric surface model for membranes: Finsler geometry modeling. Axioms 6, 10 (2017)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Dipartimento di Scienza ed Alta Tecnologia and To.Sca.LabUniversità dell’InsubriaComoItaly
  2. 2.INFN – Sezione di PaviaPaviaItaly

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