Skip to main content

Computer Simulations of Undercooled Fluids and Glasses

  • Chapter
Materials for Tomorrow

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 93))

Abstract

An introduction to the Molecular Dynamics (MD) simulation of chemically realistic models for undercooled fluids and glasses is given, emphasizing silicatic materials such as molten silicon dioxide and its mixtures with sodium oxide and aluminium oxide, and comparing the simulation results to experimental data whenever possible.

A key ingredient to the computer simulation of materials is a sufficiently accurate description of the force fields with which the atoms interact. The need to simulate large systems for sufficiently long times makes the use of effective potentials for classical MD methods desirable. The validation of such effective potentials is best done studying the corresponding crystalline states of the material. As an example, the use of the so-called BKS-potential studying the structural and thermal properties of quartz crystals is described, and a comparison to other potentials is discussed.

When one studies undercooled fluids and glasses, a second problem enters, the disparity between experimental cooling rates and the much larger rates of the simulation. The extent to which a meaningful comparison to experiments is nevertheless possible is discussed. It is shown that the simulations can reproduce the structural and dynamic properties of molten silica (including self diffusion coefficients, viscosity, sound velocity, etc.) and its mixtures with other oxides. Evidence for the formation of sodium-rich channels responsible for anomalously large diffusion constants of sodium in mixtures containing sodium oxide will be discussed. No enhanced diffusion of aluminium occurs, however, due to “tricluster” formation in such mixtures.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.P. Allen, D.J. Tildesley: Computer Simulation of Liquids (Clarendon Press, Oxford, 1987)

    Google Scholar 

  2. K. Binder, G. Ciccotti (Eds.): Monte Carlo and Molecular Dynamics of Condensed Matter Systems (Societá) Italiana di Fisica, Bologna, 1996)

    Google Scholar 

  3. D. Frenkel, B. Smit: Understanding Molecular Simulation: From Algorithms to Applications (Academic Press, San Diego, 1996)

    Google Scholar 

  4. D.P. Landau, K. Binder: A Guide to Monte Carlo Simulations in Statistical Physics (Cambridge Univ. Press, Cambridge, 2000)

    Google Scholar 

  5. J. Grotendorst, D. Marx, M. Muramatsu (Eds.): Quantum Theory of Complex Many-Body Systems: From Theory to Algorithms — Lecture Notes (NIC, Jülich, 2002)

    Google Scholar 

  6. N. Attig, K. Binder, H. Grubmüller, K. Kremer (Eds.): Computational Soft Matter: From Synthetic Polymers to Proteins — Lecture Notes (NIC, Jülich, 2004)

    Google Scholar 

  7. M. Karttunen, I. Vattulainen, A. Lukkarinen (Eds.) Novel Methods of Soft Matter Simulations. Lecture Notes in Physics, Vol 640 (Springer, Berlin, 2004)

    Google Scholar 

  8. K. Kremer, G.S. Grest: J. Chem. Phys. 92, 5057 (1990)

    Article  CAS  Google Scholar 

  9. K. Binder (ed.): Monte Carlo and Molecular Dynamics Simulations in Polymer Science (Oxford University Press, New York, 1995)

    Google Scholar 

  10. K. Binder, D.W. Heermann: Monte Carlo Simulations in Statistical Physics. An Introduction (4th Ed.) (Springer, Berlin, 2002)

    Google Scholar 

  11. A. Sariban, K. Binder: J. Chem. Phys. 86, 5859 (1987)

    Article  CAS  Google Scholar 

  12. S.K. Das, J. Horbach, K. Binder: J. Chem. Phys. 119, 1547 (2003)

    Article  CAS  Google Scholar 

  13. K. Binder, J.L. Lebowitz, M.K. Phani, M.H. Kalos: Acta Metall. 29, 1655 (1981)

    Article  CAS  Google Scholar 

  14. R. Car, M. Parrinello: Phys. Rev. Lett. 55, 2471 (1985)

    Article  CAS  Google Scholar 

  15. W. Kohn: In: Monte Carlo and Molecular Dynamics of Condensed Matter Systems ed. by K. Binder, G. Cicotti (Societá Italiana di Fisica, Bologna, 996) p. 561; R. Car: ibid. p. 601

    Google Scholar 

  16. B.J. Berne, D. Thirumalai: Annu. Rev. Phys. Chem. 37, 401 (1986)

    Article  CAS  Google Scholar 

  17. D.M. Ceperley: Rev. Mod. Phys. 67, 279 (1995)

    Article  CAS  Google Scholar 

  18. D.M. Ceperley: In: Monte Carlo and Molecular Dynamics of Condensed Matter Systems ed. by K. Binder, G. Ciccotti (Societa Italiana di Fisica, Bologna, 1996) p. 443

    Google Scholar 

  19. P. Nielaba: In: Annual Reviews of Computational Science, Vol. 5 ed. by D. Stauffer (World Scientific, Singapore, 1997) p. 137

    Google Scholar 

  20. D. Marx, M.H. Müser: J. Phys.: Condens. Matter 11, R117 (1999)

    Article  CAS  Google Scholar 

  21. M.E. Tuckerman, B.J. Berne, G.J. Martyna, M.L. Klein: J. Chem. Phys. 99, 2796 (1993)

    Article  Google Scholar 

  22. M.E. Tuckerman, A. Hughes: Classical and Quantum Dynamics in Condensed Phase Simulation (World Scientific, Singapore, 1998)

    Google Scholar 

  23. M.H. Müser: J. Chem. Phys. 114, 6364 (2001)

    Article  Google Scholar 

  24. P. Schöffel, M. H. Müser: Phys. Rev. B 63, 224180 (2001)

    Article  Google Scholar 

  25. D. Marx: Science 303, 634 (2004); D. Marx, M.E. Tuckerman, G.J. Martyna: Comput. Phys. Commun. 118, 166 (1999); D. Marx, M. Parrinello: Z. Phys. B 95, 143 (1994)

    Article  CAS  Google Scholar 

  26. L. Verlet: Phys. Rev. 159, 98 (1967)

    Article  CAS  Google Scholar 

  27. H.C. Andersen: J. Comput. Phys. 52, 24 (1983)

    Article  CAS  Google Scholar 

  28. M. Tuckerman, G.J. Martyna, B.J. Berne: J. Chem. Phys. 97, 1990 (1992)

    Article  CAS  Google Scholar 

  29. J.L. Lebowitz, J.K. Percus, L. Verlet: Phys. Rev. 153, 250 (1967)

    Article  CAS  Google Scholar 

  30. S. Nose: J. Chem. Phys. 81, 511 (1984)

    Article  CAS  Google Scholar 

  31. W.G. Hoover: Phys. Rev. A 31, 1695 (1985)

    Article  Google Scholar 

  32. C. Bennemann, W. Paul, K. Binder, B. Dünweg: Phys. Rev. 57, 843 (1998)

    CAS  Google Scholar 

  33. H.C. Andersen: J. Chem. Phys. 72, 2384 (1980)

    Article  CAS  Google Scholar 

  34. L.P. Kadanoff, P.C. Martin: Ann. Phys. (N.Y.) 24, 419 (1963)

    Article  Google Scholar 

  35. J.-P. Hansen, I.R. McDonald: Theory of Simple Liquids (Academic, San Diego, 1986)

    Google Scholar 

  36. J.P. Boon, S. Yip: Molecular Hydrodynamics (McGraw Hill, New York, 1980)

    Google Scholar 

  37. B. van Beest, G. Kramer, R. van Santen: Phys. Rev. Lett. 64, 1955 (1990)

    Article  Google Scholar 

  38. S. Tsuneyuki, M. Tsukada, H. Aoki, F. Matsui: Phys. Rev. Lett. 61, 869 (1988)

    Article  CAS  Google Scholar 

  39. K. Vollmayr, W. Kob, K. Binder: Phys. Rev. B54, 15808 (1996)

    Article  CAS  Google Scholar 

  40. C.A. Angell, J.H.R. Clark, L.V. Woodcock: Adv. Chem. Phys. 48, 397 (1981)

    CAS  Google Scholar 

  41. J. Horbach, W. Kob, K. Binder: Phil. Mag. B 77, 297 (1998)

    Article  CAS  Google Scholar 

  42. J. Horbach, W. Kob, K. Binder: J. Non-Cryst. Solids 235–237, 320 (1998)

    Article  Google Scholar 

  43. J. Horbach, W. Kob: Phys. Rev. B 60, 3169 (1999)

    Article  CAS  Google Scholar 

  44. J. Horbach, W. Kob, K. Binder: J. Phys. Chem. B 103, 4104 (1999)

    Article  CAS  Google Scholar 

  45. J. Horbach, W. Kob, K. Binder, A.C. Angell: Phys. Rev. E 54, R5897 (1996)

    Article  CAS  Google Scholar 

  46. D.L. Price, S.M. Carpenter: J. Non-Cryst. Solids 92, 153 (1987)

    Article  CAS  Google Scholar 

  47. P.J. Heaney, C.T. Prewitt, G.V. Gibbs (eds.): Silica — Physical Behavior, Geochemistry and Materials Applications (Mineral Soc. Am., Washington D.C., 1994)

    Google Scholar 

  48. M.H. Müser, K. Binder: Phys. Chem. Minerals 28, 746 (2001)

    Article  Google Scholar 

  49. D. Herzbach, K. Binder, M.H. Müser: J. Chem. Phys. 123, 124711 (2005)

    Article  Google Scholar 

  50. M. Parrinello, A. Rahman: Phys. Rev. Lett. 45, 1196 (1980)

    Article  CAS  Google Scholar 

  51. K. Binder: In: Phase Transformations in Materials ed. by G. Kostorz. Wiley-VCH, Weinheim (2001), p. 239

    Chapter  Google Scholar 

  52. P.C. Hohenberg, B.I. Halperin: Rev. Mod. Phys. 49, 435 (1977)

    Article  CAS  Google Scholar 

  53. K. Binder: In: Computational Methods in Field Theory ed. by H. Gausterer and C.B. Lang (Springer, Berlin, 1992), p. 59

    Google Scholar 

  54. K. Binder: Rep. Progr. Phys. 60, 487 (1997)

    Article  CAS  Google Scholar 

  55. M.A. Carpenter, E.K.H. Salje, A. Graeme-Barber, B. Wruck, M.T. Dove, K.S. Knight: Am. Mineral 83, 2 (1998)

    Google Scholar 

  56. K. Binder: Z. Phys. B 43, 119 (1981)

    Article  Google Scholar 

  57. M.E. Fisher: Rev. Mod. Phys. 46, 587 (1974)

    Article  Google Scholar 

  58. H. Grimm, B. Dorner: J. Phys. Chem. Solids 36, 407 (1975)

    Article  CAS  Google Scholar 

  59. J.S. Tse, D.D. Klug: J. Chem. Phys. 95, 9176 (1991)

    Article  CAS  Google Scholar 

  60. S. Tsuneyuki, H. Aoki, M. Tsukuda: Phys. Rev. Lett. 64, 776 (1990)

    Article  CAS  Google Scholar 

  61. E. Demiralp, T. Cagin, W.A. Goddard III: Phys. Rev. Lett. 82, 1708 (1999)

    Article  CAS  Google Scholar 

  62. P. Tangney, S. Scandolo: J. Chem. Phys. 117, 8898 (2002)

    Article  CAS  Google Scholar 

  63. D. Herzbach: Dissertation (Johannes Gutenberg Universität Mainz, 2004)

    Google Scholar 

  64. R.B. Sosman: The Properties of Silica, (Chemical Catalog Co., New York, 1927)

    Google Scholar 

  65. R.C. Zeller, R.O. Pohl: Phys. Rev. B4, 2029 (1971)

    Article  Google Scholar 

  66. P. Richet, Y. Bottinga, D. Denielou, J.P. Petitet, C. Tegui: Geochem. Cosmochim. Acta 46, 2639 (1982)

    Article  CAS  Google Scholar 

  67. J. Horbach, W. Kob, K. Binder: Eur. Phys. J. B 19, 539 (2001)

    Article  Google Scholar 

  68. A. Polian, D. Vo-Tanh, P. Richter: Europhys. Lett. 57, 375 (2002)

    Article  CAS  Google Scholar 

  69. J.C. Mikkelsen: Appl Phys. Lett. 45, 1187 (1984)

    Article  CAS  Google Scholar 

  70. G. Brébec, P. Seguin, C. Sella, J. Bevenot, J.C. Martin: Acta Metall. 28, 327 (1970)

    Google Scholar 

  71. W. Götze, J. Sjögren: Rep. Prog. Phys. 55, 214 (1992)

    Article  Google Scholar 

  72. W. Kob: J. Phys.: Cond. Matter 11, R85 (1999)

    Article  CAS  Google Scholar 

  73. K. Binder, W. Kob: Statistical mechanics of disordered materials (World Scientific, Singapore, 2005)

    Google Scholar 

  74. G. Urbain: Geochim. Cosmochim. Acta 46, 1061 (1982)

    Article  CAS  Google Scholar 

  75. J. Horbach, W. Kob, K. Binder: Chem. Geol. 174, 87 (2001)

    Article  CAS  Google Scholar 

  76. J. Horbach, W. Kob, K. Binder: Phys. Rev. Lett. 88, 125502 (2002)

    Article  Google Scholar 

  77. A. Winkler, J. Horbach, W. Kob, K. Binder: J. Chem. Phys. 120, 384 (2003)

    Article  Google Scholar 

  78. K. Binder, J. Horbach, W. Kob, A. Winkler: In: Complex Inorganic Solids III ed. by P.E.A. Turchi et al., (Springer, Berlin, 2005), p. 35

    Google Scholar 

  79. G.J. Kramer, A.J.M. de Man, R.A. van Santen: J. Am. Chem. Soc. 64, 6435 (1991)

    Article  Google Scholar 

  80. M. Misawa, D.L. Price, K. Suzuki: J. Non-Cryst. Solids 37, 85 (1980)

    Article  CAS  Google Scholar 

  81. A. Meyer, H. Schober, D.B. Dingwell: Europhys. Lett. 59, 708 (2002)

    Article  CAS  Google Scholar 

  82. A. Meyer, J. Horbach, W. Kob, F. Kargl, H. Schober: Phys. Rev. Lett. 93, 027801 (2004)

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Binder, K., Herzbach, D., Horbach, J., Müser, M.H. (2007). Computer Simulations of Undercooled Fluids and Glasses. In: Gemming, S., Schreiber, M., Suck, JB. (eds) Materials for Tomorrow. Springer Series in Materials Science, vol 93. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-47971-0_1

Download citation

Publish with us

Policies and ethics