Random and Nonrandom Structures in Higher Dimensions

  • R. Zallen
Part of the Institute for Amorphous Studies Series book series (IASS)


Higher-dimensional considerations are being increasingly invoked in connection with structural issues in noncrystalline solids. In this paper I survey some of these developments, including the dimensionality dependence of models of glass structure, the use of projections from higher dimensions for generating quasicrystal models for the icosahedral phase of Al−Mn, and the use of curved-space polytopes for modelling metallic glasses. I also briefly review part of what is known about close-packed lattices in higher dimensions.


Metallic Glass Close Packing Amorphous Solid Icosahedral Phase Random Close Packing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    N. F. Mott and E. A. Davis,Electronic Processes in Noncrystalline Materials(Clarendon Press, Oxford, 1979)Google Scholar
  2. 2.
    N. F. Mott, Phil. Mag. 19, 835 (1969)ADSCrossRefGoogle Scholar
  3. 3.
    R. Zallen, The Physics of Amorphous Solids(Wiley, New York, 1983)CrossRefGoogle Scholar
  4. 4.
    P. Chaudhari and D. Turnbull, Science 199, 11 (1978).ADSCrossRefGoogle Scholar
  5. 5.
    E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).ADSCrossRefGoogle Scholar
  6. 6.
    J. G. Berryman, Phys. Rev. A 27, 1053 (1983).ADSCrossRefGoogle Scholar
  7. 7.
    J. P. Straley, Phys. Rev. B 30, 6592 (1984).ADSCrossRefGoogle Scholar
  8. 8.
    D. R. Nelson, Phys. Rev. Lett. 50, 982 (1983)ADSCrossRefGoogle Scholar
  9. 8.
    D.R. Nelson, Phys. Rev. B 28, 5515 (1983)MathSciNetADSCrossRefGoogle Scholar
  10. 9.
    D. Shechtman, I. Blech, D. Gratias, and J.W. Cahn, Phys. Rev. Lett. 53, 1951 (1984).ADSCrossRefGoogle Scholar
  11. 10.
    R. D. Field and H. L. Fraser, Mat. Sci. and Eng. 68, L17 (1985).CrossRefGoogle Scholar
  12. 11.
    P. A. Bancel, P. A. Heiney, P. W. Stephens, A. I. Goldman, and P. M. Horn, preprint.Google Scholar
  13. 12.
    R. Penrose, Math. Intell. 2, 32 (1979)MathSciNetMATHCrossRefGoogle Scholar
  14. 12.
    M. Gardner, Sci. Am. 236, 110 (1977).Google Scholar
  15. 13.
    D. Levine and P. J. Steinhardt, Phys. Rev. Lett. 53, 2477 (1984).ADSCrossRefGoogle Scholar
  16. 14.
    P. Kramer and R. Neri, Acta Cryst. A. 40, 580 (1984).MathSciNetMATHCrossRefGoogle Scholar
  17. 15.
    V. Elser, preprint.Google Scholar
  18. 16.
    R. K. P. Zia and W. J. Dallas, J. Phys. A (1985, in press).Google Scholar
  19. 17.
    D. R. Nelson and M. Widom, Nucl. Phys. B 240, 113 (1984)MathSciNetADSCrossRefGoogle Scholar
  20. 17.
    S. S. Chdev and D. R. Nelson, Phys. Rev. Lett. 53, 1947 (1984).ADSCrossRefGoogle Scholar
  21. 18.
    H. S. M. Coxeter, Regular Polytopes. 3rd ed., ( Dover, New York, 1973 ).Google Scholar
  22. 19.
    J. F. Sadoc and R. Mosseri; and in Topological Disorder in Condensed Matter, ed. by F. Yonezawa and T. Ninomiya ( Springer-Verlag, Berlin, 1983 ), p. 30.CrossRefGoogle Scholar
  23. 20.
    M. H. Brodsky and D. P. DiVincenzo, J. Non-Cryst. Solids 59 and 60, 101 (1983)CrossRefGoogle Scholar
  24. 20.
    D. P. DiVincenzo, R. Mosseri, M. H. Brodsky, and J. F. Sadoc, Phys. Rev. B 29, 5934 (1984).ADSCrossRefGoogle Scholar
  25. 21.
    J. Leech and N. J. A. Sloane, Can. J. Math. 23, 718 (1971)MathSciNetMATHCrossRefGoogle Scholar
  26. 21.
    J. H. Conway and N. J. A. Sloane, Ann. Math. 116, 593 (1982)MathSciNetMATHCrossRefGoogle Scholar
  27. 21.
    T. M. Thompson, From Error-Correcting Codes Through Sphere Packings To Simple Groups(Math. Assoc. Am., 1983 ); N. J. A. Sloane, private communication.Google Scholar
  28. 21.
    N. J. A. Sloane, private communicationGoogle Scholar
  29. 22.
    H. S. M. Coxeter, Proc. Sympos. Pure Math 7, 53 (1963).MathSciNetGoogle Scholar
  30. 23.
    N. F. Mott, Current Contents 51, 18 (Dec. 22, 1980 ).Google Scholar

Copyright information

© Plenum Press , New York 1985

Authors and Affiliations

  • R. Zallen
    • 1
  1. 1.Department of PhysicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

Personalised recommendations