Three-Phonon Zone-Boundary Processes and Melting of Solids

  • B. H. Armstrong
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 68)


Vibrational theories of melting [1,2], which presuppose a critical amplitude of vibration, have enjoyed considerable empirical success. But the critical amplitude determined empirically for a vibrational catastrophe is surprisingly small and a fundamental definition of such a catastrophe is lacking. An hypothesis is advanced herein addressing these issues. Lindemann’s law is obtained from the 3-phonon transition rate without reference to a critical amplitude upon the assumption that zone-boundary (ZB) phonons cease to be valid excitations at the melting point. Corollary to this assumption is the onset of single-particle random movement on the time scale (2ωD)-1 where ωD is the Debye angular frequency. Results obtained for the Lindemann constant and for diffusion constants compare favorably with experiment for alkali metals and halides.


Diffusion Constant Debye Temperature Critical Amplitude Large Wave Number Anharmonic Lattice 
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  1. 1.
    L.L. Boyer: Phase Transitions 5, 1 (1985)CrossRefGoogle Scholar
  2. 2.
    A.R. Ubbelohde: The Molten State of Matter (Wiley, New York 1978)Google Scholar
  3. 3.
    P.A. Fleury: in Anharmonic Lattices, Structural Transitions and Melting, ed. by T. Riste (Noordhoff, Leiden 1974)Google Scholar
  4. 4.
    J. Skalyo, Jr., Y. Endoh, and G. Shirane: Phys. Rev. B9, 1797 (1974)ADSGoogle Scholar
  5. 5.
    B. Hennion and M. Schott: J. Phys. Lett. (France) 45, L621 (1984)CrossRefGoogle Scholar
  6. 6.
    D.J. Ecsedy and P.G. Klemens: Phys. Rev. B15, 5957 (1977)ADSGoogle Scholar
  7. 7.
    M. Roufosse and P.G. Klemens: Phys. Rev. B7, 5379 (1973)ADSGoogle Scholar
  8. 8a.
    B.H. Armstrong: Phys. Rev B23, 883 (1981);ADSGoogle Scholar
  9. 8b.
    B.H. Armstrong: Phys. Rev. B32, 3381 (1985)ADSGoogle Scholar
  10. 9.
    O.L. Anderson: in Physical Acoustics, ed. by W.P. Mason (Academic, New York 1965)Google Scholar
  11. 10.
    K.A. Gschneidner, Jr.: in Solid State Physics Vol. 16, ed. by F. Seitz and D. Turnbull (Academic, New York 1964)Google Scholar
  12. 11.
    Y.G. Yaks, E.V. Zarochentsev, S.P. Kravchuk, Y.P. Safronov, and A.V. Trefilov: Phys. Stat. Sol. (b) 85, 749 (1978)CrossRefADSGoogle Scholar
  13. 12.
    Z.P. Chang and G.R. Barsch: J. Phys. Chem. Sol. 32, 27 (1971)CrossRefADSGoogle Scholar
  14. 13.
    K.D. McLean and C.S. Smith: J. Phys. Chem. Sol. 33, 279 (1972)CrossRefADSGoogle Scholar
  15. 14.
    A.A.Z. Ahmad, H.G. Smith, N. Wakabayashi, and M.K. Wilkinson: Phys. Rev, B6, 3956 (1972)ADSGoogle Scholar
  16. 15.
    T.E. Faber: Introduction to the Theory of Liquid Metals (Cambridge, London 1972)Google Scholar
  17. 16.
    R.E. Young and J.P. O’Connell: Ind. Eng. Chem. Fundam. 10, 418 (1971)CrossRefGoogle Scholar
  18. 17.
    J.H.C. Thompson: Phil. Mag. 44, 131 (1953)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • B. H. Armstrong
    • 1
  1. 1.Department of Materials Science and EngineeringUniversity of WashingtonSeattleUSA

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