Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
L.L. Boyer: Phase Transitions 5, 1 (1985)
A.R. Ubbelohde: The Molten State of Matter (Wiley, New York 1978)
P.A. Fleury: in Anharmonic Lattices, Structural Transitions and Melting, ed. by T. Riste (Noordhoff, Leiden 1974)
J. Skalyo, Jr., Y. Endoh, and G. Shirane: Phys. Rev. B9, 1797 (1974)
B. Hennion and M. Schott: J. Phys. Lett. (France) 45, L621 (1984)
D.J. Ecsedy and P.G. Klemens: Phys. Rev. B15, 5957 (1977)
M. Roufosse and P.G. Klemens: Phys. Rev. B7, 5379 (1973)
B.H. Armstrong: Phys. Rev B23, 883 (1981);
B.H. Armstrong: Phys. Rev. B32, 3381 (1985)
O.L. Anderson: in Physical Acoustics, ed. by W.P. Mason (Academic, New York 1965)
K.A. Gschneidner, Jr.: in Solid State Physics Vol. 16, ed. by F. Seitz and D. Turnbull (Academic, New York 1964)
Y.G. Yaks, E.V. Zarochentsev, S.P. Kravchuk, Y.P. Safronov, and A.V. Trefilov: Phys. Stat. Sol. (b) 85, 749 (1978)
Z.P. Chang and G.R. Barsch: J. Phys. Chem. Sol. 32, 27 (1971)
K.D. McLean and C.S. Smith: J. Phys. Chem. Sol. 33, 279 (1972)
A.A.Z. Ahmad, H.G. Smith, N. Wakabayashi, and M.K. Wilkinson: Phys. Rev, B6, 3956 (1972)
T.E. Faber: Introduction to the Theory of Liquid Metals (Cambridge, London 1972)
R.E. Young and J.P. O’Connell: Ind. Eng. Chem. Fundam. 10, 418 (1971)
J.H.C. Thompson: Phil. Mag. 44, 131 (1953)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1986 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Armstrong, B.H. (1986). Three-Phonon Zone-Boundary Processes and Melting of Solids. In: Anderson, A.C., Wolfe, J.P. (eds) Phonon Scattering in Condensed Matter V. Springer Series in Solid-State Sciences, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82912-3_96
Download citation
DOI: https://doi.org/10.1007/978-3-642-82912-3_96
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-82914-7
Online ISBN: 978-3-642-82912-3
eBook Packages: Springer Book Archive