Extraordinary Caustics in the Phonon Focusing Patterns of Crystals

  • A. G. Every
Conference paper
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 68)


Catastrophe theory provides a convenient framework for classifying the phonon focusing caustics of crystals [1–4]. There are however many prominent focusing singularities which, because they arise in the vicinity of degeneracy between different branches of the phonon dispersion relation, or because they are consequent upon the special properties of the Christoffel wave equation, are not readily accommodated in elementary catastrophe theory. The “extraordinary” caustics described here have been obtained from computer generated phonon images. The search for such structures is not complete, and a mathematical analysis of the possibilities would be very useful.


Elastic Constant Conical Point Catastrophe Theory Hexagonal Symmetry Slowness Surface 
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  1. 1.
    For a recent review on phonon imaging see G.A. Northrop and J.P. Wolfe: In Nonequilibrium Phonon Dynamics, ed. by W.E. Bron (Plenum, New York 1985) p. 165Google Scholar
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    P. Taborek and D. Goodstein: Phys. Rev. B22, 1550 (1980)ADSGoogle Scholar
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    A.G. Every: Phys. Rev. B24, 3456 (1981)ADSGoogle Scholar
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    D. Armbruster and G. Dangelmayr: Z. Phys. B52, 87 (1983)CrossRefADSMathSciNetGoogle Scholar
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    A.G. Every: Phys. Rev. B, to be publishedGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • A. G. Every
    • 1
  1. 1.Department of PhysicsUniversity of the WitwatersrandJohannesburgSouth Africa

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