Journal of Statistical Physics

, Volume 47, Issue 3–4, pp 409–438 | Cite as

One-dimensional model of the quasicrystalline alloy

  • S. E. Burkov


A one-dimensional chain of atoms of two types is investigated. It is proven exactly for the model of attracting hard spheres that if the ratio of the numbers of atoms of the two types is irrational, then the state of absolutely minimal energy is quasicrystalline. The quasicrystalline state is also investigated in the case of the Lennard-Jones interatomic potential. All the microscopic values (interatomic spacing, electronic density, etc.) are shown to be quasiperiodic functions varying on Cantor sets. Diffraction patterns, electronic properties, and vibrational spectra are also discussed.

Key words

Quasicrystals incommensurability localization groundstate 


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Copyright information

© Plenum Publishing Corporation 1987

Authors and Affiliations

  • S. E. Burkov
    • 1
  1. 1.Landau Institute for Theoretical PhysicsMoscowUSSR

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