Onedimensional model of the quasicrystalline alloy
Abstract
A onedimensional 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 LennardJones 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.
 Publication:

Journal of Statistical Physics
 Pub Date:
 May 1987
 DOI:
 10.1007/BF01007518
 Bibcode:
 1987JSP....47..409B
 Keywords:

 Quasicrystals;
 incommensurability;
 localization;
 groundstate