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Elementary Excitations and Physical Properties

  • Jürgen Hafner
  • Marian Krajčí
Part of the Springer Series in Solid-State Sciences book series (SSSOL, volume 126)

Abstract

It has been known for more than twenty years that perfect structural order can exist in systems with broken translational symmetry. In the seventies the scientific interest concentrated on the so-called incommensurably modulated crystalline (IC) phases (see, e.g., Currat and Janssen 1988). The discovery by Shechtman et al. (1984) of icosahedral (i) symmetry (which implies the absence of translational periodicity) in certain alloys introduced the new field of quasicrystals (QCs). Soon after it was found that quasicrystallinity is not restricted to the i phases. Today we know QCs characterized by the classically forbidden fivefold (icosahedral), eightfold (octagonal), tenfold (decagonal), and twelvefold (dodecagonal) symmetry axes (for an introduction and reviews, see Steinhardt and Ostlund 1987, DiVinzenzo and Steinhardt 1991, Janot 1994). Icosahedral QCs are quasiperiodic in all three dimensions, while the other QCs are quasiperiodic only in the plane perpendicular to the non-crystallographic axis and periodic along it. IC phases and QCs are members of a family of quasiperiodic materials. Quasiperiodic structures can be characterized by a diffraction pattern characterized by sharp spots at the positions given by
$$k = \sum\limits_{i = 1}^n {{h_i}a_i^*,{\text{where }}{h_i}{\text{ is an integer}}{\text{.}}}$$
(7.1)
where h i is an integer.

Keywords

Elementary Excitation Participation Ratio Approximant Phase Quasiperiodic Structure Quasicrystalline Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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  • Jürgen Hafner
  • Marian Krajčí

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