Modulated quasicrystals

Reference:

Sing, B., 2008. Modulated quasicrystals. Zeitschrift für Kristallographie, 223 (11-12), pp. 765-769.

Related documents:

Official URL:

http://dx.doi.org/10.1524/zkri.2008.1073

Abstract

There is some confusion in the literature what "modulated quasicrystals" are: Some people treat "modulated quasicrystals" and "deformed model sets" as exchangeable termini (compare [6, 9, 5]), others claim that "[...] the projection method becomes powerless against incommensurate modulated structures" (e.g., [12 p. 148]). We use a mathematical approach and propose the following classification: While deformed model sets are characterised by a deformation that does not change the location of the Bragg peaks, a modulated phase yields "satellites" in the diffraction pattern and is achieved "by enlarging the internal space" with a torus.

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