Special Issue "Quasicrystals"

Guest Editor
Dr. Vance Williams
Department of Chemistry, Simon Fraser University, 8888 University Drive, Burnaby B.C., V5A 1S6, Canada
Website: http://www.chemistry.sfu.ca/people/profiles/vancew
E-Mail: vancew@sfu.ca
Phone: +1 778 782 8059
Fax: +1 778 782 3765
Interests: organic synthesis; liquid crystals; conjugated polymers; gels; self-assembly; molecular recognition; electronic materials; photochromism; novel aromatic systems

Dear Colleagues,

“We report herein the existence of a metallic solid which diffracts electrons like a single crystal but has point group symmetry m (icosahedral) which is inconsistent with lattice translations.”  This was the opening sentence of Shechtman and coworkers’ paper (Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J.W. Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 1984, 53, 1951–1953), which, to date, has been cited more than 3300 times.  With this seemingly modest statement, a new branch of science was born: the study of quasicrystals. That paper, and those that followed, challenged the conventional wisdom of X-ray crystallography that allowed for only rotational axes with two, three, four or six-fold symmetry.  The observation of five-fold symmetry in an ordered structure, which had been predicted by the mathematical physicist Roger Penrose in the preceding decade, forced materials scientists to revise their understanding of the rules that governed the assembly of atoms and molecules; in recognition of this fundamental contribution, Daniel Shechtman was awarded the 2011 Nobel Prize for Chemistry. The study of aperiodic crystals and quasicrystals continues to be a dynamic field, and this special issue is dedicated to the ongoing theoretical and experimental developments in this fascinating topic.

Dr. Vance Williams
Guest Editor

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• aperiodic crystals
• chemistry
• physics
• alloys
• quasicrystals
• crystallography

Title: The Metric for the Quasi-Bragg Law Measured for the First Time
Author: Antony J. Bourdillon
Affiliation: UHRL, P.O.Box 700001, San Jose, CA 95170, USA; E-Mail: ourdillona@sbcglobal.net
Abstract: Quasicrystals display diffraction orders in geometric series. They do not therefore follow Bragg’s law of diffraction, where the series are in linear order on a reciprocal lattice. The geometric series is a restricted form of Fibonacci series and has special properties since the sequence ratio between members is a constant, the golden section. The diffraction patterns are indexed in three dimensions with notational economy, with demonstrated completeness, and without redundancy. Simulations on a hierarchic model show that the ‘quasi lattice parameter’ that is measured in the diffraction, differs from the Bragg equivalent in crystals. This is due partly to a compromise in the multiple interplanar spacings that contribute to the diffraction. The spacings provide approximately half integral coherence at short range, with near integral coherence at long range. A special metric relates the diffraction pattern to the corresponding structure. The simulations match data in several ways: diffracted beam intensities are correctly calculated; a high resolution electron micrograph is modeled in detail; and the edge sharing unit cell fits known atomic sizes. Comparisons are made between various alloys.
Keywords: quasicrystal; metric; quasi-Bragg law; geometric, logarithmically periodic