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Aperiodic CrystalsFrom Modulated Phases to Quasicrystals:  Structure and Properties$
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Ted Janssen, Gervais Chapuis, and Marc de Boissieu

Print publication date: 2018

Print ISBN-13: 9780198824442

Published to Oxford Scholarship Online: August 2018

DOI: 10.1093/oso/9780198824442.001.0001

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Aperiodic Crystals

Ted Janssen

Gervais Chapuis

Marc de Boissieu

Oxford University Press

The law of rational indices to describe crystal faces was one of the most fundamental law of crystallography and is strongly linked to the three-dimensional periodicity of solids. This chapter describes how this fundamental law has to be revised and generalized in order to include the structures of aperiodic crystals. The generalization consists in using for each face a number of integers, with the number corresponding to the rank of the structure, that is, the number of integer indices necessary to characterize each of the diffracted intensities generated by the aperiodic system. A series of examples including incommensurate multiferroics, icosahedral crystals, and decagonal quaiscrystals illustrates this topic. Aperiodicity is also encountered in surfaces where the same generalization can be applied. The chapter discusses aperiodic crystal morphology, including icosahedral quasicrystal morphology, decagonal quasicrystal morphology, and aperiodic crystal surfaces; magnetic quasiperiodic systems; aperiodic photonic crystals; mesoscopic quasicrystals, and the mineral calaverite.

Keywords:   aperiodic crystal morphology, calaverite, icosahedral quasicrystal morphology, decagonal quasicrystal morphology, aperiodic crystal surface, magnetic quasiperiodic system, incommensurate multiferroic, aperiodic photonic crystal, mesoscopic quasicrystal

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