PREFACE

doi:10.1093/acprof:oso/9780198567776.002.0004

Front Matter

PREFACE

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https://doi.org/10.1093/acprof:oso/9780198567776.002.0004

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v–vi

Published:

May 2007

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In the eighteenth and nineteenth centuries the idea developed that, on the atomic level, crystals are constructed by regularly spaced unit cells. The mathematical theory for this idea was created by Bravais, Schoenflies, and Fedorov. After the discovery of X-rays in 1912 one really could prove this underlying periodic structure. Since then the prevailing idea has been that the ground state of matter at zero temperature is lattice periodic with a lattice constant of the order of a nanometre. Although there was actually no theoretical proof for this idea, it was generally accepted. In that view disordered systems, like glasses, form at most metastable configurations.

In the 1960s, several materials became known where besides the reflections at the points of a reciprocal lattice, there are also sharp peaks which do not fit into this scheme. The first to describe this situation was Pim de Wolff from Delft, who realized that the satellite peaks observed in anhydrous γ-Na₂CO₃ are not defects, but belong really to the structure, which is in this case an aperiodic modulated crystal phase. Although at very low temperature, the ground state is again periodic, the intermediate state between the periodic high-temperature and low-temperature phases is thermodynamically stable and aperiodic, but not disordered! Later several such materials were found. In fact, a substantial part of the minerals of the earth's crust turn out to be aperiodic. However, the term ‘aperiodic’ is not the proper characterization. As can be seen from the sharpness of the diffraction spots, these materials are just as well ordered as the usual crystals. One must agree that these materials should be called crystals as well. They have sharp diffraction peaks and flat facets. Nevertheless, these materials were not generally considered to be interesting. This changed with the discovery in 1982 of quasicrystals by Shechtman and collaborators. These materials were intriguing because they show sharp diffraction spots and a rotation symmetry which is not crystallographic, in the sense that the symmetry is not compatible with lattice periodicity. This shows that the new materials are well ordered, but aperiodic. In fact, they are quasiperiodic in the mathematical sense, and therefore they are called quasicrystals. After some years it turned out that the non-crystallographic symmetry is not an essential property. In that sense quasicrystals are not really different from modulated phases. They are all quasiperiodic crystals.

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