Summary

This volume collects key papers and commentary from the first two decades of research on icosahedral quasicrystals, following Dan Shechtman’s 1984 discovery of a phase in a rapidly solidified Al-Mn alloy that exhibited sharp diffraction patterns with fivefold symmetry—forbidden by classical crystallography. The central thesis is that icosahedral quasicrystals are a genuine new form of solid matter, ordered but not periodic, requiring a paradigm shift in the definition of a crystal. The book presents the initial experimental evidence, the theoretical development of higher-dimensional crystallography (projecting from a 6D periodic lattice), and the subsequent discovery of stable quasicrystals in systems like Al-Cu-Fe. A reader takes away a concrete understanding of how quasicrystals challenged the 200-year-old foundations of crystallography, the mathematical tools used to describe their aperiodic order, and the experimental methods (electron diffraction, high-resolution microscopy) that confirmed their structure.

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Key concepts

Icosahedral point group — A symmetry group with six fivefold axes, incompatible with periodic translational order in three dimensions.
Quasiperiodic order — A deterministic, non-repeating pattern that can be described as a projection of a higher-dimensional periodic lattice.
Penrose tiling — A two-dimensional aperiodic tiling with fivefold symmetry, used as a conceptual model for icosahedral quasicrystal structure.
Phason strain — A type of structural defect unique to quasicrystals, involving local rearrangements of atoms that preserve long-range order.
Indexing with six integers — The method of assigning Miller-like indices to diffraction peaks using a 6D reciprocal lattice basis.
Stable quasicrystal — A thermodynamically equilibrium phase (e.g., Al-Cu-Fe) that does not require rapid solidification, enabling large single-grain growth.