quasicrystals

quasicrystals
Name	Quasicrystals
Formula	variable
Discovery	1982
Discoverer	Dan Shechtman
Category	Solid-state matter

quasicrystals are a class of ordered solids that display nonperiodic atomic arrangements and symmetry incompatible with conventional crystalline translational periodicity. They exhibit sharp diffraction patterns like X-ray crystallography, possess rotational symmetries forbidden by classical crystal structure rules, and bridge concepts from solid state physics, mathematics, and materials science. Interest from Nobel Prize committees, research groups at institutions such as Weizmann Institute of Science and Oak Ridge National Laboratory, and industrial laboratories has grown since their initial identification.

Definition and Properties

Quasicrystals are defined by long-range order without translational periodicity, producing discrete Bragg peaks in diffraction experiments carried out using X-ray diffraction, electron microscopy, and neutron diffraction. Their defining properties include aperiodic tiling consistent with higher rotational symmetries, electrical and thermal transport anomalies studied alongside superconductivity and magnetism phenomena, and mechanical hardness comparable to intermetallics examined by researchers at MIT, University of California, Berkeley, and Max Planck Society. Experimental identification often references standards from International Union of Crystallography guidelines and analysis methods developed in collaboration with groups at Harvard University and ETH Zurich.

History of Discovery

The first clear report associating an ordered aperiodic alloy with forbidden symmetry was published in 1984 by Dan Shechtman at National Institute of Science and Technology-linked labs, provoking debate with proponents from IBM and critics such as Linus Pauling who favored twinning explanations. Early experimental support came from teams at Ames Laboratory, Birkbeck, University of London, and Cambridge University, and theoretical frameworks were advanced by Roger Penrose and collaborators following earlier mathematical work by Harold Scott MacDonald Coxeter. Recognition culminated in a Nobel Prize in Chemistry awarded to Shechtman in 2011 and subsequent expansion of research programs at Lawrence Berkeley National Laboratory and Argonne National Laboratory.

Structure and Symmetry

Quasicrystalline order often maps to mathematical constructs such as Penrose tilings introduced by Roger Penrose and higher-dimensional cut-and-project schemes related to work by Hermann Minkowski and Nicolas de Bruijn. Symmetry types observed experimentally include icosahedral symmetry linked to Kepler-inspired polyhedra, decagonal symmetry studied at California Institute of Technology, and dodecagonal motifs explored at University of Oxford. Structural refinement uses techniques from Fourier analysis and algorithms developed by groups at IBM Research, Los Alamos National Laboratory, and Cornell University. Connections to group theory and representations related to E8 lattices have been proposed by teams at Princeton University and Imperial College London.

Formation and Synthesis

Quasicrystalline phases have been synthesized via rapid solidification techniques pioneered at Ames Laboratory and by vapor deposition methods refined at Bell Labs and Siemens. Alloy systems include Al–Mn first reported in early studies, later expanded to Al–Cu–Fe, Al–Pd–Mn, and binary systems investigated at Delft University of Technology and Tohoku University. Synthesis protocols employ methods such as physical vapor deposition used by National Institute for Materials Science researchers, melt spinning developed at University of Tokyo, and high-pressure synthesis undertaken at Argonne National Laboratory. Thin-film growth for surface quasicrystals has been advanced by teams at EPFL and University of Michigan.

Physical and Chemical Properties

Quasicrystals show low thermal conductivity and high electrical resistivity relative to related alloys, prompting studies into thermoelectric behavior by groups at Stanford University and Rutgers University. Chemically, they exhibit oxidation resistance and low surface energy influencing friction and non-stick properties explored by NASA and Airbus materials programs. Mechanical properties such as high hardness and brittleness have been characterized using nanoindentation at facilities including Fraunhofer Society and National Physical Laboratory (UK). Magnetic and electronic spectroscopies from teams at Brookhaven National Laboratory and Rutherford Appleton Laboratory probe localized electronic states linked to pseudogaps observed in angle-resolved photoemission studies by SLAC National Accelerator Laboratory.

Applications and Technological Uses

Applied research has targeted quasicrystalline coatings for wear resistance in aerospace programs at Boeing and European Space Agency, as non-stick surfaces in cookware developed in collaboration with Alessi (company), and as low-friction phases in automotive industry components tested by Toyota and General Motors. Thermal barrier concepts informed by quasicrystal low thermal conductivity are considered by Siemens and General Electric for turbine components. Potential uses in photonic bandgap materials link to work at Bell Labs and Columbia University, while catalytic and hydrogen-storage studies have involved teams at Oak Ridge National Laboratory and French Alternative Energies and Atomic Energy Commission.

Theoretical Models and Mathematical Foundations

Mathematical foundations draw on aperiodic tilings by Roger Penrose, cut-and-project methods formalized in studies associated with Hermann Weyl and John von Neumann, and spectral theory connected to work by Israel Gelfand and André Weil. Physical modeling uses density functional theory calculations performed at Los Alamos National Laboratory and Lawrence Livermore National Laboratory, molecular dynamics simulations from research groups at Argonne National Laboratory and National Renewable Energy Laboratory, and phason dynamics described in theoretical work by Paul Steinhardt and colleagues at Princeton University. Links to quasicrystalline order in mathematics include motifs related to Möbius transformations and algebraic structures studied by Emmy Noether and Évariste Galois.

Category:Materials science