quasicrystal approximants

quasicrystal approximants
Name	Quasicrystal approximants
Category	Intermetallic phases
Formula	Various
Crystal system	Complex
Symmetry	Aperiodic approximant
Discovery	1980s

quasicrystal approximants Quasicrystal approximants are periodic intermetallic phases that locally mimic the atomic motifs of aperiodic quasicrystals while preserving three-dimensional translational symmetry. They bridge the structural and conceptual gap between periodic crystals exemplified by Max von Laue-era diffraction studies and aperiodic order associated with the work of Dan Shechtman and Roger Penrose. Approximants have been studied by research groups at institutions such as IBM, Los Alamos National Laboratory, and University of California, Santa Barbara.

Introduction

Approximants were recognized following the discovery of quasicrystals by Dan Shechtman and subsequent theoretical developments by Alan Mackay and Roger Penrose, with experimental exploration at facilities including Oak Ridge National Laboratory and Argonne National Laboratory. They appear in alloy systems investigated by teams at Harvard University, Massachusetts Institute of Technology, and Tokyo Institute of Technology, and have been the subject of reviews published in journals by American Physical Society and Nature Publishing Group.

Structural Characteristics

Approximants consist of large unit cells that contain clusters or tiles resembling those in quasicrystals studied by Dan Shechtman and modeled by Roger Penrose tilings; examples include motifs analogous to the Mackay icosahedron from Alan Mackay's work and Bergman clusters analyzed at Max Planck Society institutes. Their diffraction patterns show sharp Bragg peaks like those measured at European Synchrotron Radiation Facility and Diamond Light Source, and their atomic arrangements have been resolved using methods developed at Lawrence Berkeley National Laboratory and Stanford University.

Formation and Stability

Formation pathways for approximants have been elucidated by experimental groups at University of Cambridge and École Normale Supérieure, and by theoretical teams connected to CERN and Princeton University. Stabilization depends on electron concentration concepts traced to Hume-Rothery rules and energetic arguments discussed in conferences at International Union of Crystallography and workshops at Bell Labs. Phase diagrams including approximants have been mapped by researchers at Tohoku University and National Institute for Materials Science.

Classification and Examples

Approximants are classified by unit cell size, cluster type, and chemical system with representative examples from the Al–Pd–Mn system studied at ENSAM and the Al–Cu–Fe system investigated at University of Geneva. Notable approximants include phases related to those first characterized by I. R. Fisher's group and later by teams at Kyoto University and Pennsylvania State University. Classification schemes were proposed in symposia organized by International Centre for Theoretical Physics.

Physical Properties and Applications

Physical properties such as thermal conductivity, electrical resistivity, and hardness have been measured in laboratories at Argonne National Laboratory and Max Planck Institute for Metals Research, informing potential applications explored by researchers at Nissan Motor Company, Siemens, and Hitachi. Approximants exhibit features studied in contexts like low thermal conductivity relevant to thermoelectric research pursued at MIT and low-friction coatings developed with partners including Toyota Motor Corporation.

Experimental Identification and Characterization

Identification employs techniques established at facilities such as CERN-affiliated beamlines, European Synchrotron Radiation Facility, Brookhaven National Laboratory, and National Synchrotron Light Source II. Methods include single-crystal X-ray diffraction refined using software developed at Fritz Haber Institute collaborators, transmission electron microscopy protocols from Japan Atomic Energy Agency, and scanning probe microscopy work at IBM Research. Chemical analysis is performed using mass spectrometry and electron probe techniques standardized at United States Geological Survey labs.

Theoretical Models and Simulations

Theoretical descriptions draw on models advanced by Roger Penrose, Alan Mackay, and researchers at Los Alamos National Laboratory and California Institute of Technology; simulation studies use density functional theory implementations from groups at Oak Ridge National Laboratory and molecular dynamics packages developed at Lawrence Livermore National Laboratory. Computational classifications have been pursued on supercomputers at National Energy Research Scientific Computing Center and in collaborations with European Centre for Medium-Range Weather Forecasts-hosted facilities for large-scale calculations.

Category:Intermetallic phases Category:Crystallography