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Pseudo-fivefold diffraction symmetries in tetrahedral packing.

Stephen Lee1, Ryan Henderson, Corey Kaminsky

  • 1Department of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853-1301, USA. sl137@cornell.edu

Chemistry (Weinheim an Der Bergstrasse, Germany)
|June 20, 2013
PubMed
Summary
This summary is machine-generated.

Atomic tetrahedra pack into fused icosahedra, creating pseudo-fivefold symmetry in metallic crystals. A geometric model using the 600-cell explains these symmetries and predicts electron counts for metal stability.

Keywords:
diffractionintermetallic phasesnoble metalsquasicrystalssolid state structures

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Area of Science:

  • Crystallography and Materials Science
  • Solid-State Physics
  • Inorganic Chemistry

Background:

  • Metallic elements naturally form atomic tetrahedra that pack into fused icosahedral structures.
  • These structures exhibit pseudo-fivefold rotational diffraction symmetry across various Bravais lattice types.
  • Existing models do not fully unify the geometric principles behind these symmetries and packing arrangements.

Purpose of the Study:

  • To present a unified geometric model based on the 600-cell to explain pseudo-fivefold symmetries in intermetallic crystals.
  • To introduce a reciprocal space cluster model that correlates with diffraction peaks and metal stability theories.
  • To validate the model by calculating electron per atom bounds and comparing them with known intermetallic compounds.

Main Methods:

  • Development of a unified geometric model utilizing the 600-cell to rationalize fused-icosahedral clusters (vertex-, edge-, polygon-, and cell-centered).
  • Introduction and analysis of a tetrahedrally-packed reciprocal space cluster derived from pseudosymmetry.
  • Application of the Jones model for metal stability, calculating electron per atom bounds for pseudosymmetric Jones zone faces.

Main Results:

  • The 600-cell model successfully accounts for pseudo-fivefold symmetries in orthorhombic, hexagonal, and cubic intermetallic crystals.
  • The reciprocal space cluster accurately corresponds to principal diffraction peaks and provides insights into the Jones model.
  • Calculated electron per atom bounds align with experimental data for Group 10-12 tetrahedrally-packed structures, including Cu/Cd compounds.
  • The crystal structure of Zn11Au15Cd23, a 1:1 MacKay cubic quasicrystalline approximant, was determined.

Conclusions:

  • The 600-cell provides a unifying geometric framework for understanding pseudo-fivefold symmetries in fused-icosahedral metallic crystals.
  • The reciprocal space cluster concept and pseudosymmetry-based Jones model offer predictive power for metal stability and electron counts.
  • The study validates the geometric model with experimental data and presents a new quasicrystalline approximant structure.