Atomic clusters and atomic surfaces in icosahedral quasicrystals

Area of Science:

• Materials Science
• Crystallography
• Condensed Matter Physics

Background:

• Quasicrystals exhibit unique quasiperiodic atomic structures.
• Describing these structures requires specialized tools, particularly for icosahedral phases.
• Existing models often lack a systematic approach to atomic structure determination.

Purpose of the Study:

• To present fundamental tools for describing quasicrystal atomic structures, focusing on icosahedral phases.
• To introduce two physical rules for generating ideal quasiperiodic models.
• To demonstrate the application of these rules on specific quasicrystal examples.

Main Methods:

• Recalling properties of quasiperiodic objects.
• Applying two physical rules: maximizing density with polyhedral atomic surfaces (ASs) and maximizing high-symmetry orbits.
• Utilizing six-dimensional space and lattice parameters for AS description.
• Analyzing atomic surfaces located at high-symmetry special points.

Main Results:

• A limited number of atomic structures are identified as ideal quasiperiodic models.
• Two sets of atomic surfaces are derived based on the six-dimensional lattice parameter (0.63-0.79 nm).
• Construction of large atomic clusters is facilitated by maximizing complete orbits.
• Successful application of the rules to i-AlMnSi and i-CdRE quasicrystal phases.

Conclusions:

• The two proposed rules provide a systematic method for determining quasicrystal atomic structures.
• These rules simplify the complexity of quasicrystal descriptions, yielding a small set of ideal models.
• The findings offer a pathway to better understand and model real quasicrystals.