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On the algebra of binary codes representing close-packed stacking sequences.

Ernesto Estevez-Rams1, Cristy Azanza-Ricardo, Jorge Martínez García

  • 1Institute for Materials and Reagents (IMRE), University of Havana, San Lazaro y L, CP 10400, C. Habana, Cuba. estevez@imre.oc.uh.cu

Acta Crystallographica. Section A, Foundations of Crystallography
|February 23, 2005
PubMed
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Binary codes derived from Hagg symbols systematically study close-packed polytypes. This method counts polytypes and determines their symmetry groups by reducing problems to eigenvector calculations.

Area of Science:

  • Crystallography
  • Materials Science
  • Computational Chemistry

Background:

  • Close-packed polytypes are crucial in materials science.
  • Understanding polytype formation and symmetry is complex.
  • Existing methods for counting polytypes can be limited.

Purpose of the Study:

  • To develop a systematic method for studying close-packed polytypes using binary codes.
  • To count the number of non-equivalent polytypes of a specific length.
  • To determine the number of polytypes belonging to a given symmetry group.

Main Methods:

  • Derivation of binary codes from Hagg symbols.
  • Definition and application of Seitz operators on binary codes.
  • Reduction of counting problems to eigenvector calculations in binary code space.

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Main Results:

  • A method for systematically studying close-packed polytypes is established.
  • The number of non-equivalent polytypes of a given length can be calculated.
  • The number of polytypes conforming to specific symmetry groups is determined.

Conclusions:

  • Binary codes and Seitz operators provide an efficient framework for polytype analysis.
  • The approach simplifies the counting of polytypes and their associated symmetry groups.
  • This method offers a novel computational approach to crystallographic problems.