Pragmatic Application of Abstract Algebra to Two-Dimensional Lattice Matching

• Kawahara Kazuaki

  Department of Advanced Materials Science, Graduate School of Frontier Science, The University of Tokyo Research Fellow of Japan Society for the Promotion of Science

• Arafune Ryuichi

  International Center for Materials Nanoarchitectonics (WPI-MANA), National Institute for Materials Science

• Kawai Maki

  Department of Advanced Materials Science, Graduate School of Frontier Science, The University of Tokyo

• Takagi Noriaki

  Department of Advanced Materials Science, Graduate School of Frontier Science, The University of Tokyo

Abstract

We investigated the lattice matching condition of two-dimensional (2D) lattices based on the group isomorphism of 2D Euclidean space to complex plane. This isomorphism enables us to avoid the inconvenience derived from the algebraic structure of 2D vectors and provides the systematic analysis. We found that the lattice matching is closely connected with ideal class group which is an invariant in the algebraic number field. We also provide an algorithm to construct a structure model for a superstructure formed by overlapping two 2D lattices, which is helpful for making trial models in the structure analysis. [DOI: 10.1380/ejssnt.2015.361]

Journal

• e-Journal of Surface Science and Nanotechnology

  e-Journal of Surface Science and Nanotechnology 13 (0), 361-365, 2015

  The Japan Society of Vacuum and Surface Science

Keywords

• Surface structure
• morphology
• roughness
• and topography
• Structure analysis
• Lattice matching
• Abstract algebra

Details

• CRID: 1390282680163286912
• NII Article ID: 130005087505
• DOI: 10.1380/ejssnt.2015.361
• ISSN: 13480391
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed