Tiling models for decagonal quasicrystals with quasiperiodic potentials

Hee Tae Jeong, Won Tae Kim, Do Hyang Kim, Hyeong Chai Jeong

Research output: Contribution to journalConference article

2 Citations (Scopus)

Abstract

We study the thermal equilibrium properties of tiling models for decagonal quasicrystals using Monte Carlo simulations. Two-dimensional (2D) rhombus tilings with a ten-fold quasiperiodic potential are used to model the layers in the decagonal quasicrystals where the potential mimics interlayer interactions from the neighboring layers. When the long wavelength density wave with the ten-fold symmetry is used for the potential, the ground state becomes Penrose tiling. At high temperature, equilibrium configurations are locally similar to the maximal random tiling indicating almost free proliferation of phasons as in the unlocked phason phase. However, their phason-space fluctuations seem to remain finite indicating the long-range quasiperiodic ordering, whereas the logarithmic divergence of phason-space fluctuations is expected in an unlocked phase 2D tiling.

Original languageEnglish
Pages (from-to)115-119
Number of pages5
JournalJournal of Alloys and Compounds
Volume342
Issue number1-2
DOIs
Publication statusPublished - 2002 Aug 14
EventQC2001 - Sendai, Japan
Duration: 2001 Sep 242001 Sep 28

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Quasicrystals
Crystal symmetry
Ground state
Wavelength
Temperature
Monte Carlo simulation
Hot Temperature

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Metals and Alloys
  • Materials Chemistry

Cite this

Jeong, Hee Tae ; Kim, Won Tae ; Kim, Do Hyang ; Jeong, Hyeong Chai. / Tiling models for decagonal quasicrystals with quasiperiodic potentials. In: Journal of Alloys and Compounds. 2002 ; Vol. 342, No. 1-2. pp. 115-119.
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Tiling models for decagonal quasicrystals with quasiperiodic potentials. / Jeong, Hee Tae; Kim, Won Tae; Kim, Do Hyang; Jeong, Hyeong Chai.

In: Journal of Alloys and Compounds, Vol. 342, No. 1-2, 14.08.2002, p. 115-119.

Research output: Contribution to journalConference article

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AU - Jeong, Hee Tae

AU - Kim, Won Tae

AU - Kim, Do Hyang

AU - Jeong, Hyeong Chai

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N2 - We study the thermal equilibrium properties of tiling models for decagonal quasicrystals using Monte Carlo simulations. Two-dimensional (2D) rhombus tilings with a ten-fold quasiperiodic potential are used to model the layers in the decagonal quasicrystals where the potential mimics interlayer interactions from the neighboring layers. When the long wavelength density wave with the ten-fold symmetry is used for the potential, the ground state becomes Penrose tiling. At high temperature, equilibrium configurations are locally similar to the maximal random tiling indicating almost free proliferation of phasons as in the unlocked phason phase. However, their phason-space fluctuations seem to remain finite indicating the long-range quasiperiodic ordering, whereas the logarithmic divergence of phason-space fluctuations is expected in an unlocked phase 2D tiling.

AB - We study the thermal equilibrium properties of tiling models for decagonal quasicrystals using Monte Carlo simulations. Two-dimensional (2D) rhombus tilings with a ten-fold quasiperiodic potential are used to model the layers in the decagonal quasicrystals where the potential mimics interlayer interactions from the neighboring layers. When the long wavelength density wave with the ten-fold symmetry is used for the potential, the ground state becomes Penrose tiling. At high temperature, equilibrium configurations are locally similar to the maximal random tiling indicating almost free proliferation of phasons as in the unlocked phason phase. However, their phason-space fluctuations seem to remain finite indicating the long-range quasiperiodic ordering, whereas the logarithmic divergence of phason-space fluctuations is expected in an unlocked phase 2D tiling.

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