Abstract
In this paper, the fractal structure model, fractal dimensional calculation and the expressions of quasicrystal lattice with fivefold or eightfold symmetry have been discussed. In a fivefold symmetry quasicrystal, the foundational cell is an icosahedron, and the enlargement coefficient is l+(√5+l)/2, and D = 2.6652. In an eightfold symmetry quasicrystal, the foundational cell is a hexakaidecahedron, and the enlargement coefficient is 1+ √2, and D = 2.7206. The fractal structure model has many advantages over the Penrose model. These quasicrystal fractal lattices patterns drawn by my mapping program are close to the high-resolution electron microscopic image of real quasicrystal.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benced PA, Heiney PA (1986) Structure of rapidly quenched Al-Mn. Phys. (Paris) Colloq 47: C–348.
Hiraga K, Hirabayashi, A (1985) Icosahedral quasicrystals of a melt-quenched Al-Mn alloy. The science reports of the research institutes Tohoku University 32 Series A, 309–314.
Levine D, Steinhardt, PJ (1984) Quasicrystals: a new class of ordered structures. Phys Rev Lett 53: 2477–2480.
Mandelbrot BB. (1983) The Fractal Geometry of Nature. Freeman, New York
Peng Z (1985) Building principles of quasicrystal and particle fractal structure model. Earth Science 4: 159–174 (in Chinese).
Peng Z (1989) Deduction of quasilattice with fivefold symmetry and particle fractal structure model. Science in China (series B) 32: 215–226.
Shechtman DJ (1986) Quasiperiodic crystal-experimental evidence. Phys. (Paris) Colloq 47: C–2.
Shechtman D, Blech I, Gratias D, Chahn J (1984) A metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett 53: 1951–1953.
Shen B (1989a) A expression of lattice and calculation of dimension of the fractal structure in quasicrystal. Chinese Science Bulletin 34: 1548–1550.
Shen B (1989b) A expression of lattice and calculation of dimension of the fractal structure in quasicrystal. Chinese Science Bulletin 5: 362–364 (in Chinese).
Shen B (1992) A model of fractal structure of quasicrystals. Scientia Geologica Sinica 1: 63–71.
Shen B, Shi N (1990) The fractal structure for eightfold symmetry quasicrystal. Chinese Science Bulletin 19: 1484–1486 (in Chinese).
Shen B, Shi N (1991) The fractal structure for eightfold symmetry quasicrystal. Chinese Science Bulletin 36: 210–213.
Shi N, Liao L (1989) Point groups and single forms of quasicrystals with eightfold and twelvefold symmetry. Acta Geologica Sinica 2: 39–43.
Shi N, Min L, Shen B (1991) The configuration of quasicrystal unit cell and deduction of quasilattice. Science in China 11: 1216–1223 (in Chinese).
Shi N, Min L, Shen B (1992) The configuration of quasicrystal unit cell and deduction of quasilattice. Science in China 6: 735–744 (in Chinese).
Stephens PW, Goldman AI (1991) The structure of quasicrystal. Scientific American 264: 44–53.
Takayashu H (1986) Fractals (translated by Shen B et al). Seismological Publishing House, 1989 (in Chinese).
Wang N, Chen H, Kuo K (1987) Two-dimensional quasicrystal with rotational symmetry. Phys Rev Lett 59: 1010–1013.
Wang ZM, Kuo K (1988) The octagonal quasilattice and electron diffraction patterns of the octagonal phase. Acta cryst A44: 857–863.
Watanabe Y, Ito M, Soma T (1987) Noperiodic tessellation with eightfold rotational symmetry. Acta Cryst A43: 133–134.
Whittaker EJW, Whittaker RM (1988) Some generalized Penrose patterns from projections of n-dimensional lattices. Acta Cryst A44: 105–112.
Zobetz E (1992) A pentagonal quasicrystal tiling with fractal acceptance domain. Acta Cryst A48: 328–335.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Shen, B. (1994). Fractal Structure of Quasicrystals. In: Kruhl, J.H. (eds) Fractals and Dynamic Systems in Geoscience. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07304-9_25
Download citation
DOI: https://doi.org/10.1007/978-3-662-07304-9_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-07306-3
Online ISBN: 978-3-662-07304-9
eBook Packages: Springer Book Archive