Abstract
We prove the possibility to use the method of modeling of a quasi-lattice with octagonal symmetry similar to that proposed earlier for the decagonal quasicrystal. The method is based on the multiplication of the groups of basis sites according to specified rules. This model is shown to be equivalent to the method of the periodic lattice projection, but is simpler because it considers merely two-dimensional site groups. The application of the proposed modeling procedure to the reciprocal lattice of octagonal quasicrystals shows a fairly good matching with the electron diffraction pattern. Similarly to the decagonal quasicrystals, the possibility of three-index labeling of the diffraction reflections is exhibited in this case. Moreover, the ascertained ratio of indices provides information on the intensity of diffraction reflections.
This is a preview of subscription content, log in via an institution to check access.
Access this article
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Similar content being viewed by others
References
S. E. Burkov, Phys. Rev. B: Condens. Matter 47, 12325 (1993).
Yanfa Yan and S. J. Pennycook, Phys. Rev. B: Condens. Matter 61, 14291 (2000).
V. V. Kovshevny, D. V. Olenev, and Yu. Kh. Vekilov, J. Exp. Theor. Phys. 86(2), 375 (1998).
Yu. Kh. Vekilov and E. I. Isaev, Crystallogr. Rep. 52(6), 932 (2007).
W. Steurer and S. Deloudi, Crystallography of Quasicrystals: Concepts, Methods, and Structures (Springer-Verlag, Berlin, 2009), p. 384.
R. Ammann, B. Grünbaum, and G. C. Shephard, Discrete Comput. Geom. 8, 1 (1992).
F. P. N. Beenker, Algebraic Theory of Non-Periodic Tilings of the Plane by Two Simple Building Blocks: A Square and a Rhombus (Eindhoven University of Technology, Eindhoven, The Netherlands, 1982), TH-Report 82-WSK04.
P. J. Lu, K. Deffeyes, P. J. Steinhardt, and N. Yao, Phys. Rev. Lett. 87, 275507 (2001).
V. E. Dmitrienko, V. A. Chizhikov, S. B. Astaf’ev, and M. Kléman, Crystallogr. Rep. 49(5), 547 (2004).
A. Singh and S. Ranganathan, J. Mater. Res. 14, 11 (1999).
S. Ranganathan, E. A. Lord, N. K. Mukhopadhyay, and A. Singh, Acta Crystallogr., Sect. A: Found. Crystallogr. 63, 1 (2007).
Y. K. Vekilov and M. A. Chernikov, Phys.-Usp. 53(6), 537 (2010).
C. Janot, Quasicrystals: A Primer, 2nd ed. (Oxford University Press, New York, 1994), p. 409.
J. W. Cahn, D. Shechtman, and D. Gratias, J. Mater. Res. 1, 13 (1986).
V. V. Girzhon, V. M. Kovalyova, O. V. Smolyakov, and M. I. Zakharenko, J. Non-Cryst. Solids 358, 137 (2012).
J.-M. Dubois, Useful Quasicrystals (World Scientific, Singapore, 2005), p. 481.
M. Bicknell, Fibonacci Q. 13, 345 (1975).
Y. Roichman and D. G. Grier, arXiv:cond-mat/0506283.
D. Levine and P. Steinhardt, Phys. Rev. Lett. 53, 26 (1984).
K. H. Kuo, J. Non-Cryst. Solids 117/118, 754 (1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
The article is published in the original.
Rights and permissions
About this article
Cite this article
Girzhon, V.V., Smolyakov, O.V. & Zakharenko, M.I. Modeling quasi-lattice with octagonal symmetry. J. Exp. Theor. Phys. 119, 854–860 (2014). https://doi.org/10.1134/S1063776114110053
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776114110053