The Effects of Golden Mean on the Diffraction by Monatomic One-Dimensional Quasicrystal

M. Sa’Id¹, G. Babaji² and S.G. Abdu^3,

¹Department of Physics, Sa’adatu Rimi College of Education, Kano-Nigeria

²Department of Physics, Bayero University, Kano-Nigeria

³Department of Physics, Kaduna State University, Kaduna-Nigeria

Cite this paper:
M. Sa’Id, G. Babaji and S.G. Abdu. The Effects of Golden Mean on the Diffraction by Monatomic One-Dimensional Quasicrystal. Applied Mathematics and Physics. 2014; 2(2):53-58. doi: 10.12691/amp-2-2-5

Abstract

In this work, the code ‘Laue’ was used to simulate the diffraction pattern and to investigate the effects of varying the golden mean in a monatomic linear quasicrystal having a pseudo atomic potential. The work involved setting the parameters of the code required to simulate the diffraction, running the code and exporting the data generated to excel for analysis. It was found that the shape of the diffraction pattern and the background intensity for a given value of the golden mean is unique. Both the width of the diffraction pattern and the intensity of the central peak decrease with increasing golden mean. Results obtained illustrated the features of the diffraction by quasicrystal and proved the suitability and accuracy of the code in simulating the dynamics of quasicrystals.

Keywords:
quasicrystal diffraction pattern golden mean central peak

This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]	Cahn, J.W. (1996), Epiloque: Proceedings of the International Conference on Quasicrystals, edited by C. Janot and R. Mosseri, World Scientific, Singapore, pp. 807.
[2]	De Bruijn, N,G, (1981), Ned. Acad. Weten. Proc. Ser. A 43, 39-53.
[3]	Ferralis, N., A. W. Szmodis and R. D. Diehl (2004), Diffraction from One- and Two-Dimensional Quasicrystalline Gratings, American Association of Physics Teachers, University Park, Pennsylvania, 16802, 1241-1246.
[4]	Ishimasa, T., H.U. Nissen, and Y. Fukano (1985), New Ordered State Between Crystalline and Amorphous Ni-Cr Particles, Phys. Rev. Lett. 55 (5), 511-513.
[5]	Latvin, S.Y. (1988), Generation and Experimental Measurement of One-Dimensional Quasicrystal Diffraction Pattern, Am. J. phys. 56 (1), 72-75.
[6]	Levine, D. (1985), Quasicrystals, Journal De Physique, vol. 46 (8), 397-402.
[7]	Lifshitz, R. (1996), The Symmetry of Quasiperiodic Crystal, Physica. A 232, 633-647.
[8]	Lifshitz, R. (1997). Theory of Color Symmetry for Periodic and Quasiperiodic Crystal, Rev. Mod. Phys. 69, 1181.
[9]	Lifshitz, R. (2003), Quasicrystal; A Matter of Definition, Found. Phys. 33 (12) 1703-1711.
[10]	Lifshitz, R. and S. E. Mandel (2004), Symmetry of Magnetically Ordered Quasicrystals, Acta Cryst. A 60, 167.
[11]	Shechtman, D., I. Blech, D. Gratias, and J. Cahn (1984), Phys. Rev. let, 53.
[12]	Silsbee R.H. and Drager (2005), Simulations for Solid State Physics, Cambridge University Press, London, Chapter Three.