Dodecagonal quasicrystals: Construction of 2D lattices and demonstrations using laser pointers

Authors

  • Vladimir M. Petrushevski Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University in Skopje, Macedonia https://orcid.org/0000-0002-4796-4929
  • Sašo Kalajdžievski University of Manitoba, Winnipeg, Manitoba, Canada

DOI:

https://doi.org/10.20450/mjcce.2022.2368

Keywords:

Quasicrystals, Chemical demonstrations

Abstract

Photographic slides of an aperiodic dodecagonal tiling were used as two-dimensional diffraction gratings to describe and demonstrate the basic properties of dodecagonal quasicrystals. This paper complements our earlier publication on Penrose (decagonal) and Ammann (octagonal) quasicrystals, where we constructed and presented the corresponding diffraction gratings.

Author Biography

Vladimir M. Petrushevski, Institute of Chemistry, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University in Skopje, Macedonia

References

(1) http://jwilson.coe.uga.edu/emat6680fa05/schultz/

penrose/penrose_main.html, Penrose Tilings, Kyle

Schultz (accessed October 19, 2021).

(2) Penrose, R.; The role of aesthetics in pure and applied mathematical research, Bull. Inst. Maths. Appl. 1974, 10, 266–271.

(3) Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J. W. Me-tallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett. 1984, 53, 1951–1953. https://doi.org/10.1103/PhysRevLett.53.1951

(4) Levine, D.; Steinhardt, P. J. Quasicrystals: A New Class of Ordered Structures, Phys. Rev. Lett. 1984, 53, 2477–2480. https://doi.org/10.1103/PhysRevLett.53.2477

(5) https://guides.lib.umich.edu/citation/WebofScience, Research Impact Metrics: Citation Analysis (accessed October 19, 2021).

(6) http://physics.aps.org/story/v28/st14, Nobel Prize-Discovery of Quasicrystals (Google search, accessed October 19, 2021).

(7) Ishimasa, T., Dodecagonal quasicrystals still in pro-gress, Isr. J. Chem. 2011, 51, 1216–1225.

https://doi.org/10.1002/ijch.201100134

(8) Sadoc, J.-F.; Mosseri, R., Quasicrystalline structures: examples in 2D of a new generation method. In Jarić, M. V. & Lundqvist, S. (Editors), Quasicrystals, World Scientific, Singapoore, 1990; pp 169–179.

(9) Petruševski, V. M.; Kalajdžievski, S. M.; Najdoski, M. Ž., Quasicrystals: comparison with crystals, construc-tion of 2-D lattices, and demonstrations using a laser pointer, Chem. Educator 2003, 8, 358–363.

https://doi.org/10.1333/s00897030738a, 860358vp.pdf.

(10) Lisensky, G. C.; Kelly, T. F.; Neu, D. R.; Ellis, A. B., The optical transform: simulating diffraction experi-ments in introductory courses, J. Chem. Educ. 1991, 68, 91–96. https://doi.org/10.1021/ed068p91

(11) Berger, R., The undecidability of the domino problem, Memoirs Amer. Math. Soc 1966, 66, pp 1–72.

(12) https://www.google.com/search?q=dodecagonal+quasi-crys-tals+diffraction+pattern&tbm=isch&tbo=u&source= univ&sa=X&ei=5R3JUoSwBIe0ywPLvoG4CA&ved=0CCIQsAQ&biw=1024&bih=367. Dodecagonal Quasi¬crystals Diffraction Pattern (accessed October 19, 2021).

(13) Conrad, M.; Krumeich, F.; Reich, C.; Harbrecht, B., Hexagonal approximants of a dodecagonal tantalum telluride – the crystal structure of Ta21Te13, Mat. Sci. Eng. 2000, 294–296, 37–40.

https://doi.org/10.1016/S0921-5093(00)01150-3

Downloads

Published

2022-05-21 — Updated on 2022-07-01

Versions

How to Cite

Petrushevski, V. M., & Kalajdžievski, S. (2022). Dodecagonal quasicrystals: Construction of 2D lattices and demonstrations using laser pointers. Macedonian Journal of Chemistry and Chemical Engineering, 41(1), 133–137. https://doi.org/10.20450/mjcce.2022.2368 (Original work published May 21, 2022)

Issue

Section

Education