Generally, one can predict the shape of molecules by applying the VSEPR theory and knowledge of intermolecular and intramolecular bonds to a molecule. However, how can one predict the shape of a crystal when the atoms are shaped in such a unique pattern that never repeats?
A quasicrystal is a naturally occurring type of crystal that defies our previous knowledge in crystallography and molecular shape of crystals. Crystal lattices, until now, were represented by their geometric repetitive patterns. Regularity in the molecular structure of crystals was supported by countless numbers of experiments and was one of the main things that defined crystalline structure and arrangement (Petrucci, R.H., 2011). Thus, the discovery of the quasicrystal is major; the formal definition of a crystal will have to be altered now that a crystal has been found that does not show periodicity in its molecular structure.
The quasicrystal’s unique arrangement is a complex one that cannot be mathematically defined in the 3D-axis. Since there is no pattern in the 3D axis, one would have to define this shape in greater dimensions. To accurately communicate positions of certain molecules in a quasicrystal in 3D, thousands of parameters would have to be used to describe position in a specific unit of the structure (Weber, S., N/A). It has a fivefold symmetry – meaning that it can rotate one fifth of a revolution and overlap itself (Nelson, S.A., 2011). This was considered to be impossible in naturally occurring substances until this discovery was made. For instance, Figure 1 shows that when crystals are rotated 90 degrees in any direction, it will overlap. This is known as fourfold symmetry and is common amongst many crystals. A molecule that will rotate one fifth of a revolution and overlap was unheard of – until now.
Figure 1 – A crystal with fourfold symmetry will rotate 90 degrees and fully overlap itself. This means that in one revolution (360 degrees), the molecule will overlap four times (Nelson S.A., 2011).
The first naturally occurring quasicrystal was found in 2009 in a mineral sample by Princeton University researchers Paul J. Steinhardt, Peter J. Lu and Nan Yaos in Russia. The mineral (shown in Figure 2) was found in the Koryak mountains in samples of khatyrkite and cupalite. It was aluminum-copper-iron based and contained quasicrystallic grains (Jacoby, M., N/A).
Figure 2: A sample from the Koryak Mountains in Russia containing quasicrystal grains. It is a mix of minerals including khatyrkite and cupalite, and is roughly one millimeter in diameter (Jacoby, M., 2009).
Interestingly enough, the patterns seen in quasicrystals can be seen in Islamic tiling from the 13th century in The Alhambra in Spain, as well as in the Darb-Imam shrine in Esfahan, Iran (Connor, S., 2011).
Figure 3: A part of the intrinsic pattern in the dome-ceiling of the Shah Mosque in Iran, displaying patterns that are regular, yet never repeat and display five and ten-fold symmetry (Abdul-Ahad, G., N/A)
On a similar note, the same pattern can be observed in Roger Penrose’s mathematical Penrose tilings that also display 5 and 10-fold symmetry, put forth in the 1970’s (Weber, S., N/A). It is evident that such patterns have been known to man for centuries but no naturally occurring examples of this pattern had been proven to exist. With such redefining discoveries, our scientific knowledge can truly be broadened to include all hidden wonders on Earth.
References
Abdul-ahad, G., N.A. Isfahan: Iran’s Hidden Jewel. The Smithsonian, [online] Available at:http://www.smithsonianmag.com/multimedia/photos/?articleID=41381302&c=y [Accessed October 7, 2011]
Connor, S., 2011. Unbelievable discovery wins chemistry prize for Daniel Shechtman. The Independent, [online] Available at:http://www.independent.co.uk/news/science/unbelievable-discovery-wins-chemistry-prize-for-daniel-shechtman-2366168.html[Accessed October 7, 2011]
Jacoby, M., 2009. Quasicrystals in Nature. Chemical and Engineering News, [online] Available at: http://pubs.acs.org/cen/news/87/i23/8723news4.html[Accessed October 7, 2011]
Nelson, S. A., 2011. Mineralogy. Tulane University, [online] Available at: http://www.tulane.edu/~sanelson/eens211/introsymmetry.htm [Accessed October 7, 2011]
Petrucci, R.H. [et al.], 2011. General Chemistry;Principles and Modern Applications. 10th ed. Toronto, Pearson Canada Inc.
Weber, S., N/A. Quasicrystals. JCrystal, [online] Available at: http://www.jcrystal.com/steffenweber/qc.html [Accessed October 7, 2011]