Friday, September 26, 2014

Dan Shechtman's crystals

Dan Shechtman, the Philip Tobias Professor of Materials Science at the Technion-Israel Institute of Technology, was awarded the Nobel Prize in Chemistry in 2011, for his work on quasi-crystals. What is interesting is that for a long time, the scientific community could not accept the possibility of non-periodic or quasi-periodic crystals. Linus Pauling is even noted as saying, "There is no such thing as quasi-crystals, only quasi-scientists."

The atoms in Shechtman's crystals, an alloy made up chiefly of aluminium and manganese, exhibited a ten-fold symmetry, hitherto deemed impossible in nature. Shechtman could rotate the diffraction pattern he was seeing, by a tenth of a full circle, i.e. 36 degrees, and still obtain the same pattern. The answers came from from the world of art, and mathematics.






Aperiodic patterns have been used in medieval Islamic patterns, with a set of repeating tiles. Known as "Girih" patterns, using two to five unique tiles, they have been used to decorate portals and vaults of shrines for long:


Pattern from the archway in the Darb-i Iman shrine in Iran


The mathematical explanations came later.     Roger Penrose created aperiodic mosaics, with just two unique tiles: a fat and a thin rhombus. Substituting circles representing atoms, in Penrose's mosaic, and using this pattern as a diffraction grating, produced the same ten fold symmetry that Shechtman was seeing: ten bright dots in a circle.




The repeating structures in Shechtman's quasi-crystals





The Islamic artisans were obviously using advanced concepts of quasi-crystal geometry. In an interesting case of science-following-art, the patterns obtained by Shechtman look no different!

Quasi-crystals have since also been found to exist naturally.







Sources: http://en.wikipedia.org/wiki/Dan_Shechtman
http://www.themuslimtimes.org/2011/07/photography-2/london-museum-hosts-contemporary-islamic-art-show
http://www.telegraph.co.uk/news/uknews/1543585/Islamic-tilers-may-have-led-scientific-field.html