Gheorghe Curelet-Balan Blog

Tuesday, September 26, 2006

The possible, impossible crystals.

The structure of one of them, pictured below, was presented as a geometry game by Paul J. Steinhardt during the 100th PI public lecture, Impossible Crystals. He called it a non-periodic icosahedrally symmetric quasicrystal lattice, if I gathered correctly.

Bellow I will make time references to specific parts of the online playback of the lecture.

Complexity is beautiful if it can be reduced to simple parts. If you look closely you'll notice that only four building blocks are needed to build the below structure. Go to minute 35:10 of the lecture to learn about the building blocks and how they are built. To see how the structure was built watch from minute 38:18.

You'll learn a little bit about the game of deriving one object (zonehedron) from another. The sequence of derivations is Red-Blue-Yellow-White. Each element has five fold symmetry axis. The quasiperiodic symmetry is explained at minute 28:10, demonstrated on a quilt type 2D tiled structure. Non-periodic symmetry could be identified in other quilt type patterns.

So what an impossible crystal is? It is a quasicrystal. By Paul J. Steinhard's definition a quasicrystal is an orderly arrangement (non-periodic) structure with rotational forbidden symmetry that can be reduced to a finite number of repeating units (similar with Penrose chickens). The story of how quasicrystals were born starts at minute 20:39.

A five-fold symmetry solid is pictured in this image. If you think though that it is soccer ball shaped, think again since it is actually a hole in the quasicrystal that looks this way.

Ok, besides being beautiful and looking like a soccer ball, what quasicrystals are good for? Due to their new physical properties (elasticity, diffraction, etc.), minute 66:49, their applications are diverse. They could be used to make stronger airplane wings, non-scratch pots (minute 67:44) or photonic circuits (minute 69:00). On minute 72:00 starts the story of how the lucky combination between quasicrystals and cosmology research could yield to a unique photonic quasicrystal. Who says that cosmology research doesn't have practical applications?

It looks like besides being possible, the impossible crystals could improve the everyday life and hold the key to some of the next technological breakthroughs.

Follow this link to see some of the pictures I took during the lecture.

Other links:
Photonic crystal
Photonic computing
Paul Steinhardt's quasiphoton web page.


Post a Comment

<< Home