May 31, 2007
Quasicrystals are metal alloys with surprising properties. Discovered about 25 years ago, they appear to have a crystalline structure, yet their constituent atoms don't fall into the repeating patterns typical of conventional crystals. "Mathematically speaking," says Rice University mathematician David Damanik, "quasicrystals fall into a middle ground between order and disorder."
Now, Damanik and his colleague Serguei Tcheremchantsev have new proof of the strangeness of quasicrystals. They focused on a particular mathematical model of quasicrystals and proved that, in this model, a quasicrystal is clearly not an electrical conductor. Their results appear in the July issue of the Journal of the American Mathematical Society.
Computer simulations have shown that electrons move (very slowly) through quasicrystals in a way that's very different from the way they move through an electrical conductor. Damanik and Tcheremchantsev claim that their mathematics provides a clearer picture of the electronic properties of quasicrystals. It also shows that standard approaches, based on the Schrödinger equation, for modeling electronic behavior in materials don't work effectively for elucidating the electronic properties of quasicrystals.
"This is the first time this has been done," Damanik says, "and given the broad academic interest in quasicrystals we expect the paper to generate significant interest."
Source: Rice University, May 23, 2007