Senior collaborator: Dr. Marek Mihalkovic, Slovak Acad. Sciences. Prof. Richard Hennig (Cornell Materials Science Dept.) did a project with me as part of his Ph.D. thesis (2000) from Washington U. Past undergrads: Nan Gu '05, Sejoon Lim '08; current undergrad, Amulya Bhagat '10. My colleague, Prof. Veit Elser, was formerly active in quasicrystals.
On the atomic scale, we try to use microscopcially-derived effective potentials to resolve details of the atomic arrangements which would be unclear from diffraction fitting. With Dr. Marek Mihalkovic (from Slovakia and Chemnitz, Germany) and Prof. Mike Widom (Carnegie-Mellon University), since 1997 we have developed a successful computer model of decagonal AlNiCo in this fashion: see "Total-energy-based prediction of a quasicrystal structure". In 2004, this work was extended to the Co-rich phase of d(AlCoNi) by Nan Gu (undergrad '04) (see an example image of the idealized atomic pattern found by this simulation.)
Most recently, we discovered an model which implemented Penrose's matching rules -- the first time a set of (fairly realistic) microscopic interactions was linked to such local rules, which enforce a practically unique ideal structure analogous to a perfect crystal.
For 20 years I've pursued the "random tiling" model which seems to describe the order of icosahedral quasicrystals. A few years ago, Dr. Marek Mihalkovic and I simulated random-tiling like models with Hamiltonians that, in the low-temperature limit, approach a particular random tiling of the tiles called "canonical cells".