### Prof. Rolfe Petschek

### Case Western Reserve University

### Condensed Orientation Waves: Understanding Some Complex Crystals and Quasicrystals

Many crystal-fluid transitions seem weakly first order in the sense that local properties such as the radial pair distribution change slightly and not qualitatively at the transition and the entropies of transition are small - a few tenths of Boltzmann’s constants per particle. Nevertheless fluid-crystal and fluid-quasicrystal transitions are relatively seldom approached using Landau Theory, the basic phenomenological method most used for understanding continuous and weakly first order transitions. I believe that this is, at least in part, because it has not previously been appreciated that the important Landau order parameters for some interesting crystals, including particularly that formed by the hard tetrahedron fluid, are spatially varying orientations, rather than spatially varying densities. Such order parameters are not easily measured experimentally in many crystals and seem not to have been previously appreciated theoretically as likely order parameters for any system with crystalline or quasicrystalline symmetry other than Blue Phase Liquid Crystals. Analysis of simulations of the hard Platonic solids shows that orientation waves are crucial to the Landau Theory for the tetrahedron, important for the cube, octahedron and dodecahedron, and secondary only for the icosahedron. Insight that can be obtained by analyzing these crystals and quasicrystals using orientation wave order parameters will be discussed. I will speculate about the application of such order parameters to other crystals and quasicrystals.