The main objectives of this proposal are: (1) To determine atomic structure of real quasicrystals; (2) To identify kinetic and equilibrium factors responsible for quasicrystal formation and stability; (3) To characterize nature of disorder in quasicrystals. The average quasiperiodic structure of observed quasicrystals will be determined, and its utility vis-a-vis icosahedral glass models assessed, using the available diffraction data and novel approach of exploiting structural similarity of crystal approximants. Accurate determination of the structure is a necessary prerequisite for calculations of other physical quantities. Quasicrystal stability and formation will be investigated through classical cohesive energy, variational thermodynamic potentials, and simulations of freezing of 2D and icosahedral liquids. The results will also expand the understanding of kinetic and equilibrium pattern formation in general. Phase fluctuations and more general disorder in quasicrystals will be studied in the context of the growth of Penrose tilings, in hard-disk and random tiling models, and in terms of the freezing of 2D and icosahedral liquids. Understanding of growth induced disorder and phase fluctuations is not only crucial in the case of quasicrystals, but will also have important ramifications in theories of glasses.
