The main objectives of this condensed matter theory project are to: (1) develop general computational methods and tools for determination and analysis of quasicrystal structures using experimental diffraction data; (2) identify kinetic and equilibrium factors responsible for quasicrystal formation and stability; (3) characterize the nature of disorder in quasicrystals. Determination of quasicrystal structure is a necessary first step leading to an understanding and calculations of physical properties of quasicrystals, such as their electronic and magnetic properties. A computer package for calculating the average quasiperiodic structure of a quasicrystal from its diffraction data will be developed using a method recently introduced by the principal investigator. Studying the growth-induced disorder and phase fluctuations in quasicrstals will significantly advance the understanding of the competition between crystal, quasicrystal and glass formation in real materials. Quasicrystal stability and thermal fluctuations will be investigated through Monte Carlo simulations of tilings. Other more general disorder will be simulated using tiling growth algorithms. Special emphasis will be placed on the competition between crystal and quasicrystal structures. Quasicrystal formation will also be studied with renormalization group calculations of the liquid-icosahedratic transitions. %%% This theoretical and computational research will contribute to the understanding of the properties of quasicrystals. Ten years after the discovery of this new state of matter the basic conditions for the formation of this unique state of matter versus that of the crystalline or glassy state are still undefined. These basic conditions need to be determined before comprehensive models of specific materials properties can be implemented. The proposed research will provide a major impetus to resolution of these conditions.
