Theoretical research will be conducted on the structural and thermodynamic properties of complex, partially ordered materials. Two types of materials, quasicrystalline alloys and ferrofluids, will be described by models which capture the most relevant energetic and geometrical constraints, while remaining simple enough to perform accurate, analytic calculations of statistical properties. Quasicrystals, a common but complex structure type in intermetallic alloys, appear to be intermediate between conventional crystals and metallic glass. Employing geometrical tiling models as a shorthand description of real atomic positions, the phase diagram and phase transitions among equilibrium structures will be investigated as functions of interactions, composition and temperature. Ferrofluids are colloidal suspensions of microscopic permanent magnets. In addition to technological applications, these materials are of intrinsic scientific interest because they provide an approximate realization of a dipolar hard sphere fluid. This work will establish the nature of phases between the dilute isotropic gas and the close-packed magnetically ordered solid. %%% Theoretical research will be conducted on the basic properties of two partially ordered complex materials. Quasicrystals, which were discovered over a decade ago in certain intermetallic alloys, remain a mystery as to the mechanisms which produce this unusual structure. Ferrofluids, artificial magnetic materials with many applications, are interesting on a fundamental basis and as a real material system. Both of these fascinating materials will be studied using the latest techniques in statistical physics and computational science.
