Studies on aperiodic and quasiperiodic crystal

In this work Fixman's self-consistent phonon theory has been extended and applied to one- and two-component aperiodic and quasiperiodic crystals. First the free energy as a function of density is calculated using an average environment approximation. Then this approximation is lifted and all particles are allowed to move and search out their local free energy minima. Upon relaxation it was found that the one-component quasicrystal undergoes a structural transition to an aperiodic crystal near $rho cong$ 1.03. In the binary quasicrystal there was not a pronounced structural transition, but rather local regions of stability and instability. In both the one- and two-component aperiodic crystal it was found that the quenched free energy was dependent upon the density as well as the number of particles in the system. Lastly, the quasicrystalline lattice was transformed into a lattice of water molecules. Molecular dynamics was used to determine that the lattice was unstable.