Discommensurations in icosahedral phases

The nature of the icosahedral phase is studied in the presence of competing commensurate ordering terms in the free energy. It is shown that the phase is a discommensurate one with a periodic array of domain walls (discommensurations) separating regions with long-period structure. These long-period structures have local icosahedral symmetry and their diffraction patterns closely resemble those of the icosahedral phase. In the discommensurate state the coherence length of the icosahedral phases would be determined by the domain-wall spacing. Recent experimental observations of antiphase-boundary-type defects in such systems probably indicate that the discommensurate state of the icosahedral phase is the one that is experimentally observed. We discuss the possibility of the discommensurations getting pinned by the lattice and the appearance of metastable states with random distribution of domain walls. These states are known to exhibit certain characteristic properties of glasses