Inner Modulation in Quasicrystals and Approximants

Through a detailed analysis,it is found out that a quasilattice can be considered as one consisting of several mutually incommensurate interpenetrating sublattices,each sublattice being a modulated crystalline lattice.The modulation periods in one sublattice are given by the basic periodicities of the other sublattices.Also analyzed is the approximant quasilattice whose sublattices being mutually commensurate.In the density wave picture,the combination of crystal structures into one quasicrystal(or approximant)phase can be done in a natural procedure.