numerical study of the vibrational properties of quasicrystals and the effects of the defects and impurities

quasicrystals are a group of materials with the quasi-periodic structure, and since their discovery in 1980 their specially interesting physical properties have attracted the attention of many researchers. the lack of translational periodicity makes the numerical calculations of their physical properties much more difficult than the crystalline solids. in this work we present a detailed numerical study of the vibrational properties of quasi- periodic systems. for our purpose, we use the forced oscillator method (fom), which is relatively fast and basically simple, and originally designed for the calculation of the phonon density of states in the disordered solids. the quasi-periodic structure is also produced by the fibonacci series. in this framework we calculate the vibrational properties of the quasi-periodic structures in one, two, and thee dimensions, which compare well with experimental results. in addition to these, we performs similar calculations for the perfectly ordered and disordered systems. thus we are provided with a basis for comparison of the vibrational properties of quasi- crystalline materials with the perfect crystals and amorphous materials. we also study the effects of bond and site impurities in vibrational properties of materials.