Abstract:The lattice vibration of one-dimensional atomic chain, the lattice vibration and the distribution of the localized model after adding impurity atoms, and the lattice vibration under free boundary condition were researched in detail. Firstly, the lattice vibration of integrated lattice was introduced, the one-dimensional monoatomic chain was discussed and clear pictures of the lattice vibration were given. Secondly, the influence of the impurities both on the lattice vibration of one-dimensional atomic chain and on the localized model was discussed. Finally, the lattice vibration of one-dimensional chain was analyzed under the free boundary condition.