Lattice dynamics and elastic waves scattering by surrogate atoms in quasi-one dimensional atomic assemblies

An analytical and numerical formalism is developed to study the influence of the various positions of substitution atoms B on the scattering and transmission vibration modes in quasi-1D monatomic structures A. The matching technique is employed to calculate the dynamical properties and transmittance spectra of two substituted atomic sites. The theoretical formalism gives a complete description of the lattice dynamics and the vibration-waves propagation in the presence of the impurity sites. Numerical calculations are performed for three different positions of the two substituted atoms B in the low-dimensional structure consisting of double monatomic parallel chains. First, we examine the position where the two B atoms are adjacent in the y-direction, afterwards, we place the two sites side by side in the x-direction. Lastly, the two sites are placed in oblique configuration. The obtained results show that phonons associated to the inhomogeneous structures are strongly dependent on the scattering frequency, elastic force parameters and the position of the atomic substituted sites. In the three considered positions, the presence of the B atoms gives rise to localized vibration effects. The fluctuations observed in the vibration spectra are related to resonances due to the coherent coupling between travelling phonons and the localized vibration modes in the neighborhood of the impurity sites.