The dynamics and low-temperature heat capacity of a monatomic linear chain with a two-parametric substitutional impurity

Exact analytic expressions for spectral densities, the spectral shift function, and the total change in the phonon spectrum as well as the low-temperature heat capacity of a one-dimensional crystal containing a two-parametric substitutional impurity are obtained and analyzed as functions of the defect parameters (changes in the mass and in force constants). Calculations are made by using the chain fraction apparatus. Special attention is paid to the results that cannot be obtained in the model of the defect taking into account only the change in mass. These results include, for example, the possibility of formation of quasilocalized states in the intermediate region of continuous spectrum by a light weakly coupled impurity. In addition, it is shown that two local vibrations are formed for any (however large) mass of an impurity atom if the force of coupling of the impurity with its nearest neighbors is two or more times stronger than the force of coupling between atoms in the matrix lattice.

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