Eugenii S. Syrkin

Localization of vibrational defects in one-dimensional structures with a complex unit cell

Exact analytic expressions are obtained for Green’s functions of a linear chain with a diatomic unit cell containing an isotopic substitutional impurity. An infinite chain as well as a semi-infinite chain with an impurity at the free end are considered. The total change in the phonon spectrum and the spectral densities of vibrations of the impurity and its nearest neighbors are investigated. The conditions for the formation and characteristics of local and gap vibrations are analyzed. A general method of obtaining exact solutions by using Jacobi matrices is proposed for a wide class of one-dimensional systems.

Localization of vibrations near impurity atoms in semi-infinite and infinite linear chains

Exact analytic expressions for local densities of atoms of the system as functions of the distance to a defect as well as defect parameters (variations of mass and force constants) are derived for an semi-infinite linear chain with an impurity at the end as well as for an infinite linear chain with an interstitial or substitutional impurity (a triatomic defect cluster in the general case). The dependences of the conditions of formation and frequencies of local vibrations and of the amplitudes of vibrations of these frequencies (i.e., the form of their damping) on defect parameters are determined for different atoms of the system. Exact analytic expressions determining the threshold values of the defect parameters as functions of the distance between and impurity atom and the end of the chain are derived and analyzed.

Effect of local defects on vibrational characteristics of infinite and semi-infinite one-dimensional structures in an external periodic field

Exact analytic expressions for Green’s functions of the chain type structures with defects in an external periodic field are obtained by the method of Jacobi matrices. A diatomic impurity molecule in a monatomic chain as well as adsorbed chains with a monatomic and a diatomic unit cell are considered. The conditions for the formation and the characteristics of local and gap vibrations are investigated. The evolution of the threshold values of mass of the defect required for the formation of localized vibrations by two isotopic impurities upon a change in the separation between them is analyzed.

LATTICE DYNAMICS OF FCC-CRYOCRYSTALS WITH MANY-PARAMETRIC IMPURITIES

AbstractThe vibrational characteristics of the FCC–cryocrystals with substitutional impurities have been analyzed. A “non–central” impurity atom in environment of the “central” host atoms is considered. The difference between equilibrium interatomic distancesn

Theory of the Phase and Twin Boundaries in Solid Helium and Reversibility of the bcc-hcp Phase Transition

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Localized and quasi-low-dimensional phonons in multilayered crystals of HTS type

nand r0of the impurity and host atoms, respectively, causes their non–central interaction. A very strong dependence of the impurity frequency spectra on the ration

Dependence of the properties of single-component surface waves on direction of their propagation and surface orientation

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