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А. С. Долгов, Ю. Л. Жабчик
«Миграция двухатомных комплексов в структуре графена»
731–741 (2014)

PACS numbers: 05.20.Dd, 05.40.Fb, 61.48.Gh, 61.72.Bb, 66.30.Pa, 68.43.Jk, 81.05.ue

The kinetics of diatomic-formations’ movements in two-dimensional hexagonal structure, which is a single-layer graphene, is considered. The pattern of Hollow-positioning of the pair components under the continuity conditions is used. The choice of positioning type is conditioned by widespread conceptions of features of impurity sedimentation on the graphene and predetermines some simplification of the analysis and nature of results. Placement of the pair components in two contiguous hexagons in the conditions of cohesiveness preservation defines a limited set of jumps’ variants for each atom that, in turn, specifies a pattern of pair movement, which is different from that one for single atoms. The description of the general jumps’ pattern is performed in terms of continuous dependences for probabilities of finding of particles in one or another admissible positions. The technique of the analysis is based on the introduction of Fourier sums (generating functions) for all available positions in the structure. The found dependences for generating functions are convenient for definition of mean characteristics of development of the migration process (the moments of distribution functions) and allow monitoring the probabilities’ change for filling of various individual positions. Exact solutions of unlimited set of the equations for probabilities of filling of any positions are written down. The evolution in time of the main moments of particles’ distribution is defined. Strong decrease in mobility of the object as compared with similar individual characteristics is revealed, and it looks as disproportionate suppression of mobility of both components. Asymptotic properties of the objects do not depend on features of initial polarization of pairs; however, terms of formation of asymptotic modes are sensitive to a ratio of individual characteristics. Alternative special cases are discussed. They are identity of components and their great distinction. The general decrease in mobility is more expressed in case of coincidence (proximity) of individual characteristics. The average square of shift of the object from its initial placement grows in proportion to time in asymptotic conditions that is an indication of traditional diffusive movement. However, quite probable processes of formation and (or) destruction of binding between elements lead to essential change of the general mobility of the impurity component that determines similarity of process features to a pattern of abnormal diffusion and can take a form of both subdiffusion and superdiffusion.