Molecular-dynamics study of collective modes and dislocation ordering in mismatched overlayers

Abstract

A molecular-dynamics study of the finite-length Frenkel-Kontorova model is presented. A dislocation depinning and ordering transition driven by soliton interactions is described. Complete phonon and collective-soliton-mode dispersion relations are determined for both well-ordered and pinned-disordered soliton arrays. Local modes, and zone folding due to phonon-soliton scattering, are identified. Possible applications of these results to experimental systems are suggested.There has been a widespread and long-standing interest in the behavior of incommensurate and quasi-incommensurate systems as found in surface overlayer s, charge-density waves, intercalated materials, and other quasi-two-dimensional systems.Recently, this interest has intensified,

Exotic features in the lattice dynamics of an incommensurate overlayer/substrate structure as modeled via the Frenkel-Kontorova system

“…5 Theoretical attempts to understand the vibrational dynamics of the incommensurate phase of the FK chain have used diverse approaches and approximations. [6][7][8][9][10] Although these treatments have reproduced some of the features observed in the experimental phonon dispersion curves, [1][2][3] none of them can capture all of the characteristic features of an incommensurate system such as the Goldstone ͑or free-sliding͒ mode, phason ͑dispersion-less͒ modes, quasigaps, quasizone centers, zone folding, etc. In the continuum version of the FK model, Goldstone mode was obtained, but all other characteristic features of an incommensurate system are absent from the phonon dispersion curve.…”

“…[6][7][8]10 A molecular dynamics study of the FK chain exhibits the Goldstone mode, zone folding, dispersionless modes, etc. 9 However, this dispersionless mode is found to appear in the middle of the gap and has been interpreted as an edgelocalized mode associated with the finite length of the chain. The origin of this mode is different from the dispersionless phason modes which appear in the vicinity of quasigaps.…”