Eur. Phys. J. B (2013) 86: 381
https://doi.org/10.1140/epjb/e2013-40513-5

Regular Article

The Kuramoto-Sivashinsky equation for adatoms interacting through quasi-Rayleigh waves and formation of ordered adatom structures

Physics Faculty, Lomonosov Moscow State University, 119991 Moscow, Russia

^a e-mail: emel@em.msk.ru

Received: 21 May 2013
Received in final form: 29 July 2013
Published online: 16 September 2013

Abstract

It is shown that the defect-deformational (DD) cooperative nucleation of ordered ensembles of nanoparticles on isotropic surfaces of solids with the participation of quasi-Rayleigh waves can be described by a closed two-dimensional nonlinear DD equation of the Kuramoto-Sivashinsry (KS) type. A solution to the linearized DDKS equation describes the threshold appearance of the periodic surface strain modulation accompanied by the simultaneous formation of adatom (surface defect) piles at extrema of the surface strain. Numerical solutions to the DDKS equation in linear and nonlinear regimes describe the formation of three types of surface structures of adatom piles (clusters): lamellar-like structures, cellular disordered and hexagonal ordered ones. In the well-developed nonlinear regime, generated ensembles of nanoparticles become trimodal regarding their size distribution due to the generation of the second harmonics, degenerate parametric decay and summation of wavevectors of DD gratings taking part in the DD selforganization. The selforganizing periodic cellular DD surface structure can serve as a selforganized template for the subsequent growth of nanoparticles in the processes of atoms deposition.