Quasiparticle approach to diffusional atomic scale self-assembly of complex structures: from disorder to complex crystals and double-helix polymers

A self-organisation is an universal phenomenon in nature and, in particular, is highly important in materials systems. Our goal was to develop a new theory that provides a computationally effective approach to this problem. In this paper a quasiparticle theory of a diffusional self-organisation of atoms in continuum space during the diffusional time scale has been introduced. This became possible due to two novelties, a concept of quasiparticles, fratons, used for a description of dynamic degrees of freedom and model Hamiltonian taking into account a directionality, length and strength of interatomic bonds. To illustrate a predictive power and achievable level of complexity of self-assembled structures, the challenging cases of self-assembling of the diamond, zinc-blende, helix and double-helix structures, from a random atomic distribution, have been successfully modelled. This approach opens a way to model a self-assembling of complex atomic and molecular structures in the atomic scale during diffusional time.