A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology . However, at present, there are still significant difficulties to prototype the atomic self-organization of complex structures for comparatively large number of atoms if it starts from initially disordered distribution and develops during the time commensurate with the typical time of diffusion. This time scale may potentially be within a range between a fraction of seconds and years.
Recently we proposed a new modelling technique [2,3], Atomic Fraton Theory (AFT), that naturally incorporate structural and elastic properties of system and allows to model the most challenging cases of atomic self-assembling whose complexity prevented their modelling before. A theoretical foundation of the AFT is based on the minimisation of non-equilibrium Helmholtz free energy of a system that is a functional F[ρ] of fraton density function, ρ(r). Several examples of modelling, based on this approach, including a crystallization of the zinc-blende structure, formation of double-stranded helix polymers from a solution of monomers, dynamics of fcc-bcc transition in iron, kinetics of carbon diffusion in martensite, structure of grain boundarie , microstructure evolution in Al-based alloys will be discussed. Link between continuous and discrete AFT theory will be establish.
1. H. Zapolsky "Kinetics of Pattern Formation: Mesoscopic and Atomistic Modelling" pp. 154-196, chapter in the book "ORDER, DISORDER AND CRITICALITY. Advanced Problems of Phase Transition Theory" Ed. Yu. Holovatch, World Scientific, Singapore (2015).
2.M. Lavrskyi, H. Zapolsky and A.G. Khachaturyan «Atomic Fragment Theory in Self-Assembly of Complex Structures: from Disorder to Complex Crystals and Double Helix Polymer » arxiV : 1411.5587v2 (will be published).
3. Y. M. Jin and A. G. Khachaturyan « Atomic density function theory and modeling of microstructure evolution at the atomic scale » J. Appl. Phys., Vol. 100, p. 013519 (2006).
4. A. Kapikranyan, H. Zapolsky, C. Domain, R. Patte, C. Pareige, B. Radiguet, P. Pareige, "Atomic density function modeling of atomic structure of grain boundaries" Phys.Rev. B., 89, 014111, 2014.