A self-organization is an universal phenomenon in nature and, in particular, is highly important in materials systems and biology1. 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 technique2, 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[?] of fraton density function, ?(r). Several examples of modelling, based on this approach, including a crystallization of the zinc-blende structure, diffusional phase transitions, dynamics of the displacives phase transitions in iron, kinetics of carbon diffusion in martensite and the structure of grain boundaries3,4 will be discussed. Link between continuous and discrete AFT theory will be establish.
1.H. Zapolsky “Kinetics of pattern formation: mesoscopic and atomistic modelling” ORDER, DISORDER AND CRITICALITY, Advanced Problems of Phase Transition Theory, Volume IV, ,pp 153-193, Ed. Y. Holovach, World Scientific Publishing Co. 2015.
1.M. Lavrskyi, H. Zapolsky, A.G. Khachaturyan « Quasiparticle Approach to Diffusional Atomic Scale Self-Assembly of Complex Structures: from Disorder to Complex Crystals and Double Helix Polymers », Nature Parther Journal Computational Materials, 18 janvier, 2016.
3.O. Kapikranian, H. Zapolsky, R. Patte, C. Pareige, B. Radiguet, and P. Pareige Point defect absorption by grain boundaries in alpha iron by atomic density function modelling” Phys.Rev.B 92, (2015) pp.224106.
4.O. Kapikranian, H. Zapolsky, C. Domain, R. Patte, C. Pareige, B. Radiguet, and P. Pareige “Atomic structure of grain boundaries in iron modeled using atomic density function” , Phys.Rev.B 89, (2014) pp.014111.