Alternative closure of the Yvon - Bron - Green hierachy

Abstract

Lacking an efficient operation on the correct time scales has caused atomistic level simulation methods to encounter some limitations as they can not study phe nomenas like phase transition. One of the obstacles in achieving convincing results is unsound theory, which is the fundamental in atomistic level simulations. Another issue is restriction to specific types of interaction which limits the overall simulation length. In order to study the phase change, we have developed a novel model which provides an accurate evolution equation for atomic systems with arbitrary interatomic potentials on diffusive time scales. This method can be alternative to available simula tion methods in this branch of study which are molecular dynamics, dynamical density functional theory and phase field crystal model. The method provides the one-body distribution function in a closed form with explicit interatomic potential and is able to model the behavior of crystals on atomic length scales and leads to simulations that are many orders of magnitude times faster than other approaches. By using this approach, the crystal structure and properties could be specified directly without deriving a free energy functional as for DDFT, or fitting the coefficients in the gradient-expansion of the direct correlation function as for the PFCM. Method could be extended to con struct a phase diagram for the given interatomic potential and applied to longer times to follow the nucleation and growth of a crystal from the initially disordered solid. This method can have the ability to model other crystal structures with more diverse ki netic phenomena like diffusion. The result of this thesis is intended to more accurately reproduce the atomic behavior of solids and liquids as observed by molecular dynamics simulations.