Deriving macroscopic diffusivity from a microscopic master equation approach

In this thesis, the prediction of macroscopic (continuum) diffusion properties of a crystalline material from microscopic (atomistic) considerations is investigated. Basis of this work is an existing mathematical formalism modelling uncorrelated particles in a physical system by a Markov chain, from which a master equation in time and space is constructed. This approach is discussed, reformulated, and generalised to be applicable to any three-dimensional crystal system. It is implemented in numeric form and applied to select systems, among them MAX phase and Laves phase compounds. Analytic expressions for some model system diffusivities are obtained, and ab initio potential data is utilised to gain concrete physical insights. The formalism’s promising capabilities to describe large systems involving crystal defects or interfaces are discussed, and possible extensions to include correlation effects are sketched.