Point process microstructural model of metallic thin films with implications for coarsening

Abstract

We develop a thin-film microstructural model that represents structural markers (i.e., triple junctions in the two-dimensional projections of the structure of films with columnar grains) in terms of a stochastic, marked point process and the microstructure itself in terms of a grain-boundary network. The advantage of this representation is that it is conveniently applicable to the characterization of microstructures obtained from crystal orientation mapping, leading to a picture of an ensemble of interacting triple junctions, while providing results that inform grain-growth models with experimental data. More specifically, calculated quantities such as pair, partial pair and mark correlation functions, along with the microstructural mutual information (entropy), highlight effective triple junction interactions that dictate microstructural evolution. To validate this approach, we characterize microstructures from Al thin films via crystal orientation mapping and formulate an approach, akin to classical density functional theory, to describe grain growth that embodies triple-junction interactions.

Evolving information complexity of coarsening materials microstructures

“…Finally, we note that there are alternative descriptions of complexity in which a microstructure is described in terms of correlations of an underlying point process. For example, in a recent paper 47 , we quantify the entropy of a microstructure in terms of a two-point correlation function (the radial distribution function) of grain triple junctions. From the radial distribution function one can extract a so-called direct correlation function that may be employed in a classical density-functional model of microstructure evolution.…”

Local well-posedness of a nonlinear Fokker–Planck model

“…Grain growth is a very complex multiscale and multiphysics process influenced by the dynamics of grain boundaries, triple junctions and the dynamics of lattice misorientations (difference in the lattice orientations between two neighboring grains that share the grain boundary, figure 1), e.g. [3,38,39]. In case of the grain growth modeling [18], in the Fokker-Planck system, f may describe the joint distribution function of the lattice misorientation of the grain boundaries and of the position of the triple junctions, ϕ may describe the grain boundary energy density, and D is related to the absolute temperature of the entire system [32] (it can be viewed as a function of the fluctuation parameters of the lattice misorientations and of the position of the triple junctions due to fluctuation-dissipation principle [18]).…”