Related papers: Modeling of grain boundary dynamics using amplitud…
Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived…
We study the Poisson Boolean model where the grains are random convex bodies with a rotation-invariant distribution. We say that a grain distribution is dense if the union of the grains covers the entire space and robust if the union of the…
We use confocal microscopy and time-resolved light scattering to investigate plasticity in a col- loidal polycrystal, following the evolution of the network of grain boundaries as the sample is submitted to thousands of shear deformation…
Based on the formula for the number density of vacancies in a solid under the stress or tension, the model of grain boundary diffusion in crystalline solids is developed. We obtain the activation energy of grain boundary diffusion…
Knowledge about grain boundary migration is a prerequisite for understanding and ultimately modulating the properties of polycrystalline materials. Evidence from experiments and molecular dynamics (MD) simulations suggests that the…
A model for ionic and electronic grain boundary transport through thin films, scales or membranes with columnar grain structure is introduced. The grain structure is idealized as a lattice of identical hexagonal cells - a honeycomb pattern.…
Grain growth is a ubiquitous and fundamental phenomenon observed in the cellular structures with the grain assembly separated by a network of grain boundaries, including metals and ceramics. However, the underlying mechanism of grain growth…
We study a nonlinear kinetic model of mass exchange between interacting grains. The transition rates follow the Arrhenius equation with an activation energy that depends on the grain mass. We show that the activation parameter can be…
Grain boundaries affect properties of polycrystalline materials. The influence of a boundary is largely determined by its energy. Grain boundary energy is often portrayed as a function of macroscopic boundary parameters representing grain…
A curve shortening equation related to the evolution of grain boundaries is presented. This equation is derived from the grain boundary energy by applying the maximum dissipation principle. Gradient estimates and large time asymptotic…
Multiscale modelling aims to systematically construct macroscale models of materials with fine microscale structure. However, macroscale boundary conditions are typically not systematically derived, but rely on heuristic arguments,…
Composite of two kinds of grains is modeled in two-dimension and the elasticity is calculated using molecular dynamics method implementing Gear predictor-corrector of fifth order. It has been observed that same composite concentration can…
The thermodynamic theory of dislocation/grain boundary interaction, including dislocation pile-up against, absorption by, and transfer through the grain boundary, is developed for nonuniform plastic deformations in polycrystals. The case…
With the increasing availability of experimental and computational data concerning the properties and distribution of grain boundaries in polycrystalline materials, there is a corresponding need to efficiently and systematically express…
Volume-fraction expressions are obtained for the systems of an infinite number of parallel planes arranged both regularly and randomly. As a special case of random arrangement, a non-Poissonian point process (the second-order Erlang…
We identify a finite wavenumber instability of a 90$^{\circ}$ tilt grain boundary in three dimensional lamellar phases which is absent in two dimensional configurations. Both a stability analysis of the slowly varying amplitude or envelope…
The evolution of two grains, which lie on a substrate and are in contact with each other, can be roughly described by a model in which the exterior surfaces of the grains evolve by surface diffusion and the grain boundary, namely the…
Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The energetics and connectivities of the grain…
We study here the spontaneous clustering of a submonolayer of grains under horizontal circular shaking. The clustering of grains occurs when increasing the oscillation amplitude beyond a threshold. The dense area travels in a circular…
Amplitude representations of a binary phase field crystal model are developed for a two dimensional triangular lattice and three dimensional BCC and FCC crystal structures. The relationship between these amplitude equations and the standard…