Survey of computed grain boundary properties in face-centered cubic metals: I. Grain boundary energy

http://mimp.materials.cmu.edu/rohrer/papers/2009_09.pdf

Relative grain boundary area and energy distributions in nickel

We present and study a new algorithm for simulating the N-phase mean curvature motion for an arbitrary set of (isotropic) surface tensions. The departure point is the threshold dynamics algorithm of Merriman, Bence, and Osher for the two-phase case.



A new energetic interpretation of this algorithm allows us to extend it in a natural way to the case of N phases, for arbitrary surface tensions and arbitrary (isotropic) mobilities. For a large class of surface tensions, the algorithm is shown to be consistent in the sense that at every time step, it decreases an energy functional that is an approximation (in the sense of Gamma convergence) of the interfacial energy. A broad range of numerical tests shows good convergence properties.



An important application is the motion of grain boundaries in polycrystalline materials: It is also established that the above-mentioned large class of surface tensions contains the Read-Shockley surface tensions, both in the two-dimensional and three-dimensional settings.© 2015 Wiley Periodicals, Inc.

https://www.mis.mpg.de/preprints/2013/preprint2013_2.pdf

Threshold dynamics for networks with arbitrary surface tensions

Atomic-scale analysis of liquid-gallium embrittlement of aluminum grain boundaries

A dual-beam focused ion beam scanning electron microscope was used to collect a series of parallel electron backscatter diffraction maps of polycrystalline yttria. Using characteristics of the triple junctions, the individual layers were aligned and the geometries of the grain-boundary planes between the layers were determined. This information was used to calculate the five-parameter grain-boundary character distribution (GBCD) and grain-boundary energy distribution (GBED). The GBCD derived from the three-dimensional data was qualitatively the same as that derived from a stereological analysis of the same data. The anisotropy in the GBCD of yttria is relatively weak compared with other ceramics and is inversely correlated to the GBED.

/pdf/characterization-of-the-grain-boundary-character-and-energy-22487lcg0r.pdf

Characterization of the Grain-Boundary Character and Energy Distributions of Yttria Using Automated Serial Sectioning and EBSD in the FIB

A mesoscale, variational simulation of grain growth in two-dimensions has been used to explore the effects of grain boundary properties on the grain boundary character distribution. Anisotropy in the grain boundary energy has a stronger influence on the grain boundary character distribution than anisotropy in the grain boundary mobility. As grain growth proceeds from an initially random distribution, the grain boundary character distribution reaches a steady state that depends on the grain boundary energy. If the energy depends only on the lattice misorientation, then the population and energy are related by the Boltzmann distribution. When the energy depends on both lattice misorientation and boundary orientation, the steady state grain boundary character distribution is more complex and depends on both the energy and changes in the gradient of the energy with respect to orientation.

Mesoscale Simulation of the Evolution of the Grain Boundary Character Distribution

This paper presents coarse-graining methodologies for the passage from Molecular Dynamics (MD) models of fluids to the Navier-Stokes equations via an intermediate scale model. The microscopic and macroscopic descriptions of fluids are bridged by taking spatial and temporal averages of atomic quantities. The result is a set of discrete stochastic equations governing the evolution of coarse-grained mass, momentum, and energy, which can be shown to converge to a finite-difference representation of the Navier-Stokes equations in the large scale limit.

Peng Yu

Papers

Mesoscale Simulation of the Evolution of the Grain Boundary Character Distribution

Bridging Micro and Macro Scales in Fluids