Grain Boundary Network Structure Research Articles

Representative and statistical volume elements for grain boundary networks: A stereological approach

Experimental and computational studies have demonstrated that the structure of grain boundary networks (GBNs), e.g. the connectivity of certain types of grain boundaries (GBs), has a significant impact on macroscopic material properties. Because minor changes in GBN structure can cause large changes in effective properties, it is common to use large microstructures or report averages over many microstructural instantiations with the assumption that results become more representative as the size or number of samples increases. For crystallographic texture, and composite materials, such ideas have been made rigorous through the definition of representative volume elements (RVEs) and statistical volume elements (SVEs). However, for GBNs, the size of an RVE and the cardinality of a set of SVEs have not yet been determined. In this study, we employ stereological methods to evaluate the convergence of triple junction fractions in both idealized and realistic 2D GBNs to quantitatively define RVEs and SVE sets for GBNs. We compare these results to those for crystallographic texture in the same polycrystals and find that the trends for GBNs and texture are remarkably different. Because the vast majority of experimental work currently relies on 2D microstructure characterization, the results obtained for 2D systems have great practical value in and of themselves. However, the stereological approach employed also allows us to make quantitative predictions of RVEs and SVEs for fully 3D microstructures. These results are expected to aid future experimental and computational work in selecting appropriately sized material volumes to achieve robust quantitative results.

Effects of grain-boundary networks on the macroscopic diffusivity of hydrogen in polycrystalline materials

The diffusion heterogeneities of grain boundaries are known to affect the effective diffusivity in polycrystalline materials. However, the correlation between both has not been clearly established. In this work, the influence of the grain boundary topology and connectivity on hydrogen effective diffusivity was investigated, for membranes with different grain sizes. We modeled a polycrystal in two dimensions, as a composite containing three phases, one for the grains and the others for grain boundaries. These phases are characterized by their diffusion coefficient, with a contrast of six orders of magnitude between grain boundaries of different character and three between grains and grain boundaries. The path length and correlation length of high diffusivity boundaries were statistically characterized. We found three different behaviors of the effective diffusivity depending on the grain-boundary networks structure. We observed two linear regimes between the connectivity parameters and the effective diffusivity, and a percolated regime. We quantitatively analyzed the impact of the grain-boundary network structure on the variation of the effective diffusivity, in the two first regimes.

The distribution of internal interfaces in polycrystals

Recent advances both in experimental instrumentation and computing power have made it possible to interrogate the distribution of internal interfaces in polycrystals and the three dimensional structure of the grain boundary network with an unprecedented level of detail. The purpose of this paper is to review techniques that can be used to study the mesoscopic crystallographic structure of grain boundary networks and to summarize current findings. Recent studies have shown that grain surfaces within dense polycrystals favor the same low energy planes that are found on equilibrium crystal shapes and growth forms of crystals in contact with another phase. In the materials for which comprehensive data exists, the distribution of grain boundaries is inversely correlated to the sum of the energies of the surfaces of the grains on either side of the boundary.