Characterization of heterogeneities in grain size by network analysis

• A new method to measure heterogeneities in grain size is put forward.
• Graph theory is used to build an adjacent matrix from a single-phase microstructure.
• Centrality degree determines very accurately microstructure heterogeneities.

Heterogeneities in grain size are very common, mainly when phenomena such as abnormal grain growth is taking place. A new method to measure them is put forward. It is based on network analysis in which an adjacent matrix is built from a microstructure consisting of single-phase grains. In this approach, grains are nodes whereas their boundaries are ties. Both the degree centrality of nodes and the degree centrality of group of grains were calculated as well as their significance and deviations. Results have shown that the present method is capable to show significant differences in these properties, one order of magnitude, even if the microstructures are slightly heterogeneous. Methods involving statistical and non-linear regression analysis are also presented and compared with the new one and it is shown that these methods have more arbitrariness than the new one.

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