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The connectivity of so-called "special" and "general" grain boundaries at a quadruple node is known to be nonrandom as a result of crystallographic constraints. Although a quadruple node is a three-dimensional feature, there exist two-dimensional features which are topologically identical. Therefore, the distribution of these two-dimensional features may be used to determine the three-dimensional connectivity. Computer simulations of a three-dimensional microstructure which is virtually serial sectioned are used to validate the proposed approach.

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This is an author-produced, peer-reviewed version of this article. © 2009, Elsevier. Licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License ( The final, definitive version of this document can be found online at Scripta Materialia, doi: 10.1016/j.scriptamat.2007.04.008