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.
Frary, Megan. (2007). "Determination of Three-Dimensional Grain Boundary Connectivity from Two-Dimensional Microstructures". Scripta Materialia, 57(3), 205-208. http://dx.doi.org/10.1016/j.scriptamat.2007.04.008