On the three-dimensional twin-limited microstructure

Abstract Grain boundary networks consisting entirely of Σ3 and Σ9 boundaries (twin-limited microstructures) are analyzed. Analyses of thought examples and theoretical considerations show that there are fundamental differences between two-dimensional and three-dimensional networks. The notion of the upper limit of the fraction of Σ3 boundaries is reassessed, and implications for the concept of grain boundary engineering are discussed.