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The structure of the cubic coincident site lattice rotation group

Acta Cryst. (2004). A60, 263–277 [doi:10.1107/S010876730400772X]

[map of portion of group]A map of a portion of the twin-related group Σ3ω, which governs the grain boundary networks in ideal twin-dominated materials.

The field of grain boundary engineering aims to improve the properties (e.g. fracture toughness) of polycrystalline materials by optimizing their networks of grain boundaries. The idea  is to enhance the frequency and connectivity of so-called “special boundaries,” which arise from particular relative orientations of adjacent crystal grains and which tend to have relatively high strength, diffusion resistance, etc. The group theory of crystallographic misorientations imposes strong constraints on the network only now beginning to be understood. This article develops the mathematical underpinnings of these kinds of constraints, synthesizing and generalizing previous work in a simple, unified, and extensible framework.

B. W. Reed, R. W. Minich, R. E. Rudd and M. Kumar