A unified framework for grain boundary distributions in textured materials

Grain boundary plane distributions are widely used to infer the mechanisms governing grain boundary formation in polycrystalline materials. We show that such interpretations are inherently ambiguous. Using a unified eight-parameter boundary distribution framework, we derive both the grain boundary character distribution (GBCD) and the grain boundary normal distribution (GBND) and identify two limiting cases of boundary network formation. We show that in macroscopically driven networks, e.g. controlled by strain, the crystal-frame GBND is given by a convolution of the specimen GBND with the orientation distribution function (ODF), whereas in crystallographically driven networks, e.g. controlled by anisotropic boundary energy, the specimen GBND is obtained by convolution of the crystal GBND with the ODF. This duality implies that anisotropy in the GBND may arise from macroscopic alignment effects rather than intrinsic crystallographic selection. Conversely, this relationship may be used to identify the dominant formation process in the measured microstructures. Evaluation of a wide variety of simulated microstructures confirms the theoretically predicted relationships between texture, GBND and GBCD. In particular, our examples confirm that neither the GBND nor the GBCD alone is sufficient for identifying grain boundary formation mechanisms.