A unified framework for grain boundary distributions in textured materials

TL;DR

This paper introduces a unified framework for analyzing grain boundary distributions in textured materials, revealing inherent ambiguities and dualities in interpreting microstructural data.

Contribution

It develops an eight-parameter boundary distribution framework that links grain boundary character and normal distributions, clarifying formation mechanisms.

Findings

The framework derives GBCD and GBND from a unified model.

In macroscopically driven networks, GBND is a convolution of specimen GBND and ODF.

In crystallographically driven networks, specimen GBND results from convolution of crystal GBND and ODF.

Abstract

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, the crystal-frame GBND is given by a convolution of the specimen GBND with the orientation distribution function (ODF), whereas in crystallographically driven networks 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 mcirostructures. Evaluation of a wide variety of simulated microstructures confirm the theoretically predicted relationships between texture, GBND and GBCD. In particular, our examples confirm that the GBND or GBCD alone are not sufficient for identifying grain boundary formation mechanisms.