The uncorrelated triple junction distribution function: Towards grain boundary network design

Abstract Triple junctions are recognized as important microstructural features in the context of grain boundary network topology and grain boundary sensitive materials properties. In spite of this prominence, mathematical tools for quantifying distributions of misorientations around triple junctions have been limited to special cases. Here we derive a general formula for the uncorrelated triple junction distribution function (TJDF) for materials of arbitrary texture. Additionally, we provide the mathematical link between TJDF and the orientation distribution function, which should facilitate the use of materials design paradigms on the grain boundary network.