A Grain Growth Study: the Five Parameter Grain Boundary Curvature Distribution and the Evolution of Grain Face Area

A distribution of grain boundary curvature as a function of five independent crystallographic parameters is proposed and tested on some simple geometries. The results show that the grain boundary mean curvature distribution (GBHD) is able to capture the curvature of a digitized microstructure though noise may arise from several sources.
The GBHD is measured in two sets of three-dimensional electron backscattered diffraction (EBSD) data collected in an austenitic and a ferritic steel. It is found that the grain boundary mean curvature varies with the boundary crystallography and is more sensitive to the grain boundary plane orientation than to the disorientation. The grain boundaries with the smallest curvatures also have low grain boundary energy and large relative areas while the curvature and energy of more general grain boundaries are, on average, inversely correlated.
The GBHD is also computed from a set of electron backscattered diffraction (EBSD) data collected from SrTiO3 annealed at 1470 ℃. Unlike the steels, the average grain boundary curvature is found to be directly correlated with the grain boundary energy, suggesting that the microstructure of SrTiO3 at 1470 ℃ may contain many singular grain boundaries.
The integral mean curvature of grain faces (𝑀_s) is analyzed for the grains in the steel samples and in SrTiO₃. Similar results are obtained in the three datasets. For a given grain, its 𝑀_s is closely related to its topological characteristics. Grains with a small number of faces have positive 𝑀_s and grains with many faces have negative 𝑀𝑠. The grains with zero 𝑀_s are those whose number of neighbors equal the average number of faces of their nearest neighbors.
Various geometric, topological, and mean-field features are hypothesized to capture the evolution of grain faces in a high purity Ni sample. The dataset was collected by the Suter group at Carnegie Mellon University using the high energy diffraction microscopy (HEDM) technique. It consists of two orientation maps of a given volume, one for the pre-anneal state and one for the after-anneal state between which the sample was annealed at 800 ℃ for 25 minutes. By fitting the various features with a few machine learning models, we show that curvature does affect the evolution of grain faces but the effect is not deterministic.
A face-averaged approximation is proposed to study the evolution of grain boundary properties. The effectiveness of this face-averaged assumption is validated by a comparison between the true GBHD and the face-averaged GBHD. The results show that the grain boundary area and curvature change vary with the grain boundary inclination systematically.