Orientation mapping linked to fractal analysis: A method for studying abnormal grain growth in nanocrystalline PdAu

Abstract

In a nanocrystalline alloy, we recently discovered a novel form of abnormal grain growth involving the emergence of grain boundaries having fractal-like morphologies. Although abnormal growth has long presented a challenge to materials scientists, new insights into this phenomenon might be gained from a study of its extreme manifestation in nanocrystalline Pd 90Au 10, where some grains not only grow to much larger sizes than their neighbors but also take on dendritic, highly convoluted shapes. To unravel the origin and mechanism of grain growth in this case, it is essential to determine the fractal dimension of the resulting grain boundaries with high accuracy. To achieve this goal, we turn to orientation mapping based on electron backscatter diffraction, the output of which is subjected to image processing and subsequent box-counting analysis. The robustness, reproducibility, and accuracy of this protocol are ensured by optimizing parameters related to sample preparation, orientational imaging, image processing, and the box-counting algorithm. We have validated the approach against non-fractal Euclidean structures as well as a mathematical fractal, finding that the method yields values for the fractal dimension that are precise up to three decimal places. Moreover, the parameters of the methodology can be adapted readily to other scenarios in which elements of a given microstructure manifest a fractal character.