Abstract
A method to determine the basic parameters describing planar two-dimensional (2D) spatial arrangements of precipitates is presented. It is based on the observation that the total number of particles (precipitates), the total area, and total perimeter length of features examined in the microstructure at each step of dilation/erosion transformation uniquely depend on their initial 2D geometry (size, shape, and mutual spatial arrangements). These parameters have a clear physical interpretation such as the distribution of distances between precipitate boundaries that are measured along the shortest pathway between them. It is also argued that the network of the shortest pathway represents the dendrite and sub-grain boundaries. On this basis, the width distributions of the dendrites and sub-grains were determined.
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