On the Characterization of Directionally Solidified Dendritic Microstructures

A novel method for the stereological assessment of arrays of directionally solidified dendrites is presented. It is suitable particularly for the evaluation of the distribution of primary dendrite arm spacings and the dendrite coordination number. The method involves (1) determination of the center of gravity of each dendrite in the array under consideration, (2) calculation of the distances to all neighboring dendrites in the data set (3) sorting of the distances determined into ascending order (4) under the assumption of a minimum number of nearest neighbors—typically three—calculation of the average distance to these and associated standard deviation, (5) an assessment of whether the remaining neighbors are within the range of proposed nearest-neighbor distances and (6) repetition of the previous to determine a set of values for the entire data set and, thus, the distributions of dendrite arm spacings and coordination numbers. By application of the method to experimental microstructures, it is demonstrated that a detailed statistical assessment of directionally solidified dendritic arrays can be accomplished.