On the grain size proportionality constants calculated in MI Mendelson's Average Grain Size in Polycrystalline Ceramics

In 1969, M.I. Mendelson published a paper in the Journal of the American Ceramic Society that introduced a proportionality constant of 1.558 for estimating the average 3D grain size from the mean 2D lineal intercept under the assumption of lognormally distributed grains. Recent simulations by the authors revealed that the lognormal parameterization in the original work actually calculates the median grain size instead of the mean. The relationship between the mean caliper diameter and mean lineal intercept was found to be 1.60 when using common parameterizations. In addition, it is demonstrated through simulations that the correct proportionality constant can range from 1.776 to below unity depending on a material's grain size dispersion, such that 1.60 should only be used as a crude approximation.