On the grain size proportionality constants calculated in M.I. Mendelson's “Average Grain Size in Polycrystalline Ceramics”

Abstract

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. K E Y W O R D Scharacterization, grain size distribution microstructure, particle size distribution, simulations, stereology

The grain‐boundary resistance of CeO2 ceramics: A combined microscopy‐spectroscopy‐simulation study of a dilute solution

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Non-linear Transfer Functions for Accurately Estimating 3D Particle Size, Distribution, and Expected Error from 2D Cross Sections of a Lognormal Distribution of Spherical Particles

“…The inherent flaw in a constant value transfer function is regardless of the metrics chosen for l 2D and l 3D , K is necessarily dependent on the distribution of both the 3D feature's shapes and sizes. [1][2][3][4][5][6][7] As such, equations using a constant K require restrictive and often unrealistic prior assumptions. An example is the frequently employed Eq.…”

Segregation‐controlled densification and grain growth in rare earth‐doped Y2O3

“…For determining the average grain size, at least 250 grains were considered and a correction factor of 1.6 was used. 41 Additional to sintering experiments in the field-assisted sintering device, grain growth studies were conducted in air to determine the grain boundary mobility for doped and undoped Y 2 O 3 . Therefore, samples, which were densified by FAST/SPS at 1400°C to density >99.5%, were thermally treated in a muffle furnace for 10 h at temperature of 1400, 1500, and 1600°C.…”

“…The grain size was analyzed using the average linear intercept method. For determining the average grain size, at least 250 grains were considered and a correction factor of 1.6 was used 41 …”