A Transfer Function for Relating Mean 2D Cross-Section Measurements to Mean 3D Particle Sizes

It is common practice to estimate mean 3D particle and grain size of polycrystalline materials by multiplying 2D cross-sectional measurements by a multiplication factor. However, the most frequently used multiplication factors apply only to uniform or specific dispersions of particles, and therefore can provide misleading results. In the present work, empirical equations are developed to more accurately predict the mean 3D grain size of a lognormal spherical particle dispersion, regardless of the dispersion’s width. The equations provide an improvement over scalar multiplier values by allowing the effects of particle size distribution to be accounted for using inputs that can be obtained by cross-sectional analysis.