Extreme value analysis of tail departure from log-normality in experimental and simulated grain size distributions

Abstract

Grain size data were taken from four three- and two-dimensional microstructures, including simulated grain growth, thin film and superalloy data sets. Probability plots revealed approximately log-normal distributions for experimental grain size data sets, but with systematic differences in the upper tails. A simulated grain size data set obtained from Potts model growth exhibited strong deviation from log-normality. A peaks-over-threshold analysis was applied to quantify the differences in the upper tails. Potts model simulation of normal grain growth shows the shortest tail, whereas the thin film data showed the longest tail (i.e. closest to log-normal), with an intermediate tail shape in the superalloy.