Calculating probability densities associated with grain-size distributions

• Approximate, analytical expressions for grain-size distributions are calculated.
• A novel cumulant expansion is employed to obtain these expressions.
• We test our methodology using two experimentally obtained data sets.

We describe a methodology for calculating approximate, yet accurate analytical expressions for the probability density function of grain diameter as obtained from experimental microstructures. This methodology relies on a novel cumulant expansion that is tailored to the lognormal distribution and provides a systematic description of departures from lognormality. We test our methodology by characterizing two data sets obtained from the microstructures associated with polycrystalline, high-purity Al2O3 samples. The utillity of this approach is demonstrated by a detailed statistical analysis.