Evaluation of Stereological Strategies for Estimating Mean Volume, Number Per Unit Volume, and Grain Volume Distribution: The Disector and Selector Methods

Abstract

This paper performs a virtual evaluation of six techniques for determining number of grains or particles per unit volume, $N_{V}$, mean volume, $\bar{V}$, and cumulative volume distribution by number frequency, F(V) and number per unit volume, N_V>. The methods evaluated include several unbiased stereological techniques: the disector, selector, unbiased brick and center-of-mass and two biased methods that are sometimes inadvertently adopted by experimentalists: including or excluding all boundary grains. Focus is given to the efficient but relatively unknown disector and selector techniques. The disector determines $N_{V}$and $\bar{V}$ from several serial sections without grain reconstruction. The disector/selector combination determines grain volume distributions over an extended area of microstructure, to reduce effects of material inhomogeneity, segmenting and reconstructing only a relatively small fraction of grains. All the above methods are evaluated and compared as a function of the number of grains included in the analyses using virtual experiments with a large 3D computer-generated grain structure of known global metrics. The unbiased methods show good estimation of the above properties while the two biased methods show over- or underestimation. All methods show the same statistical dependence of coefficient of variation, CV on the inverse square root of the number of grains sampled.