Stereological Techniques for Quantitative Characterization of Microstructures

It is well known that material chemistry and processing dictate material microstructure and microstructure influences properties and performance of materials. Consequently, quantitative characterization and statistical representation of microstructure are of considerable importance in materials science. Microstructure is essentially a collection of three-dimensional volumes (for example, grains, precipitates, inclusions, pores, etc.), two-dimensional interfaces and grain boundaries, onedimensional lines (for example, grain edges), and zero-dimensional points (for example, quadruple points in grain structure) dispersed in a three-dimensional reference space (a specimen or a component). Consequently, a microstructure can be quantitatively characterized via unbiased estimation of important geometric attributes such microstructural features. It is important to emphasize that material microstructures are three-dimensional (3D) and, therefore, the attributes of three-dimensional microstructural geometry are of fundamental interest. Although techniques such as computed tomography are available for direct observation of 3D microstructures [1], it is often convenient and efficient to observe and characterize microstructure in two-dimensional (2D) metallographic sections through 3D microstructure. Nonetheless, geometric attributes of 3D microstructures are of interest. Consequently, techniques for assumption-free, unbiased, and efficient estimation of attributes of 3D microstructures from the observations/measurements performed on 2D metallographic sections are of interest. Stereology (a branch of stochastic geometry) provides mathematical basis for such estimation techniques. The objective of this contribution is to review important stereological techniques and their applications for unbiased quantitative characterization and representation of 3D opaque material microstructures via interrogation of 3D microstructure using lower dimensional probes such as planes (or surfaces), lines (straight or curved), and points, or projected images [2-4]. Interestingly, these techniques can be also applied for quantitative characterization of the microstructure (pores, inclusions, facets, dimples, etc.) present in the non-planar tortuous material fracture surfaces [5-7].