This article reviews many commonly used stereological counting measurements and the relationships based on these parameters. The discussion covers the processes involved in sampling and specimen preparation. Quantitative microstructural measurements are described including volume fraction, number per unit area, intersections and intercepts per unit length, grain size, and inclusion content.

Quantifying microstructural parameters has received considerable attention and success in developing procedures and using such data to develop structure/property relationships has been achieved. This article reviews many of the simple stereological counting measurements of volume fraction, grain structure (two-phase grain structures, and nonequiaxed grain structures), grain size, and inclusion content. It also reviews simple relationships between number of grains per unit area, number of intersections of a line of known length with particle or grain, and number of interceptions of particles or grains by a line of known length.

The principal objective of quantitative fractography is to express the characteristics of features in the fracture surface in quantitative terms, such as the true area, length, size, spacing, orientation, and location. This article provides a detailed account of the development of more quantitative geometrical methods for characterizing nonplanar fracture surfaces. Prominent techniques for studying fracture surfaces are based on the projected images, stereoscopic viewing, and sectioning. The article provides information on various roughness and materials-related parameters for profiles and surfaces. The applications of quantitative fractography for striation spacings, precision matching, and crack path tortuosity are also discussed.