Stereology for Phase Quantification

It is sometimes necessary to extract quantitative data on three-dimensional features from two-dimensional sections or surface micrographs taken by OM, SEM, or TEM. Such data extraction requires a careful consideration of how the two-dimensional representation samples the true three-dimensional objects. This branch of metrology, or measurement science, is known as stereology. Detailed techniques for the 

Presently, the most common method of specifying grain size is by the mean lineal intercept. For this to be a valid measure, one must sample grains along lines that are randomly oriented across an optical, SEM, or TEM micrograph. Ideally, micrographs are taken from sections cut perpendicular to each other in the material so that measurements in all three specimen dimensions are incorporated. The mean intercept L is found simply by Z = where the lineal fraction Li is the length of the 

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