Date of Award
Doctor of Philosophy
Materials Science and Engineering
Sectioning methods are frequently used to measure grain sizes in materials. These methods do not provide accurate grain sizes for two reasons. First, the sizes of features observed on random sections are always smaller than the true sizes of solid spherical shaped objects, as noted by Wicksell . This is the case because the section very rarely passes through the center of solid spherical shaped objects randomly dispersed throughout a material. The sizes of features observed on random sections are inversely related to the distance of the center of the solid object from the section . Second, on a plane section through the solid material, larger sized features are more frequently observed than smaller ones due to the larger probability for a section to come into contact with the larger sized portion of the spheres than the smaller sized portion. As a result, it is necessary to find a method that takes into account these reasons for inaccurate particle size measurements, while providing a correction factor for accurately determining true particle size measurements. I present a method for deducing true grain size distributions from those determined from specimen cross sections, either by measurement of equivalent grain diameters or linear intercepts.
Reference:  S. D. Wicksell, "The Corpuscle Problem: A Mathematical Study of a Biometric Problem," Biometrika. 17, 84-99 (1925).
Kristina Alyse Lord
Lord, Kristina Alyse, "Methods for obtaining true particle size distributions from cross section measurements" (2013). Graduate Theses and Dissertations. 13221.