Grain Size and Mean Lineal Intercept

For simple cases, the relationship between three-dimensional sizes and L can be geometrically determined. It can be shown, for example, that uniformly sized spherical particles have a diameter given by = 1. 5L. Note also that the internal surface area per unit volume, Sy, is simply related to the mean lineal intercept for a three-dimensional structure of space-filling grains by the equation = 2/ Z. 

This makes it possible for the analyst to obtain quantities such as the grain boundary area in a polycrystalline material from simple linear measurements on 

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