Abstract
It is shown, from a study of geometric probabilities, that the average number of intercepts per unit length of a random line drawn through a three-dimensional structure is exactly half the true ratio of surface to volume. Since the surfaces can be internal or external, the area of grain boundary or of the interface between any two constituents in a microstructure can be measured. Other metric relations are tabulated that may be of use in studies of the microstructure of polycrystalline, cellular, or particulate matter generally.
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