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Measurement of Internal Boundaries in Three-Dimensional Structures By Random Sectioning

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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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References

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Author information

Authors and Affiliations

  1. Institute for the Study of Metals, University of Chicago, Chicago, USA

    Cyril Stanley Smith (Member AIME, Director) & Lester Guttman

Authors
  1. Cyril Stanley Smith
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  2. Lester Guttman
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Additional information

Discussion on this paper, TP 3430E, may be sent, 2 copies, to AIME by March 1, 1953. Manuscript, April 16, 1952.

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Smith, C.S., Guttman, L. Measurement of Internal Boundaries in Three-Dimensional Structures By Random Sectioning. JOM 5, 81–87 (1953). https://doi.org/10.1007/BF03397456

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