Microstructural Shape Factors: Relation of Random Planar Sections to Three-Dimensional Microstructures

The relation of random planar sections of anisometric microstructures to the actual three‐dimensional anisometry is considered for oblate and prolate spheroids and cylinders. Simple formulae are obtained relating the two‐dimensional (2‐D) to three‐dimensional (3‐D) aspect ratios; for oblate systems...

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Bibliographic Details
Published in:Journal of the American Ceramic Society 1995-06, Vol.78 (6), p.1532-1536
Main Authors: Laraia, Vincent J., Rus, Ioan L., Heuer, Arthur H.
Format: Article
Language:English
Subjects:
Applied sciences
Building materials. Ceramics. Glasses
Ceramic industries
Chemical industry and chemicals
Exact sciences and technology
General studies
Technical ceramics
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Summary:The relation of random planar sections of anisometric microstructures to the actual three‐dimensional anisometry is considered for oblate and prolate spheroids and cylinders. Simple formulae are obtained relating the two‐dimensional (2‐D) to three‐dimensional (3‐D) aspect ratios; for oblate systems with large aspect ratios, the area‐weighted average 2‐D aspect ratio varies linearly with the actual aspect ratio, whereas for prolate systems of large aspect ratio, the 2‐D aspect ratio varies logarithmically with actual aspect ratio. Extension to polydisperse systems yields a shape factor, R, which gives greatest weight to grains (or particles) having the highest volume fraction. This not only preserves the linear and logarithmic functionalities found in monodisperse systems, but favorably affects the sensitivity of R to visually apparent differences among microstructures.
ISSN:0002-7820
1551-2916
DOI:10.1111/j.1151-2916.1995.tb08848.x