The stereology of grain boundary allotriomorphs

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Department of Materials Science and Engineering


Grain boundary allotriomorphs have been modeled as two abutting spherical caps of equal radius. The effects of the distance from the center of the allotriomorph, kh{cyrillic}, and the angle with respect to the plane normal to the grain boundary, ψ, at which a plane of polish sections the allotriomorph have been investigated. Expressions were derived relating the apparent to the true thickness, length, aspect ratio and dihedral angle. The effects of kh{cyrillic} and φ{symbol} upon measurements of the lengthening and thickening kinetics of allotriomorphs were found to be significant, particularly at larger values of ψ. Analysis of published high-temperature measurements of allotriomorph growth kinetics indicated that an appreciable portion of the scatter in this data may have been due to nonzero values of kh{cyrillic} and ψ. A room temperature technique for making these measurements which minimizes such effects is concluded to be stereologically more reliable.

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Metallurgical Transactions A