Man, Chi-Sing and Paroni, Roberto and Xiang, Yu and Kenik, Edward A. (2006) On the geometric autocorrelation function of polycrystalline materials. Journal of Computational and Applied Mathematics, Vol. 190 (1-2), p. 200-210. ISSN 0377-0427. Article.
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Herein we derive an expression for direct determination of the geometric autocorrelation function W of a polycrystalline material from images of its grain boundary network (e.g., those delivered by orientation imaging microscopy). We also obtain an identity that relates the mean linear intercept function to a directional derivative of the geometric autocorrelation function. These formulae were applied to examine whether a widely-used formula for W, particularly in theoretical studies of attenuation of elastic waves in polycrystalline media, would be valid for the grain boundary structure of a commercial aluminum alloy. The conclusion was negative.
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