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Stereological Corrections for Grain Boundary Number Fractions in Three Dimensions

Published online by Cambridge University Press:  15 March 2011

Bryan W. Reed  and
Mukul Kumar
Bryan W. Reed
Affiliation:
Materials Science and Technology Division, Lawrence Livermore National Laboratory Livermore, CA 94550
Mukul Kumar
Affiliation:
Materials Science and Technology Division, Lawrence Livermore National Laboratory Livermore, CA 94550
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Abstract

Two-dimensional (2D) cross sections through three-dimensional (3D) polycrystalline materials present a biased picture of the statistical properties of grain boundary networks. These properties are essential to many practical applications such as grain boundary engineering. We show a simple correction that will partly correct for the sampling biases by removing the effect of the correlation between grain boundary type and grain boundary area. This correction alters number fraction estimates by as much as ∼60% for σ3 boundaries in the highly-twinned copper samples we consider. We also estimate the bias introduced by the correlation between boundary type and boundary shape, which for many materials represents perhaps a 10% shift in the measured statistics, so that the simple method we propose should correct for the majority of the bias in favorable cases.

This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 819: Symposia N/P – Interfacial Engineering for Optimized Properties III , 2004 , N7.6
Copyright
Copyright © Materials Research Society 2004

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