AbstractTwo-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.
Descriptive zoopraxography; or, the science of animal locomotion made popular : with selected outline tracings reduced from some of the illustrations of "Animal Locomotion" an electro-photographic investigation of consecutive phases of animal movements, commenced 1872, completed 1855, and published, 1887, under the auspices of the University of Pennsylvania. Published as a memento of a series of lectures given by the author under the auspices of the United States Government Bureau of Education at the World's Columbian Exposition, in Zoopraxographical Hall 1893 /
