Reconstruction of full elements of Nye tensor by coupling precession electron diffraction (PED) measurements with computation method in simulated Nano-scaled crystal sample

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Liu, Haidong
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Symposium on Undergraduate Research and Creative Expression
Iowa State University Conferences and Symposia

The Symposium provides undergraduates from all academic disciplines with an opportunity to share their research with the university community and other guests through conference-style oral presentations. The Symposium represents part of a larger effort of Iowa State University to enhance, support, and celebrate undergraduate research activity.

Though coordinated by the University Honors Program, all undergraduate students are eligible and encouraged to participate in the Symposium. Undergraduates conducting research but not yet ready to present their work are encouraged to attend the Symposium to learn about the presentation process and students not currently involved in research are encouraged to attend the Symposium to learn about the broad range of undergraduate research activities that are taking place at ISU.

The first Symposium was held in April 2007. The 39 students who presented research and their mentors collectively represented all of ISU's Colleges: Agriculture and Life Sciences, Business, Design, Engineering, Human Sciences, Liberal Arts and Sciences, Veterinary Medicine, and the Graduate College. The event has grown to regularly include more than 100 students presenting on topics that span the broad range of disciplines studied at ISU.

Materials Science and Engineering

The study of dislocations is fundamental to the understanding the mechanical properties of materials, and is especially useful in metallurgy. Nye proposed to characterize the geometrically necessary dislocation density by a second rank tensor that characterizes the state of dislocation of subvolumes. The misorientation maps obtained by transmission electron microscopy (TEM) of the crystal sample are used to calculate the Nye tensor, however since the TEM could only take through-thickness measurements, the complete spatial information of the sample could not be acquired and only five elements of Nye tensor could be calculated. The measurement of precession electron diffraction (PED) contains the spatial orientation information as the average of a volume in the certain direction. The focus of this study is to couple the PED measurements in multiple directions with computation techniques to calculate all nine components of Nye tensor in nanoscale samples. In a simulated Nano-sized crystal known the Nye tensors, curvature tensors are calculated backward from Nye tensors, and then the curvature tensors are used to calculate the orientations through the sample. Measurements symmetric about the normal axis are taken. Orientations are represented in {hkl} notation as vector field and separated into matrix for each slice to reconstruct the tensors.