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

Abstract

<p>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.</p>