Experimental characterization of the mesoscale dislocation density tensor

Abstract

The dislocation density tensor has been an important variable in the theoretical characterization of dislocations in deformed crystals since its introduction over 5 decades ago. However, the non-destructive, three-dimensional (3D) measurements of lattice rotations and elastic strain needed to determine dislocation density tensors with micron spatial resolution over mesoscopic length scales have until now not been available. We have used 3D X-ray microscopy with sub-micron point-to-point spatial resolution to demonstrate 3D, spatially resolved measurements of the dislocation density tensor in elastically and plastically deformed silicon single crystal plates. Measurements were made of the dislocation density tensor along a line in a ∼35 µm thick silicon plate that was bent (elastically) to a 5.42 mm radius of curvature at room temperature, and in a similar sample deformed plastically by annealing to 700°C under bending stress. We discuss the theoretical background for the dislocation density tensor with respect to lattice rotation and elastic strain, we describe the X-ray microscopy technique used to make non-destructive measurement of local rotations and elastic strains with sub-micron resolution in 3D, and we discuss the analysis procedures for extracting dislocation tensors on mesoscopic length scales.