Residual-strain Determination by Least-squares Refinement of Tof Neutron-diffraction Measurements of Deformed Uranium

We report the complete macroscopic average strain tensor for a cold-rolled uranium plate. The strain tensor was determined by the least-squares refinement of interplanar spacings for 19 Bragg reflections, as determined from the neutron TOF measurements at LANSCE. An annealed uranium plate was used as a reference sample, thus providing reference interplanar spacings for all 19 reflections. We also discuss the mathematical background for the calculation of the average macroscopic strain tensor as applied to the orthorhombic crystal symmetry and general triclinic sample symmetry of the uranium sample, based on a recently proposed method to determine texture-weighted strain orientation distribution function for arbitrary crystal and sample symmetries.