The Weighted Burgers Vector: A Quantity for Constraining Dislocation Densities and Types Using Electron Backscatter Diffraction on 2D Sections through Crystalline Materials

摘要: The Weighted Burgers Vector (WBV) is defined as the sum, over all types of dislocations, [(density intersections dislocation lines with a map) x (Burgers vector)]. It can be calculated, for any crystal system, solely from orientation gradients in map view, unlike full density tensor, which requires third dimension. No assumption made about dimension and they may non-zero. only involved that elastic strains are small so lattice distortion entirely due to dislocations. Orientation estimated gridded measurements obtained by EBSD mapping, WBV calculated vector field on an map. magnitude gives lower bound tensor when coordinate invariant way. direction constrain vectors geometrically necessary dislocations present microstructure, most clearly it broken down terms vectors. has five advantages other measures local distortion. 1. hence carries more information than scalar measure misorientation. 2. explicit mathematical link individual 3. Since derived via calculus, not dependent contrast existing misorientation but system used. 4. Calculation involves no assumptions energy minimisation. 5. numerical differentiation calculating introduce errors, there direct contour integral. net content intersecting area simply integration round edge area, method fast complements point-by-point calculations. Errors measurement will have much smaller effect here, detected otherwise lost noise calculation.