The Weighted Burgers Vector: a new quantity for constraining dislocation densities and types using electron...

Area of Science:

• Materials Science
• Crystallography
• Solid Mechanics

Background:

• Dislocation density and Burgers vectors are crucial for understanding material properties and plastic deformation.
• Current methods for quantifying lattice distortion often require complex 3D data or make simplifying assumptions.
• The need for a robust, map-based method to characterize dislocation content in materials is evident.

Purpose of the Study:

• To introduce and define the Weighted Burgers Vector (WBV) as a novel measure of local lattice distortion.
• To demonstrate that WBV can be calculated solely from 2D orientation gradients obtained via EBSD mapping.
• To highlight the advantages of WBV over existing methods for analyzing dislocation structures.

Main Methods:

• Definition of WBV as the sum of (intersection density) x (Burgers vector) over all dislocation types.
• Calculation of WBV using orientation gradients derived from EBSD map data.
• Analysis of WBV magnitude and direction in relation to dislocation density tensor and Burgers vectors.

Main Results:

• WBV can be computed from 2D orientation gradients, independent of third-dimensional gradients.
• WBV magnitude provides a lower bound for the dislocation density tensor magnitude.
• WBV direction offers constraints on the types of geometrically necessary dislocations present.

Conclusions:

• The WBV is a powerful, versatile vector field for characterizing lattice distortion and dislocation content directly from EBSD maps.
• WBV offers advantages in information content, mathematical linkage to Burgers vectors, and coordinate system independence.
• WBV calculations, including integration around map edges, provide a fast and complementary approach to detailed microstructural analysis.