The Weighted Burgers Vector

A quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials

J. Wheeler*, E. Mariani, S. Piazolo, D. J. Prior, P. J. Trimby, M. R. Drury

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)

Abstract

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

Original languageEnglish
Title of host publicationRecrystallization and Grain Growth IV
Editors E.J. Palmiere, B.P. Wynne
Place of PublicationZurich
PublisherSciTePress
Pages732-736
Number of pages5
Volume715-716
ISBN (Print)9783037853900
DOIs
Publication statusPublished - 2012
Event4th International Conference on Recrystallization and Grain Growth, ReX and GG IV - Sheffield, United Kingdom
Duration: 4 Jul 20109 Jul 2010

Publication series

NameMaterials Science Forum
Volume715-716
ISSN (Print)02555476

Other

Other4th International Conference on Recrystallization and Grain Growth, ReX and GG IV
CountryUnited Kingdom
CitySheffield
Period4/07/109/07/10

Keywords

  • Dislocation density
  • Electron Backscatter Diffraction
  • Geometrically necessary dislocation
  • Nye tensor

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    Wheeler, J., Mariani, E., Piazolo, S., Prior, D. J., Trimby, P. J., & Drury, M. R. (2012). The Weighted Burgers Vector: A quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials. In E. J. Palmiere, & B. P. Wynne (Eds.), Recrystallization and Grain Growth IV (Vol. 715-716, pp. 732-736). (Materials Science Forum; Vol. 715-716). Zurich: SciTePress. https://doi.org/10.4028/www.scientific.net/MSF.715-716.732