## 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 language | English |
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Title of host publication | Recrystallization and Grain Growth IV |

Editors | E.J. Palmiere, B.P. Wynne |

Place of Publication | Zurich |

Publisher | SciTePress |

Pages | 732-736 |

Number of pages | 5 |

Volume | 715-716 |

ISBN (Print) | 9783037853900 |

DOIs | |

Publication status | Published - 2012 |

Event | 4th International Conference on Recrystallization and Grain Growth, ReX and GG IV - Sheffield, United Kingdom Duration: 4 Jul 2010 → 9 Jul 2010 |

### Publication series

Name | Materials Science Forum |
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Volume | 715-716 |

ISSN (Print) | 02555476 |

### Other

Other | 4th International Conference on Recrystallization and Grain Growth, ReX and GG IV |
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Country/Territory | United Kingdom |

City | Sheffield |

Period | 4/07/10 → 9/07/10 |

## Keywords

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