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\begin{document}

\title{Using crystal lattice distortion data for geological investigations: the
Weighted Burgers Vector method}



\author[1]{John Wheeler}%
\author[2]{Sandra Piazolo}%
\author[3]{David John Prior}%
\author[4]{Patrick W Trimby}%
\author[5]{Jacob A Tielke}%
\affil[1]{University of Liverpool}%
\affil[2]{School of Earth and Environment, The University of Leeds}%
\affil[3]{University of Otago}%
\affil[4]{Oxford Instruments}%
\affil[5]{Lamont-Doherty Earth Observatory}%


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  \date{June 10, 2024}


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\begin{abstract}
Distorted crystals carry useful information on processes involved in
their formation, deformation and growth. The distortions are
accommodated by geometrically necessary dislocations, and therefore
characterising those dislocations is an informative task, to assist in,
for example, deducing the slip systems that produced the dislocations.
Electron Backscatter Diffraction (EBSD) allows detailed quantification
of distorted crystal orientations and we summarise here a method for
extracting information on dislocations from such data. The Weighted
Burgers Vector (WBV) method calculates a vector at each point on an EBSD
map, or an average over a region. The vector is a weighted average of
the Burgers vectors of dislocation lines intersecting the map surface.
It is weighted towards dislocation lines at a high angle to the map but
that can be accounted for in interpretation. The method is fast and does
not involve specific assumptions about dislocation types. It can be
used, with care, to analyse subgrain walls (sharp orientation changes)
as well as gradational orientation changes within individual grains. We
describe new and published examples of the use of the technique to
illustrate its potential; case studies to date mainly use the WBV
direction not the magnitude. EBSD orientation data have angular errors,
and so does the WBV. We present an analysis of these angular errors,
showing there is a trade-off between directional accuracy and area
sampled. In summary the technique is fast, free from assumptions, and
errors can be taken into account to allow testing of hypotheses about
dislocation types.%
\end{abstract}%



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