Using crystal-lattice distortion data for geological investigations: the weighted Burgers vector method

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 crystals 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 assumes only that elastic strains have little effect on the calculation. It can be used, with care, to analyse subgrain walls (sharp orientation changes) as well as gradational orientation changes within individual grains. There are four linked parts to this contribution. 1We describe the mathematical background to the WBV and then how it is modified to deal with spaced, discrete orientation measurements. 2EBSD orientation data have angular errors, and so does the WBV. We present a new analysis of these angular errors, showing there is a trade-off between directional accuracy and area sampled. Angular errors can now be accounted for during testing of hypotheses about dislocation types. 3We present new studies on olivine and plagioclase to illustrate how to use the method. 4We discuss published studies on ice and titanite to further illustrate the method.We note that the methods discussed here are applicable to any crystalline material encompassing minerals (including ice), metals and ceramics.