Weighted Burgers Vector

The Weighted Burgers Vector algorithm is described in detail in section 3.4.5. As the name suggests, it is a vector quantity calculated from 2D map data, and so has a magnitude and a direction, which provide an estimate a lower bound on the magnitude of the dislocation density tensor, and 3D information about dislocation types present (i.e. directions of likely Burgers vectors), respectively (Wheeler et al., 2009). The WBV data presented here was calculated from a square region of 9 pixels, with the calculated WBV value being assigned to the central point.

168 6.4 Results

For the comparison of the two techniques, the WBV algorithm was first applied to conventional EBSD maps of the two samples, and then the WBV algorithm was applied to the same data, after it had been processed by the HR-EBSD technique.

6.4.1 Albite

The WBV can be used to calculate the net Burgers vector content of a given region of interest in an EBSD map by an integration around the edge of the area. Wheeler et al. (2009) first suggested such an integration would reduce the effect of noise within the data, and this has been confirmed in unpublished numerical experiments (Wheeler, pers. comm.). When the integral WBV is calculated around a loop, a histogram is generated which shows lengths of the WBV calculated at each pixel within the loop. WBVs of the smallest magnitude are those most prone to error, and should thus be discarded; hence the histogram provides a simple way to threshold minimum and maximum reliable WBV magnitude values.

Figure 6.3 a) Frequency histogram of WBV magnitudes calculated for the conventional EBSD map of albite. b) Frequency histogram of WBV magnitudes calculated for the HR-EBSD map of albite. Note the greater maximum WBV magnitude calculated from the HR-EBSD dataset.

169

Figure 6.4 a) WBV magnitude map of albite from conventional EBSD dataset, thresholded between 0.02 and 0.07 μm−1_{. b) WBV magnitude map of the same area using HR-EBSD-processed}

data, using the same thresholds. Intracrystalline features are more sharply defined in the HR- EBSD-processed map. Red boxes show the position of data presented in Fig. 6.7.

170 When the WBV is calculated, frequency histograms of WBV magnitude are automatically generated (e.g. Figs. 6.3 & 6.8), which can be used to remove noise from a WBV magnitude map by thresholding minimum and maximum values. The main peak in the histogram is predominantly composed of noise, so most of the peak should be removed. The histogram generated by the conventional EBSD map of albite suggests a minimum value of 0.02 μm−1 _{and a maximum value of around 0.07 μm}−1 _{should be}

used (Fig. 6.3; note different x axis scales). The histogram shows that the highest value for WBV magnitude actually occurs at a little under 0.45 μm−1_{. However, using this}

value as a maximum when plotting WBV magnitude maps means intracrystalline features containing lower magnitude WBVs do not show up well in such maps, so a lower maximum value is recommended. Thresholding at the values stated above and plotting the WBV magnitude on to the albite map results in certain intracrystalline features, such as subgrain walls, emerging in the magnitude map (Fig. 6.4a). The WBV directions of pixels with the highest magnitudes can also be plotted using the IPF colour scheme (key in inset). The maximum magnitude used for this plot was increased to 0.45

μm−1_{, to include all of the longest WBVs, as these are the most accurate (Fig. 6.5a). This}

is because the WBV is calculated from orientation gradients, which, in turn, relate to misorientations (angles and axes) between the point of interest and adjacent pixels. Low dislocation densities lead to smaller misorientations, bigger errors on misorientation axes and hence bigger errors in WBV. There is a clear dominance of blue pixels in the image, which corresponds to the [010] Burgers vector. This is not a Burgers vector that has been identified to be part of a common slip system in plagioclase, suggesting the observed intracrystalline distortion is a product of other processes. See Chapter 3 for a full discussion of these ideas.

The accuracy of the integral WBV depends on the angular resolution of the EBSD data (Piazolo et al., 2015), which suggests applying the WBV to HR-processed EBSD datasets should yield more accurate results. The histogram produced by integration of the HR-processed data shows the maximum WBV magnitude calculated for a single pixel has more than doubled, although the peak in the histogram has not shifted to higher values (Fig. 6.3b). Using the same threshold values as applied to the conventional EBSD dataset (min = 0.02, max = 0.07 μm−1_{), more detail, with sharper}

boundaries, can be observed in the magnitude plot. The noise, apparent in the background of the HR-EBSD magnitude plot as stippling of colour, is reduced compared to the conventional EBSD dataset (Fig. 6.4b), and the same dominant central feature is resolved in sharper detail. Plotting WBV directions using the IPF colour

171

Figure 6.5 WBV direction plots of a) conventional and b) HR-EBSD albite data. Noise reduction during HR-EBSD processing removes many single pixels with a range of IPF colours (i.e. orientations), leaving dominantly blue (i.e. the [010] crystallographic direction) WBV orientations in both linear features and isolated pixels.

172

Figure 6.6 Contoured IPF plots of the WBV directions plotted on the maps in Fig. 6.5. a) a range of directions are calculated from the conventional EBSD data. b) a clear maxima centred on the [010] crystallographic direction can be observed.

scheme shows a stronger dominance of the ‘blue’ (i.e. [010]) crystallographic direction within the central feature (Fig. 6.5b). In addition, the WBV calculated for isolated pixels tends to be dominated by the [010] direction, unlike the isolated pixels plotted from the conventional EBSD data, which have a much wider spread (compare Figs. 6.5a & b). Contoured IPF plots confirm the dominance of the [010] Burgers vector in the HR- processed dataset (Fig. 6.6).

A close-up of part of a prominent looping feature in the HR-EBSD dataset that is not picked out in the conventional EBSD dataset serves to reinforce the extra detail that can be gathered using HR-EBSD data (Fig. 6.7; see box in Figs. 6.4a and b for location; map grid reference: [415 440 135 150]). Figures 6.7a and c show WBV magnitude maps, thresholded between 0.005 and 0.05 μm−1_{, for the conventional and HR-EBSD datasets,}

respectively. In the conventional EBSD dataset, no linear feature can be determined, in contrast to a clear linear feature (subgrain wall?) visible in the HR-EBSD dataset.

173 Likewise, in WBV direction IPF plots (both thresholded between 0.02 and 0.5 μm−1_{, no}

regular directional feature is observed in the conventional EBSD dataset (Fig. 6.7b), but a clear feature with WBVs consistently oriented in the [010] crystallographic direction is resolved (Fig. 6.7d); indeed, systematic changes in orientation within the linear feature – from the edges to the centre of the line – can also be observed.

Figure 6.7 Close-up of the region identified by the red box in Figs. 6.4a&b. In a) and b), from the conventional EBSD dataset, no linear feature is resolved, whereas after HR-EBSD processing a linear feature can be observed in both the c) WBV magnitude and d) WBV direction plots. Not only is the feature identifiable in the HR plots, some degree of detail within the line can be resolved, e.g. there is a systematic shift in orientation from either edge to the centre of the feature.