2.5. Automated Analysis of Slip Lines

Such a series of vector rotations is most easily done via a (semi-)automated analysis. Here, we give an example of MATLAB code (Version 2015 or newer) with MTEX toolbox (Version 5.3.1) developed for this purpose within our group. Figure 4 shows the workflow of the code, and the various options available when automating the slip line analysis. The code is split into three sections, in which the orientation data is entered, the slip lines identified, and the active slip planes determined. For the initial entry of orientation data, a further three modes are available, based upon (i) EBSD maps, most often used in the case of polycrystals, (ii) single orientations where the indents are contained within a single grain, or (iii) where the sample orientation in the indented area has not been directly measured, and a set of orientations should be generated given either an assumed texture or one measured separately by X-ray diffraction (XRD) for example.

Workflow of the automated slip line analysis code. Orange segments show analysis steps corresponding to the input of EBSD maps (mode 1), purple shows mode 2 and green shows mode 3. All the blue segments then run to give the final assignment of a slip line to a slip system.

This mode is most commonly used where indents are made in a polycrystalline sample, such that the number of orientations to include in the analysis approaches the number of indents made. The code therefore takes EBSD data collected over the area of interest and aligns it to secondary electron (SE) images of the indents to correlate the location data with the orientation data before the user indicates the slip lines of interest and the slip planes are calculated. The EBSD data are typically OSC formatted data, but the code leverages MTEX and is therefore flexible. The specific steps to achieve the slip plane calculation are:

Step 1: Alignment. If there is misalignment between the SEM image of the indents and the EBSD map, an artificial angle deviation could be introduced between the experimental slip lines and those theoretically possible based on the crystal symmetry slip traces. To avoid this, in this step the code will firstly plot and save the EBSD-IQ map and then guide the user to upload an alignment SE image taken under low magnification. Afterward, the user can select three different indents (e.g., the corners of the array of indents) to use as fiducial markers to align the two images. The code will determine the best fitted alignment parameters based on the selected positions of the indents.

Step 2: Indent Selection. In this step, a grain of interest on the output IQ image is selected and the corresponding SE/AFM image of the indent to be analysed should be uploaded.

In this mode, no upload of the EBSD data is necessary. Instead, the code will ask for the Euler angles of the orientation and then for the upload of the corresponding SE/AFM image of the indent of interest.

In mode 3, the active fraction of slip systems is then calculated only considering the effect of the bulk texture and the Schmidt factor for each slip system. The user must upload the texture of the specimen as an input–typically measured by X-ray diffraction- and the code subsequently discretises this texture into 10,000 orientations. The (nanoindentation) Schmid factor of each slip system is calculated based upon a series of points distributed over the assumed stress field under the indenter [41,42,43]. It is assumed that those with a Schmid factor greater than 0.4 will be activated. This mode, therefore, allows an analysis in the absence of direct orientation measurement; however, it relies on the assumptions that the given texture is representative of the indented region, and that the stress field is homogenous enough to be described by pure theory.

In the first two modes, the code will firstly rotate the SE/AFM image automatically according to the alignment parameters determined in Section 1. The user subsequently needs to mark the slip traces of interest on the rotated image by clicking the start and end points of each of the traces. The traces will be marked with black dashed lines. In mode 3, the code will go through the 10,000 orientations one by one and generate different slip lines (0–180 degrees relative to the x-vector).

Simultaneously, the code can also calculate the theoretical slip lines of different slip planes of interest on the observed surface.

The deviation angle between the user-identified and/or automatically generated lines and the lines that each theoretical slip plane would produce can then be calculated. When this angle is small, i.e., the misorientation threshold, ∆, is under ~5°, it can be assumed that the slip plane of interest is active. This misorientation threshold can be varied according to the needs of the user; larger values will be more forgiving to experimental error, cross slip, slip line curvature, etc, but will result in an increase in over-counting, as each experimental slip trace could correspond to an increased number of potential slip planes.

The MATLAB code operating in modes 1 and 2 will colour the slip traces corresponding to the slip plane operating, e.g., basal planes, pyramidal planes, etc. For mode 3, the activity of this slip plane will simply be counted. An example of these modes are shown in Figure 5.

Examples of indents analysed in mode 1, mode 2 and mode 3. (a) In mode 1, the three points indicated by the yellow circles are used to align the EBSD and SE images. (b) The indent of interest is selected from the EBSQ-IQ map, (c) the corresponding SE image is uploaded, and the slip lines are marked by the user. (d) The code subsequently identifies the operating slip planes, and colours them accordingly. (e) In mode 2, the Euler angles are provided by the user, (f) the slip lines are marked by the user on the AFM image, (g) and then these are assigned to slip planes and coloured accordingly. (h) In mode 3, the global texture of the sample is defined as an input and discritised into 10,000 orientations. (i) The stress field under an indent is calculated for these orientations, and slip systems showing a Schmid factor >0.4 are assumed to be active. The indents shown in (b–d) are made in a Nb₆Co₇ μ-phase, produced by arc melting and annealed for 1000 h at 1100 °C and mechanically polished down to a colloidal silica finish. The indents in (f,g) are in the same Fe₇Mo₆ µ-phase sample described in Figure 3.