Grain- and phase-boundary analysis

As grain and phase boundaries are preferred loci of intergranular micro-crack initiation, also the grain- and phase-boundary orientation distribution was analysed. For this purpose, the automatic “rotating polarizer stage” was used. Parts of the horizontal sample slices were used for the preparation of thin sections. In each of these thin sections, five representative sections were selected of five of the samples and analysed by microscopy with a magnification of 2.5.

Only for sample 104, six sections were analysed because of the large grain size.

For each section, 200 images with different polarisations were automatically captured by the computer-controlled rotating polarizer stage (Fig. 3.2). During this procedure, the polariser within the microscope stage is rotated stepwise (with an interval of 1 gon).

The resulting dataset therefore consists of 200 individual images that were subsequently combined (Fig. 3.2 A) and analysed with the automatic edge-detection routine of the software

“GEOVISION 6.0”. This routine automatically detects grain and phase boundaries by indentifying contrast gradients in the stacked image and completing these to grain boundaries (Fig. 3.2 B). This works properly with pure quartzites, but it is somewhat problematic if the sample contains larger amounts of other minerals, in this case feldspars and mica, or small inclusions in the minerals. Therefore, the results of the automatic edge-detection were refined manually, e.g. by disregarding twin lamellae identified as grain boundaries, to improve the results (Fig. 3.2 B). It has to be considered that the automatic edge-detection measures each edge length between two triple points (Fig. 3.3). For this reason, particularly longer boundaries are often cut in several sections that are counted separately by the software. As a result, the grain-boundary direction of long grains is statistically falsified by an amplification

Fig. 3.2: Example of grain- and phase-boundary determination by the automatic edge detection of the software

“GEOVISION 6.0”. A) Photomicrograph of sample 87 under crossed polars. The analysed dataset consists of 200 stacked images captured with the “rotating polarizer stage” assembled by “GEOVISION 6.0”. B) Image of A) after processing the automatic edge detection with “GEOVISION 6.0” without manual refining. White lines represent the automatically-detected grain and phase boundaries. The yellow asterisk marks an intra-granular micro-crack, identified as a grain boundary by the software, which was deleted during the manual refining. The grain boundary marked by a red line has a curvature factor of 1, while the blue-marked grain boundary has a curvature factor of -1, depending on their orientation in the reference system of the “rotating polarizer stage”. The green-marked inclusions have a curvature factor of 0 and are neglected during data analysis.

Fig. 3.3: During edge detection with “GEOVISION 6.0”

grain and phase boundaries are separated at triple points.

Consequently, long grain and phase boundaries are disected more often than short boundaries. Therefore, the direction of the long axis of these long grains appears disproportionally more often in the statistics.

crack emits an EMR pulse, a wrong number of micro-cracks per direction would falsify the results.

To quantify this statistical effect, the rose diagrams were (1) plotted separately for different boundary lengths, and (2) an additional analysis was carried out, where the grain-boundary lengths were grouped according to their direction, and the grain-boundary length was summed for all boundaries in each group. Consequently, the true boundary length in relation to the strike of the boundaries could be evaluated.

The curvature of the boundary segments detected by the automatic edge-detection represents another statistical problem. Since an EMR contribution by grain/phase-boundary cracks occurs parallel to their strike, curved boundaries can contribute in a more or less wide angular range to the EMR. Furthermore, small inclusions detected by the software and not manually rejected (see Fig. 3.2 B) result in completely round and closed boundaries and have to be ignored in the

Fig. 3.4: Exemplary statistic test for sample 83: influence of reduced number of data as a result of filtering grain/phase-boundary data as a function of curvature. A) For grain/phase boundaries with a curvature factor of 0.8 and 1, and -0.8 and -1 respectively, 65% of grain/phase boundaries and 60% of the corresponding grain/phase-boundary length remain for further analysis. B) - E) overpage.

evaluation, because no preferred radiation direction can be expected. To quantify this effect, every calculated grain boundary is attributed a curvature factor called R-statistics in

“GEOVISION 6.0”. The curvature factor has a range of -1 to 1, where -1 and 1 are straight boundaries without curvature. A curvature factor of 0 describes completely circular and closed forms. For the evaluation of the data, only grain/phase boundaries with a curvature factor of 0.8 to 1, and -0.8 to -1 respectively, were used. To ensure that the results were not statistically falsified by this data restriction, the effects were exemplarily tested for sample 83 (Fig. 3.4). For this purpose, the complete dataset was grouped according to curvature factor, and the strike distribution of each group was determined as function of the number of grain boundaries and as a function of the boundary length per direction. The results indicate that about two thirds of the data lie in a range of the curvature factor 0.8 and 1 (and -0.8 to -1) and that this data contributes with about 60% to the total grain- and phase-boundary length. By including boundaries with higher curvature (R < 0.8 and R > -0.8) the results to become less well defined; however, they show the same main trends. In the following, the grain- and phase-boundary data of all samples was filtered by curvature prior to further analysis.

Fig. 3.4: Exemplary statistic test for sample 83: influence of reduced number of data as a result of filtering grain/phase-boundary data as a function of curvature. B) - E) A further increase of the data range by adding stronger-curved grain/phase boundaries has no significant effect on the resulting main strike.