Microsc. Microanal. 20, 852–863, 2014 doi:10.1017/S143192761400035X
© MICROSCOPY SOCIETY OF AMERICA 2014
Orientation Precision of Electron Backscatter Diffraction Measurements Near Grain Boundaries Stuart I. Wright,1,* Matthew M. Nowell,1 René de Kloe,2 and Lisa Chan3 1
EDAX, 392 East 12300 South, Draper, UT 84020, USA EDAX BV, Ringbaan Noord 103, 5046 AA Tilburg, The Netherlands 3 TESCAN USA, 508 Thomson Park Drive, Cranberry TWP, PA 16066, USA 2
Abstract: Electron backscatter diffraction (EBSD) has become a common technique for measuring crystallographic orientations at spatial resolutions on the order of tens of nanometers and at angular resolutions < 0.1°. In a recent search of EBSD papers using Google Scholar™, 60% were found to address some aspect of deformation. Generally, deformation manifests itself in EBSD measurements by small local misorientations. An increase in the local misorientation is often observed near grain boundaries in deformed microstructures. This may be indicative of dislocation pile-up at the boundaries but could also be due to a loss of orientation precision in the EBSD measurements. When the electron beam is positioned at or near a grain boundary, the diffraction volume contains the crystal lattices from the two grains separated by the boundary. Thus, the resulting pattern will contain contributions from both lattices. Such mixed patterns can pose some challenge to the EBSD pattern band detection and indexing algorithms. Through analysis of experimental local misorientation data and simulated pattern mixing, this work shows that some of the rise in local misorientation is an artifact due to the mixed patterns at the boundary but that the rise due to physical phenomena is also observed. Key words: electron backscatter diffraction, EBSD, orientation imaging microscopy, OIM, orientation precision, kernel average misorientation, KAM
I NTRODUCTION Electron backscatter diffraction (EBSD) in the scanning electron microscope (SEM) is well suited to the characterization of deformed microstructures in crystalline materials. EBSD is capable of measuring crystallographic orientations at spatial resolutions on the order of tens of nanometers (or even nanometers) and at angular resolutions < 0.1° (cf. Steinmetz & Zaefferer, 1993; Trimby, 2012; Wright et al., 2012). When EBSD measurements are automatically collected at each point on a regular measurement grid, it is possible to compare the orientations of neighboring points in the grid to characterize local misorientations present in the microstructure. One common method for characterizing the local misorientation is using the kernel average misorientation (KAM) measurement (Wright et al., 2011). A kernel is a set of grid points in the immediate vicinity of a point of interest in the measurement grid. The kernel will contain the first nearest neighbors out to a user-specified set of neighbors, such as the third nearest neighbors. The misorientation of each point in the kernel with respect to the orientation of the point at the center of the kernel is calculated. The average of these misorientations is then determined. This is the KAM value. It can be calculated for each point in the measurement grid and mapped to a color scale to form a KAM map. This allows the spatial arrangement of local misorientation within the microstructure to be visualized. Received July 26, 2013; accepted January 29, 2014 *Corresponding author. [email protected]
An increase in the local misorientation as determined by KAM is often observed near grain boundaries in deformed microstructures, relative to the grain interiors (Mishra et al., 2009; Perrin et al., 2010; Rollett et al., 2012; Beausir & Fressengeas, 2013). This is expected due to dislocation pile-up at the boundaries. However, the increase in local misorientation may also be due to a decrease in orientation precision of the EBSD measurements in the immediate vicinity of a boundary. When the electron beam is positioned at a grain boundary, the diffraction volume contains the crystal lattices from the two grains separated by the boundary. Thus, the resulting pattern will contain contributions from both lattices, as shown in Figure 1. Such mixed patterns can pose a challenge to both the EBSD pattern band detection and indexing algorithms. Generally, the software is successful in finding the solution of one of the two contributing patterns, but occasionally it will find a solution that does not correspond with either. Figure 2 shows indexing results from a grain boundary in fully recrystallized nickel (Ni). Of 363 boundary points only six (1.6%) do not correspond to either of the orientations on either side of the boundary. It should also be noted that both the image quality (IQ) and confidence index (CI) maps show lower values in the immediate vicinity of the grain boundary. This work seeks to differentiate the artificial rise in KAM measurements at grain boundaries due to pattern mixing from the real increases due to physical phenomena. KAM measurements in recrystallized and deformed materials using both direct measurements at grain boundaries as well as statistical approaches are compared. In addition, the effect
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Figure 1. Schematic illustrating mixed pattern at a grain boundary due to interaction volume containing crystal lattices from both sides of the boundary.
Figure 2. a: Image quality, (b) confidence index (red is high, blue is low), and (c) orientation map from a grain boundary in nickel.
of the mixing on the band detection and indexing algorithms is explored using a simulation of pattern mixing. The algorithms used for band detection and indexing differ between systems. In this paper we have used the algorithms as implemented in the EDAX® orientation imaging microscopy (OIM) EBSD data collection systems. The data collection software uses a triplet indexing approach to determine the orientation, given a set of detected bands (Wright & Adams, 1992). Each possible triplet of bands is constructed. The angle between each pair of bands in a triplet is determined. These angles are compared against a lookup table of interplanar angles constructed from the planes in the crystal producing the strongest diffraction bands. From this comparison, a set of possible orientations is determined. This procedure is repeated for every possible triplet. The orientation that appears most often from the set of triplet orientations is then assumed to be the correct solution for the pattern. As the detection of the bands in the diffraction pattern is never perfect, the “same” orientation solutions determined by each triplet will differ slightly from triplet to triplet. Solutions from different triplets that are found to be similar (i.e., within just a few degrees of each other, typically 3°) are averaged together using a quaternion
Figure 3. Schematic showing band triplets contributing to the averaged orientation solution for two patterns (a, b) and a 50/50 mix of the two patterns (c). g denotes an orientation, fa denotes an orientation averaging function.
averaging approach (Kunze et al., 1993) to refine the final solution. Mixed patterns have a direct impact on the solution refinement. Consider the case where seven bands are detected in a pattern from grain A and seven are also detected in the pattern from a neighboring grain B. Thirty-five triplets can be formed from seven bands, so if all the bands are accurately detected, then 35 slightly different orientations will be used in the refinement averaging process. However, if a pattern is obtained from the immediate vicinity of the boundary separating grain A and grain B, then it is possible that the band detection would find four bands for grain A and three bands for grain B. In this case, the orientation associated with grain A would be that selected by the indexing algorithm. But, only four triplets can be formed from four bands so the refinement of the solution through averaging would be reduced, this is illustrated in Figure 3. Thus, the orientation precision would be less in mixed patterns as opposed to patterns from the grain interior.
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This is also evident in Figure 2b, where the CI is lower at the boundary. This is a direct result of the splitting of the votes between the two orientation solutions. The Hough transform is used to detect the bands in the EBSD patterns (Krieger-Lassen et al., 1992). Kunze et al. (2010) details the particulars associated with implementation of the Hough transform in the software used. The Hough transform seeks to find a specified number of bands in the patterns as set by the operator. This is typically the number of strongest bands expected in the patterns. However, if the two patterns are mixed then the relative strength of the bands will be weakened. This is evidenced in pattern quality or IQ maps, as shown in Figure 2a. A metric describing the quality of the diffraction pattern is measured at each point in the scan. This value in the OIM software is the sum of the Hough peak heights divided by the number of peaks specified by the user—a slight modification of the method proposed by Kunze et al. (2010). Maps can be constructed from the IQ value by mapping the values onto a gray scale. The grain boundaries are clearly delineated in such maps as they generally appear much darker (Wright & Nowell, 2006). This is clear evidence that detection of the bands in the mixed patterns will be more difficult than for nonmixed patterns. This may have a couple of potential effects on the accuracy of the band detection. The first is the detection of “rogue” or false bands. If too many rogue bands are detected then this can lead to the software finding neither of the two orientations separated by the grain boundary. Such points will typically be evident as individual points in the grid not associated with any neighboring points and are filtered out in the postprocessing. We will not investigate such effects in this work. However, another effect of rogue bands is a reduction of the number of bands used in the indexing algorithm leading to either of the correct solutions. As noted in the previous section this reduces the number of points in the solution cloud used in averaging, which can lead to less orientation precision. The second effect of mixed patterns on the Hough transform is that the number of “strong” bands in a mixed pattern is increased. This essentially leads to a relative weakening of the strength of the individual bands from both patterns contributing to the mixed patterns. This would potentially lead to less accuracy in determination of the band positions as determined from the associated Hough peaks. These effects are explored using both experimental data from both recrystallized and deformed samples for comparison as well as simulated mixing of patterns. Both the impact of the magnitude of the loss in orientation precision and the spatial extent of the diminished orientation precision are investigated.
M ATERIALS AND M ETHODS Six samples from three different materials were used in this study. The first was a copper (Cu) sample that had been subjected to repeated equal channel angular processing and
Table 1. Various Factors Describing the Quality of the Scan Data for each of the Materials Investigated. Reduction (%) 4.5 11 20 30
Measured
Interpolated
Difference
0.48 1.32 1.64 2.78
0.39 0.93 1.30 1.39
0.09 0.39 0.34 0.88
was then fully recrystallized. This material has a grain size in the range of 5–10 μm. The second sample was a fully recrystallized Ni alloy with an approximate grain size of 20 μm. The third was a series of samples of cold-rolled brass with a 70% Cu/30% Zn ratio. Samples were obtained after 4.5, 11, 20, and 30% rolling reductions. The approximate grain size in these materials was 100 μm. All of the samples were prepared using mechanical polishing using standard procedures. The final polish was performed using a vibratory polisher and 0.05 μm colloidal silica. Automated EBSD scans were obtained from each sample. For the Cu sample a scan containing 3.47 million points was collected over a 33.5 × 35.9 μm area with a 20 nm step size. For the recrystallized Ni sample, scans from five different twinned grains were obtained. Twin boundaries that appeared nearly vertical in the image were scanned for reasons, which will be detailed later in the text. These scans encompassed the full twinned grain and used a step size of 20 nm. The brass scans were performed using a 250 nm step size over a 1.5 × 1.5 mm area resulting in 2.53 million individual orientation measurements in each scan. Pertinent values relating to these scans are shown in Table 1. The indexing success rate was determined by first performing a grain CI standardization (Nowell & Wright, 2005) and then finding the number of points with CI values >0.1. It should be noted that the CI standardization is essentially a CI upgrade process, the orientation data is not altered in this process. This was the only postprocessing applied to the data. The rates, average CI values, and average fit values all reflect the high quality of the measured scan data. It should be noted that for CI >0.1, there is a >95% likelihood that the pattern is indexed correctly (Field, 1997). Field’s (1997) results showed that the indexing reliability for a CI of 0 and a CI of 0.1 is quite different—40 versus 95%, respectively; whereas for CIs between 0.1 and 1, the indexing reliability rises gradually from 95 to 100%. The measurements were made using an FEI™ XL30 field-emission SEM. A 20 keV accelerating voltage was used for all measurements with ~8 nA of current. A relatively high current was used so that the scans could be done in a practical time frame without having to use any electronic gain on the EBSD camera, which would introduce additional noise into the patterns. KAM maps for the brass samples are shown in Figure 4. First nearest neighbor KAMs with a 5° tolerance angle maps were used in all of the calculations.
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Figure 4. First nearest neighbor kernel average misorientation maps for the (a) 4.5, (b) 11, (c) 20, and (d) 30% coldrolled brass.
Ideally, the same step size would have been used for all of the studies. However, the Cu sample had a relatively fine grain size of 5–10 μm in diameter whereas the brass samples had a coarser grain size of ~100 μm. Thus, larger step sizes were used in the brass samples so as to characterize many grain boundaries. The KAM values are affected by the step size (Wright et al., 2000; Wright et al., 2011; Takayama et al., 2005) thus some care must be exercised in interpreting the KAM results where different step sizes are used. In order to confirm the validity of the observations reported, scans with 20 nm step sizes containing at least one triple point were performed on the 4.5, 11, and 20% cold-rolled brass samples. Scans from two separate triple points were performed on the 4.5% cold-rolled brass sample. Since only a few boundaries were sampled in each scan area, the results from the two scans did differ from each other. However, given the grain size in the brass samples these measurements are by no means meant to provide a comprehensive statistical characterization of these materials, rather they were performed only to verify the comparison between the measurements at 20 nm step size in the Cu with the 250 nm step size measurements in the brass samples. As noted, the KAM tolerance angle was set to 5°. This value was selected so that the KAM results would be
focused on the low-angle misorientations characteristic of deformation and not the grain boundaries themselves. In principle, a smaller tolerance angle could enable the subgrain structures within the grains to be investigated. However, characterizing phenomena such as subgrain size, edge versus screw dislocations, or stacking fault is difficult in the SEM, and is generally more suited to investigation in the transmission electron microscope. Although the recent work of Gutierrez-Urrutia et al. (2013) shows that new imaging techniques may make such work possible in the SEM. Such techniques would allow correlation between the deformation substructure and the orientation measurements to be explored, but this is beyond the focus of this work. However, it was noted in the 20 nm step scans on the deformed brass samples that some boundaries showed very different KAM distributions on one side of the boundary compared to the other, indicating a difference in dislocation pile-up at the boundaries.
KAM Profiles KAM profiles were determined across selected grain boundaries in the Cu sample, as shown in Figure 5. This was done by
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Figure 5. Boundaries for which kernel average misorientation profiles were measured overlaid on an image quality map from copper. The blue profile lines denote twin boundaries and the red denote random boundaries. The number next to the random boundaries (red) is the angle of misorientation and the number next to the twin boundaries (blue) denotes the inclination of the twin plane with respect to the sample surface. Figure 7. A series of simulated mixed patterns formed by mixing two patterns obtained from the copper sample. The pair of numbers below shows the percent contribution of the left hand and right hand end patterns.
Figure 6. Schematic illustrating the averaging scheme used in calculating the kernel average misorientation profiles.
drawing a straight line normal to the boundary on a KAM map originating at the grain interior in one grain and ending at the grain interior of the adjacent grain, as shown schematically in Figure 6. For each point on the profile line, KAM values at grid points perpendicular to the profile line within seven times the step size are averaged together. This allows an averaged KAM profile line to be determined. This procedure was also followed for the twin boundaries in the five Ni scans.
Averaged KAM Profiles Instead of focusing on selected boundaries, a more statistical approach was taken using every point in the recrystallized Cu and the cold-rolled brass scans. The average KAM value
at each point in the scan grid was calculated. The average KAM value as a function of distance from the grain boundary was calculated. These calculations were carried out to a distance equal to ten times the step size (200 nm for the Cu and 2.5 μm for the brass). In addition, an average KAM value for the grain interiors excluding the points used in the KAM versus distance calculations was calculated as a baseline. Note that for some of the smaller grains, the narrow twins in particular, the number of neighbors for which the KAM averages can be calculated will be limited and the grain interior values cannot be calculated.
Simulated Pattern Mixing Pairs of individual patterns were obtained from points in the grain interiors from neighboring grains in the Cu sample. This was done for 22 random boundaries and 21 twin boundaries. Simulated mixed patterns were created using the following equation where IiMj denotes the intensity of the mixed pattern at pixel i, j, and IiAj denotes the first pattern and IiBj the second. f is the fraction of pattern B in the mixed pattern: IiMj ¼ ð1 - f ÞIiAj + fIiBj :
(1)
An example of a series of mixed patterns formed from one pair of patterns is shown in Figure 7. These patterns were
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Figure 8. Averaged kernel average misorientation profiles for the random boundaries, highlighted in Figure 5.
indexed using the standard automated band detection and indexing procedures in the OIM software. The results were compared against results obtained for the two end-point patterns using manual detection of the bands and the standard automated indexing procedure. In both cases, nine bands were used. These results include (1) the misorientation between the solution obtained for each mixed pattern and the closest (in orientation) of the two end solutions, (2) the number of votes toward each end solution, and (3) the peak positions relative to those found in the end patterns. The effect of noise on these results was investigated by artificially adding noise to the patterns. This was done for a given pattern by switching the pixel intensity to random values between the minimum and maximum values for the pattern at a specified fraction of pixels in the pattern.
RESULTS AND D ISCUSSION Individual KAM Profiles in Cu The KAM profiles for the random boundaries are shown in Figure 8. The numbers in the legend refer to the misorientation angle at the boundary. There does not appear to be any relationship between the boundary misorientation and the maximum KAM value in the profiles nor the general shape of the profiles. Figure 9 shows the average profiles for the random boundaries and the twin boundaries. The KAM profile value at the interface is clearly less for the twin boundaries than for the random boundaries.
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Figure 9. Average kernel average misorientation profiles for the twin and random boundaries, highlighted in Figure 5.
parallel to the 70° tilt of the sample (for EBSD), i.e. the vertical twins, to eliminate any influence from the sample tilt. The primary recrystallization twins in Cu can both be identified by their linear appearance in the IQ maps as well as by their misorientation, 60° about . The twinning plane in these twins is the (111) plane. For twin boundaries it is possible to determine the inclination of the boundary plane with respect to the measurement surface plane. First, we identify the (111) plane, which produces a trace parallel to the boundary in the two-dimensional measurement. The inclination of this (111) plane is then assumed to be parallel to the boundary plane and can be determined from the orientation data for either of the grains separated by the twin boundary. Thus, we can compare the profiles of the twins in the microstructure to determine whether the boundary plane inclination plays a role in the KAM profiles. KAM profiles and normalized IQ profiles are shown in Figure 10 for three of the five twin boundaries measured. The IQ normalization was done to bring the lowest IQ to 1 and the maximum IQ to 0 for easy comparison with the KAM profiles. No discernible correlation was found between the boundary inclinations and the KAM and normalized IQ profiles. While a smaller step size could be used to search for the inclination effect, the 20 nm step size used in these measurements is already nearing the generally accepted limit for the lateral resolution of the technique. Smaller step sizes are difficult to achieve and require operating conditions not typically used for the large-scale maps used in this study (Steinmetz & Zaefferer, 2010).
Individual KAM Profiles in Ni
Averaged KAM Profiles in Cu and Brass
There is some expectation that the KAM profiles would be broader for planes inclined more closely toward parallel to the surface than for planes perpendicular to the surface. To investigate whether this effect can be observed we have performed scans on twins in the Ni, which have boundary traces
Results from the averaged KAM profiles for all scan points in the Cu and brass samples are shown in Figure 11. The first item of note in these plots is that the average KAM profile for the 4.5% cold-rolled brass is quite similar in value at the boundary (0) compared to that for the recrystallized Cu.
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Figure 11. Average kernel average misorientation as a function of distance from the grain boundaries in fully recrystallized copper and cold-rolled brass to reductions indicated in the legend.
Figure 10. a: Orientation map of a vertical twin in Nickel. b: Individual kernel average misorientation and (c) normalized image quality profiles for three vertical twin boundaries with different inclination angles indicated in the legend.
However, the rise in KAM starts much farther away from the boundary—at ~150 nm versus over 1 μm away. This result suggests that the increase in misorientation at the grain boundaries due to artifacts is in the immediate vicinity of the grain boundary; whereas the increase due to physical phenomena is on the order of a micron or more (cf. Ohashi et al., 2009). This is further confirmed by the lack of correlation of the boundary plane inclination with the KAM results. The averaged KAM measured on the deformed brass samples with 20 nm step sizes also showed a rise in the KAM, farther away from the boundary, but not nearly so strong as seen in the 250 nm step size scans. The 4.5% cold-rolled brass was very similar to the Cu and with increasing deformation the initiation of the rise in KAM increases by ~15% with each successive reduction step.
The second feature of note is that the KAM plots generally shift upwards with increasing deformation. However, with increasing deformation the KAM increases more at the grain boundary than at the grain interior. At reduction levels of 11% and greater there is a large jump from the points one grid step away from the boundary to those at the boundary. This may be due in part to the reduced indexing precision of the mixed patterns at the boundary. Figure 12 compares additional parameters as a function of distance from the boundary for the Cu sample and the 30% reduced brass sample. This plot was generated by calculating the percent difference in the KAM, IQ, CI, and fit parameters from those calculated in the grain interiors. It is interesting to note that the IQ, CI, and fit parameters are fairly similar between these two plots but that the rise in the KAM differences at the grain boundary differs substantially. These results suggest that misorientations >0.5° (based on the Cu baseline material and the 4.5% cold-rolled brass) are directly related to physical phenomena whereas below 0.5° the misorientations observed are more likely due to artifacts of pattern mixing at the boundaries. As expected, at the smaller 20 nm step sizes the rise in KAM values with deformation is smaller than at the 250 nm step size. As noted in the introduction, one potential reason for the increase in the KAM at the boundary is that less band triplets contribute to the solution averaging in a mixed pattern. Figure 13 shows that this presumption is valid. If we use seven bands versus 14 bands in the indexing procedure we see a decrease in the KAM values. While there is a general decrease in the KAM values, the decrease at the boundary
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Figure 13. Average kernel average misorientation as a function of distance from the grain boundaries for scans calculated using seven bands and 14 bands, as detected by the Hough transform.
Figure 12. Plots showing the percent difference in the average kernel average misorientation, image quality, confidence index, and fit values relative to the grain interior average values as a function of distance from the grain boundaries for (a) the recrystallized copper and (b) the 30% cold-rolled brass sample.
(50 nm) is more marked than at the grain interiors (0.1 versus 0.06°). Fourteen is more than the number of bands we typically use (nine) for face-centered cubic materials. Even in nonmixed patterns, one or two out of the 14 bands detected are rogue bands. This is confirmed by the fact that the average CI values for the seven and 14 band scans are 0.87 and 0.69, respectively, indicating that more false bands are found when using 14 bands than seven. However, even if one or two bands out of the 14 are misidentified, the number of triplet combinations for the 12 or 13 correct bands increases significantly (220 triplets for 12 bands and 286 for 13). This explains the decrease in KAM values in the grain interiors.
However, the benefit of using more bands is amplified at the boundary where for an evenly mixed pattern ideally seven bands would be found for one pattern and seven for the other pattern. This is an even greater increase in the number of triplets over the three or four bands detected when only seven bands are used. One surprising detail in these results is the curve for the 11% CR brass is below that for the 20% CR brass beyond about 750 nm from the boundary. One possibility could simply be that the number of grains sampled in the deformed materials was insufficient. Another possibility is that with increased deformation the dislocations become organized into distinct subgrains instead of being more randomly dispersed within the grain interiors. The same sample preparation was applied to all samples so it is assumed that differences in sample preparation were not the cause.
Simulated Pattern Mixing The orientation solution obtained for each mixed pattern was compared against the solution obtained for the two end patterns (patterns A and B). This was done using pattern pairs from 22 random boundaries and 21 twin boundaries. The results are plotted as a function of the percentage of the contribution of pattern B to the mixed pattern. The results are shown in Figure 14. It is interesting to note that even with only 1% pattern mixing there is already an effect on the orientation precision. If we assume the resolution of the technique is on the order 20–50 nm, then in a perfectly recrystallized material we would not expect to see a rise in the KAM values until ~50 nm from the grain boundary due to pattern mixing. The fact that
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Figure 14. Average values for the misorientations between the mixed patterns and the end patterns for the twin and random boundaries.
we observed the rise beginning at ~150 nm in the recrystallized Cu suggests that a slight dislocation accumulation was introduced during sample preparation (although very careful polishing was performed on these samples, it is possible that some deformation was introduced). Another observation of note is that the switch from solution A to solution B as the identified solution from the mixed pattern generally occurred very close to 50% mixing. However, with increasing noise, a shift of the cross-over from one pattern to another tended to stray away from 50%. It is presumed that this is due to the dominant pattern having more high structure factor bands more ideally suited to the various settings used in the Hough such as the mask size, which favors bands of an optimal width over other bands or strong bands being in higher quality regions of the pattern (i.e., passing through near the center of the pattern as opposed to the edges). As in the individual KAM profiles between the random and twin boundaries, the rise in misorientation in the mixed patterns was found to be smaller in the twin boundaries than in the random boundaries. If we assume some of the increase in KAM values is because of some deformation introduced during mechanical polishing then these results suggest that twin boundaries are more conducive to slip transmission than random high-angle grain boundaries. However, there does not seem to be a consensus in the literature on the effect of twin boundaries on slip transmission (cf. Bieler et al., 2009). The simulated pattern mixing results exclude any slip transmission effects and yet show the same results as the individual KAM profiles. This suggests another plausible explanation for the decreased rise in KAMs at twin boundaries could be that patterns from either side of twin boundaries share bands. This will lead to less competition between the primary bands in the pattern and less splitting of the votes in the triplet indexing between the two end solutions. Random noise was added to the patterns to ascertain its impact on the pattern mixing results. Figure 15 shows the
Figure 15. Average misorientation between the mixed pattern and the end patterns for all pattern pairs with random noise added at levels, as indicated in the legend.
results up to an added noise of 40% and only the misorientations >5°. After 50% noise is added, the indexing algorithm tends to find an orientation solution that is no longer related to either of the endpoints. It is interesting to note that the pattern mixing simulations show that after adding 40% noise, large misorientations from the end points are observed, which would indicate that the fraction of incorrectly indexed points (i.e., orientation solutions that do not correspond to the orientations of the grains on either side of the grain boundaries) will increase with increasing noise as opposed to an incremental rise in the KAM. However, it was also observed that there is a rise in misorientation relative to the 0% noise patterns, which suggests that even in the grain interiors, a rise in KAM due to noise would be expected. This is also observed in the KAM statistics on the deformed brass samples. This is not unexpected. We have focused on the mixing of patterns at large-angle grain boundaries. However, with the formation of subgrains during deformation, the interaction volume may contain a series of geometrically necessary dislocations with a net nonzero Burgers vector (i.e., a subgrain boundary). This will also lead to a mixed pattern; albeit, one containing two or more very similar patterns. Instead of the contributing patterns producing extra bands in the mixed pattern as at a highangle grain boundary, the resulting mixed pattern will show more diffuse bands. The contribution of statistically stored dislocations (i.e., those with net Burgers vectors of zero) will also further degrade the quality of the pattern. Such patterns simply appear more diffuse or noisy, which the simulations have shown, reduces the orientation precision. Thus, while KAM values will rise with increasing deformation, some of that rise is due to the actual physical increase in the
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Figure 17. The average difference in the Hough peak positions in mixed patterns relative to the end patterns as a function of the degree of mixing. Figure 16. Plot of misorientation between the mixed pattern and the end patterns for three pattern pairs with misorientations between the end point patterns, as shown in the legend.
SUMMARY
magnitude of local misorientation and some is due to decreased orientation precision as pattern quality diminishes with increasing deformation. In order to confirm the effect of subgrain rotations on the orientation precision, simulated pattern mixing was performed on patterns from single crystal silicon after slight rotations. Three pairs of patterns were used, with orientation differences of 0.43, 0.70, and 1.1°. Figure 16 shows the effect of the pattern mixing of these pattern pairs on the orientation precision. It is worth noting in these results that the rise in misorientation for these mixed patterns was on the order of that observed in the recrystallized Cu. It should be noted that the effect of subgrains will be greater the larger the interaction volume. Thus, a tungsten SEM will generally show this effect more than a field-emission gun SEM. Any SEM condition that affects the interaction volume will have an impact on the magnitude of this effect. Figure 17 shows the variation in the Hough peak positions as a function of mixing of patterns A and B. This plot is created by averaging the results for all of the twin and random pattern pairs. The difference in peak position is calculated using the square root of the sum of the squared difference in ρ and θ for the Hough peaks. The ρ value is the perpendicular distance of a band relative to the center of the pattern and θ is the angle the band normally makes relative to the horizontal. The reference for these difference calculations are the Hough peaks for the end patterns. This result clearly shows that the superposed patterns have an impact on the ability of the Hough transform to precisely locate the position of the bands in the pattern. This is further evidenced by the lower IQ values at boundaries. The IQ values are based on the Hough peak heights so a lowering of the IQ value corresponds to a decline in the band detection reliability.
The overall conclusion of this work is that for low levels of deformation it is difficult to differentiate the physical phenomena from the indexing artifacts. At higher levels it is possible for EBSD to measure misorientations at grain boundaries with enough precision to characterize the deformation mechanisms leading to the increased misorientation at grain boundaries such as dislocation pile-up. However, it is important to note that there will very likely be a nonnegligible contribution from indexing artifacts, likely in the range of 0.5°. Two reasons were found for these artifacts: (1) pattern mixing at high-angle grain boundaries and (2) increased “noise” in the patterns due to higher dislocation density at the boundaries. The KAM profiles suggest that these artifacts would be limited to >150 nm from the grain boundary; however, the fact that no correlation between the tilt of the boundary plane and the KAM profiles was observed suggests that the localization of the artifacts would be on the order of the interaction volume, which would be conservatively estimated as 50 nm in a field-emission gun SEM. Some differences between twin and random boundaries were observed. There is a twofold reason for this observation. First, the patterns from the boundaries separated by the twin are likely to have certain elements in common, i.e. bands and/or zone axes. Second, the results suggest that the twin boundaries in the materials examined tend to be more conducive to slip transmission. The results of this study show that the orientation precision at grain boundaries can be improved by using more bands than typically recommended. This will likely lead to lower overall CI values and slower indexing speeds, but this is easily overcome by offline indexing. In the OIM data collection software as many as 30 Hough peaks are recorded for each pattern (if this many are detected), even though less are requested during the initial online indexing, making it straightforward to use more bands during offline indexing.
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CONCLUSIONS
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While we have focused on the use of KAM in this work, it is important to note that any other metrics employing local differences in orientation such as dislocation density measurements (Sun et al., 2000; El-Dasher et al., 2003; Field et al., 2005; Pantleon, 2008; Wilkinson & Randman, 2010) would also be affected by the artifacts studied here. One example that has been explored is the effect of pattern mixing on the crosscorrelation techniques used for strain measurement from EBSD patterns (Clarke, 2008; Britton, 2010). Effects of 0.01° were observed between the root patterns and the mixed pattern. However, it is expected that metrics that do not use crosscorrelation type analyses but, rather, local misorientations, as determined during the conventional automated EBSD scanning process will be similar to those observed in this work. The boundaries in IQ maps are generally delineated by darker pixels due to weaker Hough patterns at the boundaries. We have found an exception to this in scans of coarse grained materials mapped with relatively large step sizes performed by moving the sample stage under a stationary beam. This suggests that in the general case for scans performed by moving the beam from point to point in the scan grid that the beam is not stationary during collection of the beam pattern, but may be moving—the beam movement is not as instantaneous as assumed. The movement of the beam during pattern collection would create an artificially mixed pattern. We have explored the impact of the beam movement on the orientation precision by performing a scan over an area of the Cu sample in the usual manner and with a slight delay before pattern collection to allow the beam to settle. The differences in KAM results with and without the delay were negligible suggesting that this effect is inconsequential for the fine step sizes and camera settings typically used for characterizing local misorientation in deformed materials. As with any characterization technique, the results of this study reiterate the need for a baseline to ascertain the magnitude of any measurement uncertainty in order to carefully study the evolution of structure during deformation.
ACKNOWLEDGMENTS The authors gratefully acknowledge Ben Britton of the Imperial College London for information on the effects of mixed patterns on cross-correlation calculations. Josh Kacher of Lawrence Berkeley and Travis Rampton of Brigham Young University and Eric Payton of Alfred University are also acknowledged for helpful discussions on twin boundaries.
REFERENCES BEAUSIR, B. & FRESSENGRASS, C. (2013). Disclination densities from EBSD orientation mapping. Int J Solids Struct 50, 137–146. BIELER, T.R., EISENLOHR, P., ROTERS, F., KUMAR, D., MASON, D.E., CRIMP, M.A. & RAABE, D. (2009). The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals. Int J Plast 25, 1665–1683. BRITTON, T.B. (2010). A high resolution electron backscatter diffraction study of titanium and its alloys. PhD Thesis. Oxford, England: The University of Oxford.
CLARKE, E.E. (2008). Internal stresses and dislocation densities generated by phase transformations in steel. PhD Thesis. Oxford, England: The University of Oxford. EL-DASHER, B.S., ADAMS, B.L. & ROLLETT, A.D. (2003). Viewpoint: Experimental recovery of geometrically necessary dislocation density in polycrystals. Scripta Mater 48(2), 141–145. FIELD, D.P. (1997). Recent advances in the application of orientation imaging. Ultramicroscopy 67, 1–9. FIELD, D.P., TRIVEDI, P.B., WRIGHT, S.I. & KUMAR, M. (2005). Analysis of local orientation gradients in deformed single crystals. Ultramicroscopy 103(1), 33–39. GUTIERREZ-URRUTIA, I., ZAEFFERER, S. & RAABE, D. (2013). Coupling of electron channeling with EBSD: Towards the quantitative characterization of deformation structures in the SEM. J Minerals, Metal Mater Soc 65(9), 1229–1236. KRIEGER LASSEN, N.C., CONRADSEN, K. & JUUL-JENSEN, D. (1992). Image-processing procedures for analysis of electron back scattering patterns. J Microsc 6(1), 115–121. KUNZE, K., WRIGHT, S.I., ADAMS, B.L. & DINGLEY, D.J. (1993). Advances in automatic EBSP single orientation measurements. Text Microstruct 20(1–4), 41–54. MISHRA, S.K., PANT, P., NARASIMHAN, K., ROLLETT, A.D. & SAMAJDAR, I. (2009). On the widths of orientation gradient zones adjacent to grain boundaries. Scripta Mater 61, 273–276. NOWELL, M.M. & WRIGHT, S.I. (2005). Orientation effects on indexing of electron backscatter diffraction patterns. Ultramicroscopy 103, 41–58. OHASHI, T., BARABASH, R.I., PANG, J.W.L., ICE, G.E. & BARABASH, O.M. (2009). X-ray microdiffraction and strain gradient crystal plasticity studies of geometrically necessary dislocations near a Ni bicrystal grain boundary. Int J Plast 25(5), 920–941. PANTLEON, W. (2008). Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction. Scripta Mater 58, 994–997. PERRIN, C., BERBENNI, S., VEHOFF, H. & BERVEILLER, M. (2010). Role of discrete intra-granular slip on lattice rotations in polycrystalline Ni: Experimental and micromechanical studies. Acta Mater 58, 4639–4649. ROLLETT, A.D., WAGNER, F., ALLAIN-BONASSO, N., FIELD, D.P. & LEBENSOHN, R.A. (2012). Comparison of gradients in orientation and stress between experiment and simulation. Mater Sci Forum 702–703, 463–468. STEINMETZ, D.R. & ZAEFFERER, S. (2010). Towards ultrahigh resolution EBSD by low accelerating voltage. Mater Sci Tech 26(6), 640–645. SUN, S., ADAMS, B.L. & KING, W.E. (2000). Observations of lattice curvature near the interface of a deformed aluminum bicrystal. Philos Mag 80, 9–25. TAKAYAMA, Y., SZPUNAR, J.A. & KATO, H. (2005). Analysis of intragranular misorientation related to deformation in an Al-Mg-Mn alloy. Mater Sci Forum 495–497, 1049–1054. TRIMBY, P.W. (2012). Orientation mapping of nanostructured materials using transmission Kikuchi diffraction in the scanning electron microscope. Ultramicroscopy 120, 16–24. WILKINSON, A.J. & RANDMAN, D. (2010). Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction. Philos Mag 90, 1159–1177. WRIGHT, S.I. & ADAMS, B.L. (1992). Automatic-analysis of electron backscatter diffraction patterns. Metall Trans A 23(3), 759–767. WRIGHT, S.I., BASINGER, J.A. & NOWELL, M.M. (2012). Angular precision of automated electron backscatter diffraction measurements. Mater Sci Forum 702–703, 548–553.
EBSD at Grain Boundaries WRIGHT, S.I., FIELD, D.P. & DINGLEY, D.J. (2000). Advanced software capabilities for automated EBSD. In Electron Backscatter Diffraction in Materials Science, Schwartz, A.J., Kumar, M. & Adams, B.L. (Eds.), pp. 141–152. New York: Kluwer Academic/ Plenum Publishers.
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© MICROSCOPY SOCIETY OF AMERICA 2014
Orientation Precision of Electron Backscatter Diffraction Measurements Near Grain Boundaries Stuart I. Wright,1,* Matthew M. Nowell,1 René de Kloe,2 and Lisa Chan3 1
EDAX, 392 East 12300 South, Draper, UT 84020, USA EDAX BV, Ringbaan Noord 103, 5046 AA Tilburg, The Netherlands 3 TESCAN USA, 508 Thomson Park Drive, Cranberry TWP, PA 16066, USA 2
Abstract: Electron backscatter diffraction (EBSD) has become a common technique for measuring crystallographic orientations at spatial resolutions on the order of tens of nanometers and at angular resolutions < 0.1°. In a recent search of EBSD papers using Google Scholar™, 60% were found to address some aspect of deformation. Generally, deformation manifests itself in EBSD measurements by small local misorientations. An increase in the local misorientation is often observed near grain boundaries in deformed microstructures. This may be indicative of dislocation pile-up at the boundaries but could also be due to a loss of orientation precision in the EBSD measurements. When the electron beam is positioned at or near a grain boundary, the diffraction volume contains the crystal lattices from the two grains separated by the boundary. Thus, the resulting pattern will contain contributions from both lattices. Such mixed patterns can pose some challenge to the EBSD pattern band detection and indexing algorithms. Through analysis of experimental local misorientation data and simulated pattern mixing, this work shows that some of the rise in local misorientation is an artifact due to the mixed patterns at the boundary but that the rise due to physical phenomena is also observed. Key words: electron backscatter diffraction, EBSD, orientation imaging microscopy, OIM, orientation precision, kernel average misorientation, KAM
I NTRODUCTION Electron backscatter diffraction (EBSD) in the scanning electron microscope (SEM) is well suited to the characterization of deformed microstructures in crystalline materials. EBSD is capable of measuring crystallographic orientations at spatial resolutions on the order of tens of nanometers (or even nanometers) and at angular resolutions < 0.1° (cf. Steinmetz & Zaefferer, 1993; Trimby, 2012; Wright et al., 2012). When EBSD measurements are automatically collected at each point on a regular measurement grid, it is possible to compare the orientations of neighboring points in the grid to characterize local misorientations present in the microstructure. One common method for characterizing the local misorientation is using the kernel average misorientation (KAM) measurement (Wright et al., 2011). A kernel is a set of grid points in the immediate vicinity of a point of interest in the measurement grid. The kernel will contain the first nearest neighbors out to a user-specified set of neighbors, such as the third nearest neighbors. The misorientation of each point in the kernel with respect to the orientation of the point at the center of the kernel is calculated. The average of these misorientations is then determined. This is the KAM value. It can be calculated for each point in the measurement grid and mapped to a color scale to form a KAM map. This allows the spatial arrangement of local misorientation within the microstructure to be visualized. Received July 26, 2013; accepted January 29, 2014 *Corresponding author. [email protected]
An increase in the local misorientation as determined by KAM is often observed near grain boundaries in deformed microstructures, relative to the grain interiors (Mishra et al., 2009; Perrin et al., 2010; Rollett et al., 2012; Beausir & Fressengeas, 2013). This is expected due to dislocation pile-up at the boundaries. However, the increase in local misorientation may also be due to a decrease in orientation precision of the EBSD measurements in the immediate vicinity of a boundary. When the electron beam is positioned at a grain boundary, the diffraction volume contains the crystal lattices from the two grains separated by the boundary. Thus, the resulting pattern will contain contributions from both lattices, as shown in Figure 1. Such mixed patterns can pose a challenge to both the EBSD pattern band detection and indexing algorithms. Generally, the software is successful in finding the solution of one of the two contributing patterns, but occasionally it will find a solution that does not correspond with either. Figure 2 shows indexing results from a grain boundary in fully recrystallized nickel (Ni). Of 363 boundary points only six (1.6%) do not correspond to either of the orientations on either side of the boundary. It should also be noted that both the image quality (IQ) and confidence index (CI) maps show lower values in the immediate vicinity of the grain boundary. This work seeks to differentiate the artificial rise in KAM measurements at grain boundaries due to pattern mixing from the real increases due to physical phenomena. KAM measurements in recrystallized and deformed materials using both direct measurements at grain boundaries as well as statistical approaches are compared. In addition, the effect
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Figure 1. Schematic illustrating mixed pattern at a grain boundary due to interaction volume containing crystal lattices from both sides of the boundary.
Figure 2. a: Image quality, (b) confidence index (red is high, blue is low), and (c) orientation map from a grain boundary in nickel.
of the mixing on the band detection and indexing algorithms is explored using a simulation of pattern mixing. The algorithms used for band detection and indexing differ between systems. In this paper we have used the algorithms as implemented in the EDAX® orientation imaging microscopy (OIM) EBSD data collection systems. The data collection software uses a triplet indexing approach to determine the orientation, given a set of detected bands (Wright & Adams, 1992). Each possible triplet of bands is constructed. The angle between each pair of bands in a triplet is determined. These angles are compared against a lookup table of interplanar angles constructed from the planes in the crystal producing the strongest diffraction bands. From this comparison, a set of possible orientations is determined. This procedure is repeated for every possible triplet. The orientation that appears most often from the set of triplet orientations is then assumed to be the correct solution for the pattern. As the detection of the bands in the diffraction pattern is never perfect, the “same” orientation solutions determined by each triplet will differ slightly from triplet to triplet. Solutions from different triplets that are found to be similar (i.e., within just a few degrees of each other, typically 3°) are averaged together using a quaternion
Figure 3. Schematic showing band triplets contributing to the averaged orientation solution for two patterns (a, b) and a 50/50 mix of the two patterns (c). g denotes an orientation, fa denotes an orientation averaging function.
averaging approach (Kunze et al., 1993) to refine the final solution. Mixed patterns have a direct impact on the solution refinement. Consider the case where seven bands are detected in a pattern from grain A and seven are also detected in the pattern from a neighboring grain B. Thirty-five triplets can be formed from seven bands, so if all the bands are accurately detected, then 35 slightly different orientations will be used in the refinement averaging process. However, if a pattern is obtained from the immediate vicinity of the boundary separating grain A and grain B, then it is possible that the band detection would find four bands for grain A and three bands for grain B. In this case, the orientation associated with grain A would be that selected by the indexing algorithm. But, only four triplets can be formed from four bands so the refinement of the solution through averaging would be reduced, this is illustrated in Figure 3. Thus, the orientation precision would be less in mixed patterns as opposed to patterns from the grain interior.
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This is also evident in Figure 2b, where the CI is lower at the boundary. This is a direct result of the splitting of the votes between the two orientation solutions. The Hough transform is used to detect the bands in the EBSD patterns (Krieger-Lassen et al., 1992). Kunze et al. (2010) details the particulars associated with implementation of the Hough transform in the software used. The Hough transform seeks to find a specified number of bands in the patterns as set by the operator. This is typically the number of strongest bands expected in the patterns. However, if the two patterns are mixed then the relative strength of the bands will be weakened. This is evidenced in pattern quality or IQ maps, as shown in Figure 2a. A metric describing the quality of the diffraction pattern is measured at each point in the scan. This value in the OIM software is the sum of the Hough peak heights divided by the number of peaks specified by the user—a slight modification of the method proposed by Kunze et al. (2010). Maps can be constructed from the IQ value by mapping the values onto a gray scale. The grain boundaries are clearly delineated in such maps as they generally appear much darker (Wright & Nowell, 2006). This is clear evidence that detection of the bands in the mixed patterns will be more difficult than for nonmixed patterns. This may have a couple of potential effects on the accuracy of the band detection. The first is the detection of “rogue” or false bands. If too many rogue bands are detected then this can lead to the software finding neither of the two orientations separated by the grain boundary. Such points will typically be evident as individual points in the grid not associated with any neighboring points and are filtered out in the postprocessing. We will not investigate such effects in this work. However, another effect of rogue bands is a reduction of the number of bands used in the indexing algorithm leading to either of the correct solutions. As noted in the previous section this reduces the number of points in the solution cloud used in averaging, which can lead to less orientation precision. The second effect of mixed patterns on the Hough transform is that the number of “strong” bands in a mixed pattern is increased. This essentially leads to a relative weakening of the strength of the individual bands from both patterns contributing to the mixed patterns. This would potentially lead to less accuracy in determination of the band positions as determined from the associated Hough peaks. These effects are explored using both experimental data from both recrystallized and deformed samples for comparison as well as simulated mixing of patterns. Both the impact of the magnitude of the loss in orientation precision and the spatial extent of the diminished orientation precision are investigated.
M ATERIALS AND M ETHODS Six samples from three different materials were used in this study. The first was a copper (Cu) sample that had been subjected to repeated equal channel angular processing and
Table 1. Various Factors Describing the Quality of the Scan Data for each of the Materials Investigated. Reduction (%) 4.5 11 20 30
Measured
Interpolated
Difference
0.48 1.32 1.64 2.78
0.39 0.93 1.30 1.39
0.09 0.39 0.34 0.88
was then fully recrystallized. This material has a grain size in the range of 5–10 μm. The second sample was a fully recrystallized Ni alloy with an approximate grain size of 20 μm. The third was a series of samples of cold-rolled brass with a 70% Cu/30% Zn ratio. Samples were obtained after 4.5, 11, 20, and 30% rolling reductions. The approximate grain size in these materials was 100 μm. All of the samples were prepared using mechanical polishing using standard procedures. The final polish was performed using a vibratory polisher and 0.05 μm colloidal silica. Automated EBSD scans were obtained from each sample. For the Cu sample a scan containing 3.47 million points was collected over a 33.5 × 35.9 μm area with a 20 nm step size. For the recrystallized Ni sample, scans from five different twinned grains were obtained. Twin boundaries that appeared nearly vertical in the image were scanned for reasons, which will be detailed later in the text. These scans encompassed the full twinned grain and used a step size of 20 nm. The brass scans were performed using a 250 nm step size over a 1.5 × 1.5 mm area resulting in 2.53 million individual orientation measurements in each scan. Pertinent values relating to these scans are shown in Table 1. The indexing success rate was determined by first performing a grain CI standardization (Nowell & Wright, 2005) and then finding the number of points with CI values >0.1. It should be noted that the CI standardization is essentially a CI upgrade process, the orientation data is not altered in this process. This was the only postprocessing applied to the data. The rates, average CI values, and average fit values all reflect the high quality of the measured scan data. It should be noted that for CI >0.1, there is a >95% likelihood that the pattern is indexed correctly (Field, 1997). Field’s (1997) results showed that the indexing reliability for a CI of 0 and a CI of 0.1 is quite different—40 versus 95%, respectively; whereas for CIs between 0.1 and 1, the indexing reliability rises gradually from 95 to 100%. The measurements were made using an FEI™ XL30 field-emission SEM. A 20 keV accelerating voltage was used for all measurements with ~8 nA of current. A relatively high current was used so that the scans could be done in a practical time frame without having to use any electronic gain on the EBSD camera, which would introduce additional noise into the patterns. KAM maps for the brass samples are shown in Figure 4. First nearest neighbor KAMs with a 5° tolerance angle maps were used in all of the calculations.
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Figure 4. First nearest neighbor kernel average misorientation maps for the (a) 4.5, (b) 11, (c) 20, and (d) 30% coldrolled brass.
Ideally, the same step size would have been used for all of the studies. However, the Cu sample had a relatively fine grain size of 5–10 μm in diameter whereas the brass samples had a coarser grain size of ~100 μm. Thus, larger step sizes were used in the brass samples so as to characterize many grain boundaries. The KAM values are affected by the step size (Wright et al., 2000; Wright et al., 2011; Takayama et al., 2005) thus some care must be exercised in interpreting the KAM results where different step sizes are used. In order to confirm the validity of the observations reported, scans with 20 nm step sizes containing at least one triple point were performed on the 4.5, 11, and 20% cold-rolled brass samples. Scans from two separate triple points were performed on the 4.5% cold-rolled brass sample. Since only a few boundaries were sampled in each scan area, the results from the two scans did differ from each other. However, given the grain size in the brass samples these measurements are by no means meant to provide a comprehensive statistical characterization of these materials, rather they were performed only to verify the comparison between the measurements at 20 nm step size in the Cu with the 250 nm step size measurements in the brass samples. As noted, the KAM tolerance angle was set to 5°. This value was selected so that the KAM results would be
focused on the low-angle misorientations characteristic of deformation and not the grain boundaries themselves. In principle, a smaller tolerance angle could enable the subgrain structures within the grains to be investigated. However, characterizing phenomena such as subgrain size, edge versus screw dislocations, or stacking fault is difficult in the SEM, and is generally more suited to investigation in the transmission electron microscope. Although the recent work of Gutierrez-Urrutia et al. (2013) shows that new imaging techniques may make such work possible in the SEM. Such techniques would allow correlation between the deformation substructure and the orientation measurements to be explored, but this is beyond the focus of this work. However, it was noted in the 20 nm step scans on the deformed brass samples that some boundaries showed very different KAM distributions on one side of the boundary compared to the other, indicating a difference in dislocation pile-up at the boundaries.
KAM Profiles KAM profiles were determined across selected grain boundaries in the Cu sample, as shown in Figure 5. This was done by
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Figure 5. Boundaries for which kernel average misorientation profiles were measured overlaid on an image quality map from copper. The blue profile lines denote twin boundaries and the red denote random boundaries. The number next to the random boundaries (red) is the angle of misorientation and the number next to the twin boundaries (blue) denotes the inclination of the twin plane with respect to the sample surface. Figure 7. A series of simulated mixed patterns formed by mixing two patterns obtained from the copper sample. The pair of numbers below shows the percent contribution of the left hand and right hand end patterns.
Figure 6. Schematic illustrating the averaging scheme used in calculating the kernel average misorientation profiles.
drawing a straight line normal to the boundary on a KAM map originating at the grain interior in one grain and ending at the grain interior of the adjacent grain, as shown schematically in Figure 6. For each point on the profile line, KAM values at grid points perpendicular to the profile line within seven times the step size are averaged together. This allows an averaged KAM profile line to be determined. This procedure was also followed for the twin boundaries in the five Ni scans.
Averaged KAM Profiles Instead of focusing on selected boundaries, a more statistical approach was taken using every point in the recrystallized Cu and the cold-rolled brass scans. The average KAM value
at each point in the scan grid was calculated. The average KAM value as a function of distance from the grain boundary was calculated. These calculations were carried out to a distance equal to ten times the step size (200 nm for the Cu and 2.5 μm for the brass). In addition, an average KAM value for the grain interiors excluding the points used in the KAM versus distance calculations was calculated as a baseline. Note that for some of the smaller grains, the narrow twins in particular, the number of neighbors for which the KAM averages can be calculated will be limited and the grain interior values cannot be calculated.
Simulated Pattern Mixing Pairs of individual patterns were obtained from points in the grain interiors from neighboring grains in the Cu sample. This was done for 22 random boundaries and 21 twin boundaries. Simulated mixed patterns were created using the following equation where IiMj denotes the intensity of the mixed pattern at pixel i, j, and IiAj denotes the first pattern and IiBj the second. f is the fraction of pattern B in the mixed pattern: IiMj ¼ ð1 - f ÞIiAj + fIiBj :
(1)
An example of a series of mixed patterns formed from one pair of patterns is shown in Figure 7. These patterns were
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Figure 8. Averaged kernel average misorientation profiles for the random boundaries, highlighted in Figure 5.
indexed using the standard automated band detection and indexing procedures in the OIM software. The results were compared against results obtained for the two end-point patterns using manual detection of the bands and the standard automated indexing procedure. In both cases, nine bands were used. These results include (1) the misorientation between the solution obtained for each mixed pattern and the closest (in orientation) of the two end solutions, (2) the number of votes toward each end solution, and (3) the peak positions relative to those found in the end patterns. The effect of noise on these results was investigated by artificially adding noise to the patterns. This was done for a given pattern by switching the pixel intensity to random values between the minimum and maximum values for the pattern at a specified fraction of pixels in the pattern.
RESULTS AND D ISCUSSION Individual KAM Profiles in Cu The KAM profiles for the random boundaries are shown in Figure 8. The numbers in the legend refer to the misorientation angle at the boundary. There does not appear to be any relationship between the boundary misorientation and the maximum KAM value in the profiles nor the general shape of the profiles. Figure 9 shows the average profiles for the random boundaries and the twin boundaries. The KAM profile value at the interface is clearly less for the twin boundaries than for the random boundaries.
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Figure 9. Average kernel average misorientation profiles for the twin and random boundaries, highlighted in Figure 5.
parallel to the 70° tilt of the sample (for EBSD), i.e. the vertical twins, to eliminate any influence from the sample tilt. The primary recrystallization twins in Cu can both be identified by their linear appearance in the IQ maps as well as by their misorientation, 60° about . The twinning plane in these twins is the (111) plane. For twin boundaries it is possible to determine the inclination of the boundary plane with respect to the measurement surface plane. First, we identify the (111) plane, which produces a trace parallel to the boundary in the two-dimensional measurement. The inclination of this (111) plane is then assumed to be parallel to the boundary plane and can be determined from the orientation data for either of the grains separated by the twin boundary. Thus, we can compare the profiles of the twins in the microstructure to determine whether the boundary plane inclination plays a role in the KAM profiles. KAM profiles and normalized IQ profiles are shown in Figure 10 for three of the five twin boundaries measured. The IQ normalization was done to bring the lowest IQ to 1 and the maximum IQ to 0 for easy comparison with the KAM profiles. No discernible correlation was found between the boundary inclinations and the KAM and normalized IQ profiles. While a smaller step size could be used to search for the inclination effect, the 20 nm step size used in these measurements is already nearing the generally accepted limit for the lateral resolution of the technique. Smaller step sizes are difficult to achieve and require operating conditions not typically used for the large-scale maps used in this study (Steinmetz & Zaefferer, 2010).
Individual KAM Profiles in Ni
Averaged KAM Profiles in Cu and Brass
There is some expectation that the KAM profiles would be broader for planes inclined more closely toward parallel to the surface than for planes perpendicular to the surface. To investigate whether this effect can be observed we have performed scans on twins in the Ni, which have boundary traces
Results from the averaged KAM profiles for all scan points in the Cu and brass samples are shown in Figure 11. The first item of note in these plots is that the average KAM profile for the 4.5% cold-rolled brass is quite similar in value at the boundary (0) compared to that for the recrystallized Cu.
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Figure 11. Average kernel average misorientation as a function of distance from the grain boundaries in fully recrystallized copper and cold-rolled brass to reductions indicated in the legend.
Figure 10. a: Orientation map of a vertical twin in Nickel. b: Individual kernel average misorientation and (c) normalized image quality profiles for three vertical twin boundaries with different inclination angles indicated in the legend.
However, the rise in KAM starts much farther away from the boundary—at ~150 nm versus over 1 μm away. This result suggests that the increase in misorientation at the grain boundaries due to artifacts is in the immediate vicinity of the grain boundary; whereas the increase due to physical phenomena is on the order of a micron or more (cf. Ohashi et al., 2009). This is further confirmed by the lack of correlation of the boundary plane inclination with the KAM results. The averaged KAM measured on the deformed brass samples with 20 nm step sizes also showed a rise in the KAM, farther away from the boundary, but not nearly so strong as seen in the 250 nm step size scans. The 4.5% cold-rolled brass was very similar to the Cu and with increasing deformation the initiation of the rise in KAM increases by ~15% with each successive reduction step.
The second feature of note is that the KAM plots generally shift upwards with increasing deformation. However, with increasing deformation the KAM increases more at the grain boundary than at the grain interior. At reduction levels of 11% and greater there is a large jump from the points one grid step away from the boundary to those at the boundary. This may be due in part to the reduced indexing precision of the mixed patterns at the boundary. Figure 12 compares additional parameters as a function of distance from the boundary for the Cu sample and the 30% reduced brass sample. This plot was generated by calculating the percent difference in the KAM, IQ, CI, and fit parameters from those calculated in the grain interiors. It is interesting to note that the IQ, CI, and fit parameters are fairly similar between these two plots but that the rise in the KAM differences at the grain boundary differs substantially. These results suggest that misorientations >0.5° (based on the Cu baseline material and the 4.5% cold-rolled brass) are directly related to physical phenomena whereas below 0.5° the misorientations observed are more likely due to artifacts of pattern mixing at the boundaries. As expected, at the smaller 20 nm step sizes the rise in KAM values with deformation is smaller than at the 250 nm step size. As noted in the introduction, one potential reason for the increase in the KAM at the boundary is that less band triplets contribute to the solution averaging in a mixed pattern. Figure 13 shows that this presumption is valid. If we use seven bands versus 14 bands in the indexing procedure we see a decrease in the KAM values. While there is a general decrease in the KAM values, the decrease at the boundary
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Figure 13. Average kernel average misorientation as a function of distance from the grain boundaries for scans calculated using seven bands and 14 bands, as detected by the Hough transform.
Figure 12. Plots showing the percent difference in the average kernel average misorientation, image quality, confidence index, and fit values relative to the grain interior average values as a function of distance from the grain boundaries for (a) the recrystallized copper and (b) the 30% cold-rolled brass sample.
(50 nm) is more marked than at the grain interiors (0.1 versus 0.06°). Fourteen is more than the number of bands we typically use (nine) for face-centered cubic materials. Even in nonmixed patterns, one or two out of the 14 bands detected are rogue bands. This is confirmed by the fact that the average CI values for the seven and 14 band scans are 0.87 and 0.69, respectively, indicating that more false bands are found when using 14 bands than seven. However, even if one or two bands out of the 14 are misidentified, the number of triplet combinations for the 12 or 13 correct bands increases significantly (220 triplets for 12 bands and 286 for 13). This explains the decrease in KAM values in the grain interiors.
However, the benefit of using more bands is amplified at the boundary where for an evenly mixed pattern ideally seven bands would be found for one pattern and seven for the other pattern. This is an even greater increase in the number of triplets over the three or four bands detected when only seven bands are used. One surprising detail in these results is the curve for the 11% CR brass is below that for the 20% CR brass beyond about 750 nm from the boundary. One possibility could simply be that the number of grains sampled in the deformed materials was insufficient. Another possibility is that with increased deformation the dislocations become organized into distinct subgrains instead of being more randomly dispersed within the grain interiors. The same sample preparation was applied to all samples so it is assumed that differences in sample preparation were not the cause.
Simulated Pattern Mixing The orientation solution obtained for each mixed pattern was compared against the solution obtained for the two end patterns (patterns A and B). This was done using pattern pairs from 22 random boundaries and 21 twin boundaries. The results are plotted as a function of the percentage of the contribution of pattern B to the mixed pattern. The results are shown in Figure 14. It is interesting to note that even with only 1% pattern mixing there is already an effect on the orientation precision. If we assume the resolution of the technique is on the order 20–50 nm, then in a perfectly recrystallized material we would not expect to see a rise in the KAM values until ~50 nm from the grain boundary due to pattern mixing. The fact that
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Figure 14. Average values for the misorientations between the mixed patterns and the end patterns for the twin and random boundaries.
we observed the rise beginning at ~150 nm in the recrystallized Cu suggests that a slight dislocation accumulation was introduced during sample preparation (although very careful polishing was performed on these samples, it is possible that some deformation was introduced). Another observation of note is that the switch from solution A to solution B as the identified solution from the mixed pattern generally occurred very close to 50% mixing. However, with increasing noise, a shift of the cross-over from one pattern to another tended to stray away from 50%. It is presumed that this is due to the dominant pattern having more high structure factor bands more ideally suited to the various settings used in the Hough such as the mask size, which favors bands of an optimal width over other bands or strong bands being in higher quality regions of the pattern (i.e., passing through near the center of the pattern as opposed to the edges). As in the individual KAM profiles between the random and twin boundaries, the rise in misorientation in the mixed patterns was found to be smaller in the twin boundaries than in the random boundaries. If we assume some of the increase in KAM values is because of some deformation introduced during mechanical polishing then these results suggest that twin boundaries are more conducive to slip transmission than random high-angle grain boundaries. However, there does not seem to be a consensus in the literature on the effect of twin boundaries on slip transmission (cf. Bieler et al., 2009). The simulated pattern mixing results exclude any slip transmission effects and yet show the same results as the individual KAM profiles. This suggests another plausible explanation for the decreased rise in KAMs at twin boundaries could be that patterns from either side of twin boundaries share bands. This will lead to less competition between the primary bands in the pattern and less splitting of the votes in the triplet indexing between the two end solutions. Random noise was added to the patterns to ascertain its impact on the pattern mixing results. Figure 15 shows the
Figure 15. Average misorientation between the mixed pattern and the end patterns for all pattern pairs with random noise added at levels, as indicated in the legend.
results up to an added noise of 40% and only the misorientations >5°. After 50% noise is added, the indexing algorithm tends to find an orientation solution that is no longer related to either of the endpoints. It is interesting to note that the pattern mixing simulations show that after adding 40% noise, large misorientations from the end points are observed, which would indicate that the fraction of incorrectly indexed points (i.e., orientation solutions that do not correspond to the orientations of the grains on either side of the grain boundaries) will increase with increasing noise as opposed to an incremental rise in the KAM. However, it was also observed that there is a rise in misorientation relative to the 0% noise patterns, which suggests that even in the grain interiors, a rise in KAM due to noise would be expected. This is also observed in the KAM statistics on the deformed brass samples. This is not unexpected. We have focused on the mixing of patterns at large-angle grain boundaries. However, with the formation of subgrains during deformation, the interaction volume may contain a series of geometrically necessary dislocations with a net nonzero Burgers vector (i.e., a subgrain boundary). This will also lead to a mixed pattern; albeit, one containing two or more very similar patterns. Instead of the contributing patterns producing extra bands in the mixed pattern as at a highangle grain boundary, the resulting mixed pattern will show more diffuse bands. The contribution of statistically stored dislocations (i.e., those with net Burgers vectors of zero) will also further degrade the quality of the pattern. Such patterns simply appear more diffuse or noisy, which the simulations have shown, reduces the orientation precision. Thus, while KAM values will rise with increasing deformation, some of that rise is due to the actual physical increase in the
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Figure 17. The average difference in the Hough peak positions in mixed patterns relative to the end patterns as a function of the degree of mixing. Figure 16. Plot of misorientation between the mixed pattern and the end patterns for three pattern pairs with misorientations between the end point patterns, as shown in the legend.
SUMMARY
magnitude of local misorientation and some is due to decreased orientation precision as pattern quality diminishes with increasing deformation. In order to confirm the effect of subgrain rotations on the orientation precision, simulated pattern mixing was performed on patterns from single crystal silicon after slight rotations. Three pairs of patterns were used, with orientation differences of 0.43, 0.70, and 1.1°. Figure 16 shows the effect of the pattern mixing of these pattern pairs on the orientation precision. It is worth noting in these results that the rise in misorientation for these mixed patterns was on the order of that observed in the recrystallized Cu. It should be noted that the effect of subgrains will be greater the larger the interaction volume. Thus, a tungsten SEM will generally show this effect more than a field-emission gun SEM. Any SEM condition that affects the interaction volume will have an impact on the magnitude of this effect. Figure 17 shows the variation in the Hough peak positions as a function of mixing of patterns A and B. This plot is created by averaging the results for all of the twin and random pattern pairs. The difference in peak position is calculated using the square root of the sum of the squared difference in ρ and θ for the Hough peaks. The ρ value is the perpendicular distance of a band relative to the center of the pattern and θ is the angle the band normally makes relative to the horizontal. The reference for these difference calculations are the Hough peaks for the end patterns. This result clearly shows that the superposed patterns have an impact on the ability of the Hough transform to precisely locate the position of the bands in the pattern. This is further evidenced by the lower IQ values at boundaries. The IQ values are based on the Hough peak heights so a lowering of the IQ value corresponds to a decline in the band detection reliability.
The overall conclusion of this work is that for low levels of deformation it is difficult to differentiate the physical phenomena from the indexing artifacts. At higher levels it is possible for EBSD to measure misorientations at grain boundaries with enough precision to characterize the deformation mechanisms leading to the increased misorientation at grain boundaries such as dislocation pile-up. However, it is important to note that there will very likely be a nonnegligible contribution from indexing artifacts, likely in the range of 0.5°. Two reasons were found for these artifacts: (1) pattern mixing at high-angle grain boundaries and (2) increased “noise” in the patterns due to higher dislocation density at the boundaries. The KAM profiles suggest that these artifacts would be limited to >150 nm from the grain boundary; however, the fact that no correlation between the tilt of the boundary plane and the KAM profiles was observed suggests that the localization of the artifacts would be on the order of the interaction volume, which would be conservatively estimated as 50 nm in a field-emission gun SEM. Some differences between twin and random boundaries were observed. There is a twofold reason for this observation. First, the patterns from the boundaries separated by the twin are likely to have certain elements in common, i.e. bands and/or zone axes. Second, the results suggest that the twin boundaries in the materials examined tend to be more conducive to slip transmission. The results of this study show that the orientation precision at grain boundaries can be improved by using more bands than typically recommended. This will likely lead to lower overall CI values and slower indexing speeds, but this is easily overcome by offline indexing. In the OIM data collection software as many as 30 Hough peaks are recorded for each pattern (if this many are detected), even though less are requested during the initial online indexing, making it straightforward to use more bands during offline indexing.
AND
CONCLUSIONS
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While we have focused on the use of KAM in this work, it is important to note that any other metrics employing local differences in orientation such as dislocation density measurements (Sun et al., 2000; El-Dasher et al., 2003; Field et al., 2005; Pantleon, 2008; Wilkinson & Randman, 2010) would also be affected by the artifacts studied here. One example that has been explored is the effect of pattern mixing on the crosscorrelation techniques used for strain measurement from EBSD patterns (Clarke, 2008; Britton, 2010). Effects of 0.01° were observed between the root patterns and the mixed pattern. However, it is expected that metrics that do not use crosscorrelation type analyses but, rather, local misorientations, as determined during the conventional automated EBSD scanning process will be similar to those observed in this work. The boundaries in IQ maps are generally delineated by darker pixels due to weaker Hough patterns at the boundaries. We have found an exception to this in scans of coarse grained materials mapped with relatively large step sizes performed by moving the sample stage under a stationary beam. This suggests that in the general case for scans performed by moving the beam from point to point in the scan grid that the beam is not stationary during collection of the beam pattern, but may be moving—the beam movement is not as instantaneous as assumed. The movement of the beam during pattern collection would create an artificially mixed pattern. We have explored the impact of the beam movement on the orientation precision by performing a scan over an area of the Cu sample in the usual manner and with a slight delay before pattern collection to allow the beam to settle. The differences in KAM results with and without the delay were negligible suggesting that this effect is inconsequential for the fine step sizes and camera settings typically used for characterizing local misorientation in deformed materials. As with any characterization technique, the results of this study reiterate the need for a baseline to ascertain the magnitude of any measurement uncertainty in order to carefully study the evolution of structure during deformation.
ACKNOWLEDGMENTS The authors gratefully acknowledge Ben Britton of the Imperial College London for information on the effects of mixed patterns on cross-correlation calculations. Josh Kacher of Lawrence Berkeley and Travis Rampton of Brigham Young University and Eric Payton of Alfred University are also acknowledged for helpful discussions on twin boundaries.
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