texture analysis

From Collecting EBSD at 20 Patterns per second (pps) to Collecting at 4,500 pps

John Haritos, Regional Sales Manager Southwest USA. EDAX

I recently had the opportunity to host a demo for one of my customers at our Draper, Utah office. This was a long-time EDAX and EBSD user, who was interested in seeing our new Velocity CMOS camera, and to try it on some of their samples.

When I started in this industry back in the late 90s, the cameras were running at a “blazing” 20 points per second and we all thought that this was fast. At that time, collection speed wasn’t the primary issue. What EBSD brought to the table was automated orientation analysis of diffraction patterns. Now users could measure orientations and create beautiful orientation maps with the push of a button, which was a lot easier than manually interpreting these patterns.

Fast forward to 2019 and with the CMOS technology being adapted from other industries to EBSD we are now collecting at 4,500 pps. What took hours and even days to collect at 20 pps now takes a matter of minutes or seconds. Below is a Nickel Superalloy sample collected at 4,500 pps on our Velocity™ Super EBSD camera. This scan shows the grain and twinning structure and was collected in just a few minutes.

Figure 1: Nickel Superalloy

Of course, now that we have improved from 20 pps to 4,500 pps, it’s significantly easier to get a lot more data. So the question becomes, how do we analyze all this data? This is where OIM Analysis v8™ comes to the rescue for the analysis and post processing of these large data sets. OIM Analysis v8™ was designed to take advantage of 64 bit computing and multi-threading so the software can handle large datasets. Below is a grain size map and a grain size distribution chart from an Aluminum friction stir weld sample with over 7 Million points collected with the Velocity™ and processed using OIM Analysis v8™. This example is interesting because the grains on the left side of the image are much larger than the grains on the right side. With the fast collection speeds, a small (250nm) step size could still be used over this larger collection area. This allows for accurate characterization of grain size across this weld interface, and the bimodal grain size distribution is clearly resolved. With a slower camera, it may be impractical to analyze this area in a single scan.

Figure 2: Aluminum Friction Stir Weld

In the past, most customers would setup an overnight EBSD run. You could see the thoughts running through their mind: will my sample drift, will my filament pop, what will the data look like when I come back to work in the morning? Inevitably, the sample would drift, or the filament would pop and this would mean the dreaded “ugh” in the morning. With the Velocity™ and the fast collection speeds, you no longer need to worry about this. You can collect maps in a few minutes and avoid this issue in practice. It’s a hard thing to say in a brochure, but its easy to appreciate when seeing it firsthand.

For me, watching my customer see the analysis of many samples in a single day was impressive. These were not particularly easy samples. They were solar cell and battery materials, with a variety of phases and crystal structures. But under similar conditions to their traditional EBSD work, we could collect better quality data much faster. The future is now. Everyone is excited with what the CMOS technology can offer in the way of productivity and throughput for their EBSD work.

Old Eyes?

Dr. Stuart Wright, Senior Scientist EBSD, EDAX

I was recently asked to write a “Tips & Tricks” article for the EDAX Insight Newsletter as I had recently done an EDAX Webinar (www.edax.com/news-events/webinars) on Texture Analysis. I decided to follow up on one item I had emphasized in the Webinar. Namely, the need for sampling enough orientations for statistical reliability in characterizing a texture. The important thing to remember is that it is the number of grain orientations as opposed to the number of orientations measured. But that lead to the introduction of the idea of sub-sampling a dataset to calculate textures when the datasets are very large. Unfortunately, there was not enough room to go into the kind of detail I would have liked to so I’ve decided to use our Blog forum to cover some details about sub-sampling that I found interesting

Consider the case where you not only want to characterize the texture of a material but also the grain size or some other microstructural characteristic requiring a relatively fine microstructure relative to the grain size. According to some previous work, to accurately capture the texture you will want to measure approximately 10,000 grains [1] and about 500 pixels per average grain in order to capture the grain size well [2]. This would result in a scan with approximately 5 million datapoints. Instead of calculating the texture using all 5 million data points, you can use a sub-set of the points to speed up the calculation. In our latest release of OIM Analysis, this is not as big of a concern as it once was as the texture calculations have been multithreaded so they are fast even for very large datasets. Nonetheless, since it is very likely that you will want to calculate the grain size, you can use the area weighted average grain orientation for each grain as opposed to using all 5 million individual orientation measurements for some quick texture calculation. Alternatively, a sub-set of the points through random or uniform sampling of the points in the scan area could be used.

Of course, you may wonder how well the sub-sampling works. I have done a little study on a threaded rod from a local hardware store to test these ideas. The material exhibits a (110) fiber texture as can be seen in the Normal Direction IPF map and accompanying (110) pole figure. For these measurements I have simply done a normalized squared difference point-by-point through the Orientation Distribution Function (ODF) which we call the Texture Difference Index (TDI) in the software.


This is a good method because it allows us to compare textures calculated using different methods (e.g. series expansion vs binning). In this study, I have used the general spherical harmonics series expansion with a rank of L = 22 and a Gaussian half-width of  = 0.1°. The dataset has 105,287 points with 92.5% of those having a CI > 0.2 after CI Standardization. I have elected only to use points with CI > 0.2. The results are shown in the following figure.

As the step size is relatively coarse with respect to the grain size, I have experimented with using grains requiring at least two pixels before considering a set of similarly oriented points a grain versus allowing a single pixel to be a grain. This resulted in 9981 grains and 25,437 grains respectively. In both cases, the differences in the textures between these two grain-based sub-sampling approaches with respect to using the full dataset are small with the 1 pixel grain based sub-sampling being slight closer as would be expected. However, the figure above raised two questions for me: (1) what do the TDI numbers mean and (2) why do the random and the uniform sampling grids differ so much, particularly as the number of points in the sub-sampling gets large (i.e. at 25% of the dataset).

TDI
The pole figure for the 1000 random points in the previous figure certainly captures some of the characteristics of the pole figure for the full dataset. Is this reflected in the TDI measurements? My guess is that if I were to calculate the textures at a lesser rank, something like L = 8 then the TDI’s would go down. This is already part of the TDI calculation and so it is an easy thing to examine. For comparison I have chosen to look at four different datasets: (a) all of the data in the dataset above (named “fine”), (b) a dataset from the same material with a coarser step size (“coarse”) containing approximately 150,000 data points, (c) sub-sampling of the original dataset using 1000 randomly sampled datapoints (“fine-1000”) and (d) the “coarse” dataset rotated 90 degrees about the vertical axis in the pole figures (“coarse-rotated”). It is interesting to note that the textures that are similar “by-eye” show a general increase in the TDI as the series expansion rate increases. However, for very dissimilar textures (i.e “coarse” vs “coarse-rotated”) the jump to a large TDI is immediate.

Random vs Uniform Sampling
The differences between the random and uniform sampling were a bit curious so I decided to check the random points to see how they were positioned in the x-y space of the scan. The figure below compares the uniform and random sampling for 4000 datapoints – any more than this is hard to show. Clearly the random sampling is reasonable but does show a bit of clustering and gaps within the scan area. Some of these small differences show up with higher differences in TDI values than I would expect. Clearly, at L = 22 we are picking up quite subtle differences – at least subtle with respect to my personal “by-eye” judgement. It seems to me, that my “by-eye” judgement is biased toward lower rank series expansions.


Of course, another conclusion would be that my eyesight is getting rank with age ☹ I guess that explains my increasingly frequent need to reach for my reading glasses.

References
[1] SI Wright, MM Nowell & JF Bingert (2007) “A comparison of textures measured using X-ray and electron backscatter diffraction”. Metallurgical and Materials Transactions A, 38, 1845-1855
[2] SI Wright (2010) “A Parametric Study of Electron Backscatter Diffraction based Grain Size Measurements”. Practical Metallography, 47, 16-33.