microstructural analysis

Intersections

Dr. Stuart Wright, Senior Scientist EBSD, EDAX

The city has recently started burying a pipe down the middle of one of the roads into my neighborhood. There were already a couple of troublesome intersections on this road. The construction has led to several accidents in the past couple of weeks at these intersections and I am sure there are more to come.

A question from a reviewer on a paper I am co-authoring got me thinking about the impact of intersections of bands in EBSD patterns on the Hough transform. The intersections are termed ‘zone axes’ or ‘poles’ and a pattern is typically composed of some strong ones where several high intensity bands intersect as well as weak ones where perhaps only two bands intersect.

To get an idea of the impact of the intersections on the Hough transform, I have created an idealized pattern. The intensity of the bands in the idealized pattern is derived from the peaks heights from the Hough transform applied to an experimental pattern. For a little fun, I have created a second pattern by blacking out the bands in the original idealized pattern, leaving behind only the intersections. I created a third pattern by blacking out the intersections and leaving behind only the bands. I have input these three patterns into the Hough transform. As I expected, you can see the strong sinusoidal curves from the pattern with only the intersections. However, you can also see peaks, where these sinusoidal curves intersect and these correspond (for the most part) to the bands in the pattern.

In the figure, the middle row of images are the raw Hough Transforms and the bottom row of images are the Hough Transforms after applying the butterfly mask. It is interesting to note how much the Hough peaks differ between the three patterns. It is clear that the intersections contribute positively to finding some of the weaker bands. This is a function not only of the band intensity but also the number of zone axes along the length of the band in the pattern.

Eventually the construction on my local road will be done and hopefully we will have fewer accidents. But clearly, intersections are more than just a necessary evil 😊

Hats Off/On to Dictionary Indexing

Dr. Stuart Wright, Senior Scientist EBSD, EDAX

Recently I gave a webinar on dynamic pattern simulation. The use of a dynamic diffraction model [1, 2] allows EBSD patterns to be simulated quite well. One topic I introduced in that presentation was that of dictionary indexing [3]. You may have seen presentations on this indexing approach at some of the microscopy and/or materials science conferences. In this approach, patterns are simulated for a set of orientations covering all of orientation space. Then, an experimental pattern is tested against all of the simulated patterns to find the one that provides the best match with the experimental pattern. This approach does particularly well for noisy patterns.

I’ve been working on implementing some of these ideas into OIM Analysis™ to make dictionary indexing more streamlined for datasets collected using EDAX data collection software – i.e. OIM DC or TEAM™. It has been a learning experience and there is still more to learn.

As I dug into dictionary indexing, I recalled our first efforts to automate EBSD indexing. Our first attempt was a template matching approach [4]. The first step in this approach was to use a “Mexican Hat” filter. This was done to emphasize the zone axes in the patterns. This processed pattern was then compared against a dictionary of “simulated” patterns. The simulated patterns were simple – a white pixel (or set of pixels) for the major zone axes in the pattern and everything else was colored black. In this procedure the orientation sampling for the dictionary was done in Euler space.
It seemed natural to go this route at the time, because we were using David Dingley’s manual on-line indexing software which focused on the zone axes. In David’s software, an operator clicked on a zone axis and identified the <uvw> associated with the zone axis. Two zone axes needed to be identified and then the user had to choose between a set of possible solutions. (Note – it was a long time ago and I think I remember the process correctly. The EBSD system was installed on an SEM located in the botany department at BYU. Our time slot for using the instrument was between 2:00-4:00am so my memory is understandably fuzzy!)

One interesting thing of note in those early dictionary indexing experiments was that the maximum step size in the sampling grid of Euler space that would result in successful indexing was found to be 2.5°, quite similar to the maximum target misorientation for modern dictionary indexing. Of course, this crude sampling approach may have led to the lack of robustness in this early attempt at dictionary indexing. The paper proposed that the technique could be improved by weighting the zone axes by the sum of the structure factors of the bands intersecting at the zone axes.
However, we never followed up on this idea as we abandoned the template matching approach and moved to the Burn’s algorithm coupled with the triplet voting scheme [5] which produced more reliable results. Using this approach, we were able to get our first set of fully automated scans. We presented the results at an MS&T symposium (Microscale Texture of Materials Symposium, Cincinnati, Ohio, October 1991) where Niels Krieger-Lassen also presented his work on band detection using the Hough transform [6]. After the conference, we hurried back to the lab to try out Niels’ approach for the band detection part of the indexing process [7].
Modern dictionary indexing applies an adaptive histogram filter to the experimental patterns (at left in the figure below) and the dictionary patterns (at right) prior to performing the normalized inner dot-product used to compare patterns. The filtered patterns are nearly binary and seeing these triggered my memory of our early dictionary work as they reminded me of the nearly binary “Sombrero” filtered patterns– Olé!
We may not have come back full circle but progress clearly goes in steps and some bear an uncanny resemblance to previous ones. I doff my hat to the great work that has gone into the development of dynamic pattern simulation and its applications.

[1] A. Winkelmann, C. Trager-Cowan, F. Sweeney, A. P. Day, P. Parbrook (2007) “Many-Beam Dynamical Simulation of Electron Backscatter Diffraction Patterns” Ultramicroscopy 107: 414-421.
[2] P. G. Callahan, M. De Graef (2013) “Dynamical Electron Backscatter Diffraction Patterns. Part I: Pattern Simulations” Microscopy and Microanalysis 19: 1255-1265.
[3] S.I. Wright, B. L. Adams, J.-Z. Zhao (1991). “Automated determination of lattice orientation from electron backscattered Kikuchi diffraction patterns” Textures and Microstructures 13: 2-3.
[4] Y.H. Chen, S. U. Park, D. Wei, G. Newstadt, M.A. Jackson, J.P. Simmons, M. De Graef, A.O. Hero (2015) “A dictionary approach to electron backscatter diffraction indexing” Microscopy and Microanalysis 21: 739-752.
[5] S.I. Wright, B. L. Adams (1992) “Automatic-analysis of electron backscatter diffraction patterns” Metallurgical Transactions A 23: 759-767.
[6] N.C. Krieger Lassen, D. Juul Jensen, K. Conradsen (1992) “Image processing procedures for analysis of electron back scattering patterns” Scanning Microscopy 6: 115-121.
[7] K. Kunze, S. I. Wright, B. L. Adams, D. J. Dingley (1993) “Advances in Automatic EBSP Single Orientation Measurements.” Textures and Microstructures 20: 41-54.

Saying What You Mean and Meaning What You Say!

Shawn Wallace, Applications Engineer, EDAX

A recent conversation on a list serv discussed sloppiness in the use of words and how it can cause confusion. This made me consider that in the world of microanalysis, we are not immune. We are probably sloppiest with two particular words. They are resolution and phase.

Let us start with how we use the word phase and how phases are commonly defined in microanalysis. In Energy Dispersive Spectroscopy (EDS), we use phase for everything, for example, phase mapping, phase library. In Electron Backscatter Diffraction (EBSD), the usage is a little more straightforward.

So, what is a phase? Well to me, a geologist, a phase has both a distinct chemistry and a distinct crystal structure. Why does this matter to a geologist? Two different minerals with the same chemistry, but with different structures, can behave in very different ways and this gives me useful information about each of them.
The classic example for geologists is the Al2SIO5 system (figure 1). It has three members, Kyanite, Sillimanite, and Andalusite. They each have the same chemistry but different structures. The structure of each is controlled by the pressure and temperature at which the mineral equilibrated. Simple chemistry tells me nothing. I need the structure to tease out that information.

Figure 1. Phase Diagram of the Al2SiO5 system in geological conditions. Different minerals form at different pressures and temperatures, letting geologists know how deep and/or the temperature at which the parent rock formed.**

EDS users use the term phase much more loosely. A phase is something that is chemically distinct. Our phase maps look at a spectrum pixel by pixel and see how they compare. In the end, the software goes through the entire map and groups each pixel with like pixels. The phase library does chi squared fits to compare the spectrum to the library (figure 2).

Figure 2. Our Spectrum Library Match uses as Chi-squared fit to determine the best possible matches. This phase is based on compositional data, not compositional and structural data.

While the definition of phase is relatively straight forward, the meaning of resolution gets a little murkier. If you asked someone what the EDS resolution is, you may get different answers depending on who you ask. The main way we use the term resolution when talking about EDS is spectral resolution. This defines how tight the peaks in a spectrum are (figure 3).

Figure 3. Comparison of EDS vs. WDS spectral resolution. WDS has much higher resolution (tighter peaks) than EDS, but fewer counts and more set-up are required.

The other main use of resolution, in EDS is the spatial resolution of the EDS signal itself (figure 4). There are many factors which determine this, but the main ones are the accelerating voltage and sample characteristics. This resolution can go from nanometers to microns.

Figure 4. Distribution of the electron energy deposited in an aluminum sample (top row) and a gold sample (bottom row) at 15 kV (left column) and 5 kV (right column). Note the dramatic difference in penetration given by the right hand side scale bar.

The final use of resolution for EDS is mapping resolution. This is by far the easiest to understand. It is just the step size of the beam while you are mapping.

Luckily for us, the easiest way to find out what people mean when they use the terms resolution or phase, is just to ask. Of course, the way to avoid any confusion is to be as precise as possible with your choice of words. I resolve to do my part and communicate as clearly as I can!

** Source: Wikipedia

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.

Back to Basics

Dr. René de Kloe, Applications Specialist, EDAX

When you have been working with EBSD for many years it is easy to forget how little you knew when you started. EBSD patterns appear like magic on your screen, indexing and orientation determination are automatic, and you can produce colourful images or maps with a click of a mouse.

Image 1: IPF on PRIAS™ center EBSD map of cold-pressed iron powder sample.

All the tools to get you there are hidden in the EBSD software package that you are working with and as a user you don’t need to know exactly how all of it happens. It just works. To me, although it is my daily work, it is still amazing how easy it sometimes is to get high quality data from almost any sample even if it only produces barely recognisable patterns.

Image 2: Successful indexing of extremely noisy patterns using automatic band detection.

That capability did not just appear overnight. There is a combination of a lot of hard work, clever ideas, and more than 25 years of experience behind it that we sometimes just forget to talk about, or perhaps even worse, expect everybody to know already. And so it is that I occasionally get asked a question at a meeting or an exhibition where I think, really? For example, some years ago I got a very good question about the EBSD calibration.

Image 3: EBSD calibration is based on the point in the pattern that is not distorted by the projection. This is the point where the electrons reach the screen perpendicularly (pattern center).

As you probably suspect EBSD calibration is not some kind of magic that ensures that you can index your patterns. It is a precise geometrical correction that distorts the displayed EBSD solution so that it fits the detected pattern. I always compare it with a video-projector. That is also a point projection onto a screen at a small angle, just like the EBSD detection geometry. And when you do that there is a distortion where the sides of the image on the screen are not parallel anymore but move away from each other. On video projectors there is a smart trick to fix that: a button labelled keystone correction which pulls the sides of the image nicely parallel again where they belong.

Image 4: Trapezoid distortion before (left) and after (right) correction.

Unfortunately, we cannot tell the electrons in the SEM to move over a little bit in order to make the EBSD pattern look correct. Instead we need to distort the indexing solution just so that it matches the EBSD pattern. And now the question I got asked was, do you actually adjust this calibration when moving the beam position on the sample during a scan? Because otherwise you cannot collect large EBSD maps. Apparently not everybody was doing that at that time, and it was being presented at a conference as the invention of the century that no EBSD system could do without. It was finally possible to collect EBSD data at low magnification! So, when do you think this feature will be available in your software? I stood quiet for a moment before answering, well, eh, we actually already have such a feature that we call the pattern centre shift. And it had been in the system since the first mapping experiments in the early 90’s. We just did not talk about it as it seemed so obvious.

There are more things like that hidden in the software that are at least as important, such as smart routines to detect the bands even in extremely noisy patterns, EBSD pattern background processing, 64-bit multithreading for fast processing of large datasets, and efficient quaternion-based mathematical methods for post-processing. These tools are quietly working in the background to deliver the results that the user needs.
There are some other original ideas that date back to the 1990’s that we actually do regularly talk about, such as the hexagonal scanning grid, triplet voting indexing, and the confidence index, but there is also some confusion about these. Why do we do it that way?

The common way in imaging and imaging sensors (e.g. CCD or CMOS chips) is to organise pixels on a square grid. That is easy and you can treat your data as being written in a regular table with fixed intervals. However, pixel-to-pixel distances are different horizontally and diagonally which is a drawback when you are routinely calculating average values around points. In a hexagonal grid the point-to-point distance is constant between all neighbouring pixels. Perhaps even more importantly, a hexagonal grid offers ~15% more points on the same area than a square grid, which makes it ideally suited to fill a surface.

Image 5: Scanning results for square (left) and hexagonal (right) grids using the same step size. The grain shape and small grains with few points are more clearly defined in the hexagonal scan.

This potentially allows improvements in imaging resolution and sometimes I feel a little surprised that a hexagonal imaging mode is not yet available on SEMs.
The triplet voting indexing method also has some hidden benefits. What we do there is that a crystal orientation is calculated for each group of three bands that is detected in an EBSD pattern. For example, when you set the software to find 8 bands, you can define up to 56 different band triangles, each with a unique orientation solution.

Image 6: Indexing example based on a single set of three bands – triplet.

Image 7: Equation indicating the maximum number of triplets for a given number of bands.

This means that when a pattern is indexed, we don’t just find a single orientation, we find 56 very similar orientations that can all be averaged to produce the final indexing solution. This averaging effectively removes small errors in the band detection and allows excellent orientation precision, even in very noisy EBSD patterns. The large number of individual solutions for each pattern has another advantage. It does not hurt too much if some of the bands are wrongly detected from pattern noise or when a pattern is collected directly at a grain boundary and contains bands from two different grains. In most cases the bands coming from one of the grains will dominate the solutions and produce a valid orientation measurement.

The next original parameter from the 1990’s is the confidence index which follows out of the triplet voting indexing method. Why is this parameter such a big deal that it is even patented?
When an EBSD pattern is indexed several parameters are recorded in the EBSD scan file, the orientation, the image quality (which is a measure for the contrast of the bands), and a fit angle. This angle indicates the angular difference between the bands that have been detected by the software and the calculated orientation solution. The fit angle can be seen as an error bar for the indexing solution. If the angle is small, the calculated orientation fits very closely with the detected bands and the solution can be considered to be good. However, there is a caveat. What now if there are different orientation solutions that would produce virtually identical patterns? This may happen for a single phase where it is called pseudosymmetry. The patterns are then so similar that the system cannot detect the difference. Alternatively, you can also have multiple phases in your sample that produce very similar patterns. In such cases we would typically use EDS information and ChI-scan to discriminate the phases.

Image 8: Definition of the confidence index parameter. V1 = number of votes for best solution, V2 = mumber of votes for 2nd best solution, VMAX= Maximum possible number of votes.

Image 9: EBSD pattern of silver indexed with the silver structure (left) and copper structure (right). Fit is 0.24″, the only difference is a minor variation in the band width matching.

In both these examples the fit value would be excellent for the selected solution. And in both cases the solution has a high probability of being wrong. And that is where the confidence index or CI value becomes important. The CI value is based on the number of band triangles or triplets that match each possible solution. If there are two indistinguishable solutions, these will both have the same number of triangles and the CI will be 0. This means that there are two or more apparently valid solutions that may all have a good fit angle. The system just does not know which of these solutions is the correct one and thus the measurement is rejected. If there is a difference of only 10% in matched triangles between alternative orientation solutions in most cases the software is capable of identifying the correct solution. The fit angle on its own cannot identify this problem.

After 25 years these tools and parameters are still indispensable and at the basis of every EBSD dataset that is collected with an EDAX system. You don’t have to talk about them. They are there for you.

Picture postcards from…

Dr. Felix Reinauer, Applications Specialist, EDAX

Display of postcards from my travels.

…L. A. – this is the title of a popular song from Joshua Kadison which one may like or dislike but at least three words in this title describe a significant part of my work at EDAX. Truth be told I’ve never been to Los Angeles, but as an application specialist traveling in general is a big part of my job. I´m usually on the move all over Europe meeting customers for trainings or attending exhibitions and workshops. This part of my job gives me the opportunity to meet with lots of people from different places and have fruitful discussions at the same time. If I am lucky, there is sometimes even some time left for sightseeing. The drawback of the frequent traveling is being separated from family and friends during these times.

Nowadays it is easy to stay in touch thanks to social media. You send a quick text message or make phone calls, but these are short-term. And here we get back to the title of this post and Joshua Kadison´s pop song, because quite some time ago I started the tradition of sending picture postcards from the places I travel to. And yes, I am talking about the real ones made from cardboard, documenting the different cities and countries I get to visit. Additionally, these cards are sweet notes highly appreciated by the addressee and are often pinned to a wall in our apartment for a period of time.

Within the last couple of years, I notice that it is getting harder to find postcards, this is especially true in the United States. Sometimes keeping on with my tradition feels like an Iron Man challenge. First, I run around to find nice picture postcards, then I have to look for stamps and the last challenge is finding a mailbox. Finally, all these exercises must be done in a limited span of time because the plane is leaving, the customer is waiting, or the shops are closing. But it is still worth it.

It is not only the picture on the front side, which is interesting, each postcard holds one or more stamps – tiny pieces of artfully designed paper – as well. Postage stamps were first introduced in Great Britain in 1840. The first one showed the profile of Queen Victoria and is called “Penny Black” due to the black background and its value. Thousands of different designs have been created ever since attracting collectors all over the world. Sadly, this tradition might be fading. Nowadays the quick and easy way of printed stamps from a machine with only the value on top seems to be becoming the norm. But the small stamps are often beautiful to look at and are full of interesting information, either about historical events, famous persons or remarkable locations.

A selection of postage stamps from countries I have visited.

For me, as a chemist I was also curious about the components of the stamps. Like a famous painting, investigated by XRF to collect information about the pigments and how the artist used them. For the little pieces of art, the SEM in combination with EDS is predestinated to investigate them in low vacuum mode without damaging them. The stamps I looked at are from my trips to Sweden, Great Britain, the Netherlands and the Czech Republic. In addition, I added one German stamp as a tribute to one of the most important chemists, Justus von Liebig after whom the Justus-Liebig University in Gießen is named, where he was professor (1824 – 1852) and I did my Ph. D. (a few years later).

All the measurements shown below were done under the same conditions using an acceleration voltage of 20 kV, with a pressure of 30 Pa and 40x magnification. With the multifield map option the entire stamp area was covered, using a single field resolution of 64×48 each and 128 frames.

Czech Republic Germany

 

Netherlands Sweden

United Kingdom

The EDS results show that modern paper is a composite material. The basic cellulose fibers are covered with a layer of calcium carbonate to ensure a good absorption of the different pigments used. This can be illustrated with the help of phase mappings. Even after many kilometers of travelling and all the hands treating the postcards all features of the stamps are still intact and can be detected. The element mappings show that the colors are not only based on organic compounds, but the existence of metal ions indicate a use of inorganic pigments. Typical elements detected were Al, S, Fe, Ti, Mn and others. The majority of the analysis work I do for EDAX and with EDAX customers is very specialized and involves materials, which would not be instantly familiar to non-scientists. It was fun to be able to use the same EDS analysis techniques on recognizable, everyday objects and to come up with some interesting results.

“Strained” Friendship

Dr. Stuart Wright, Senior Scientist EBSD, EDAX

Don’t just read the title of this post and skip to the photos or you might think it is some soap opera drama about strained relations – instead, the title is, once again, my feeble attempt at a punny joke!

I was recently doing a little reference checking and ended up on the website for Microscopy and Microanalysis (the journal, not the conference). On my first glance, I was surprised to see my name in the bottom right corner. Looking closer, I noticed that the paper Matt Nowell, David Field and I wrote way back in 2011 entitled “A Review of Strain Analysis Using Electron Backscatter Diffraction” is apparently the most cited article in Microscopy and Microanalysis. I am pleased that so many readers have found it useful. I remember, at the time, that we were getting a lot of questions about the tools within OIM Analysis™ for characterizing local misorientation and how they relate to strain. It was also a time when HREBSD was really starting to gain some momentum and we were getting a lot of questions on that front as well. So, we thought it would be helpful to write a paper that hopefully would answer some practical questions on using EBSD to characterize strain. From all the citations, it looks as though we actually managed to achieve what we had strived for.

My co-authors on that paper have been great to work with professionally; but I also count them among my closest personal friends. David Field joined Professor Brent Adams’ research group at BYU way back in 1987 if my memory is correct. We both completed master’s degrees at BYU and then followed Brent to Yale in 1988 to do our PhDs together. David then went on to Alcoa and I went to Los Alamos National Lab. Brent convinced David to leave and join the new startup company TSL and I joined about a year later. David left TSL for Washington State University shortly after EDAX purchased TSL.

Before, I joined TSL, Matt Nowell* had joined the company and he has been at TSL/EDAX ever since. Even with all the comings and goings we’ve remained colleagues and friends.

I’ve been richly blessed by both their excellent professional talents and their fun spirited friendship. We’ve worked, traveled and attended conferences together. We’ve played basketball, volleyball and golf together. I must also brag that we formed the core of the soccer team to take on the Seoul National University students after ICOTOM 13 in Seoul. Those who attended ICOTOM 13 may remember that it was held shortly after the 2002 World Cup hosted jointly by Korea and Japan; in which Korea had such a good showing – finishing 4th. A sequel was played at SNU where the students pretty much trounced the rest of the world despite our best efforts 😊. Here are a few snapshots of us with our Korean colleagues at ICOTOM 13 – clearly, we were always snappy dressers!

* Don’t miss Matt’s upcoming webinar: “Applications of High-Speed CMOS Cameras for EBSD Microstructural Analysis”