Grain size

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.

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.

Crown Caps = Fresh Beer?

Dr. Felix Reinauer, Applications Specialist Europe, EDAX

A few days ago, I visited the Schlossgrabenfest in Darmstadt, the biggest downtown music festival in Hessen and even one of the biggest in Germany. Over one hundred bands and 12 DJs played all kinds of different music like Pop, Rock, Independent or House on six stages. This year the weather was perfect on all four days and a lot of people, celebrated a party together with well known, famous and unknown artists. A really remarkable fact is the free entrance. The only official fee is the annual plastic cup, which must be purchased once and is then used for any beverage you can buy in the festival area.

During the festival my friend and I listened to the music and enjoyed the good food and drinks sold at different booths in the festival grounds. In this laid-back atmosphere we started discussing the taste of the different kinds of beer available at the festival and throughout Germany. Beer from one brewery always tastes the same but you can really tell the difference if you try beer from different breweries. In Germany, there are about 1500 breweries offering more than 5000 different types of beer. This means it would take 13.5 years if you intended to taste a different beer every single day. Generally, breweries and markets must guarantee that the taste of a beer is consistent and that it stays fresh for a certain time.

In the Middle Ages a lot of people brewed their own beer and got sick due to bad ingredients. In 1516 the history of German beer started with the “Reinheitsgebot”, a regulation about the purity of beer. It says that only three ingredients, malt, water, and hops, may be used to make beer. This regulation must still be applied in German breweries. At first this sounds very unspectacular and boring, but over the years the process was refined to a great extent. Depending on the grade of barley roasting, the quantity of hops and the brewing temperature, a great variety of tastes can be achieved. In the early times the beer had to be drunk immediately or cooled in cold cellars with ice. To take beer with you some special container was invented to keep it drinkable for a few hours. Today beer is usually sold in recyclable glass bottles with a very tight cap keeping it fresh for months without cooling. This cap protects the beer from oxidation or getting sour.

Coming back to our visit to the Schlossgrabenfest; in the course of our discussions about the taste of different kind of beer we wondered how the breweries guarantee that the taste of the beer will not be influenced by storage and transport. The main problem is to seal the bottles gas-tight. We were wondered about the material the caps on the bottles are made of and whether they are as different as the breweries and maybe even special to a certain brewery.

I bought five bottles of beers from breweries located in the north, south, west, and east of Germany and one close to the EDAX office in Darmstadt. After opening the bottles, a cross section of the caps was investigated by EDS and EBSD. To do so, the caps were cut in the middle, embedded in a conductive resin and polished (thanks to René). The area of interest was the round area coming from the flat surface. The EDS maps were collected so that the outer side of the cap was always on the left side and the inner one on the right side of the image. The EBSD scans were made from the inner Fe metal sheet.

Let´s get back to our discussion about the differences between the caps from different breweries. The EDS spectra show that all of them are made from Fe with traces of Mn < 0.5 wt% and Cr, Ni at the detection limit. The first obvious difference is the number of pores. The cap from the east only contains a few, the cap from north the most and the cap from the middle big ones, which are also located on the surface of the metal sheet. The EBSD maps were collected from the centers of the caps and were indexed as ferrite. The grains of the cap from the middle are a little bit smaller and with a larger size distribution (10 to 100 microns) than the others, which are all about 100 microns. A remarkable misorientation is visible in some of the grains in the cap from the north.

Now let´s have a look at the differences on the inside and outside of the caps. EDS element maps show carbon and oxygen containing layers on both sides of all the caps, probably for polymer coatings. Underneath, the cap from the east is coated with thin layers of Cr with different thicknesses on each side. On the inside a silicone-based sealing compound and on the outside a varnish containing Ti can also be detected. The cap from the south has protective coatings of Sn on both sides and a silicon sealing layer can also be found on the inside. The composition of the cap from the west is similar to the cap from the east but with the Cr layer only on the outside. The large pores in the cap from the middle are an interesting difference. Within the Fe metal sheet, these pores are empty, but on both sides, they are filled with silicon-oxide. It seems that this silicon oxide filling is related to the production process, because the pores are covered with the Sn containing protective layers. The cap from the north only contains a Cr layer on the inside. The varnish contains Ti and S.

In summary, we didn’t expect the caps would have these significant differences. Obviously, the differences on the outside are probably due to the different varnishes used for the individual labels from each of the breweries. However, we didn’t think that the composition and microstructure of the caps themselves would differ significantly from each other. This study is far from being complete and cannot be used as a basis for reliable conclusions. However, we had a lot of fun before and during this investigation and are now sure that the glass bottles can be sealed to keep beer fresh and guarantee a great variety of tastes.

Building an EBSD Sample

Matt Nowell, EBSD Product Manager, EDAX

Father’s Day is this weekend, and I like to think my kids enjoy having a material scientist for a father. They have a go-to resource for math questions, science projects are full of fun and significant digits, and when they visit the office they get to look at bugs and Velcro with the SEM. I’m always up to take them to museums to see crystals and airplanes and other interesting things as we travel around. That’s one way we have tried to make learning interactive and engaging. Another activity we have recently tried is 3D printing. This has allowed us to find or create 3D digital models of things and then print them out at home. Here are some fun examples of our creations.
At home we are printing with plastics, but in the Material Science world there is a lot of interest and development in printing with metals as well. This 3D printing, or additive manufacturing, is rapidly developing as a new manufacturing approach for both prototyping and production in a range of industries including aerospace and medical implants. Instead of melting plastics with a heated nozzle, metal powders are melted together with lasers or electron beams to create these 3D shapes that cannot be easily fabricated by traditional approaches.

In these applications, it is important to have reliable and consistent properties and performance. To achieve this, the microstructure of the metals must be both characterized and understood. EBSD is an excellent tool for this requirement.

The microstructures that develop during 3D printing are very interesting. Here is an example from a Ni-based superalloy created using Selective Laser Melting (SLM). This image shows a combined Image Quality and Orientation (IQ + IPF) Map, with the orientations displayed relative to the sample normal direction. Rather than equiaxed grains with easily identifiable twin boundaries, as are common with many nickel superalloys, this image shows grains that are growing vertically in the structure. This helps indicate the direction of heat flow during the manufacturing process. Understanding the local conditions during melting and solidification helps determine the final grain structure.
In some materials, this heating and cooling will cause not only melting, but also phase transformations that also affect the microstructure. Ti-6Al-4V (or Ti64) is one of the most common Titanium alloys used in both aerospace and biomedical applications, and there has been a lot of work done developing additive manufacturing methods for this alloy. Here is an IQ + IPF map from a Ti64 alloy built for a medical implant device.
At high temperatures, this alloy transforms into a Body-Centered Cubic (or BCC) structure called the Beta phase. As the metal cools, it transforms into a Hexagonal Closed Pack (HCP) structure, called the Alpha phase. This HCP microstructure develops as packets of similarly oriented laths as seen above. However, not all the Beta phase transforms. Here is an IQ + Phase EBSD map, where the Alpha phase is red and the Beta phase is blue. Small grains of the Beta phase are retained from the higher temperature structure.
If we show the orientations of the Beta grains only, we see how the packets relate to the original Beta grains that were present at high temperatures.
The rate of cooling will also influence the final microstructure. In this example, pieces of Ti64 were heated and held above the Beta transition temperature. One sample was then cooled in air, and another was quenched in water. The resulting microstructures are shown below. The first is the air-cooled sample.
The second is the water-cooled sample.

Clearly there is a significant difference in the resulting structure based on the cooling rate alone. As I imagine the complex shapes built with additive manufacturing, understanding both the local heating and cooling conditions will be important for optimization of both the structure and the properties.

A Little Background on Backgrounds

Dr. Stuart Wright, Senior Scientist EBSD, EDAX

If you have attended an EDAX EBSD training course, you have seen the following slide in the Pattern Indexing lecture. This slide attempts to explain how to collect a background pattern before performing an OIM scan. The slide recommends that the background come from an area containing at least 25 grains.

Those of you who have performed re-indexing of a scan with saved patterns in OIM Analysis 8.1 may have noticed that there is a background pattern for the scan data (as well as one of the partitions). This can be useful if re-indexing a scan where the raw patterns were saved as opposed to background corrected patterns. This background pattern is formed by averaging 500 patterns randomly selected from the saved patterns. 500 is a lot more than the minimum of 25 recommended in the slide from the training lecture.

Recently, I was thinking about these two numbers – is 25 really enough, is 500 overkill? With some of the new tools (Callahan, P.G. and De Graef, M., 2013. Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations. Microscopy and Microanalysis, 19(5), pp.1255-1265.) available for simulating EBSD patterns I realized this might be provide a controlled way to perhaps refine the number of orientations that need to be sampled for a good background. To this end, I created a set of simulated patterns for nickel randomly sampled from orientation space. The set contained 6,656 patterns. If you average all these patterns together you get the pattern at left in the following row of three patterns. The average patterns for 500 and 25 random patterns are also shown. The average pattern for 25 random orientations is not as smooth as I would have assumed but the one with 500 looks quite good.

I decided to take it a bit further and using the average pattern for all 6,656 patterns as a reference I compared the difference (simple intensity differences) between average patterns from n orientations vs. the reference. This gave me the following curve:
From this curve, my intuitive estimate that 25 grains is enough for a good background appears be a bit optimistic., but 500 looks good. There are a few caveats to this, the examples I am showing here are at 480 x 480 pixels which is much more than would be used for typical EBSD scans. In addition, the simulated patterns I used are sharper and have better signal-to-noise ratios than we are able to achieve in experimental patterns at typical exposure times. These effects are likely to lead to more smoothing.

I recently saw Shawn Bradley who is one of the tallest players to have played in the NBA, he is 7’6” (229cm) tall. I recognized him because he was surrounded by a crowd of kids – you can imagine that he really stood out! This reminded me that these results assume a uniform grain size. If you have 499 tiny grains encircling one giant grain, then the background from these 500 grains will not work as a background as it would be dominated by the Shawn Bradley grain!

Seeing is Believing?

Dr. René de Kloe, Applications Specialist, EDAX

A few weeks ago, I participated in a joint SEM – in-situ analysis workshop in Fuveau, France with Tescan electron microscopes and Newtec (supplier of the heating-tensile stage). One of the activities during this workshop was to perform a live in-situ tensile experiment with simultaneous EBSD data collection to illustrate the capabilities of all the systems involved. In-situ measurements are a great way to track material changes during the course of an experiment, but of course in order to be able to show what happens during such an example deformation experiment you need a suitable sample. For the workshop we decided to use a “simple” 304L austenitic stainless-steel material (figure 1) that would nicely show the effects of the stretching.

Figure 1. Laser cut 304L stainless steel tensile test specimen provided by Newtec.

I received several samples a few weeks before the meeting in order to verify the surface quality for the EBSD measurements. And that is where the trouble started …

I was hoping to get a recrystallized microstructure with large grains and clear twin lamellae such that any deformation structures that would develop would be clearly visible. What I got was a sample that appeared heavily deformed even after careful polishing (figure 2).

Figure 2. BSE image after initial mechanical polishing.

This was worrying as the existing deformation structures could obscure the results from the in-situ stretching. Also, I was not entirely sure that this structure was really showing the true microstructure of the austenitic sample as it showed a clear vertical alignment that extended over grain boundaries.
And this is where I contacted long-time EDAX EBSD user Katja Angenendt at the MPIE in Düsseldorf for advice. Katja works in the Department of Microstructure Physics and Alloy Design and has extensive experience in preparing many different metals and alloys for EBSD analysis. From the images that I sent, Katja agreed that the visible structure was most likely introduced by the grinding and polishing that I did and she made some suggestions to remove this damaged layer. Armed with that knowledge and new hope I started fresh and polished the samples once more. And I had some success! Now there were grains visible without internal deformation and some nice clean twin lamellae (figure 3). But not everywhere. I still had lots of areas with a deformed structure and whatever I tried I could not get rid of those.

Figure 3. BSE image after optimized mechanical polishing.

Back to Katja. When I discussed my remaining polishing problems she helpfully proposed to give it a try herself using a combination of mechanical polishing and chemical etching. But even after several polishing attempts starting from scratch and deliberately introducing scratches to verify that enough material was removed we could not completely get rid of the deformed areas. Now we slowly started to accept that this deformation was perhaps a true part of the microstructure. But how could that be if this is supposed to be a recrystallised austenitic 304L stainless steel?

Table 1. 304/304L stainless steel composition.

Let’s take a look at the composition. In table 1 a typical composition of 304 stainless steel is given. The spectrum below (figure 4) shows the composition of my samples.

Figure 4. EDS spectrum with quantification results collected with an Octane Elite Plus detector.

All elements are in the expected range except for Ni which is a bit low and that could bring the composition right at the edge of the austenite stability field. So perhaps the deformed areas are not austenite, but ferrite or martensite? This is quickly verified with an EBSD map and indeed the phase map below confirms the presence of a bcc phase (figure 5).

Figure 5. EBSD map results of the sample before the tensile test, IQ, IPF, and phase maps.

Having this composition right at the edge of the austenite stability field actually added some interesting additional information to the tensile tests during the workshop. Because if the internal deformation in the austenite grains got high enough, we might just trigger a phase transformation to ferrite (or martensite) with ongoing deformation.

Figure 6. Phase maps (upper row) and Grain Reference Orientation Deviation (GROD) maps (lower row) for a sequence of maps collected during the tensile test.

And that is exactly what we have observed (figure 6). At the start of the experiments the ferrite fraction in the analysis field is 7.8% and with increasing deformation the ferrite fraction goes up to 11.9% at 14% strain.

So, after a tough start the 304L stainless steel samples made the measurements collected during the workshop even more interesting by adding a phase transformation to the deformation. If you are regularly working with these alloys this is probably not unexpected behavior. But if you are working with many different materials you have to be aware that different types of specimen treatment, either during preparation or during experimentation, may have a large influence on your characterization results. Always be careful that you do not only see what you believe, but ensure that you can believe what you see.

Finally I want to thank the people of Tescan and Newtec for their assistance in the data collection during the workshop in Fuveau and especially a big thank you to Katja Angenendt at the Max Planck Institute for Iron Research in Düsseldorf for helpful discussions and help in preparing the sample.

Looking At A Grain!

Sia Afshari, Global Marketing Manager, EDAX

November seems to be the month when the industry tries to squeeze in as many events as possible before the winter arrives. I have had the opportunity to attend a few events and missed others, however, I want to share with you how much I enjoyed ICOTOM18*!

ICOTOM (International Conference on Texture of Materials) is an international conference held every three years and this year it took place in St. George, Utah, the gateway to Zion National Park.

This was the first time I have ever attended ICOTOM which is, for the most part, a highly technical conference, which deals with the material properties that can be detected and analyzed by Electron Backscatter Diffraction (EBSD) and other diffraction techniques. What stood out to me this year were the depth and degree of technical presentations made at this conference, especially from industry contributors. The presentations were up to date, data driven, and as scientifically sound as any I have ever seen in the past 25 years of attending more than my share of technical conferences.


The industrial adaptation of technology is not new since X-ray diffraction has been utilized for over half a century to evaluate texture properties of crystalline materials. At ICOTOM I was most impressed by the current ‘out of the laboratory’ role of microanalysis, and especially EBSD, for the evaluation of anisotropic materials for quality enhancement.

The embracing of the microanalysis as a tool for product enhancement means that we equipment producers need to develop new and improved systems and software for EBSD applications that will address these industrial requirements. It is essential that all technology providers recognize the evolving market requirements as they develop, so that they can stay relevant and supply current needs. If they can’t do this, then manufacturing entities will find their own solutions!

*In the interests of full disclosure, I should say that EDAX was a sponsor of ICOTOM18 and that my colleagues were part of the organizing committee.

Aimless Wanderin’ – Need a Map?

Dr. Stuart Wright, Senior Scientist, EDAX

In interacting with Rudy Wenk of the University of California Berkeley to get his take on the word “texture” as it pertains to preferred orientation reminds me of some other terminologies with orientation maps that Rudy helped me with several years ago.

Map reconstructed form EBSD data showing the crystal orientation parallel to the sample surface normal

Joe Michael of Sandia National Lab has commented to me a couple of times his objection to the term “IPF map”. As you may know, the term is commonly used to describe a color map reconstructed from OIM data where the color denotes the crystallographic axis aligned with the sample normal as shown below. Joe points out that the term “orientation map” or “crystal direction map” or something similar would be much more appropriate and he is absolutely right.

The reason behind the name “IPF map”, is that I hi-jacked some of my code for drawing inverse pole figures (IPFs) as a basis to start writing the code to create the color-coded maps. Thus, we started using the term internally (it was TSL at the time – prior to EDAX purchasing TSL) and then it leaked out publicly and the name stuck – my apologies to Joe. We later added the ability to color the microstructure based on the crystal direction aligned with any specified sample direction as shown below.

Orientation maps showing the crystal directions aligned with the normal, rolling and transverse directions at the surface of a rolled aluminum sheet.

The idea for this map was germinated from a paper I saw presented by David Dingley where a continuous color coding schemed was devised by assigning red, green and blue to the three axes of Rodrigues-Frank space: D. J. Dingley, A. Day, and A. Bewick (1991) “Application of Microtexture Determination using EBSD to Non Cubic Crystals”, Textures and Microstructures, 14-18, 91-96. In this case, the microstructure had been digitized and a single orientation measured for each grain using EBSD. Unfortunately, I only have gray scale images of these results.

SEM micrograph of nickel, grain orientations in Rodrigues-Frank space and orientation map based on color Rodrigues vector coloring scheme. Source: Link labeled “Full-Text PDF” at www.hindawi.com/archive/1991/631843/abs/

IPF map of recrystallized grains in grain oriented silicon steel from Y. Inokuti, C. Maeda and Y. Ito (1987) “Computer color mapping of configuration of goss grains after an intermediate annealing in grain oriented silicon steel.” Transactions of the Iron and Steel Institute of Japan 27, 139-144.
Source: Link labeled “Full Text PDF button’ at www.jstage.jst.go.jp/article/isijinternational1966/27/4/27_4_302/_article

We didn’t realize it at the time; but, an approach based on the crystallographic direction had already been done in Japan. In this work, the stereographic unit triangle (i.e. an inverse pole figure) was used in a continues color coding scheme were red is assigned to the <110> direction, blue to <111> and yellow to <100> and then points lying between these three corners of the stereographic triangle are combinations of these three colors. This color coding was used to shade grains in digitized maps of the microstructure according to their orientation. Y. Inokuti, C. Maeda and Y. Ito (1986) “Observation of Generation of Secondary Nuclei in a Grain Oriented Silicon Steel Sheet Illustrated by Computer Color Mapping”, Journal of the Japan Institute of Metals, 50, 874-8. The images published in this paper received awards in 1986 by the Japanese Institute of Metals and TMS.

AVA map and pole figure from a quartz sample from “Gries am Brenner” in the Austrian alps south of Innsbruck. The pole figure is for the c-axis. (B. Sander (1950) Einführung in die Gefügekunde der Geologischen Körper: Zweiter Teil Die Korngefüge. Springer-Vienna)
Source: In the last chapter (Back Matter) in the Table of Contents there is a link labeled “>> Download PDF” at link.springer.com/book/10.1007%2F978-3-7091-7759-4

I thought these were the first colored orientation maps constructed until Rudy later corrected me (not the first, nor certainly the last time). He sent me some examples of mappings of orientation onto a microstructure by “hatching” or coloring a pole figure and then using those patterns or colors to shade the microstructure as traced from micrographs. H.-R. Wenk (1965) “Gefügestudie an Quarzknauern und -lagen der Tessiner Kulmination”, Schweiz. Mineralogische und Petrographische Mitteilungen, 45, 467-515 and even earlier in B. Sander (1950) Einführung in die Gefügekunde Springer Verlag. 402-409 . Sanders entitled this type of mapping and analysis as AVA (Achsenvertilungsanalyse auf Deutsch or Axis Distribution Analysis in English).

Such maps were forerunners to the “IPF maps” of today (you could actually call them “PF maps”) to which we are so familiar with. It turns out our wanderin’s in A Search for Structure (Cyril Stanley Smith, 1991, MIT Press) have actually not been “aimless” at all but have helped us gain real insight into that etymologically challenged world of microstructure.

Aimless Wanderin’ in 3D (Part 3)

Dr. Stuart Wright, Senior Scientist, EDAX

In my research on the origins of the term texture to describe preferred lattice orientation I spent some time looking at one of the classic texts on the subject: Bunge’s “red bible” as we called it in our research group in grad school – Texture Analysis in Materials Science Mathematical Methods (1969). As I was reading I found an interesting passage as it relates to where we are with EBSD today:

“In a polycrystalline material crystallites of different shape, size and orientation are generally present. It can thus also occur that regions of different orientation are not separated from one another by unequivocally defined grain boundaries, but that, on the contrary, the orientation changes continuously from one point to another. If one desires to completely describe the crystal orientation of a polycrystalline material, one must specify the relevant orientation g for each point with coordinates x, y, z within the sample:

g=g(x,y,z)           (3.1)

If one writes g in EULER’s angles, this mean explicitly

φ_1=φ_1 (x,y,z);  Φ=Φ(x,y,z);  φ_2=φ_2 (x,y,z);           (3.2)

One thus requires three functions, each of these variables, which are also discontinuous at grain boundaries. Such a representation of the crystal orientation is very complicated. Where therefore observe that it has as yet been experimentally determined in only a very few cases (see, for example, references 139-141, 200-203), and that its mathematical treatment is so difficult that it is not practically applicable.”

I don’t quote these lines to detract in any way from the legacy of Professor Bunge in the field of texture analysis. I did not know Professor Bunge well but in all my interactions with him he was always very patient with my questions and generous with his time. Professor Bunge readily embraced new technology as it advanced texture analysis forward including automated EBSD. I quote this passage to show that the ideas behind what we might today call 3D texture analysis were germinated very early on. The work on Orientation Coherence by Brent Adams I quoted in Part 2 of this series was one of the first to mathematically build on these ideas. Now with serial sectioning via the FIB or other means coupled with EBSD as well as high-energy x-ray diffraction it is possible to realize the experimental side of these ideas in a, perhaps not routine but certainly, tractable manner.

A schematic of the evolution from pole figure-based ODF analysis to EBSD-based orientation maps to 3D texture data.

Others have anticipated these advancements as well. In chapter 2 of Rudy Wenk’s 1985 book entitled Preferred Orientation in Deformed Metal and Rocks: An introduction to Modern Texture Analysis it states:

“Pole figures and fabric diagrams provide information only about the orientation of crystals. It may be desirable to know the relation between the spatial distribution of grains and grain shape with respect to crystallographic orientation. Orientation relations between neighboring grains further defined the fabric and help to elucidate its significance.”

But let us return to the theme of aimless wanderin’s in texture terminology. The title for Chapter 4 of Bunge’s book is “Expansion of Orientation Distribution Functions in Series of Generalized Spherical Harmonics”. This chapter describes a solution the determination of the three-dimensional ODF (orientation distribution function) from two-dimensional pole figures. The chapter has a sub-title “Three-Dimensional Textures”. The three dimensions in this chapter of Bunge’s book are in orientation space (the three Euler Angles). What we call today a 3D texture is actually a 6D description with three dimensions in orientation space and three spatial dimensions (e.g. x, y and z). And those working with High-Energy x-rays have also characterized spatially resolved orientation distributions for in-situ experiments thus adding a seventh dimension of time, temperature, strain, …

It is nice to know in the nearly 50 years since Bunge’s book was published that what can sometimes appear to be aimless wanderin’s with mixed up terminology has actually lead us to higher dimensions of understanding. But, before we take too much credit for these advances in the “metallurgical arts”, as it says on the Google Scholar home page we “stand on the shoulders of giants” who envisioned and laid the groundwork for these advances.

Fine-Tuning the Microstructure

Dr. Stuart Wright, Senior Scientist, EDAX

Since my blog about piano wires back in November 2014, I’ve continued to think about what it all means in terms of music. As I mentioned in my posting, my friend Keith Kopp provided the wires for me to look at. Keith is very generous with his time. I’ve seen him many times help out with music at various church and neighborhood socials. I’m always impressed that someone like Keith can clearly hear when an instrument is even slightly out of tune and also recognize how to fix the problem. I certainly don’t have the ear for that kind of thing. Keith mentioned to me that he can hear the difference between the two wires he supplied to me. I realized quickly I had no hope of picking that up with my insensitive ears. I then realized that Keith was saying he could hear the difference even when the two wires are tuned. I wondered what it was that he was hearing. I turned to Wikipedia for some insight and stumbled across an entry on “inharmonicity” which is “the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency”.  I realized that the sound waves are travelling through the wires at slightly different rates due to elastic anisotropy coupled with grain-to-grain differences in orientation. Thus, while the average pitch of the wire will be in tune there will actually be a spread about that pitch. I might be able to estimate that spread using the principles of elastic anisotropy.

For a single crystal the elastic behavior is anisotropic as is illustrated in a plot for the elastic modulus for an iron single crystal below (courtesy of Megan Frary at Boise State University).

Figure 1

The elastic properties of a single crystal can be expressed in terms of a tensor. This is handy, because rotating the property tensor to reflect the grain orientation with respect to a set of samples axes is fairly straight forward (C is a fourth order elasticity tensor and g is the orientation matrix):

equation

The next step was to simply go to a reference volume and find the single crystal elastic constants for fcc and bcc iron, plug them into OIM Analysis and then “Bob’s your uncle”. However, I learned it wasn’t nearly as straightforward as I thought. Once again, some searching on the internet led me to some papers on first principle calculations of elastic constants and I quickly discovered that estimating elastic constants at room temperature is not as simple as I would have thought. I found several papers by Levente Vitos and co-workers. Professor Vitos was kind enough to teach me a little about this field and after some correspondence with him I decided to use the elastic constants for Fe-Mn found in Zhang, H., Punkkinen, M. P., Johansson, B., & Vitos, L. (2012). Elastic parameters of paramagnetic iron-based alloys from first-principles calculations. Physical Review B, 85:  054107-1. My thinking was that while the absolute values of the constants were probably not accurate, the ratios between the components would be constant enough to at least give me a rough idea of the distribution. (I tried some of the other constants in this paper and the results were all pretty similar.)

I then calculated the distribution of elastic moduli parallel to the longitudinal direction of the wire thinking this might give me an idea of the differences in the distribution of pitches one might hear when a piano wire is struck. The results are shown below – on the left for actual elastic moduli and then on the right for how this might translate to a distribution of pitches. However, this second plot is only a schematic to illustrate my thinking – I have no idea how the elastic moduli variations would translate to pitch variations, the horizontal scale could be much wider, i.e. the flats and sharps could be much farther away from the center pitch and it may also not be a linear relationship. Also the choice of C is completely arbitrary – the actual pitch will depend on the diameter and tension on the wire.

Figure 2
The bad wire (in terms of breakage), which according to Keith’s ear has a clearer sound than the wire less prone to breaking, has a narrower distribution of elastic moduli. Of course, I may be completely off-base as a “fuller” sound may correspond to the broader distribution as well. Perhaps what Keith can hear is the fine balance between clarity and fullness. So if my large set of assumptions is correct then, while I may not be able to hear the difference, I can at least see the difference in the texture data.