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.
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.
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!
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.
Call me old-fashioned, but when I want to relax I always try to go outdoors, away from computers and electronic gadgets. So when I go on vacation with my family we look for quiet places where we can go hiking and if possible we visit places with interesting rocks that contain fossils. Last summer I spent my summer vacation with my family in the Hunsrück in Germany. The hills close to where we stayed consisted of shales. These are strongly laminated rocks that have been formed by heating and compaction of finegrained sediments, mostly clay, that have been deposited under water in a marine environment. These rocks are perfect for the occurrence of fossils. When an organism dies and falls on such a bed of clay and is covered by a successive stack of mud layers, it can be beautifully preserved. The small grains and airtight seal of the mud can give a very good preservation such that the shape of the plant or animal can be found millions of years later as a highly detailed fossil. Perhaps the most famous occurrence of such fossil-bearing shale is the Burgess shale in British Columbia, Canada which is renowned for the preservation of soft tissue of long-extinct creatures. The Hunsrück region in Germany may not be that spectacular, but it is a lot closer to home for me and here also beautiful fossils have been found.
Figure 1. Crinoid or sea lily fossil found in the waste heap of the Marienstollen in Weiden, Germany.
So, when we would go hiking during our stay we just had to pack a hammer in our backpack to see if we would be lucky enough to find something spectacular of our own. What we found were fragments of a sea lily or crinoid embedded in the rock (Figures 1,3) and as is typical for fossils from the area, much of the fossilised remains had been replaced by shiny sulphide crystals (Figure 2). Locally it is said that the sulphides are pyrite. FeS2. So of course, once back home I could not resist putting a small fragment of our find in the SEM to confirm the mineral using EDS and EBSD. The cross section that had broken off the fossil showed smooth fracture surfaces which looked promising for analysis (Figure 4). EDS was easy and quickly showed that the sulphide grains were not iron sulphide, but instead copper bearing chalcopyrite. Getting EBSD results was a bit trickier because although EBSD bands were often visible, shadows cast by the irregular surface confuse the band detection (Figure 5).
Figure 4. Cross section of shale with smooth sulphide grains along the fracture surface.
Figure 5. EBSD patterns collected from the fracture surface. Indexing was done after manual band selection. Surface irregularities are emphasized by the projected shadows.
Now the trick is getting these patterns indexed and here I do like computers doing the work for me. Of course, you can manually indicate the bands and get the orientations of individual patterns, but that will not be very helpful for a map. The problem with a fracture surface is that the substrate has a variable tilt with respect to the EBSD detector. Parts of the sample might be blocking the path to the EBSD detector which complicates the EBSD background processing.
The EDAX EBSD software has many functions to help you out of such tight spots when analyzing challenging samples. For example, in addition to the standard background subtraction that is applied to routine EBSD mapping there is a library of background processing routines available. These routines can be helpful if your specimen is not a “typical” flat, well-polished EBSD sample. This library allows you to create your own recipe of image processing routines to optimize the band detection on patterns with deviating intensity gradients or incomplete patterns due to shadowing.
The standard background polishing uses an averaged EBSD pattern of more than ~25 grains such that the individual bands are blended out. This produces a fixed intensity gradient that we use to remove the background from all the patterns in the analysis area. When the actual intensity gradient shifts due to surface irregularities it is not enough to just use such a fixed average background. In that case you will need to add a dynamic background calculation method to smooth out the resulting intensity variations.
This is illustrated in the EBSD mapping of the fossil in Figure 6. The first EBSD mapping of the fossil using standard background subtraction only showed those parts of the grains that happened to be close to the optimal orientation for normal EBSD. When the surface was pointing in another direction, the pattern intensity had shifted too much for successful indexing. Reindexing the map with optimised background processing tripled the indexable area on the fracture surface.
Figure 6. Analysis of the fracture surface in the fossil. -1- PRIAS center image showing the smooth sulphide grains, -2- Superimposed EDS maps of O(green), Al(blue), S(magenta), and Fe(orange) -3- EBSD IPF on IQ maps with standard background processing, -4- original IPF map, -5- EBSD IPF on IQ maps with optimized background processing, -6- IPF map with optimized background.
In addition to the pattern enhancements also the band detection itself can be tuned to look at specific areas of the patterns. Surface shadowing mainly obscures the bottom part of the pattern, so when you shift the focus of the band detection to the upper half of the pattern you can maximize the number of detected bands and minimize the disturbing effects of the edges of the shadowed area. It is unavoidable to pick up a false band or two when you have a shadow, but when there are still 7-9 correct bands detected as well, indexing is not a problem.
Figure 7. Band detection on shadowed EBSD pattern. Band detection in the Hough transform is focused at the upper half of the pattern to allow detection of sufficient number of bands for correct indexing.
In the images below are a few suggestions of background processing recipes that can be useful for a variety of applications.
Of course, you can also create your own recipe of image processing options such that perhaps you will be able to extract some previously unrecognized details from your materials.
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
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.
If my memory is functioning correctly, I believe Val Randle coined the term “meso-texture” to describe the texture associated with the misorientations at grain boundaries.
I confess that, whenever I hear the term, I chuckle. This is because of a humorous memory tied to the first paper I was involved with. I was an undergraduate at Brigham Young University (BYU) at the time. The lead author, Brent Adams, later became my PhD advisor. The ideas presented in this work became the motivation behind my PhD work to automate EBSD.
B. L. Adams, P. R. Morris, T. T. Wang, K. S. Willden and S. I. Wright (1987). “Description of orientation coherence in polycrystalline materials.” Acta Metallurgica 35: 2935-2946.
The paper describes some impressive work on the mathematical side by Brent and Peter and painstaking work by Tong-Tsung Wang who did hundreds of manual orientation measurements from individual grains in several planar sections of aluminum tubing using selected area diffraction. My role was digitize the microstructures in such a way that the two-point orientation correlations could be computed. The following is an example of one section plane from this work.
Digitized microstructure of one half of one section of a total of 10 sections used in the calculation of the orientation coherence function for aluminum tubing. Each grain number represents a individual grain orientation measurement.
The experimental work was a major undertaking. Thus, Brent Adams was so interested to hear David Dingley’s talk on EBSD at ICOTOM 8 in Santa Fe in 1987 shortly after this paper was published. Brent envisioned a fully automated system to link crystallographic orientation with microstructure via EBSD.
One of the interesting findings of this work was the discovery of a Meso-Structure:
“The strong implication of Table 2 is that there exists a new scale of microstructure in the material (and presumably in other polycrystalline materials) which has not previously been characterized, or even observed except in a qualitative manner. It seems appropriate to identify this new scale of microstructure as mesostructured since it clearly pertains to clusters or aggregates of grains or crystallites”
After this paper was published Brent received a letter from Sir Charles Frank. Sir Charles expressed his interest and appreciation for the ideas presented in the work. However, he objected to the term Meso-Structure. One of his objections was that “Meso” has its roots in Greek, but “Structure” is Latin. He didn’t like that we were mixing words of different etymological origins. I have to think this criticism was given “tongue in cheek” as the term microstructure with which Sir Charles was well familiar also mixes Greek and Latin. Thus, whenever I hear the term mesotexture used to describe grain boundary or misorientation texture I have to chuckle given it’s mix of the Greek “meso” and Latin “texture”.
I’m not sure what the best term is to describe the preferred misorientation of grain boundaries. The community uses the terms misorientation, disorientation, orientation difference and others sometimes as synonyms and at other times with differences in meaning. As all aimless wanderin’s tend to leave crisscrossing tracks, I note that my first exposure to the use of Rodrigues Vectors, which lend themselves well to describing misorientation, was by Sir Charles Frank at ICOTOM 8 in Santa Fe.
I hope my aimless wanderin’s through odd terminology and anecdotal history doesn’t leave you too disoriented 😊
(Next in this series are some ruminations on the term “3D texture”).
On a recent transatlantic flight I passed the time watching one of my favorite movies: Oh Brother! There are a lot of great quotable lines in this movie. One that seems appropriate for this blog entry is from the lead character: Ulysses Everett McGill
“Say, uh, any a you boys smithies? Or, if not smithies per se, were you otherwise trained in the metallurgic arts before straitened circumstances forced you into a life of aimless wanderin’?”
Source: Rudy Wenk
While, in theory, I am “trained in the metallurgic arts”, my travels sometimes feel like “aimless wanderin’” and sometimes my mind follows suit – especially on long flights. In this series of entries for the EDAX Blog, I would like to take you on some “wanderin’s” through some of the terminology, history and personalities surrounding EBSD. Let’s begin with “texture”.
My global wanderings aren’t always aimless and I often learn some interesting things. At some recent conferences, I saw several interesting textures measured using neutron diffraction; for example, works by Heinz-Günther Brokmeier, Sven Vogel, Raul Bolmaro and others. Generally, these textures were measured over large volumes, such as from a section of a pipe, or an entire automobile component. It struck me that the use of the word “texture” has evolved to mean different things to different people.
My source of most early historical texture knowledge is Rudy Wenk. Rudy informs me that he believes the first use of the word was in an 1833 textbook by a Belgian geologist – d’Halloy to describe a directional microstructure. This seems a little ironic now as geologists tend to use the term “fabric” to describe what a metallurgist would refer to as “texture” but the evolution of these terms has also seen some wanderin’ as described in section 6 in Chapter 1 of Rudy’s 1985 book, Preferred Orientation in Deformed Metal and Rocks: An introduction to Modern Texture Analysis. I had the great fortune of learning from Rudy during a short-course on texture held at BYU when I was an undergrad as well as during his visits to Los Alamos National Lab when I was a Post-Doc. I am excited for a symposium in his honor at this year’s edition of ICOTOM in St George, Utah.
I was first introduced to the term texture in 1985 by Peter Morris, who was a visiting researcher at BYU working with Professor Brent Adams. At the time, I was employed by a Professor in the Physics Department, Dorian Hatch, to track down papers in the library (long before libraries went digital and on-line search and retrieval tools were available). I was a junior Mechanical Engineering student but had become a bit disenchanted with my coursework. I expressed to Dorian my frustration and that I was considering switching my major (Dorian was one of my leaders in our local church congregation when I was a teenager and was very helpful in offering good advice to a young university student). He recommended I go and visit with a new Professor in Mechanical Engineering named Brent Adams. When I knocked on Brent’s office door he was busy and recommended I speak with Peter. I still remember being completely lost as Peter tried to talk to me about which kind of mathematical functions would be appropriate to describe the r-dependence of the Two-Point Orientation Coherence function. Luckily, Brent popped in before I left Peter’s office completely befuddled; he brought things down a little closer to my level (if you can imagine Brent doing such a thing) and introduced me to texture. Brent was looking for someone with programming skills which I happened to have and so I joined his research team. (I got to know Peter better as part of Brent’s team particularly on a long drive from Provo, Utah to Santa Fe, New Mexico for ICOTOM 8. At one point in the drive I thought I would try out my German on Peter but was very surprised to learn that he didn’t speak German – remarkable, because if you dig out a copy of Bunge’s Texture Analysis in Materials Science you will note it was translated from German to English by Peter).
My personal introduction to texture was through the ODF or Orientation Distribution Function (another odd description as in the formal statistical sense it is actually a density function as opposed to a distribution function) per Bunge (“Zur Darstellung allgemeiner Texturen”, Zeitschrift der Metallkunde, 56, 872-874 (1965)):
“Die Orientierungsvertailung oder Textur eines polykristallinen Materials wird charakterisiert durch den Volumenateil derjenigen Kristalle, deren Orientierung zwischeng g and g + dg liegt.”
My best attempt at a translation is “the orientation distribution or texture of polycrystalline materials is characterized through the volume fraction of the constituent crystals, with orientations lying between g and dg.”
Bunge further explains in Chapter 4 of Rudy’s book entitled Preferred Orientation in Deformed Metal and Rocks: An Introduction to Modern Texture Analysis (1985):
“The texture is thus, per definition, the orientation distribution of all crystals present in the sample irrespective of their arrangement in the sample. Since the texture is defined as a statistical quantity, the sample must at least be big enough, compared to the grain size, to allow a statistically significant description. This, in turn, depends on the degree of relevance required. If we have a sample much bigger that what is required by statistical relevance, then it may be divided into volume elements V big enough to allow the statistical description of the texture. The texture can then be measured in each of these volumes elements separately. If the textures of all volume elements of the big sample are statistically identical, then the big sample is said to have a homogeneous texture. If we speak about he the texture of a material without further specification, the homogeneity is assumed. In may important cases, however, the textures of the volume elements are not the same. Such textures are called inhomogeneous, and the definition of the term “texture” become more complex (e.g., Bung, 1982c).”
In the world of EBSD, we measure textures on surfaces. We hope this is representative of the volume but oft times we know it is not. For instance, consider the following (111) pole figure measured from the surface of an aluminum sheet. It has some of the characteristics we expect for a rolled fcc material but does not exhibit the symmetry we would expect for the texture through the volume of the sheet.
(111) pole figures from two samples of rolled aluminum. Left: recent EBSD measurements on the surface of a sample. Right: X-Ray measurements from the cross-section (this pen plot is from my M.S. Thesis which formed the basis of the paper S. I. Wright and B. L. Adams (1990) An Evaluation of the Single Orientation Method for Texture Determination in Materials of Moderate Texture Strength”, Textures and Microstructures 12, 65-76.
Could the lack of symmetry be due to a lack of statistics – i.e. the volume element investigated is too small? I don’t believe so as the average grain size for this material is approximately 25 microns (always a bit tricky to estimate in deformed materials with elongated grains and with a well-defined subgrain structure) and the step size was 4µm. The scan area was 2.1 x 1.6 mm (~250,000 orientation measurements) and thus, approximately 6900 grains were sampled. In addition, the pole figure is fairly symmetric horizontally. Rather, I assume the lack of vertical symmetry in the pole figure comes from a texture gradient from the surface to the center of the sheet. So rather than calling this a texture in the classic volumetric sense it would be more correct to add “surface” as a qualifier – i.e. a surface texture.
One concern I have, is the use of the term micro-texture. I understand the point, it is the texture measured at the “micro-scale” – in the language of the quote from Bunge, a volume element at the micro-scale. But, if the area contains just a few grains, is it really a “texture”? That isn’t to say we can’t learn a lot from such measurements but, in my mind, the term texture has a statistical component to it in terms of the number of grain orientations sampled. For example, consider the following texture measurements from the same sample. Each measurement contains approximately 250,000 EBSD measurements of orientation but the step sizes are 4µm, 400nm, 40nm and 4nm. Clearly, as the sampled area becomes smaller and smaller, the measured texture becomes less and less representative of the sample as a whole. Actually, it is remarkable that the fcc rolling texture is recognizable in all but the 4nm step size. At the smallest step size, the “texture” contains just 3 grains and thus the oscillations around the major peaks arising from the spherical harmonics used to calculate the texture are relatively prominent.
(111) pole figures and orientation maps from the surface of rolled aluminum sheet from EBSD measurements at step sizes of 4µm, 400nm, 40nm and 4nm each with just over 250,000 orientation measurements.
My concern is not enough to protest the use of the word micro-texture as I think most who use the term understand the implications, but as a community we need to be aware of sampling and statistical reliability as we draw conclusions from our EBSD measurements so that our scientific wanderin’s don’t become aimless but, to quote another classic movie, “stay on target”.
(Stay tuned for some thoughts on the term “meso-texture” 😊)
