Month: June 2021

Home Sweet Home

Dr. René de Kloe, Applications Specialist, EDAX

This last year has been different in many ways, both personally and at work. For me, it meant being in the office or working from home instead of being out and about and meeting customers and performing operator schools in person. This does not exactly mean that things are quieter, though! At home, I got confronted with lots of little maintenance things in and around my house that otherwise somehow manage to escape my attention. At work, lots of things vying for my attention have managed to land on my desk.

The upside is that with almost everything now being done through remote connections. I get to sit more at the microscope in the lab to work on customer samples, collect example datasets, perform system tests, and also practice collecting data on difficult samples so that I can support our customers better. To do that, I have the privilege of being able to choose which EBSD detector I want to mount, from the fast Velocity to the familiar Hikari to the sensitive Clarity Direct Electron System. But how do I decide what samples to use for such practice sessions?

A common garden snail (Cornu aspersum) and an empty shell used for the analysis.

Figure 1. A common garden snail (Cornu aspersum) and an empty shell used for the analysis.

In the past, I wrote about my habit of occasionally going “dumpster diving” to collect interesting materials (well, to be honest, I try to catch the things just before they land in the dumpster). That way, I have built up a nice collection of interesting alloys, rocks, and ceramics to keep me busy. But this time, I wanted to do something different, and an opportunity presented itself when I was working on a fun DIY project, a saddle stool for my daughter. On one of the days that I was shaping wood in my garden for the saddle-support, I noticed some garden snails moving about leisurely. These were the lucky chaps (Figure 1). While we occasionally feel the need to redecorate our walls to get a change of view, the snail’s home remains the same and follows him wherever he goes; sounds great! No need to do any decoration or maintenance, and always happy at home!

But all kidding aside, I have long been interested in the structure of these snail shells and have wanted to do microstructural analysis on one. So, when I found an empty shell nearby belonging to one of its cousins that had perished, I decided to try to do some Scanning Electron Microscope (SEM) imaging and collect Electron Backscatter Diffraction (EBSD) data to figure out how the shell was constructed. The fragility of the shell and especially the presence of organic material in between the carbonate crystals that make up the shell makes them challenging for EBSD, so I decided to mount my Clarity Detector and give it a very gentle try.

The outer layer that contains the shell’s color was already flaking off, so I had nice access to the shell’s outer surface without the need to clean or polish it. And with the Gatan PECS II Ion Mill that I have available, I prepared a cross-section of a small fragment. I was expecting a carbonate structure like you see in seashells and probably all made of calcite, which is the stable crystal form of CaCO3 at ambient temperatures. What I found was quite a bit more exotic and beautiful.

In the cross-section, the shell was made up of multiple layers (Figure 2). First, on the inside, a strong foundation made of diagonally placed crossed bars, then two layers of well-organized small grains, was topped by an organic layer containing the color markings.

A PECS II milled cross-section view of the shell with different layers. The dark skin on the top is the colored outer layer.

Figure 2. A PECS II milled cross-section view of the shell with different layers. The dark skin on the top is the colored outer layer.

At the edge of the PECS II prepared cross-section, a part of the outer shell surface remained standing, providing a plan view of the structure just below the surface looking from the inside-out. In the image (Figure 3), a network of separated flat areas can be recognized with a feather-like structure on the top, which is the colored outer surface of the shell. An EDS map collected at the edge suggests that the smooth areas are made up of Ca-rich grains, which you would expect from a carbonate structure. Still, the deeper “trenches” contain an organic material with a higher C and O content, explaining why the shell is so beam-sensitive.

A plan view SEM image of the structure directly below the colored surface together with EDS maps showing the C, O, and Ca distribution.

Figure 3. A plan view SEM image of the structure directly below the colored surface together with EDS maps showing the C (purple), O (green), and Ca (blue) distribution.

The EBSD data was collected from the outer surface, where I could peel off the colored organic layer. This left a clean but rough surface that allowed successful EBSD mapping without further polishing.

My first surprise here was the phase. All the patterns that I saw were not of calcite but aragonite (Figure 4). This form of calcium carbonate is stable at higher temperatures and forms nacre and pearls in shells in marine and freshwater environments. I was not expecting to see that in a land animal.

Figure 4. An aragonite EBSD pattern and orientation determination.

Figure 4. An aragonite EBSD pattern and orientation determination.

The second surprise was that the smooth areas that you can see in Figure 3 are not large single crystals but consist of a very fine-grained structure with an average grain size of only 700 nm (Figure 5). The organic bands are clearly visible by the absence of diffraction patterns – the irregular outline is caused by projection due to the surface topography.

Image Quality (IQ) and aragonite IPF maps of the outer surface of the shell. The uniform red color and (001) pole figure indicate a very strong preferred crystal orientation.

Figure 5. Image Quality (IQ) and aragonite IPF maps of the outer surface of the shell. The uniform red color and (001) pole figure indicate a very strong preferred crystal orientation.

After this surface map, I wanted to try something more challenging and see if I could get some information on the crossbar area underneath. At the edge of the fractured bit of the shell, I could see the transition between the two layers with the crossbars on the left, which were then covered by the fine-grained outer surface (Figure 6).

An IQ map of the fracture surface. The lower left area shows the crossbar structure, then a thin strip with the fine-grained structure, and at the top right some organic material remains.

Figure 6. An IQ map of the fracture surface. The lower left area shows the crossbar structure, then a thin strip with the fine-grained structure, and at the top right some organic material remains.

Because the fractured sample surface is very rough, EBSD patterns could not be collected everywhere. Nevertheless, a good indication of the microstructure could be obtained. The IPF map (Figure 7) shows the same color as the previous map, with all grains sharing the same crystal direction pointing out of the shell.

An IPF map showing the crystal direction perpendicular to the shell surface. All grains share the same color indicating that the [001] axes are aligned.

Figure 7. An IPF map showing the crystal direction perpendicular to the shell surface. All grains share the same color indicating that the [001] axes are aligned.

But looking at the in-plane directions showed a very different picture (Figure 8). Although the sample normal direction is close to [001] for all grains, the crystals in the crossbar structure are rotated by 90° and share a well-aligned [100] axis with the two main directions rotated by ~30° around it.

An IPF map along Axis 2 showing the in-plane crystal directions with corresponding color-coded pole figures.

Figure 8. An IPF map along Axis 2 showing the in-plane crystal directions with corresponding color-coded pole figures.

Detail of the IPF map of the crossbar area with superimposed crystal orientations.

Figure 9. Detail of the IPF map of the crossbar area with superimposed crystal orientations.

I often have a pretty good idea of what to expect regarding phases and microstructure in manufactured materials. Still, I am often surprised by the intricate structures in the smallest things in natural materials like these snail shells.

These maps indicate a fantastic level of biogenic crystallographic control in the snail shell formation. First, a well-organized interlocked fibrous layer with a fixed orientation relationship is then covered by a smooth layer of aragonite islands, bound together by an organic structure, and then topped by a flexible, colored protective layer. With such a house, no redecoration is necessary. Home sweet home indeed!

Disoriented

Dr. Stuart Wright, Senior Scientist, EDAX

Of all the papers I’ve written, my favorite title I’ve managed to sneak past the editors and reviewers is “Random thoughts on non-random misorientation distributions.” The paper is a write-up of a presentation I gave at a celebration of Professor David Dingley’s contributions to EBSD, which was held as a special version of the annual Royal Microscopy Society EBSD meeting at New Lanark in Scotland. It was a fun meeting as several of David’s former Ph.D. students shared some great stories and pictures of David, and the talks were a little less formal than usual, which led to some interesting discussions.

There are many terms used to describe the difference in crystallographic orientation between two crystal lattices: misorientation, disorientation, orientation difference, misorientation angle, minimum misorientation angle, grain boundary character, intercrystalline interface. One can get a bit “disoriented” trying to sort out all these different terms. Unfortunately, I am at fault for some of the confusion as I have tended to use the different terms loosely in my presentations and papers. But I am not the only one; I have seen some wandering in the definition of some of these terms as different researchers have followed up on the work of others. I will not pretend to be rigorous in this blog, but let me see if I can help sort through the different terms.

My first exposure to the idea of misorientation was from Bunge’s classic book Texture Analysis in Materials Science from 1969. I was first introduced to the book when I joined Professor Brent Adam’s Lab in 1985. We called it the “Red Bible,” as we had a very well-worn copy in the lab. We were even lucky enough to have Peter Morris with us at the time, who translated the book from German to English (a herculean task for a non-German speaker without modern tools like Google Translate). On page 44 of this book, you will find the following:

If two adjacent grains in a grain boundary have orientations g1 and g2, the orientation difference is thus given by:

g = g2 g1-1                                                                   (3.12)

This looks like a relatively simple expression, and we have generally calculated it using orientations described as matrices, and thus the result ∆g would also be a matrix. But the most common description of this orientation difference given in the literature would be an axis-angle pair. Any two crystals have at least one axis in common. A rotation about that axis will bring the two crystal lattices into coincidence.

Axis-angle description of misorientation.

Figure 1. Axis-angle description of misorientation.

While the equation above seems simple, we need to remember that, due to crystal symmetry, there are multiple symmetrically equivalent descriptions of the orientations g1 and g2. We can term the symmetry operators Li. These are the elements of the crystallographic point group symmetry for the crystals in question. For example, for a cubic crystal, there will be 24 symmetry elements. Since there are 24 symmetric equivalents for g1 and 24 for g2 that means there will be 576 symmetric equivalents for ∆g. In the expression below, the apostrophe denotes symmetrically equivalent.

g’12 = Lig2∙(Lig1)-1

As an example, here is a list for a random axis angle pair assuming cubic crystal symmetry: 12° @ 〈456〉. Note that the notation 〈uvw〉 denotes the family of crystal directions and [uvw] denotes a single crystal direction. Once again, for cubic symmetry, there are (in general) 24 [uvw] directions in the 〈uvw〉 family of directions (note in general there are 24 directions in the family, i.e. [123], [132], [-123], [-132], …. but this can be reduced for families where multiplicity plays a role, such as 〈00w〉 or 〈uuw〉…).

AngleAxisAngleAxis
12.00(4 5 6)124.26(139 132 170)
82.16(2 18 155)125.80(118 121 148)
83.62(20 4 157)131.85(44 43 45)
85.06(4 45 325)169.37(2 161 177)
95.94(33 3 262)170.34(235 6 265)
97.23(4 20 177)171.30(2 149 172)
98.51(62 7 617)171.80(10 8 167)
108.17(39 38 40)173.17(8 12 167)
114.78(137 173 177)174.54(12 10 167)
116.39(130 103 136)178.07(25 196 221)
117.99(137 177 181)179.03(188 26 207)
122.71(149 153 192)179.03(155 18 179)

So, this is a list of symmetrical misorientations given as axis-angle pairs. The minimum rotation angle in this set is the disorientation. But, you will also see the disorientation called the orientation distance (Bunge equation 2.123), rotation angle and misorientation angle (OIM), minimum misorientation angle, as well as simply the misorientation, orientation difference, grain boundary angle, . For a little comic relief at intense EBSD workshops, I have often said that I prefer the term misorientation because disorientation is what we tend to feel at the end of the day of lectures. I give Professor Marc De Graef credit for helping me finally get these terms straight. So, now I can retire that joke that probably never really translated very well into different languages anyway.

One more note on terminology. A grain boundary is a five-parameter entity: three for the misorientation and two to describe the orientation of the boundary plane.

5D Grain Boundary Character.

Figure 2. 5D Grain Boundary Character.

This five-dimensional entity is now often referred to as the Grain Boundary Character (Rohrer) but has also been termed the Intercrystalline Interface Structure (Adams). In the past and in OIM Analysis, the Grain Boundary Character Distribution or GBCD refers to the distribution of grain boundaries across three classifications, low-angle random boundaries, high-angle random boundaries, and “special” (generally CSL) boundaries. As a side note, Grain Boundary Character has been called a “full” or “complete” description of a grain boundary, but this is a bit of an overreach. There are still other parameters associated with a grain boundary that may be just as important as these five, for example, curvature, faceting, chemical composition.

It should be noted that we can calculate the misorientation between two crystals of different symmetry and get a nice, neat axis-angle pair.

Picture4

However, the concept of coincidence is not as clear as for two crystals of the same symmetry, as illustrated in the schematic shown in Figure 3. Nonetheless, this terminology (and its corresponding mathematical methods) can be helpful when analyzing the orientation relationships associated with phase transformations.

Misorientation between a hexagonal and cubic crystal.

Figure 3. Misorientation between a hexagonal and cubic crystal.

I hope this brief discussion has helped “orient” you in the right direction. I know I am now trying to be more careful in using these terms, which will probably result in a few changes in our user interface for a future version of OIM to reflect this.

References

Wright, SI (2006) Random thoughts on non-random misorientation distributions. Materials Science and Technology 22: 1287-1296.

Bunge, HJ (1969) Mathematische Methoden der Texturanalyse. Akademie-Verlag: Berlin.

Beladi H, Nuhfer NT, and Rohrer GS (2014) The five-parameter grain boundary character and energy distributions of a fully austenitic high-manganese steel using three dimensional data. Acta Materialia 70:281-289

Zhao J, Koontz JS, and Adams BL, 1988. Intercrystalline structure distribution in alloy 304 stainless steel. Metallurgical Transactions A, 19:1179-1185.