Recently, we held a webinar on Grain Analysis in OIM Analysis™. After the webinar, many users mentioned that the basic operation overview was very helpful. Since there was a very enthusiastic response, I want to take this opportunity to share these fundamental tips and tricks with the greater electron backscatter diffraction (EBSD) community.
Perhaps the most popular EBSD application is grain analysis, as it’s fundamental to characterizing many materials. Because the results of grain analysis are sometimes consistent or inconsistent with other tests, it’s great to start with a basic understanding of a grain with respect to EBSD and how grain analysis works.
The definition of a grain in OIM Analysis differs from the strict academic definition, which refers to the collection of pixels within a certain orientation range. This orientation range, namely grain tolerance angle, can be changed in OIM Analysis, which is generally set to 5° by default. You can also vary the number of pixels in a grain (the default is 2). These parameters affect the result of grain size, so we should pay attention to them in the analysis. The prerequisite of grain analysis is that the data is statistically valuable. Sometimes this requires a lot of tests to achieve the goal, repetitive studies to diminish errors, or the data should be filtered or processed before the analysis (per relevant standards, accordingly).
Figure 1. A typical grain map.
A standard display for grain size analysis is the Grain Size (diameter) chart. First, the grain is fit to a circle, and then the software calculates the diameter. The data distribution range and average grain size are on the chart’s right side. The most frequent question users ask is, “What is the formula to calculate the average grain size?”. In fact, two results of the average grain size, which are calculated by two different methods, are shown. The ‘number’ method calculates the average area of each grain first (the sum area is divided by grain number values first) before it determines the diameter. In contrast, it considers different weights due to different areas for the ‘area’ method. Since large grains have larger weight percentages, it first calculates the average grain area using different weight percentages, then calculates the average grain size.
In addition to the average grain size, OIM Analysis offers a variety of charts and plots to characterize grain shape. The most popular one is the grain shape aspect ratio, an essential parameter to display the columnar grain property (grains are fit as an ellipse). In addition to the shape aspect ratio, the Grain Shape Orientation in OIM Analysis shows the angle between the long axis and the horizontal direction, which is suitable for grains with a specific growth direction.
OIM Analysis offers numerous functions. Concerning grain analysis, there are six different charts for grain size and eight for grain shapes. Some charts are not common, but they have corresponding application scenarios. If you do not know the meaning of those charts, you can query the OIM Analysis Help file to get relative information.
Grain analysis is a very common function of EBSD applications. As a webinar speaker, I enjoyed digging up some less familiar details so users could gain a deeper understanding of software operations. I look forward to continually introducing webinar topics to meet the EBSD community’s needs and make greater progress in the new year.
Although red, green, and blue are placed at a high symmetry axis, the remaining colors are not uniformly distributed
Saturated rainbow palettes are not perceptually uniform, so the same orientation gradient will have different apparent intensities when centered around different orientations
Groups with two or four high symmetry directions do not have a natural mapping to three principal colors
Choosing red and green as principal colors result in poor contrast for individuals with red-green color vision deficiency (CVD)
OIM Analysis™ v9 implements four new Inverse Pole Figure (IPF) color palettes to address these issues, as shown in Figure 1. For fundamental sectors with three principal directions, CVD colors replace green with yellow for the second principal color. For fundamental sectors with four principal directions, red, yellow, green, and blue are used for traditional colors, and red, yellow, cyan, and blue are used for CVD colors. Notice that the new legends distribute colors smoothly while the old ones have large patches of red, green, and blue extending from the corners and sharp bands of yellow, cyan, and magenta.
Figure 1. The m3m (top) and m3 (bottom) IPF legend is shown from left to right for OIM Analysis v8 colors, new saturated colors, perceptually uniform colors, CVD saturated colors, and perceptually uniform CVD colors.
Figure 2. A nickel dataset is IPF colored with saturated (left) and perceptually uniform (right) color maps using traditional (top) and CVD (middle) colors. Notice that some significant orientation gradients in the KAM map (bottom left) are visible with perceptually uniform colors but may be invisible if the orientation falls in a low contrast region of the saturated color map. OIM Analysis v8 coloring is shown in the bottom right.
Figure 3. A partially recrystallized steel dataset is IPF colored with saturated (left) and perceptually uniform (right) color maps using traditional (top) and CVD (middle) colors. Notice that orientation gradients are over-emphasized in darker regions of the saturated color maps (blue and purple) and under-emphasized in brighter regions (green, yellow, and cyan).
Perceptually uniform color maps are designed so that a constant size step in the data being colored results in an apparent color change of constant magnitude regardless of the starting value. The uniformity of a color map can be visualized by imposing a ripple onto a ramp, as shown in Figure 3 and described by Kovesi . The ripple disappears in brighter regions of traditional saturated color maps but has a uniform relative intensity in perceptually uniform maps, as shown in Figure 4. The new perceptually uniform IPF colors in OIM Analysis v9 extend perceptually uniform cyclic color maps to a hemisphere by adding a white center point.
Figure 4. A perceptually uniform ramp is modified by a sine wave to create a test signal (green). The test signal is colored with a perceptually uniform black to white color map with maximum sine wave amplitude at the top of the image and minimum amplitude at the bottom. Note that the relative intensity of the ripple is the same at every gray level near the top edge and the ramp appears extremely smooth near the bottom edge. Figure adapted from Kovesi .
Figure 5. Traditional saturated color maps (top) are shown for heat (left) and rainbow (right) colors. Notice that the ripples are nearly invisible near red on both maps, yellow on the heat map, and green on the rainbow map. Perceptually uniform equivalents (bottom) sacrifice some color saturation/vividness to achieve a uniform sensitivity response across the entire map. Legends from Kovesi .
Deuteranomaly (red-green CVD) is the most common form of CVD and is simulated in Figure 6 to illustrate how much ambiguity is introduced in traditional colors. CVD impacts roughly 1 in 12 men and 1 in 200 women, so CVD colors should be preferred for papers and presentations.
Figure 6. Deuteranomaly is simulated with increasing severity from left to right (normal, 30%, 70%, 100%/Deuteranopia) for the traditional (top) and CVD (bottom) saturated palettes. Notice that in the far-right column, the traditional map has different directions with the same color, while the CVD map is significantly less ambiguous.
Enhanced IPF saturated color palettes maintain a similar look and feel while more uniformly distributing the available gamut. Perceptually uniform IPF color palettes sacrifice the full use of the RGB gamut to render crystal directions with increased precision, and CVD colors avoid red-green ambiguity. Together these new palettes enable visualization and accurate interpretation of orientation data for the widest range of audiences.
Kovesi, P. (2015). Good colour maps: How to design them. arXiv preprint arXiv:1509.03700.
Nolze, G., & Hielscher, R. (2016). Orientations–perfectly colored. Journal of Applied Crystallography, 49(5), 1786-1802.
Dictionary indexing compares experimental electron backscatter diffraction (EBSD) patterns against a dictionary of simulated patterns for each orientation on a uniform grid in orientation space [1,2]. Synthetic patterns are generated by rotating the Kikuchi sphere by the crystal orientation and projecting onto a plane using the experimental geometry. Comparison against a physics-based forward model gives excellent precision and noise tolerance at the cost of significant computational overhead. Spherical harmonic-based indexing uses the same Kikuchi sphere or ‘master pattern,’ but back projects experimental patterns onto the sphere instead. The orientation is indexed using the maximum spherical cross-correlation between the back-projected pattern and the Kikuchi sphere [3,4]. Mathematically, dictionary and spherical indexing are extremely similar, but the spherical approach is more numerically efficient since it can leverage fast Fourier transforms for the computations. In practice, spherical indexing provides similar precision  and noise tolerance to dictionary indexing but at much faster speeds.
A GPU implementation of spherical harmonic-based EBSD indexing implemented in OIM Analysis™ as part of the OIM Matrix module provides excellent indexing quality at hundreds or thousands of patterns per second. Here, we applied it to a range of scans to demonstrate the indexing quality and user parameters.
Spherical harmonic indexing has two parameters: bandwidth and grid size. Bandwidth is how far in frequency space to compute harmonics (analogous to a low pass filter on the EBSD pattern). Grid size is the correlation resolution with an Euler angle cube of (grid size)3 used for correlation (i.e., 0 – 360 for phi1, Phi, and phi2). In general, computation time scales with the number of Euler angle grid points, and a reasonable bandwidth is one less than half the grid size. For example, the following are some reasonable pairs of values:
Once the best Euler grid point (maximum cross-correlation) is selected, subpixel resolution can be achieved through a refinement step.
This dataset is a scan of the same region at different camera gains to intentionally produce corresponding sets of low and high-quality patterns.
Figure 1. Shows a) the result of indexing high-quality patterns, b) spherical harmonic indexing at a bandwidth of 63 and Euler grid of 1283 without refinement, and c) at a bandwidth of 63 with refinement.
Figure 1 shows a) the result of indexing high-quality patterns, b) spherical harmonic indexing at a bandwidth of 63 and Euler grid of 1283 without refinement, and c) at a bandwidth of 63 with refinement. Note that since grid point spacing is ~2.8° (360° / 128), the unrefined result has a stepped appearance due to the discrete orientation possibilities. After refinement, any orientation is possible, providing smooth results.
Figure 2. KAM maps are shown for the same region at a) 0°, b) 1°, and c) 2°.
In Figure 2, KAM maps are shown for the same region at a) 0°, b) 1°, and c) 2°. Notice that without refinement, there is no misorientation within a patch and a sharp spike between them. Even though both the Hough and refined spherical appear smooth, the slight orientation noise in the Hough indexing is visible using KAM.
Figure 3. With low-quality patterns, Hough indexing a) starts to fail, but b) spherical indexing still provides robust solutions and c) accurately captures continuous orientation gradients after refinement.
With low-quality patterns, Hough indexing a) starts to fail, but b) spherical indexing still provides robust solutions and c) accurately captures continuous orientation gradients after refinement (Figure 3).
Figure 4. a) bandwidths of 63, b) 95, and c) 127 are compared before (a – c) and after (d – f) refinement.
For very low-quality patterns, higher bandwidths may be required for better indexing results. In Figure 4, a) bandwidths of 63, b) 95, and c) 127 are compared before (a – c) and after (d – f) refinement. Note that the discrete steps in orientations before refinement become smaller with increased Euler angle grid resolution, but they refine to similar orientations. For all three bandwidths, the grid size is 2 * (bandwidth + 1).
Figure 5. 4. a) Raw pattern and b) NPAR pattern using Hough indexing and c) raw pattern and d) NPAR pattern using spherical indexing with a bandwidth of 127.
With spherical indexing integrated into OIM Analysis, existing image processing algorithms can be used for especially difficult patterns. At extremely high noise levels, Hough indexing cannot index any points, and the spherical indexing begins to fail for some points. NPAR trades spatial resolution for pattern quality by averaging each pattern with its neighbors. The improved patterns can be indexed reliably by both methods but Hough indexing struggles with the resulting overlap patterns near grain boundaries (Figure 5).
Hot Rolled Mg
Figure 6. Hough indexing struggles to index when pattern quality is reduced by a) high deformation, but b) spherical indexing is robust against significantly degraded pattern quality. Note that the d) spherical indexing confidence index strongly correlates with c) image quality but is high even in some regions with extremely low IQ.
Hough indexing struggles to index when pattern quality is reduced by a) high deformation, but b) spherical indexing is robust against significantly degraded pattern quality. Note that the d) spherical indexing confidence index strongly correlates with c) image quality but is high even in some regions with extremely low IQ (Figure 6).
Figure 7. Excellent results are possible even with a single pattern center used for the entire dataset. Vignetting is visible in a) an IPF+IQ map of Hough indexing with a fixed pattern center. The field is flat over the entire area for b) an IPF+CI map of spherical indexing with a fixed pattern center.
Spherical indexing can use a unique pattern center for each point at no extra cost for large fields of view. Excellent results are possible even with a single pattern center used for the entire dataset, as shown in Figure 7.
Deformed Duplex Steel
Figure 8. Phase discrimination depends on the similarity of the phases with a two-phase steel. In addition to the quality in orientation results with d – f) spherical indexing vs. a – c) Hough indexing, b – c & e – f) phase discrimination is improved with spherical BCC and FCC iron well separable.
Spherical indexing can be applied to multiple phases in the same way as any other indexing technique. Phase discrimination depends on the similarity of the phases with a two-phase steel shown in Figure 8. In addition to the quality in orientation results with d – f) spherical indexing vs. a – c) Hough indexing, b – c & e – f) phase discrimination is improved with spherical BCC and FCC iron well separable. Real space refinement may be required for particularly difficult cases in addition to the spherical harmonic refinement shown.
Figure 9. a) spherical CI + IPF shows similar trends as b) Hough IQ + IPF.
Again, spherical indexing’s confidence index correlates well with pattern quality. In Figure 9, a) spherical CI + IPF shows similar trends as b) Hough IQ + IPF.
Callahan, P. G., & De Graef, M. (2013). Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations. Microscopy and Microanalysis, 19(5), 1255-1265.
Callahan, P. G., & De Graef, M. (2013). Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations. Microscopy and Microanalysis, 19(5), 1255-1265.
Lenthe, W. C., Singh, S., & De Graef, M. (2019). A spherical harmonic transform approach to the indexing of electron backscattered diffraction patterns. Ultramicroscopy, 207, 112841.
Hielscher, R., Bartel, F., & Britton, T. B. (2019). Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross-correlation on the sphere. Ultramicroscopy, 207, 112836.
Sparks, G., Shade, P. A., Uchic, M. D., Niezgoda, S. R., Mills, M. J., & Obstalecki, M. (2021). High-precision orientation mapping from spherical harmonic transform indexing of electron backscatter diffraction patterns. Ultramicroscopy, 222, 113187.
Dr. Chang Lu, Application Specialist, Gatan & EDAX
In early 2022, Gatan and EDAX completed the integration, and our new division was named Electron Microscope Technology (EMT). As an EMT application scientist on the China applications team, I am responsible for almost all the Gatan and EDAX products for Northern China, on both Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM) platforms. Therefore, I work with diversified products and diversified user groups that focus on different subject matters. In the first half of this year, I found that the data analysis software from EMT Gatan’s DigitalMicrograph® (DM) and EDAX’s OIM Analysis™ are not completely isolated, but in many cases, they can cooperate with each other to help our customers.
For instance, DM can do a series of electron microscopy-related data processing. For some energy dispersive spectroscopy (EDS) mapping data from the minor content, there are various methods to achieve smoothing and enhance the contrast. While in the MSA panel, the principal component analysis (PCA) function can be helpful in terms of high-resolution EDS mapping. However, in today’s EDAX blog, I will talk a little bit more about one feature in OIM Analysis that could potentially benefit a lot of Gatan camera users.
In northern China, there are a group of Gatan users who are focused on nanoscale phases and grains in the TEM. In most scenarios, they heavily employ electron diffraction or bright field imaging to make judgments. However, it is really difficult to determine the unknown (unidentified but has a known x-ray diffraction (XRD) pattern and chemical composition, so there is a potential for it) phase by simply relying on the minor changes of grayscale bright field images. You may say diffraction could help. Yes, a clean, beautiful diffractogram of a particular crystal direction can be helpful. But, no, you need to find the zone axis carefully. If this unknown phase has a crystal structure of low symmetry, most of the time, the effort will be in vain. Generally speaking, the Difpack tool in the DM software could help in determining d-spacing and angles, however, it is not intuitive enough to know the sample at first sight.
The solution is pattern simulation with OIM Matrix™. At first, I noticed this feature because it helped an EDAX user who was studying strains. It can easily export a theoretical Kikuchi pattern for a specific sample orientation with zero stress. Then one day, I had a sudden thought during my morning shower. Maybe I can change the acceleration voltage to 200 kV (typical for TEM), and the sample tilt angle to 0° (make it flat). After entering a specific orientation, we can get a Kikuchi pattern under TEM conditions! For example, take the simulated pattern from NdCeB. With Kinematic Color Overlay, we can also find out what crystal plane corresponds to a specific Kikuchi line. Now, when we start changing the zone axis in an unidentified sample, we can first simulate several orientations and compare them with what we see under TEM. In this way, the process of finding the Kikuchi pole turns out to be very convenient.
Figure 1. A simulated pattern from NdCeB using OIM Matrix.
Now, when some Gatan users bring in some “weird” unidentified samples and say they want to find various zone axis for doing diffractions. I don’t worry about it. I think from a problem-solving point of view, the powerful software from both Gatan and EDAX, like the integration of two companies, can also be combined to solve complex and difficult problems for our customers in the future.
It has been an interesting experience to build our OIM Matrix™ software package. As you may know, OIM Matrix is partially a front-end user interface to the EMsoft package developed by Professor Marc De Graef’s group at Carnegie Mellon University to make it convenient to use within the framework of OIM Analysis™. I have learned a lot in the process and am grateful for Marc’s patience with my many questions. Will Lenthe recently joined the EBSD group at EDAX. Will worked as a Post-Doc in Marc’s group, and his additional insights have been invaluable as we are striving to build the second generation of OIM Matrix. It will be easier to use, more robust, and provide some significant speed gains.
While our initial focus for OIM Matrix was on helping users improve the indexing of EBSD patterns from difficult-to-index materials, I’ve been surprised by how useful it has been for testing our software. It has also helped us in developing some of our new features. Having well-simulated patterns for known orientations and EBSD/SEM geometries is very helpful.
I used OIM Matrix for a study on feldspars. According to Wikipedia:
“Feldspars are a group of rock-forming aluminum tectosilicate minerals containing sodium, calcium, potassium, or barium. The most common members of the feldspar group are the plagioclase (sodium-calcium) feldspars and the alkali (potassium-sodium) feldspars. Feldspars make up about 60% of the Earth’s crust and 41% of the Earth’s continental crust by weight.”
Given that feldspars are relatively common, we are frequently asked to help index them. They are difficult, as a poster at the 2019 Quantitative Microanalysis (QMA) conference detailed . I thought it might be interesting to see what we could learn about the limits of EBSD in characterizing these materials. I won’t give you all that we learned in that little study, but what I thought was an interesting snapshot. Figure 1 shows a phase diagram for the feldspar group of minerals.
Figure 1. Phase diagram for the feldspar group.
To start, I looked in the American Mineralogist Crystal Structure Database (AMCSD) for all the relevant entries I could find. There are a lot of variants. Here is a table:
Table 1. Number of entries in AMCSD for each feldspar.
I enjoy seeing pattern simulation results, but producing 149 master patterns  would take more patience than I have (each master pattern calculation can take several hours for these low-symmetry materials). So, I selected one entry for each mineral type. I tried to find one that seemed most representative of all the other entries in the set. After calculating the eight master patterns, I simulated one individual pattern at the same orientation for each mineral, as shown in Figure 2. Note that they are all similar, with the most deviation coming from the anorthite and sanidine end members of the series.
Figure 2. Patterns were simulated at Euler angles of (30°, 30°, 30°) for each feldspar.
To quantify the differences, I calculated the normalized dot-products  for all pattern pairs to get the following table. A value of “1” indicates the patterns are identical. As expected by the initial observation, the biggest difference is the sanidine to albite pair of patterns.
Table 2. Normalized dot products.
Of course, the next step would be to see how this holds up to experimental patterns and dictionary indexing . I hope to eventually do this with samples Professor Rudy Wenk of Stanford University kindly gave me. Rudy has been one of the major contributors to the entries in the AMCSD for feldspars.
There was one more virtual experiment I thought would be interesting. I wanted to ascertain how much the chemical species in the feldspar series influenced the patterns. To do this, I created an average structure instead of using the lattice parameters for each feldspar. I then populated these structures with atoms to maintain the chemical composition ratios specified for each series. A master pattern for each ideal structure was calculated. Three hundred forty patterns were simulated uniformly, covering orientation space with a spacing of approximately 30° between orientations. The average normalized dot products were calculated for each pattern against the albite pattern at the same orientation. Figure 3 shows the results.
Figure 3. The normalized dot product of simulated patterns for idealized structures against the albite simulated patterns.
Clearly, the dot products are all very near 1, indicating that the differences in the simulated patterns due to chemical composition are small for these chemical species. This suggests that coupling EBSD with EDS is critical when trying to differentiate the different feldspar minerals. While this small study has not changed the world of feldspar indexing, it has, at least, been a stimulating study of simulating for me.
 B Schneider, and J Fournelle (2019) “Using Quantitative and Qualitative Analysis to Confirm Phase Identities for Large Area EBSD Mapping of Geological Thin Sections” Poster at Microanalysis Society Topical Conference: Quantitative Microanalysis, University of Minnesota, Minneapolis MN, June 2019.
 PG Callahan, and M De Graef (2013) “Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations” Microscopy and Microanalysis, 19, 1255-1265.
 S Singh, and M De Graef (2016) “Orientation sampling for dictionary-based diffraction pattern indexing methods” Modelling and Simulation in Materials Science and Engineering, 24, 085013.
 K Marquardt, M De Graef, S Singh, H Marquardt, A Rosenthal, and S Koizuimi (2019) “Quantitative electron backscatter diffraction (EBSD) data analyses using the dictionary indexing (DI) approach: Overcoming indexing difficulties on geological materials” American Mineralogist: Journal of Earth and Planetary Materials, 102, 1843-1855.
As EBSD Product Manager, one of the things I have missed the most in the last 18 months during the COVID pandemic is visiting customers. Generally, in a year, I will attend a few meetings. Some are reoccurring: M&M for microscopy topics, TMS for materials science, and an annual EBSD meeting (either the RMS or MAS version, depending on the year) to keep up with the latest and greatest in these fields. Additionally, I will attend a new show to learn about potential markets and applications. It’s always enjoyable to meet both users and prospects to learn more about their applications and how EDAX tools can help their characterization needs.
In place of these shows, I’ve been turning towards social media to keep track of trends for EBSD. Twitter is one tool I use, where there is a strong scientific group that shares their thoughts on a range of subjects and offers support to each other in this networked community. Recently, my Twitter feed showed a beautiful EBSD map on the cover of Science. Professor Andrew Minor’s group out of UC Berkeley had used EDAX EBSD to analyze twinning in cryoforged titanium. I feel connected to this work, as I’ve looked at twinning in titanium on other samples (Bringing OIM Analysis Closer to Home blog). Seeing different posts about various applications helps me understand where EBSD is used is very exciting and rewarding.
Figure 1. September 17, 2021 issue of Science magazine featuring an EBSD orientation map of cryoforged titanium.
LinkedIn is another social media tool I use. One of my favorite things about this platform is seeing how the careers of different people I know have developed over the years. I turn 50 in a couple of weeks, and I’ve been involved in EBSD for over half of these years. With that experience, I’ve seen the generational development of scientists and engineers in my field. The post-docs who first adopted EBSD when I started are now department chairs and running their own research groups. The students who came to a training course now advise the new users at their companies on EBSD. Recent students are graduating and now asking about EBSD for their new positions. It’s easy to get a sense of how the EBSD knowledge I’ve shared with people has percolated out into the greater world.
While I expect to see some EBSD on Twitter and LinkedIn, this year, I also had a pleasant surprise finding some wonderful EBSD in Gizmodo (https://gizmodo.com/these-microscopic-maps-of-3d-printed-metals-look-like-a-1846669930). I’ve had a strong interest in additive manufacturing since visiting NASA 15 years ago. Seeing this technology develop and how EBSD can help understand the microstructures produced is very satisfying to me. I reached out to Jake Benzing, who was the driver behind this post. This led to his group at NIST being featured in our latest EDAX Insight newsletter. It also helped me connect with a user and be better positioned to get feedback on using our products to drive development and improvement.
Figure 2. Ti-6Al-4V created by a form of AM called electron-beam melting powder-bed fusion. This map of grain orientations reveals an anisotropic microstructure, with respect to the build direction (Z). In this case, the internal porosity was sealed by a standard hot isostatic pressing treatment.
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?
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.
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.
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.
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.
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).
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.
Figure 7. An IPF map showing the crystal direction perpendicular to the shell surface. All grains share the same color indicating that the  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  for all grains, the crystals in the crossbar structure are rotated by 90° and share a well-aligned  axis with the two main directions rotated by ~30° around it.
Figure 8. An IPF map along Axis 2 showing the in-plane crystal directions with corresponding color-coded pole figures.
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!
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.
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], …. but this can be reduced for families where multiplicity plays a role, such as 〈00w〉 or 〈uuw〉…).
(4 5 6)
(139 132 170)
(2 18 155)
(118 121 148)
(20 4 157)
(44 43 45)
(4 45 325)
(2 161 177)
(33 3 262)
(235 6 265)
(4 20 177)
(2 149 172)
(62 7 617)
(10 8 167)
(39 38 40)
(8 12 167)
(137 173 177)
(12 10 167)
(130 103 136)
(25 196 221)
(137 177 181)
(188 26 207)
(149 153 192)
(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.
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.
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.
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.
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.