OIM Analysis™

Spherical Indexing

Will Lenthe, Principal Software Engineer, EDAX

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 [5] 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:

BandwidthGrid Size
63128
95192
127256

Once the best Euler grid point (maximum cross-correlation) is selected, subpixel resolution can be achieved through a refinement step.

Ni Sequence

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).

Rutile

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.

References

  1. Callahan, P. G., & De Graef, M. (2013). Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations. Microscopy and Microanalysis, 19(5), 1255-1265.
  2. Callahan, P. G., & De Graef, M. (2013). Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations. Microscopy and Microanalysis, 19(5), 1255-1265.
  3. 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.
  4. 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.
  5. 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.

Simulate them!

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.

模拟他们!

Dr. Chang Lu, Application Scientist, Gatan & EDAX

2022年初,Gatan和EDAX这两家公司完成了整合,我们的部门更名为Electron Microscope Technology (EMT)。作为EMT中国团队的应用技术支持,我负责中国北方区扫描电镜(SEM)还有透射电镜(TEM)上Gatan还有EDAX的几乎全部产品。产品多样,服务的用户群体也多样。慢慢地在工作过程中,我就发现两边的数据分析软件(Gatan的Digital Micrograph以及EDAX的Orientation Imaging Microscopy)其实并不是完全分开的,很多时候它们可以在不同程度上相互支持,互通互联。

比如说,Gatan公司在TEM平台上知名的DigitalMicrograph(DM)软件。DM可以处理一系列的电镜相关的表征数据。对于部分信号较弱的EDAX能谱结果,我们也可以把数据载入,通过DM内置的图像平滑,互相关算法以及主成分分析(PCA)进行数据的优化处理。但是我今天更想要分享的是EDAX Orientation Imaging Microscopy(OIM)软件在TEM平台上的一些应用。

在我服务的客户群体中,有一些用户尤其关注一些纳米级的物相和晶粒。这时候在TEM平台,我们往往需要使用到电子衍射的手段来对样品进行判断。然而,很多时候单单依靠透射电镜下灰度值衬度的变化,一些微弱的物相的改变很难被发觉。同时,一张干净,漂亮的来自特定晶向的电子衍射,往往需要我们对样品旋转晶带轴。虽然我们可以沿着特定的菊池线去找菊池极,但是这条菊池线对应什么晶面?菊池极对应哪个晶带轴?我们往往需要在Difpack工具里面标定晶格间距和角度,再比对样品材料不同晶面和夹角才有可能清楚,这很麻烦。

我第一次注意到OIM中的Pattern Simulation功能是因为帮助某个研究应力应变的老师输出无应力的特定取向的标准菊池花样图。然后我注意到,其实我是可以对应更改电镜的加速电压,样品倾斜角度还有取向来得到一系列的菊池花样,比如下图这个200 kV加速电压下得到的NdCeB 样品的模拟花样。我们可以对左下角的orientation参数进行修改,得到一系列模拟出来的菊池花样。通过Kinematic Color Overlay,我们还可以知道对应的菊池线对应的是什么晶面。现在,当我们处于未知状态开始转晶带轴的时候我都会首先模拟几个相似的取向,进行对比。这样一来,我沿着那个晶面(菊池线)在找哪个晶带轴(菊池极)都变得异常清楚,这非常方便。

图 1. NdCeB 使用 OIM Matrix。

现在,当Gatan的用户再拿来一个“奇奇怪怪”的样品说要找到特定晶带轴做衍射,我也不像以前担心怎么搞了。需要什么,我们就在EDAX OIM中先模拟出来一个,对着这个模拟的图,旋转,调整晶面,然后在TEM电子衍射过程中去找。我想从解决问题的角度来讲,Gatan和EDAX丰富的软件资源,就像我们这两家公司的合并一样,未来也可以合并解决客户复杂和困难的问题。

Stimulating Simulations

Dr. Stuart Wright, Senior Scientist, EDAX

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 [1]. 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 [2] 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 [3] 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 [4]. 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.

[1] 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.

[2] PG Callahan, and M De Graef (2013) “Dynamical electron backscatter diffraction patterns. Part I: Pattern simulations” Microscopy and Microanalysis, 19, 1255-1265.

[3] 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.

[4] 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.

Learning From Customers

Matt Nowell, EBSD Product Manager, EDAX

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.

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?

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 [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.

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!

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.

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.

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.

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.

Boxes

Dr. Stuart Wright, Senior Scientist, EDAX

It has been a tough year for all of us – at times, I get cabin fever and feel boxed-in. The recent holiday break was a pleasant diversion. Even though we weren’t able to gather like we usually do, we did get to spend some time with a couple of our grandkids. As we opened gifts, per the usual stereotype, our youngest grandson had more fun playing with the boxes than the toys in them! Since today’s blog is on boxes, Figure 1 shows a picture of our granddaughter atop an old toy box. Yes, she is more than willing to pose for the camera.

Figure 1. My granddaughter atop a toy box I built many years ago.

So why the picture of a toy box? That toy box is 32 years old and has a tie-in to the development of EBSD (since I am getting older, I’m allowed to be a bit nostalgic.)

I joined Professor Brent Adams’ group as an undergrad at BYU in 1985. Brent was working on the orientation coherence function (OCF) at the time, which is a statistical description of crystallographic orientation arrangement within a polycrystalline microstructure. One of the Ph.D. students, T. T. Wang, went off to what was then the Alcoa Technical Center to make orientation measurements using selected area diffraction – a painstakingly slow process. He returned with a large set of Euler angles and a box of micrographs with numbered spots to indicate where the orientation measurements were from. My assignment was to digitize those micrographs – both to manually point-and-click each grain vertex and to write software to use those vertices to reconstruct and visualize the digital microstructure. Figure 2 shows one example from the set of 9 section planes. The entire set contained 5,439 grains and 21,221 boundaries. It was a lot of tedious work.

Figure 2. Digitized microstructure from aluminum tubing for work reported in 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.

When Brent saw David Dingley’s presentation on EBSD at ICOTOM in 1987, he got very excited as he realized how much it could help with our group’s data collection needs. We got the first EBSD system in the US shortly after ICOTOM. It was installed on an old SEM in the botany department. The system was all computer-controlled, but it still required a user to manually (with the mouse) identify zone axes in each EBSD pattern to be indexed. It was a huge step forward for our research group. Brent quickly envisioned a fully automated system for site-specific orientation measurements. In 1988, Professor Adams moved to Yale University. I was fortunate to be invited to be a member of the research team that accompanied him. My wife and I boxed up our belongings and moved our small family of four from Utah to Connecticut for our new adventure.

The first few weeks at Yale were spent cleaning out an old laboratory space (some items even went to the Yale museum) in preparation for receiving our new CamScan SEM and the next generation EBSD system from David Dingley. When the SEM boxes arrived at the lab, we were very excited to see the microscope uncrated and installed. It was great to have our own microscope to work with, and we waited in eager anticipation for David’s arrival to install the new EBSD system. Unfortunately, I don’t have many photos from the Yale lab, but Figure 3 shows one with three of my colleagues in front of the SEM.

Figure 3. Brent Adams, John Hack, and Karsten Kunze in the SEM lab at Yale.

After everything was installed, there were a lot of wooden boards left over from all the crates in which the equipment was shipped. Being the stereotypical poor-starving student, I saw the wood as an opportunity. I diverted the bigger pieces of wood to my car instead of the dumpster and took them to our apartment. It was enough wood to build a toy box for each of our two kids (Figure 4).

Figure 4. Building a toy box with my kids while at Yale.

A picture of the SEM at BYU (Brent returned to BYU after I graduated in 1992 and brought the system with him back to BYU) can be seen in Figure 5. Note all the boxes surrounding the instrument. In the very first system, instead of controlling the SEM beam, we moved the sample under a stationary beam using piezoelectric stages. In this photo, the camera was fixed so that it was always inserted into the microscope chamber, so there wasn’t a box to control the slide yet. Eventually, the stages were replaced with beam control, the SEM image could be viewed live on the workstation monitor, the camera was controlled through the computer, the image processing was done in the computer, the camera slide was controlled in software until we reached the modern, streamlined systems we are accustomed to today.

Figure 5. Photo of the first fully automated EBSD system in a lab at BYU (originally at Yale but later moved to BYU).

The old SEM was scrapped several years ago, but the two toy boxes are still in use and filled with “stuffies” as my granddaughter likes to say. So, just like the presents under the Christmas tree, the SEM boxes are still providing entertainment long after the toys they once held have been recycled into new ones 😊.

How to Get a Good Answer in a Timely Manner

Shawn Wallace, Applications Engineer, EDAX

One of the joys of my job is troubleshooting issues and ensuring you acquire the best results to advance your research. Sometimes, it requires additional education to help users understand a concept. Other times, it requires an exchange of numerous emails. At the end of the day, our goal is not just to help you, but to ensure you get the right information in a timely manner.

For any sort of EDS related question, we almost always want to look at a spectrum file. Why? There is so much information hidden in the spectrum that we can quickly point out any possible issues. With a single spectrum, we can quickly see if something was charging, tilted, or shadowed (Figure 1). We can even see weird things like beam deceleration caused by a certain imaging mode (Figure 2). With most of these kinds of issues, it is common to run into major quant related problems. Any quant problems should always start with a spectrum.

Figure 1. The teal spectrum shows a strange background versus what a normal spectrum (red) should look like for a material.

This background information tells us that the sample was most likely shadowed and that rotating the sample to face towards the detector may give better results.

Figure 2. Many microscopes can decelerate the beam to help with imaging. This deceleration is great for imaging but can cause EDS quant issues. Therefore, we recommend reviewing the spectrum up front to reduce the number of emails to troubleshoot this issue.

To save the spectrum, right-click in the spectrum window, then click on Save (Figure 3). From there, save the file with a descriptive name, and send it off to the applications group. These spectrum files also include other metadata, such as amp time, working distance, and parameters that give us so many clues to get to the bottom of possible issues.

Figure 3. Saving a spectrum in APEX™ is intuitive. Right-click in the area and a pop-up menu will allow you to save the spectrum wherever you want quickly.

For information on EDS backgrounds and the information they hold, I suggest watching Dr. Jens Rafaelsen’s Background Modeling and Non-Ideal Sample Analysis webinar.

The actual image file can also help us confirm most of the above.

Troubleshooting EBSD can be tricky since the issue could be from sample prep, indexing, or other issues. To begin, it’s important to rule out any variances associated with sample preparation. Useful information to share includes a description of the sample, as well as the step-by-step instructions used to prepare the sample. This includes things like the length of time, pressure, cloth material, polishing compound material, and even the direction of travel. The more details, the better!

Now, how do I know it is a sample prep problem? If the pattern quality is low at long exposure times (Figure 4) or the sample looks very rough, it is probably related to sample preparation (Figure 4). That being said, there could be non-sample prep related issues too.

Figure 4. This pattern is probably not indexable on its own. Better preparation of the sample surface is necessary to index and map this sample correctly.

For general sample prep guidelines, I would highly suggest Matt Nowell’s Learn How I Prepare Samples for EBSD Analysis webinar.

Indexing problems can be challenging to troubleshoot without a full data set. How do I know my main issues could be related to indexing? If indexing is the source, a map often appears to be very speckled or just black due to no indexing results. For this kind of issue, full data sets are the way to go. By full, I mean patterns and OSC files. These files can be exported out of TEAM™/APEX™. They are often quite large, but there are ways available to move the data quickly.

For the basics of indexing knowledge, I suggest checking out my latest webinar, Understanding and Troubleshooting the EDAX Indexing Routine and the Hough Parameters. During this webinar, we highlight attributes that indicate there is an issue with the data set, then dive into the best practices for troubleshooting them.

As for camera set up, this is a dance between the microscope settings, operator’s requirements, and the camera settings. In general, more electrons (higher current) allow the experiment to go faster and cover more area. With older CCD based cameras, understanding this interaction was key to good results. With the newer Velocity™ cameras based on CMOS technology, the dance is much simpler. If you are having difficulty while trying to optimize an older camera, the Understanding and Optimizing EBSD Camera Settings webinar can help.

So how do you get your questions answered fast? Bury us with information. More information lets us dive deeper into the data to find the root cause in the first email, and avoids a lengthy back and forth exchange of emails. If possible, educate yourself using the resources we have made available, be it webinars or training courses. And always, feel free to reach out to my colleagues and me at edax.applications@ametek.com!

What a Difference a Year Makes

Jonathan McMenamin, Marketing Communications Coordinator, EDAX

EDAX is considered one of the leaders in the world of microscopy and microanalysis. After concentrating on advancements to our Energy Dispersive Spectroscopy (EDS) systems for the Scanning Electron Microscope (SEM) over the past few years, EDAX turned its attention to advances in Electron Backscatter Diffraction (EBSD) and EDS for the Transmission Electron Microscope (TEM) in 2019.

After the introduction of the Velocity™ Plus EBSD camera in June 2018, which produces indexing speeds greater that 3,000 indexed points per second, EDAX raised the bar further in 2019. In March, the company announced the arrival of the fastest EBSD camera in the world, the Velocity™ Super, which can go 50% faster at 4,500 indexed points per second. This was truly a great accomplishment!

EBSD orientation map from additively manufactured Inconel 718 collected at 4,500 indexed points per second at 25 nA beam current.

Less than three months later, EDAX added a new detector to its TEM product portfolio. The Elite T Ultra is a 160 mm2 detector that offers a unique geometry and powerful quantification routines for comprehensive analysis solutions for all TEM applications. The windowless detector’s geometric design gives it the best possible solid angle to increase the X-ray count rates for optimal results.

EDAX Elite T Ultra EDS System for the TEM.

Just before the annual Microscopy & Microanalysis conference, EDAX launched the OIM Matrix™ software module for OIM Analysis™. This new tool gives users the ability to perform dynamic diffraction-based EBSD pattern simulations and dictionary indexing. Users can now simulate EBSD patterns based on the physics of dynamical diffraction of electrons. These simulated patterns can then be compared to experimentally collected EBSD patterns. Dictionary indexing helps improve indexing success rates over standard Hough-based indexing approaches. You can watch Dr. Stuart Wright’s <a href=”https://youtu.be/Jri181evpiA&#8221; target=”_blank”>presentation from M&M</a> for more information.

Dictionary indexing flow chart and conventional indexing results compared with dictionary indexing results for a nickel sample with patterns collected in a high-gain/noisy condition.

EDAX has several exciting product announcements on the way in early 2020. We have teased a two of these releases, APEX™ Software for EBSD and the Clarity™ Direct Electron Detector. APEX™ EBSD will give users the ability to characterize both compositional and structural characteristics of their samples on the APEX™ Platform. It gives them the ability to collect and index EBSD patterns and EBSD maps, as well as allow for simultaneous EDS-EBSD collection. You can learn more about APEX™ EBSD in the September issue of the Insight newsletter and in our “APEX™ EBSD – Making EBSD Data Collection How You Want It” webinar.

EBSD of a Gibeon Meteorite sample covering a 7.5 mm x 6.5 mm area using ComboScan for large area analysis.

The Clarity™ is the world’s first commercial direct electron detector (DeD) for EBSD. It provides patterns of the highest quality and sensitivity with no detector read noise and no distortion for optimal performance. The Clarity™ does not require a phosphor screen or light transfer system. The DeD camera is so sensitive that individual electrons can be detected, giving users unprecedented performance for EBSD pattern collection. It is ideal for analysis of beam sensitive samples and potential strain applications. We recently had a webinar “Direct Electron Detection with Clarity™ – Viewing EBSD Patterns in a New Light” previewing the Clarity™. You can also get a better understanding of the system in the December issue of the Insight newsletter or the .

EBSD pattern from Silicon
using the Clarity™ detector.

All this happened in one year! 2020 looks to be another great year for EDAX with further improvements and product releases to offer the best possible tools for you to solve your materials characterization problems.