Dr. Shangshang Mu, Application Scientist, Gatan/EDAX
Over the past year, I’ve rekindled my enjoyment of traveling as I visited customers in the Americas, Asia, and across Europe. During my return journey, I was deeply touched by an airline billboard at the Munich, Germany airport that read, “We all live under one sun. Let’s see it again.” Indeed, it is genuinely nice to see the world once more since reemerging from the pandemic.
While flying over Hudson Bay, an inland marginal sea of the Arctic Ocean, I saw numerous ice caps floating on the water from the aircraft’s belly camera view. To me, these were very reminiscent of the counts per second (CPS) map (Figure 1) in one of the wavelength dispersive spectrometry (WDS) datasets I shared with customers during these trips. Although they were orders of magnitude larger than the micron-scale sample, the resemblance was striking.
Figure 1. Ice caps in Hudson Bay (left) resemble the CPS map of a Si-W-Ta sample (right).
Throughout these journeys, our EDAX Lambda WDS system was one of the hot topics drawing customers’ attention. This parallel beam spectrometer features a compact design compatible with almost every scanning electron microscope (SEM). The improved energy resolution and sensitivity and lower limits of detection make it an excellent supplement to your energy dispersive spectroscopy (EDS) detectors. The CPS map I referred to was captured from a Si-W-Ta sample. The energy peaks of Si K, W M, and Ta M are heavily overlapped, with only approximately 30 eV energy difference between each other. Lambda WDS systems provide up to 15x better energy resolution than typical EDS systems, effectively resolving the ambiguity in analysis.
Figure 2. Overlay of EDS (red outline) and WDS (cyan color) spectra from the central area of the Si-W-Ta sample.
The overlay of EDS/WDS spectra from the central area of the map shows that the Lambda WDS system intrinsically resolves the overlapping EDS peaks (red outline), as depicted by the cyan color WDS spectrum (Figure 2). The shortcoming of EDS in resolving these overlapping peaks results in the distributions of the three elements appearing identical in EDS maps. However, the WDS maps provide clear and distinct visualizations of the individual distributions of the three elements (Figure 3).
Figure 3. EDS (top) and WDS (bottom) maps of the Si-W-Ta sample. The WDS maps resolve the artifacts due to Ta M, Si K, and W M peak overlaps in the EDS maps.
This year’s M&M meeting is just around the corner. If you are traveling to this entirely in-person event, stop by our booth (#504) to check out our integrated EDS-WDS SEM solutions and many other products that will capture your interest.
I have two sons graduating this year. My oldest son is graduating college with a Materials Science and Engineering degree and is interested in materials characterization. My middle son is graduating high school and has grown up refining ores in Minecraft, casting characters from Dungeons and Dragons, and 3D printing school projects. I’m glad they are both interested in materials and how they can affect daily living. I’ve also been a little sentimental and nostalgic thinking about how we have tried to learn more about materials in our household.
One activity they have always enjoyed is collecting pressed coins. These machines squeeze a coin between two rollers, one of which has an engraving on its surface that is then imprinted onto the stretched and flattened surface of the deformed coin. We have collected these coins from around the world. One example is shown in Figure 1, which is a pressed coin from Universal Studios. This was the most recent addition to the collection. I decided to press a second coin that we could prepare and characterize with electron backscatter diffraction (EBSD) to see the microstructural developments that occur during the pressing process.
Figure 1. A pressed coin from Universal Studios.
The pressed coin was mechanically polished down to 0.02 µm colloidal silica and then analyzed using the new EDAX Velocity Ultra EBSD detector. This new detector allowed for high-speed data collection at acquisition rates of 6,500 indexed patterns per second. Figure 2 shows the inverse pole figure (IPF) orientation map collected from a 134 µm x 104 µm area with a 100 nm step size, with the coloring relative to the orientations aligned with the sample’s surface normal direction. At these speeds, the acquisition time was less than five minutes. A copper blank was used instead of the traditional penny for this sample. This was noticeable when indexing the EBSD patterns. Since 1982, pennies have been made of zinc coated with copper. Zinc has a hexagonal crystal structure, while the EBSD patterns from this coin were face-centered cubic (FCC). EDS analysis confirmed that the material was copper.
Figure 2. An IPF orientation map collect from a 134 µm x 104 µm area of the pressed coin with a 100 nm step size. The coloring is relative to the orientations aligned with the sample’s surface normal direction.
The IPF map shows a significant amount of deformation. This can be seen in the IPF maps with the color variation within each grain. This is, of course, expected, as the elongation and thinning of the coin are easily observed while watching the machine. EBSD is an ideal tool for characterizing this deformation within the material. While there are several different map types to visualize local misorientations and deformation, Figure 3 shows one of my favorites, the grain reference orientation deviation (GROD) map. In this map, the grains are first calculated by grouping measurements of similar orientation using a 5° tolerance angle. Next, the average orientation of each grain is calculated. Finally, each pixel within a grain is colored according to its misorientation from the average orientation of its grain. The microstructure’s largest GROD angular value is 61.9°, indicating a large spread of orientations. This map also shows the grain boundaries as black lines to indicate the original grain boundary positions.
Figure 3. A GROD map of the pressed coin.
Figure 4 shows a fascinating view of how the material is deformed within a selected grain. This chart was created by drawing a line within a grain and plotting the point-to-point and point-to-origin misorientations along this line. The point-to-point distribution shows that each step is typically a small misorientation value below the grain tolerance angle. The point-to-origin distribution shows an accumulation of misorientations within this grain, with the overall misorientation changing more than 30° over the 25 µm distance within the grain. This type of result always gets me thinking about what a grain really is in a deformed material.
Figure 4. A view of how the material is deformed within a selected grain. This chart was created by drawing a line within a grain and plotting the point-to-point and point-to-origin misorientations along this line.
Figure 5. The (001), (111), and (110) pole figures calculated from the measured orientations.
Figure 5 shows the (001), (111), and (110) pole figures calculated from the measured orientations. These pole figures are incomplete and resemble what is expected for a rolled FCC material. This is due to the small number of grains sampled in this area. A second map was collected over a 1,148 µm x 895 µm area with a 2 µm step size in under a minute to get a better sampling of the entire microstructure. The pole figures for this data are shown in Figure 6. Comparing Figures 5 and 6 shows that the additional sampling within the second scan adds more symmetry to the pole figures.
Figure 6. The pole figures for the second map that was collected over a 1,148 µm x 895 µm area with a 2 µm step size.
This was a fun example to show the different data types that can be derived from EBSD measurements. In materials science, understanding the relationship between materials processing and the resulting microstructure is critical to understanding the material’s final properties. It’s clear that pressing a coin causes significant deformation within the material, which can then be measured and quantified with EBSD. Maybe the next time we go to the zoo, we will vary the speed at which we roll the coins and see what effect that has on the data.
The precision and accuracy of orientation measurements by electron backscatter diffraction (EBSD) have been of interest since the advent of EBSD [1, 2]. In contrast, reliability (in terms of correctly identifying the orientation at least within 5°) was of greater concern when indexing was first automated (there is a section of my thesis [3] devoted to precision, as well as Krieger Lassen’s thesis [4]). I’ve written a few papers on the subject [5 – 7], and there have been several more by other authors [8 – 11]. High-resolution EBSD (HREBSD) has shown success in markedly improving precision [12]. Now that dictionary indexing (DI) has become more common; there has been a resurgence in papers on the precision that can be achieved using DI [13 – 15]. I know that is a lot of references for a blog post, but I wanted to give you an idea of how many different research groups have studied angular precision in EBSD measurements – the references given are only a sampling; there are certainly more.
Will Lenthe and I have been working hard to improve the dictionary indexing capabilities in the EDAX OIM Matrix™ add-on module to EDAX OIM Analysis™. In addition, Will has added the ability to perform spherical indexing within OIM Matrix [16 – 17] (see Will’s “New Tools for EBSD Data Collection and Analysis” webinar for more information). These new capabilities will be available soon in OIM Analysis 9. I’m excited about the progress we’ve made. You will find OIM Matrix much easier to use and more robust. In addition, we’ve sped up many aspects of OIM Analysis, which will help with the big datasets routinely obtained with the EDAX Velocity™ cameras.
The precision of indexing via spherical indexing has recently been explored [18]. Using OIM Analysis 9, we’ve been exploring what we can achieve in terms of orientation precision with orientation refinement [19 – 21] applied to initial indexing results obtained by Hough transform-based indexing, dictionary indexing, and spherical indexing. We haven’t quantified our results yet. Still, the KAM maps (which indicate the orientation precision) we’ve obtained are so promising that I want to show our preliminary results. Our refinement method is essentially a hybrid of that proposed by Singh, Ram, and De Graef [19] and Pang, Larsen, and Schuh [21]. But for the spherical indexing, we also have implemented an additional refinement in the harmonic frequency space. Figure 1 shows some results I am excited to share.
Figure 1. KAM maps from nickel [22]. (Top row) As-indexed, (middle row) with NPAR for Hough-based indexing and refinement in the spherical harmonics for spherical indexing, and (bottom row) after real-space refinement. The first column is for Hough-based indexing, columns 2 – 4 are for dictionary indexing with different dictionary target disorientations, and columns 5 – 6 are for SI with different harmonic bandwidths.
It is pretty interesting that the KAM maps after refinement are all nearly the same, no matter which type of indexing was used to obtain the initial orientation measurements. We do not expect much plastic strain or permanent deformation in these samples, so the reduced KAM values are more of what we expect for the sample.
Here is another set of results for a silicon single crystal. The scan is approximately 1 x 1 mm with a 30 m step size. You can see the dramatic improvement in these results. Unfortunately, the two points with the largest KAM values are due to some dust particles on the sample’s surface.
Figure 2. KAM maps were constructed using Hough-based indexing, SI, and SI followed by refinement.
We are very excited to get these advancements into your hands and are putting in extra hours to get the software ready for release. We hope you are as precisely excited as we are to apply it to your samples!
[1] Harland CJ, Akhter P, Venables JA (1981) Accurate microcrystallography at high spatial resolution using electron backscattering patterns in a field emission gun scanning electron microscope. Journal of Physics E14:175-182
[2] Dingley DJ (1981) A Comparison of Diffraction Techniques for the SEM. Scanning Electron MicroscopyIV: 273-286
[3] Wright SI (1992) Individual Lattice Orientation Measurements Development and Applications of a Fully Automatic Technique. Ph.D. Thesis., Yale University.
[4] Krieger Lassen NC (1994) Automated Determination of Crystal Orientations from Electron Backscattering Patterns. Ph.D. Thesis, Danmarks Tekniske Universitet.
[5] Wright S, Nowell M (2008) High-Speed EBSD. Advanced Materials and Processes66: 29-31
[6] Wright SI, Basinger JA, Nowell MM (2012) Angular precision of automated electron backscatter diffraction measurements. Materials Science Forum702: 548-553
[7] Wright SI, Nowell MM, de Kloe R, Chan L (2014) Orientation Precision of Electron Backscatter Diffraction Measurements Near Grain Boundaries. Microscopy and Microanalysis20:852-863
[8] Humphreys FJ, Huang Y, Brough I, Harris C (1999) Electron backscatter diffraction of grain and subgrain structures – resolution considerations. Journal of Microscopy – Oxford195:212-216.
[9] Demirel MC, El-Dasher BS, Adams BL, Rollett AD (2000) Studies on the Accuracy of Electron Backscatter Diffraction Measurements. In: Schwartz AJ, Kumar M, Adams BL (eds) Electron Backscatter Diffraction in Materials Science. Kluwer Academic/Plenum Publishers, New York, pp 65-74.
[10] Godfrey A, Wu GL, Liu Q (2002) Characterisation of Orientation Noise during EBSP Investigation of Deformed Samples. In: Lee DN (ed) ICOTOM 13, Seoul, Korea, Textures of Materials. Trans Tech Publications Inc., pp 221-226.
[11] Ram F, Zaefferer S, Jäpel T, Raabe D (2015) Error analysis of the crystal orientations and disorientations obtained by the classical electron backscatter diffraction technique. Journal of Applied Crystallography48: 797-813
[12] Wilkinson AJ, Britton TB (2012) Strains, planes, and EBSD in materials science. Materials Today15: 366-376
[13] Ram F, Singh S, Wright SI, De Graef M (2017) Error Analysis of Crystal Orientations Obtained by the Dictionary Approach to EBSD Indexing. Ultramicroscopy181:17-26.
[14] Nolze G, Jürgens M, Olbricht J, Winkelmann A (2018) Improving the precision of orientation measurements from technical materials via EBSD pattern matching. Acta Materialia159:408-415
[15] Shi Q, Loisnard D, Dan C, Zhang F, Zhong H, Li H, Li Y, Chen Z, Wang H, Roux S (2021) Calibration of crystal orientation and pattern center of EBSD using integrated digital image correlation. Materials Characterization178:111206
[16] Lenthe W, Singh S, De Graef M (2019) A spherical harmonic transform approach to the indexing of electron backscattered diffraction patterns. Ultramicroscopy207:112841
[17] Hielscher R, Bartel F, Britton TB (2019) Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross-correlation on the sphere. Ultramicroscopy207:112836
[18] Sparks G, Shade PA, Uchic MD, Niezgoda SR, Mills MJ, Obstalecki M (2021) High-precision orientation mapping from spherical harmonic transform indexing of electron backscatter diffraction patterns. Ultramicroscopy222:113187
[19] Singh S, Ram F, De Graef M (2017) Application of forward models to crystal orientation refinement. Journal of Applied Crystallography50:1664-1676.
[20] Winkelmann A, Jablon BM, Tong V, Trager‐Cowan C, Mingard K (2020) Improving EBSD precision by orientation refinement with full pattern matching. Journal of Microscopy277:79-92
[21] Pang EL, Larsen PM, Schuh CA (2020) Global optimization for accurate determination of EBSD pattern centers. Ultramicroscopy209:112876
[22] Wright SI, Nowell MM, Lindeman SP, Camus PP, De Graef M, Jackson MA (2015) Introduction and comparison of new EBSD post-processing methodologies. Ultramicroscopy159:81-94
2022 was a year of changes. In the beginning, I set up a desk in the scanning electron microscope (SEM) lab where, without truly reaching out, I only needed to turn in my chair to switch from emails and virtual customers on my laptop to the live energy dispersive spectroscopy (EDS) and electron backscatter diffraction (EBSD) system and real data on the microscope. As travel restrictions gradually eased worldwide, we were all able to start meeting “real” people again. After almost two years of being grounded, I finally met people face to face again, discussing their analysis needs, and answering questions do not compare to online meetings. We restarted in-person training courses, and I participated in many external courses, exhibitions, and conferences, reaching out to microscopists all over Europe.
And as always, I try to correlate real life with some nice application examples. And what is similar to reaching out to people in the microanalysis world? Reaching out to things! So, what came to mind are remote thermal sensors, which most of us will have at home in the kitchen: a thermostat in an oven and a wired thermometer that you can use to measure food temperatures. And I just happened to have a broken one that was ready to be cut up and analyzed.
Figure 1. a) A food thermometer and b) an oven thermostat sensor.
On the outside, these two sensors looked very similar; both were thin metal tubes connected to a control unit. Because of this similarity, I was also expecting more or less the same measuring method, like using a thermocouple in both thermometers. But to my surprise, that was not quite the case.
The long tube of the food thermometer was mostly empty. Right at the tip, I found this little sensor about 1 mm across connected to copper wires that led to the control unit. After mounting and careful sectioning, I could collect EDS maps showing that the sensor consisted of a central block of Mn-Co-Fe-oxide material sandwiched between silver electrodes soldered to the copper-plated Ni wires.
Note that in the image, you only see one of the wires, the other is still below the surface, and I did not want to polish it any deeper.
Figure 2. The temperature sensor taken out of the tube of the food thermometer.
Figure 3. A forward scatter SEM image of the polished cross-section showing the central MnCoFe-oxide material and one of the connecting wires.
This was no thermocouple.
Figure 4. The element distribution in the sensor.
Figure 5. The EDS spectrum of the central CoMnFe-oxide area.
Instead, the principle of this sensor is based on measuring the changing resistivity with temperature. The EBSD map of the central Co-Mn-De oxide area shows a coarse-grained structure without any preferred orientation to make the resistivity uniform in all directions.
Figure 6. An EBSD IPF on Image Quality map of the sensor in the food thermometer.
Figure 7. (001) pole figure of the MnCoFe oxide phase, showing a random orientation distribution.
And where the tube of the food thermometer was mostly empty, the tube of the oven thermostat sensor was completely empty. There were not even electrical connections. The sensor was simply a thin hollow metal tube that contained a gas that expands when heated. This expansion would move a small disk with a measurement gauge that was then correlated with a temperature readout. Although this sounded very simple, some clever engineering was needed to prevent the tube from pinching shut when bending and moving it during installation.
I cut and polished the tube, and an EBSD map of the entire cross-section is shown below.
Figure 8. a) EBSD IQ and b) IPF maps of a cross-section through the entire tube of the oven thermostat sensor.
The tube is constructed out of three layers of a Fe-Cr-Ni alloy with fine-grained multiphase chromium phosphide layers in between. This microstructure is what provides corrosion protection, and it also adds flexibility to the tube. And this, in turn, is crucial to prevent cracks from forming that would cause the leaking of the contained gas, which is critical in getting a good temperature reading.
The detailed map below shows a section of the phosphide layer. There are two chromium phosphide phases, and in between, there are dendritic Ni grains that link everything together.
Figure 9. EDS maps showing the composition of one of the phosphide layers.
Figure 10. EBSD IPF maps of the different phases. a) All phases on a PRIAS center image, b) CrP, c) Fe matrix, and d) Ni dendrites, Cr3P.
When you look at the microstructure of both sensors in detail, it is possible to determine how they work, and you can appreciate why they have been designed as they are. The two devices are efficient and tailored to their intended use. The oven thermostat is designed to be mounted in a fixed position to be secure so that it can be used for a very long time. The food thermometer is very flexible and can easily be moved around.
In that respect, I feel there is another similarity between these sensors and the different kinds of meetings between people we have experienced over the past year. It does not matter how you do it; you can always reach out and feel some warmth.
Dr. Shangshang Mu, Applications Engineer, Gatan/EDAX
The new APEX™ 3.0 is the ultimate materials characterization software, integrating Energy Dispersive Spectroscopy (EDS), Electron Backscatter Diffraction (EBSD), and Wavelength Dispersive Spectrometry (WDS) to deliver previously unattainable solutions. This optimized configuration offers the uncompromised performance of each technique and allows users to combine them for the ultimate materials insight. All three techniques seamlessly operate within the APEX, blending powerful elemental and crystallographic analysis routines through an intuitive interface to deliver outstanding data collection, faster analysis, and flexible reporting for users of all levels.
What does APEX WDS look like?
WDS functionalities are implemented seamlessly with the EDS graphical user interface. The user can quickly adapt to the new functionalities and employ WDS when and where EDS reaches the limit. With one-click from start to finish, Auto WDS allows fully automated WDS scan list generation, optimum sample height determination, and spectrum collection. It simultaneously collects EDS and WDS spectra and displays them side-by-side or overlaid for easy data visualization and interpretation (Figure 1), with no overlapping or overloading of windows.
Figure 1. Simultaneous EDS-WDS spectrum acquisition user interface.
APEX allows you to set an intermediate position for the EDS detector to ensure optimal count rates for both techniques.
Figure 2. Simultaneous EDS-WDS mapping user interface.
Sets of combined EDS-WDS spectrum, linescan, and mapping data at different stage positions can be done via automated batch collection routines (Figure 2) to streamline SEM experiments. EDS and WDS data collection settings are managed in one user-friendly batch scan list (Figure 3).
Figure 3. Combined EDS-WDS batch list.
The quantitative elemental analysis supports individual technique or combined EDS-WDS standards. You can easily switch between EDS and WDS standards for each element by clicking on the icon in front of the element (Figure 4).
Figure 4. Quantitative results with combined EDS-WDS standards.
With the addition of WDS capabilities, APEX 3.0 now includes EDS, EBSD, and WDS. Each characterization tool can operate independently to utilize EDAX’s technological advancements or integrates data to provide solutions that were once unachievable.
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.
The city has recently started burying a pipe down the middle of one of the roads into my neighborhood. There were already a couple of troublesome intersections on this road. The construction has led to several accidents in the past couple of weeks at these intersections and I am sure there are more to come.
A question from a reviewer on a paper I am co-authoring got me thinking about the impact of intersections of bands in EBSD patterns on the Hough transform. The intersections are termed ‘zone axes’ or ‘poles’ and a pattern is typically composed of some strong ones where several high intensity bands intersect as well as weak ones where perhaps only two bands intersect.
To get an idea of the impact of the intersections on the Hough transform, I have created an idealized pattern. The intensity of the bands in the idealized pattern is derived from the peaks heights from the Hough transform applied to an experimental pattern. For a little fun, I have created a second pattern by blacking out the bands in the original idealized pattern, leaving behind only the intersections. I created a third pattern by blacking out the intersections and leaving behind only the bands. I have input these three patterns into the Hough transform. As I expected, you can see the strong sinusoidal curves from the pattern with only the intersections. However, you can also see peaks, where these sinusoidal curves intersect and these correspond (for the most part) to the bands in the pattern.
In the figure, the middle row of images are the raw Hough Transforms and the bottom row of images are the Hough Transforms after applying the butterfly mask. It is interesting to note how much the Hough peaks differ between the three patterns. It is clear that the intersections contribute positively to finding some of the weaker bands. This is a function not only of the band intensity but also the number of zone axes along the length of the band in the pattern.
Eventually the construction on my local road will be done and hopefully we will have fewer accidents. But clearly, intersections are more than just a necessary evil 😊
When you are in Sweden at Scandem 2019 it is the perfect time to order SOS as an appetizer or for dinner. It is made of smör, ost and sill (butter, cheese and herring) served together with potatoes. Sometimes the potatoes need a little bit of improvement in taste. It is very easy to take the salt mostly located on all tables and salt them. Doing that I thought about how easy it is to do this today and what am I really pouring on my potatoes?
Salt was very important in the past. In ancient times salt was so important that the government of Egypt and other countries setup salt taxes. Around 4000 years ago in China and during the Bronze age in Europe, people started to preserve food using brine. The Romains had soldiers guarding and securing the transportation of salt. Salt was as expensive as gold. Sal is the Latin word for salt and the soldiers used to get their salare. Today you still get a salary. Later ‘Streets of Salt’ were settled to guarantee safe transportation all over the country. As a result, cities along these roads got wealthy. Even cities, like Munich, were founded to make money with the salt tax. Salt even destroyed empires and caused big crises. Venice fought with Genoa over spices in the middle ages. In the 19th century soldiers were sent out to conquer a big mountain of salt of an Inconceivable value, lying along the Missouri River. We all know the history of India´s independence. Mohandas Gandhi organized a salt protest to demonstrate against the British salt tax. The importance of the word salt is also implemented in our languages, “Worth the salt”, “Salz in der Suppe” or “Mettre son grain de sel”.
The two principle ways of getting salt are from underground belts and from the sea. It can be extracted from underground either by mining or by using solution mining. Sea salt is produced in small pools which were filled up during high tide and water evaporates under sunny weather conditions. Two kinds of salt mining are done. Directly digging the salt out of the mountain, then dissolving it to clean it. Or hot water is directly used to dissolve the salt and then the brine is pumped up.
Buying salt today is no longer that expensive, dangerous or difficult. But now a new problem arises. I´m talking about salt for consumption, which usually means NaCl in nice white crystals. So, are there any advantages to using different kind of salts? If we believe advertisements or gourmets, it is important, where the salt we use came from and how it was produced. Today the most time-consuming issue is the selection of the kind of salt you want in the supermarket!
For my analysis I chose three kinds of salts from three different areas. The first question was, are the differences big enough to detect them using EDS or will the differences be related to minor trace elements which can only be seen in WDS. It was a surprise for me that the differences are that huge. I had a look at several crystals from one sample. Shown as examples are the typical analysis of the different compounds and elements for that provenance.
First looking at the mined salt. I selected a kind of salt from the oldest salt company in Germany established over 400 years ago. One kind from Switzerland manufactured in the middle of the Alpes and one from the Kalahari, to be as far away as possible from the others. The salt from Switzerland is the purest salt only containing NaCl with some minor traces. The German salt contains a bigger amount of potassium and the Kalahari salt a bigger amount of sulfur and oxygen (Figure 2.).
Figure 2.
Secondly, I was interested in the salt coming from the sea. I selected two types of salt from French coasts one from the Atlantic Ocean in Brittany and another one from the Mediterranean Sea. The third one came from the German coast at the Baltic Sea. The first interesting impression is that all the sea salt contains many more elements. The Mediterranean salt contains the smallest amount of trace elements. The salt from the Atlantic Ocean and the Baltic sea contains, besides the main NaCl, phases containing Ca, K, S, Mg and O. A difference in the two is the amount of Ca containing compounds (Figure 3.).
Figure 3.
Finally, I was interested in some uncommon types of salt. In magazines and television, experts often publish recipes with special types supposedly offering a special taste, or advertising offers remarkable new kinds of healthy salt. So, I was looking for three kinds which seem to be unusable. I found two, a red and a black colored, Hawaiian salt. The spectrum of the red salt shows nicely that Fe containing minerals cause the red color. Even titanium can be found and a bigger amount of Al, Si and O. The black salt contains mainly the same elements. Instead of Fe the high amount of C causes the black color. A designer salt is the Pyramid finger salt, which is placed on top of the meat to make it look nicer. Beside the shape, the only specialty is the higher amount of Ca, S and O (Figure 4).
Figure 4.
It was really interesting that salt is not even salt. As the shape of the crystals varies, so they differ in composition. In principle it is NaCl but contain more or less different kinds of compounds or even coal to color it. There are elements found in different amounts related to the type of salt and area it came from. These different salts are located in a few very small areas in and on the crystals.
And finally, I pour salt onto my potatoes and think, ok it is NaCl.
Recently I gave a webinar on dynamic pattern simulation. The use of a dynamic diffraction model [1, 2] allows EBSD patterns to be simulated quite well. One topic I introduced in that presentation was that of dictionary indexing [3]. You may have seen presentations on this indexing approach at some of the microscopy and/or materials science conferences. In this approach, patterns are simulated for a set of orientations covering all of orientation space. Then, an experimental pattern is tested against all of the simulated patterns to find the one that provides the best match with the experimental pattern. This approach does particularly well for noisy patterns.
I’ve been working on implementing some of these ideas into OIM Analysis™ to make dictionary indexing more streamlined for datasets collected using EDAX data collection software – i.e. OIM DC or TEAM™. It has been a learning experience and there is still more to learn.
As I dug into dictionary indexing, I recalled our first efforts to automate EBSD indexing. Our first attempt was a template matching approach [4]. The first step in this approach was to use a “Mexican Hat” filter. This was done to emphasize the zone axes in the patterns. This processed pattern was then compared against a dictionary of “simulated” patterns. The simulated patterns were simple – a white pixel (or set of pixels) for the major zone axes in the pattern and everything else was colored black. In this procedure the orientation sampling for the dictionary was done in Euler space. It seemed natural to go this route at the time, because we were using David Dingley’s manual on-line indexing software which focused on the zone axes. In David’s software, an operator clicked on a zone axis and identified the <uvw> associated with the zone axis. Two zone axes needed to be identified and then the user had to choose between a set of possible solutions. (Note – it was a long time ago and I think I remember the process correctly. The EBSD system was installed on an SEM located in the botany department at BYU. Our time slot for using the instrument was between 2:00-4:00am so my memory is understandably fuzzy!)
One interesting thing of note in those early dictionary indexing experiments was that the maximum step size in the sampling grid of Euler space that would result in successful indexing was found to be 2.5°, quite similar to the maximum target misorientation for modern dictionary indexing. Of course, this crude sampling approach may have led to the lack of robustness in this early attempt at dictionary indexing. The paper proposed that the technique could be improved by weighting the zone axes by the sum of the structure factors of the bands intersecting at the zone axes. However, we never followed up on this idea as we abandoned the template matching approach and moved to the Burn’s algorithm coupled with the triplet voting scheme [5] which produced more reliable results. Using this approach, we were able to get our first set of fully automated scans. We presented the results at an MS&T symposium (Microscale Texture of Materials Symposium, Cincinnati, Ohio, October 1991) where Niels Krieger-Lassen also presented his work on band detection using the Hough transform [6]. After the conference, we hurried back to the lab to try out Niels’ approach for the band detection part of the indexing process [7].
Modern dictionary indexing applies an adaptive histogram filter to the experimental patterns (at left in the figure below) and the dictionary patterns (at right) prior to performing the normalized inner dot-product used to compare patterns. The filtered patterns are nearly binary and seeing these triggered my memory of our early dictionary work as they reminded me of the nearly binary “Sombrero” filtered patterns– Olé! We may not have come back full circle but progress clearly goes in steps and some bear an uncanny resemblance to previous ones. I doff my hat to the great work that has gone into the development of dynamic pattern simulation and its applications.
[1] A. Winkelmann, C. Trager-Cowan, F. Sweeney, A. P. Day, P. Parbrook (2007) “Many-Beam Dynamical Simulation of Electron Backscatter Diffraction Patterns” Ultramicroscopy 107: 414-421. [2] P. G. Callahan, M. De Graef (2013) “Dynamical Electron Backscatter Diffraction Patterns. Part I: Pattern Simulations” Microscopy and Microanalysis 19: 1255-1265. [3] S.I. Wright, B. L. Adams, J.-Z. Zhao (1991). “Automated determination of lattice orientation from electron backscattered Kikuchi diffraction patterns” Textures and Microstructures 13: 2-3. [4] Y.H. Chen, S. U. Park, D. Wei, G. Newstadt, M.A. Jackson, J.P. Simmons, M. De Graef, A.O. Hero (2015) “A dictionary approach to electron backscatter diffraction indexing” Microscopy and Microanalysis 21: 739-752. [5] S.I. Wright, B. L. Adams (1992) “Automatic-analysis of electron backscatter diffraction patterns” Metallurgical Transactions A 23: 759-767. [6] N.C. Krieger Lassen, D. Juul Jensen, K. Conradsen (1992) “Image processing procedures for analysis of electron back scattering patterns” Scanning Microscopy 6: 115-121. [7] K. Kunze, S. I. Wright, B. L. Adams, D. J. Dingley (1993) “Advances in Automatic EBSP Single Orientation Measurements.” Textures and Microstructures 20: 41-54.
A recent conversation on a list serv discussed sloppiness in the use of words and how it can cause confusion. This made me consider that in the world of microanalysis, we are not immune. We are probably sloppiest with two particular words. They are resolution and phase.
Let us start with how we use the word phase and how phases are commonly defined in microanalysis. In Energy Dispersive Spectroscopy (EDS), we use phase for everything, for example, phase mapping, phase library. In Electron Backscatter Diffraction (EBSD), the usage is a little more straightforward.
So, what is a phase? Well to me, a geologist, a phase has both a distinct chemistry and a distinct crystal structure. Why does this matter to a geologist? Two different minerals with the same chemistry, but with different structures, can behave in very different ways and this gives me useful information about each of them.
The classic example for geologists is the Al2SIO5 system (figure 1). It has three members, Kyanite, Sillimanite, and Andalusite. They each have the same chemistry but different structures. The structure of each is controlled by the pressure and temperature at which the mineral equilibrated. Simple chemistry tells me nothing. I need the structure to tease out that information.
Figure 1. Phase Diagram of the Al2SiO5 system in geological conditions. Different minerals form at different pressures and temperatures, letting geologists know how deep and/or the temperature at which the parent rock formed.**
EDS users use the term phase much more loosely. A phase is something that is chemically distinct. Our phase maps look at a spectrum pixel by pixel and see how they compare. In the end, the software goes through the entire map and groups each pixel with like pixels. The phase library does chi squared fits to compare the spectrum to the library (figure 2).
Figure 2. Our Spectrum Library Match uses as Chi-squared fit to determine the best possible matches. This phase is based on compositional data, not compositional and structural data.
While the definition of phase is relatively straight forward, the meaning of resolution gets a little murkier. If you asked someone what the EDS resolution is, you may get different answers depending on who you ask. The main way we use the term resolution when talking about EDS is spectral resolution. This defines how tight the peaks in a spectrum are (figure 3).
Figure 3. Comparison of EDS vs. WDS spectral resolution. WDS has much higher resolution (tighter peaks) than EDS, but fewer counts and more set-up are required.
The other main use of resolution, in EDS is the spatial resolution of the EDS signal itself (figure 4). There are many factors which determine this, but the main ones are the accelerating voltage and sample characteristics. This resolution can go from nanometers to microns.
Figure 4. Distribution of the electron energy deposited in an aluminum sample (top row) and a gold sample (bottom row) at 15 kV (left column) and 5 kV (right column). Note the dramatic difference in penetration given by the right hand side scale bar.
The final use of resolution for EDS is mapping resolution. This is by far the easiest to understand. It is just the step size of the beam while you are mapping.
Luckily for us, the easiest way to find out what people mean when they use the terms resolution or phase, is just to ask. Of course, the way to avoid any confusion is to be as precise as possible with your choice of words. I resolve to do my part and communicate as clearly as I can!
