OIM

Being more precise

Dr. Stuart Wright, Senior Scientist, Gatan/EDAX

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 E 14:175-182
[2] Dingley DJ (1981) A Comparison of Diffraction Techniques for the SEM. Scanning Electron Microscopy IV: 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 Processes 66: 29-31
[6] Wright SI, Basinger JA, Nowell MM (2012) Angular precision of automated electron backscatter diffraction measurements. Materials Science Forum 702: 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 Microanalysis 20:852-863
[8] Humphreys FJ, Huang Y, Brough I, Harris C (1999) Electron backscatter diffraction of grain and subgrain structures – resolution considerations. Journal of Microscopy – Oxford 195:212-216.
[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 Crystallography 48: 797-813
[12] Wilkinson AJ, Britton TB (2012) Strains, planes, and EBSD in materials science. Materials Today 15: 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. Ultramicroscopy 181:17-26.
[14] Nolze G, Jürgens M, Olbricht J, Winkelmann A (2018) Improving the precision of orientation measurements from technical materials via EBSD pattern matching. Acta Materialia 159:408-415
[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 Characterization 178:111206
[16] Lenthe W, Singh S, De Graef M (2019) A spherical harmonic transform approach to the indexing of electron backscattered diffraction patterns. Ultramicroscopy 207:112841
[17] Hielscher R, Bartel F, Britton TB (2019) Gazing at crystal balls: Electron backscatter diffraction pattern analysis and cross-correlation on the sphere. Ultramicroscopy 207:112836
[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. Ultramicroscopy 222:113187
[19] Singh S, Ram F, De Graef M (2017) Application of forward models to crystal orientation refinement. Journal of Applied Crystallography 50:1664-1676.
[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 Microscopy 277:79-92
[21] Pang EL, Larsen PM, Schuh CA (2020) Global optimization for accurate determination of EBSD pattern centers. Ultramicroscopy 209:112876
[22] Wright SI, Nowell MM, Lindeman SP, Camus PP, De Graef M, Jackson MA (2015) Introduction and comparison of new EBSD post-processing methodologies. Ultramicroscopy 159:81-94

Grain Analysis in OIM Analysis

Dr. Sophie Yan, Applications Engineer, EDAX

Recently, we held a webinar on Grain Analysis in OIM Analysis™. After the webinar, many users mentioned that the basic operation overview was very helpful. Since there was a very enthusiastic response, I want to take this opportunity to share these fundamental tips and tricks with the greater electron backscatter diffraction (EBSD) community.

Perhaps the most popular EBSD application is grain analysis, as it’s fundamental to characterizing many materials. Because the results of grain analysis are sometimes consistent or inconsistent with other tests, it’s great to start with a basic understanding of a grain with respect to EBSD and how grain analysis works.

The definition of a grain in OIM Analysis differs from the strict academic definition, which refers to the collection of pixels within a certain orientation range. This orientation range, namely grain tolerance angle, can be changed in OIM Analysis, which is generally set to 5° by default. You can also vary the number of pixels in a grain (the default is 2). These parameters affect the result of grain size, so we should pay attention to them in the analysis. The prerequisite of grain analysis is that the data is statistically valuable. Sometimes this requires a lot of tests to achieve the goal, repetitive studies to diminish errors, or the data should be filtered or processed before the analysis (per relevant standards, accordingly).

Figure 1. A typical grain map.

A standard display for grain size analysis is the Grain Size (diameter) chart. First, the grain is fit to a circle, and then the software calculates the diameter. The data distribution range and average grain size are on the chart’s right side. The most frequent question users ask is, “What is the formula to calculate the average grain size?”. In fact, two results of the average grain size, which are calculated by two different methods, are shown. The ‘number’ method calculates the average area of each grain first (the sum area is divided by grain number values first) before it determines the diameter. In contrast, it considers different weights due to different areas for the ‘area’ method. Since large grains have larger weight percentages, it first calculates the average grain area using different weight percentages, then calculates the average grain size.

In addition to the average grain size, OIM Analysis offers a variety of charts and plots to characterize grain shape. The most popular one is the grain shape aspect ratio, an essential parameter to display the columnar grain property (grains are fit as an ellipse). In addition to the shape aspect ratio, the Grain Shape Orientation in OIM Analysis shows the angle between the long axis and the horizontal direction, which is suitable for grains with a specific growth direction.

OIM Analysis offers numerous functions. Concerning grain analysis, there are six different charts for grain size and eight for grain shapes. Some charts are not common, but they have corresponding application scenarios. If you do not know the meaning of those charts, you can query the OIM Analysis Help file to get relative information.

Grain analysis is a very common function of EBSD applications. As a webinar speaker, I enjoyed digging up some less familiar details so users could gain a deeper understanding of software operations. I look forward to continually introducing webinar topics to meet the EBSD community’s needs and make greater progress in the new year.

关于晶粒那些事儿

Dr. Sophie Yan, Applications Engineer, EDAX

最近我们办了一期OIM Analysis如何进行晶粒分析的直播，效果颇出我意料。大家对于基本操作的热情令我始料未及，在播出之后联系我的人中，也往往会提到这一场直播对他们有所帮助。我本以为，这一类关于基本操作的直播并不太吸引人，充其量也不过是成为大家在日常操作中备查的工具视频而已；但，果然是我灯下黑，事实并不是如此。我也借此机会，给大家分享一些基本的原则或窍门。

可能在EBSD的各种应用场景中，最常碰到的是就是粒度分析。绝大多数的人都会有这个需求。EBSD粒度分析的结果，有些会与其它测试的结果吻合，有些会有出入。这时，我们就必须了解EBSD的晶粒是怎么定义，粒度又是怎么测得的，才可能更好的分析EBSD测试的结果。

OIM中的晶粒不同于学术上严格的定义，是指在一定取向范围内的像素点的集合。这个取向范围，即容差角，是可以设置的，一般默认为5度。像素点的个数，也同样可以设置，默认个数为2; 这些参数的设置，其实都会影响我们统计晶粒粒径的结果，因此需要在粒径分析中予以注意。当然，进行粒径分析的前提是数据具有统计意义，有时需要进行大量的重复性的测试来减少误差，也需要在测试之前对数据进行筛选或处理（可参照相关标准进行操作）。

典型的晶粒图

最常见的粒度分析的结果是将晶粒拟合成圆，计算其平均直径，即常见的Grain Size(diameter)曲线。曲线（或柱状图）的右边是数据部分，有不同粒度分布的占比，也列出了平均粒径。这是我被客户问得最多的部分，即，我们的平均粒径的结果是怎么计算的：这个平均粒径其实列出了两种结果，由两种方法分别计算。“number”方法是指按数数目的方法，先计算每个颗粒平均的面积(总面积除以晶粒数)，然后再计算直径；”area”则要考虑因面积不同而带来的不同权重，大颗粒占权重较大，按权重计算出颗粒的平均面积，再计算平均粒径。

除平均粒径外，OIM Analysis还提供了多种表征颗粒形状的图表。最常见的是短长比（grain shape aspect ratio）,是描述非等轴晶粒径的重要参数(晶粒被拟合成椭圆)。当然，除了短边长边的比值，有些颗粒有形状还有明显的择优，按特定的方向生长，针对这一点，Grain Shape Orientation表征长边与水平方向的角度，可以描述这一特性。

OIM Analysis提供非常丰富的功能，晶粒粒径有6种不同图表，晶粒形状有8种。有些图表可能不太常用，但都有对应的应用场景。对于这些相对冷门的图表，一般用户，如不了解其功能，可以在OIM Analysis提供的帮助文件中查询，可以得到关于其功能或定义的相关信息。

粒度分析是EBSD应用非常常用的功能。这一次，作为主讲人，在准备过程中我也挖掘出一些平常不注意的细节，对软件操作也有了更深的了解。相信，随着我们随后不定期推出的一系列培训，我们能更加贴合用户的需求，协助大家把软件用得更好，在新的一年里，获得更大的进步。

Reaching Out

Dr. René de Kloe, Applications Scientist, EDAX

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.

I wish everybody a very happy and peaceful 2023.

Improved IPF Color Palettes

Will Lenthe, Principal Software Engineer, EDAX

Most IPF color schemes have several shortcomings:

  1. Although red, green, and blue are placed at a high symmetry axis, the remaining colors are not uniformly distributed
  2. Saturated rainbow palettes are not perceptually uniform, so the same orientation gradient will have different apparent intensities when centered around different orientations
  3. Groups with two or four high symmetry directions do not have a natural mapping to three principal colors
  4. Choosing red and green as principal colors result in poor contrast for individuals with red-green color vision deficiency (CVD)

OIM Analysis™ v9 implements four new Inverse Pole Figure (IPF) color palettes to address these issues, as shown in Figure 1. For fundamental sectors with three principal directions, CVD colors replace green with yellow for the second principal color. For fundamental sectors with four principal directions, red, yellow, green, and blue are used for traditional colors, and red, yellow, cyan, and blue are used for CVD colors. Notice that the new legends distribute colors smoothly while the old ones have large patches of red, green, and blue extending from the corners and sharp bands of yellow, cyan, and magenta.

Figure 1. The m3m (top) and m3 (bottom) IPF legend is shown from left to right for OIM Analysis v8 colors, new saturated colors, perceptually uniform colors, CVD saturated colors, and perceptually uniform CVD colors.

Figure 2. A nickel dataset is IPF colored with saturated (left) and perceptually uniform (right) color maps using traditional (top) and CVD (middle) colors. Notice that some significant orientation gradients in the KAM map (bottom left) are visible with perceptually uniform colors but may be invisible if the orientation falls in a low contrast region of the saturated color map. OIM Analysis v8 coloring is shown in the bottom right.

Figure 3. A partially recrystallized steel dataset is IPF colored with saturated (left) and perceptually uniform (right) color maps using traditional (top) and CVD (middle) colors. Notice that orientation gradients are over-emphasized in darker regions of the saturated color maps (blue and purple) and under-emphasized in brighter regions (green, yellow, and cyan).

Perceptual Uniformity

Perceptually uniform color maps are designed so that a constant size step in the data being colored results in an apparent color change of constant magnitude regardless of the starting value. The uniformity of a color map can be visualized by imposing a ripple onto a ramp, as shown in Figure 3 and described by Kovesi [1]. The ripple disappears in brighter regions of traditional saturated color maps but has a uniform relative intensity in perceptually uniform maps, as shown in Figure 4. The new perceptually uniform IPF colors in OIM Analysis v9 extend perceptually uniform cyclic color maps to a hemisphere by adding a white center point.

Figure 4. A perceptually uniform ramp is modified by a sine wave to create a test signal (green). The test signal is colored with a perceptually uniform black to white color map with maximum sine wave amplitude at the top of the image and minimum amplitude at the bottom. Note that the relative intensity of the ripple is the same at every gray level near the top edge and the ramp appears extremely smooth near the bottom edge. Figure adapted from Kovesi [1].


Figure 5. Traditional saturated color maps (top) are shown for heat (left) and rainbow (right) colors. Notice that the ripples are nearly invisible near red on both maps, yellow on the heat map, and green on the rainbow map. Perceptually uniform equivalents (bottom) sacrifice some color saturation/vividness to achieve a uniform sensitivity response across the entire map. Legends from Kovesi [1].


CVD Colors

Deuteranomaly (red-green CVD) is the most common form of CVD and is simulated in Figure 6 to illustrate how much ambiguity is introduced in traditional colors. CVD impacts roughly 1 in 12 men and 1 in 200 women, so CVD colors should be preferred for papers and presentations.

Figure 6. Deuteranomaly is simulated with increasing severity from left to right (normal, 30%, 70%, 100%/Deuteranopia) for the traditional (top) and CVD (bottom) saturated palettes. Notice that in the far-right column, the traditional map has different directions with the same color, while the CVD map is significantly less ambiguous.

Enhanced IPF saturated color palettes maintain a similar look and feel while more uniformly distributing the available gamut. Perceptually uniform IPF color palettes sacrifice the full use of the RGB gamut to render crystal directions with increased precision, and CVD colors avoid red-green ambiguity. Together these new palettes enable visualization and accurate interpretation of orientation data for the widest range of audiences.

References

  1. Kovesi, P. (2015). Good colour maps: How to design them. arXiv preprint arXiv:1509.03700.
  2. Nolze, G., & Hielscher, R. (2016). Orientations–perfectly colored. Journal of Applied Crystallography, 49(5), 1786-1802.

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.