grain measurement

Aimless Wanderin’ in 3D (Part 3)

Dr. Stuart Wright, Senior Scientist, EDAX

In my research on the origins of the term texture to describe preferred lattice orientation I spent some time looking at one of the classic texts on the subject: Bunge’s “red bible” as we called it in our research group in grad school – Texture Analysis in Materials Science Mathematical Methods (1969). As I was reading I found an interesting passage as it relates to where we are with EBSD today:

“In a polycrystalline material crystallites of different shape, size and orientation are generally present. It can thus also occur that regions of different orientation are not separated from one another by unequivocally defined grain boundaries, but that, on the contrary, the orientation changes continuously from one point to another. If one desires to completely describe the crystal orientation of a polycrystalline material, one must specify the relevant orientation g for each point with coordinates x, y, z within the sample:

g=g(x,y,z)           (3.1)

If one writes g in EULER’s angles, this mean explicitly

φ_1=φ_1 (x,y,z);  Φ=Φ(x,y,z);  φ_2=φ_2 (x,y,z);           (3.2)

One thus requires three functions, each of these variables, which are also discontinuous at grain boundaries. Such a representation of the crystal orientation is very complicated. Where therefore observe that it has as yet been experimentally determined in only a very few cases (see, for example, references 139-141, 200-203), and that its mathematical treatment is so difficult that it is not practically applicable.”

I don’t quote these lines to detract in any way from the legacy of Professor Bunge in the field of texture analysis. I did not know Professor Bunge well but in all my interactions with him he was always very patient with my questions and generous with his time. Professor Bunge readily embraced new technology as it advanced texture analysis forward including automated EBSD. I quote this passage to show that the ideas behind what we might today call 3D texture analysis were germinated very early on. The work on Orientation Coherence by Brent Adams I quoted in Part 2 of this series was one of the first to mathematically build on these ideas. Now with serial sectioning via the FIB or other means coupled with EBSD as well as high-energy x-ray diffraction it is possible to realize the experimental side of these ideas in a, perhaps not routine but certainly, tractable manner.

A schematic of the evolution from pole figure-based ODF analysis to EBSD-based orientation maps to 3D texture data.

Others have anticipated these advancements as well. In chapter 2 of Rudy Wenk’s 1985 book entitled Preferred Orientation in Deformed Metal and Rocks: An introduction to Modern Texture Analysis it states:

“Pole figures and fabric diagrams provide information only about the orientation of crystals. It may be desirable to know the relation between the spatial distribution of grains and grain shape with respect to crystallographic orientation. Orientation relations between neighboring grains further defined the fabric and help to elucidate its significance.”

But let us return to the theme of aimless wanderin’s in texture terminology. The title for Chapter 4 of Bunge’s book is “Expansion of Orientation Distribution Functions in Series of Generalized Spherical Harmonics”. This chapter describes a solution the determination of the three-dimensional ODF (orientation distribution function) from two-dimensional pole figures. The chapter has a sub-title “Three-Dimensional Textures”. The three dimensions in this chapter of Bunge’s book are in orientation space (the three Euler Angles). What we call today a 3D texture is actually a 6D description with three dimensions in orientation space and three spatial dimensions (e.g. x, y and z). And those working with High-Energy x-rays have also characterized spatially resolved orientation distributions for in-situ experiments thus adding a seventh dimension of time, temperature, strain, …

It is nice to know in the nearly 50 years since Bunge’s book was published that what can sometimes appear to be aimless wanderin’s with mixed up terminology has actually lead us to higher dimensions of understanding. But, before we take too much credit for these advances in the “metallurgical arts”, as it says on the Google Scholar home page we “stand on the shoulders of giants” who envisioned and laid the groundwork for these advances.

Aimless Wanderin’ at the Meso-Scale (Part 2)

Dr. Stuart Wright, Senior Scientist, EDAX

If my memory is functioning correctly, I believe Val Randle coined the term “meso-texture” to describe the texture associated with the misorientations at grain boundaries.

I confess that, whenever I hear the term, I chuckle. This is because of a humorous memory tied to the first paper I was involved with. I was an undergraduate at Brigham Young University (BYU) at the time. The lead author, Brent Adams, later became my PhD advisor. The ideas presented in this work became the motivation behind my PhD work to automate EBSD.

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.

The paper describes some impressive work on the mathematical side by Brent and Peter and painstaking work by Tong-Tsung Wang who did hundreds of manual orientation measurements from individual grains in several planar sections of aluminum tubing using selected area diffraction. My role was digitize the microstructures in such a way that the two-point orientation correlations could be computed. The following is an example of one section plane from this work.

Digitized microstructure of one half of one section of a total of 10 sections used in the calculation of the orientation coherence function for aluminum tubing. Each grain number represents a individual grain orientation measurement.

The experimental work was a major undertaking. Thus, Brent Adams was so interested to hear David Dingley’s talk on EBSD at ICOTOM 8 in Santa Fe in 1987 shortly after this paper was published. Brent envisioned a fully automated system to link crystallographic orientation with microstructure via EBSD.

One of the interesting findings of this work was the discovery of a Meso-Structure:

“The strong implication of Table 2 is that there exists a new scale of microstructure in the material (and presumably in other polycrystalline materials) which has not previously been characterized, or even observed except in a qualitative manner. It seems appropriate to identify this new scale of microstructure as mesostructured since it clearly pertains to clusters or aggregates of grains or crystallites”

Greek statue who seems to be suppressing a chuckle.
Source: www.britannica.com/art/Archaic-smile

After this paper was published Brent received a letter from Sir Charles Frank. Sir Charles expressed his interest and appreciation for the ideas presented in the work. However, he objected to the term Meso-Structure. One of his objections was that “Meso” has its roots in Greek, but “Structure” is Latin. He didn’t like that we were mixing words of different etymological origins. I have to think this criticism was given “tongue in cheek” as the term microstructure with which Sir Charles was well familiar also mixes Greek and Latin. Thus, whenever I hear the term mesotexture used to describe grain boundary or misorientation texture I have to chuckle given it’s mix of the Greek “meso” and Latin “texture”.

I’m not sure what the best term is to describe the preferred misorientation of grain boundaries. The community uses the terms misorientation, disorientation, orientation difference and others sometimes as synonyms and at other times with differences in meaning. As all aimless wanderin’s tend to leave crisscrossing tracks, I note that my first exposure to the use of Rodrigues Vectors, which lend themselves well to describing misorientation, was by Sir Charles Frank at ICOTOM 8 in Santa Fe.

I hope my aimless wanderin’s through odd terminology and anecdotal history doesn’t leave you too disoriented 😊

(Next in this series are some ruminations on the term “3D texture”).

Notes from Madison: Atom Probe Tomography Users’ Meeting

Dr. Katherine Rice, Applications Scientist at CAMECA Instruments, Inc.

Dinner at the top of the Park with a view of the Wisconsin State Capitol

The Terrace at the University of Wisconsin

Last week was a great week up here in Madison for our bi-annual users’ meeting, with about 90 atom probe enthusiasts making the trek to Madison, WI to discuss the finer points of atom probe tomography (APT).   There were plenty of great sessions involving, for example, correlative microscopy, cryo-atom probe, and new ways to detect evaporated ions.  Lest anyone think that we are too serious up here in Wisconsin, we also enjoyed talks on atom probing rodent teeth and even beer, as well as having several social events where our attendees could sample local brews.

Demo attendees watching a map being taken

Demo attendees watching a map being taken

Many of the users have been implementing transmission EBSD (or TKD, as some folks prefer) on their needle-shaped atom probe specimens which are typically shaped by a focused ion beam (FIB) microscope.  This allows for identification of any grain boundaries present, and also helps position a grain boundary close to the specimen apex so there is a good chance it will be captured in an APT analysis.  Atom probe specimens usually have a radius of ~100 nm which makes them ideally sized for transmission EBSD at SEM voltages between 20-30 kV.   The users’ group meeting also marked another special event:  the debut of Atom Probe Assist (APA) mode in the TEAM™ software.  Transmission EBSD can be challenging, but APA mode makes the analysis faster and easier by implementing recipes for background subtraction developed by EDAX and by skipping mapping of areas not intercepted by the specimen.  We had about 20 users at the Tuesday demos of APA mode and another few at an additional demo on Friday.  CAMECA’s Dr. Yimeng Chen manned the FIB and quickly targeted a grain boundary for FIB milling while our EDAX friend Dr. Travis Rampton took maps after each milling step to make sure the grain boundary was contained in the specimen.

Yimeng Chen and Travis Rampton present a poster.

Yimeng Chen and Travis Rampton present a poster.

Sample holders that work well for t-EBSD and FIB were also on debut at the meeting.  Many of CAMECA’s atom probe users mount up each specimen to our Microtip coupons, which are 3 mm X 5 mm pieces of Si that hold 22 flat topped posts.  Our Microtip Holder (affectionately nicknamed the Moth) was developed to do transmission EBSD on each of 22 mounted specimens, and then transfer the stub portion directly into the atom probe.  Even if you don’t do APT, these microtip posts are a convenient way to mount multiple thin samples for transmission EBSD.

The moth sample holder containing a microtip coupon

The moth sample holder containing a microtip coupon

It was incredible to see the explosion of transmission EBSD for atom probe, and the cool things that many LEAP users are discovering when they try it out on their atom probe samples.  Perhaps the greatest strength of this technique is how easy and integrated it is in the atom probe specimen preparation process.  You don’t even need to move your sample or the camera between steps when you are shaping a liftout wedge into a specimen that is atom probe ready.  I look forward to hearing about the new applications that are being discovered when combining t-EBSD and APT!

When a picture is worth only a single word….

Matt Nowell – Product Manager EBSD, EDAX

I’ve been at EDAX, and formerly TSL, for 20 years now, and given that OIM makes such beautiful images, one of the more ironic facts about my career is that I am color blind.  That can sometimes make interpreting colored microstructural images a bit more challenging, and I’m very grateful for the flexibility in coloring within OIM Analysis that the software guys have put in for me (although I think they keep the default first 2 colors in phase maps red and green just because I won the last golf Burrito Open).

Occasionally, however, it’s very easy to read the microstructure.  Take this image for example:

Inverse Pole Figure showing crystallographic orientation.

This image is an Inverse Pole Figure (IPF) map showing the crystallographic orientation.  While I’m sure if one were properly motivated, you might find the right vector in sample space to turn this IPF map into a test for colorblindness, even I can see that it spells out DOE.  This very cool example was created by researchers at Oak Ridge National Laboratory, where they used an additive manufacturing process called Electron Beam Melting (EBM) to spatially modify the solidification texture development in a nickel-based superalloy.  One can easily imagine that if you can control the local microstructure, you can then design and engineer the microstructure to optimize properties spatially for specific loads and applications.  You can learn more about the work at Oak Ridge at: http://3dprint.com/19477/ebm-printing-3d-ornl/ or http://web.ornl.gov/sci/manufacturing/research/additive/.

Other approaches have also been used to write into the microstructure, which I guess is the equivalent to changing the font and font size.

Dimes

In this example from the Else Kooi Laboratory, formerly known as the Dimes Technology Center, at the Delft University of Technology (http://www.dimes.tudelft.nl/EKL/Home.php) a laser beam was used to locally induce recrystallization in polycrystalline silicon.  This approach has been used to develop thin film transistors used in things like liquid crystal displays.  The writing is visible in both the OIM image quality (IQ) map(top) and the grain map (bottom), where adjacent measurement pixels of similar orientations are grouped together as grains, and then these resolved grains are randomly colored to show size and morphology.  That approach gives each letter a different color.

OIM has even been used to read the deformation in metals to recover destroyed serial numbers in metal objects like firearms.  In the images below, an “X” has been stamped into a piece of stainless steel (a), and then polished to visually remove the marker (b).

Figure2

Researchers at NIST have then used OIM to map over the area, with the corresponding IQ map shown here:

ImageJ=1.47v unit=um

The residual plastic deformation present in the microstructure causes a lower EBSD IQ value which is used to image the stamped X.  Years ago EDAX was featured on the TV show CSI for our Orbis µXRF product.  With this forensic application, we are finally ready for a sequel.  More information about this application can be found in a paper by Ryan White and Bob Keller in Forensic Science International (R.M. White and R.R Keller, Restoration of firearm serial numbers with electron backscatter diffraction (EBSD) Forensic Science International 249 (2014) pp 266-270) and at http://www.nist.gov/mml/acmd/ebsd-021115.cfm.

While all of these examples have used OIM to visualize the text within the microstructure, my first introduction to this literary metallurgical engineering was observable by eye:

RexGG

This sample was created for the International Conference on Grain Growth (ICGG), held back in 1995.  In keeping with theme of this conference, the characters were placed by locally inhibiting the grain growth while the bulk material was recrystallized.

So, while these pictures many not be worth a thousand words, they do contain at least a thousand grains.  The fact that a few words have been engineered into the microstructure by various means is pretty incredible.

Many thanks to Ryan Dehoff at Oak Ridge National Lab, Ryan White and Bob Keller at NIST, and David Field at Washington State University for allowing the use of their images for this blog.

Resolving Matters

Dr. René de Kloe, Applications Specialist, EDAX

Every now and then a new critical parameter in EBSD analysis comes up. This parameter is often related to a new trend in materials science research or industrial development. One of the latest buzz-words is “nano”. Things are getting smaller and smaller and EBSD technology has to keep up to be able to provide the microstructural answers. This drive to investigate the tiniest details led, for example, to the emergence of transmission EBSD. But it seems that not everyone means the same thing when they talk about nano; Where does nano begin and where does it end? For example, is “nano” anything smaller than 1 micron, or anything below 100 nm, or perhaps only things smaller than 10 nm? The answer is of course: all of them. The feature scale really depends on your application and field of science. For example in natural geological materials, grain sizes smaller than 1 micron are not very common and such rocks could be described as nano-structures. But in semiconductor or photovoltaic applications nano may range from single atomic layers to perhaps 100 nm.

In the EBSD community the emergence of nano-analysis has sprouted the use of another buzz-word: ‘resolution’. But exactly as with nano, ‘resolution’ can have several different meanings depending on who you talk to. So let’s start with the basics, what is resolution?

resolution
Pronunciation: /rɛzəˈluːʃ(ə)n/
The smallest interval measurable by a telescope or other scientific instrument; the resolving power.
The degree of detail visible in a photographic or television image
A firm decision to do or not to do something
The action of solving a problem or contentious matter
(from http://www.oxforddictionaries.com/definition/english/resolution)

Of these definitions the first two have obvious relevance to EBSD analysis, but at the same time define something completely different. The first one deals with the feature size on the sample, whose limits are defined by the combination of SEM beam settings and physical sample properties. The second one describes the amount of detail observable in a diffraction pattern collected from an area of a sample, which is affected by the number of pixels available on the imaging sensor. These two definitions are easily confused, but are not directly related.

And of course there is a third definition of resolving something which is a well-known strength of EBSD. It is the power to resolve the difference between different phases. For example here is a geological material, a granitic rock with several minerals with low-symmetry crystal structures. In order to resolve the phase differences, the analysis of a rock like this does not require any high resolution settings. A detector resolution of only 120 pixels and step size of 0.5 micron was sufficient.

Figure 1
But things are not always what they seem at first glance as is illustrated by the sequence of images below. All these maps are collected with the same low detector resolution of only 80 pixels, but with very different spatial resolution, or step size, on the sample. The sample is a piece of the Gibeon meteorite, an iron meteorite that was discovered in Namibia in 1836. The structure is very coarse grained and the individual grains can easily be seen with the naked eye.

Field of View_2

But looks can be deceiving. My first attempt to characterize the structure resulted in a speckled map that looked pretty bad and made me doubt my polishing skills. Subsequent maps with higher and higher spatial resolution (i.e. smaller step size) started to resolve a fine-grained structure with many grains being smaller than 100 nm. So for this example, high spatial resolution maps were obtained using low resolution camera settings.

Figure 3

For phase identification and characterization of deformation microstructures the pixel resolution of the detector becomes more important, but within reason. For phase identification you want to be able to identify small details in a pattern and this is also helpful when you are looking at small orientation changes due to dislocation structures in a material. This biotite pattern displays a pseudosymmetry where the difference between similar orientations is defined by the position of some relatively weak bands in the pattern. The correct indexing result is outlined in red.

Figure 4

Left: Biotite patterns with pseudosymmetric indexing results – red pattern is correct
Right: Kernel average misorientation map in deformed iron alloy illustrating precise locations of subgrain boundaries

In such cases, what you need to identify the difference between these orientations is having enough pixels in the band pattern across the weaker and thinner bands to be able to detect them automatically. Therefore the band detection capabilties dictate the resolution that you need to resolve the difference between these two orientations and not the number of pixels that you have available on your EBSD detector. Typically a pattern of 200 pixels is sufficient on any material. And that resolution is also enough to be able to measure orientation changes down to 0.05 degrees, which allows accurate identification of subgrain structures as shown in the kernel misorientation map.

If even smaller orientation changes are the target of your analysis or if you want to measure minute shape changes of the crystal lattice due to elastic strains, the standard band detect routines are insufficient. For such analyses you would need to use a pattern with more pixels and a dedicated technique based on cross correlation of sections of the diffraction patterns. For this tool, using many more pixels would appear to be better. But keep in mind that other variables in the system geometry such as the exact detector positioning, signal-to-noise level, lens artifacts, or pattern center calibration errors can introduce uncertainties that may easily exceed the improvements gained by using more pixels. In practice, patterns with 480 pixels or more have been used successfully. What you see is not always what you get.

The above examples have highlighted a number of different uses of the word resolution and it appears that you have to be pretty careful in describing what you really want to accomplish. Going for a high resolution camera will not give you better spatial resolution in your EBSD maps. Similarly low resolution maps may be measured using a high resolution camera which shows that the number of pixels on your detector is totally independent of the spatial resolution that may be obtained on your samples.

Therefore to conclude I would like to appeal to the last definition of resolution mentioned above: The action of solving a problem or contentious matter.
With the different meanings of resolution clouding the waters and creating confusion I would like to propose the use of “high resolution EBSD ” to describe the application of mapping with small step-size to resolve the fine details in a material. “High precision EBSD” would then describe the application to map out small orientation changes in a material in order to investigate and understand the deformation mechanisms and finally “high definition EBSD” to describe the technique of investigating minute changes in pattern geometry to characterize (elastic) strains in the crystal lattice by applying cross-correlation methods.

My $0,02

Time For A Change – New Perspectives in Grain Size Analysis

EBSD geometry

Dr. Stuart Wright, Senior Scientist EBSD, EDAX

For better or worse, I’ve been long involved in trying to set forth some guidelines for the measurement of grain size using EBSD. This involvement has included serving on some of the standard committees, advising customers and reading, reviewing and publishing papers [1]. However, I’ve always felt unsettled about the outcome of those efforts. Part of that discomfort comes from the fear that an inexperienced EBSD user could be misled to an incorrect conclusion based on using a canned procedure. However, some recent experiments have given me more confidence in obtaining reliable grain size statistics using EBSD.

There are a couple of challenges associated with the measurement of grain size using EBSD. First, there are the usual factors associated with collecting good EBSD data: determining a polishing procedure that will produce good patterns, finding good SEM and EBSD camera settings, ensuring the sample is in the expected geometry [2]. However, I will assume these factors are well under control so that good quality EBSD data is obtained, that is data with a high indexing rate so that very little clean-up is required. Now, the challenge is making sure the choices for the parameters associated with grain size are appropriate. The first of these is the grain tolerance angle. I will focus on recrystallized materials at this point so the choice of grain tolerance angle is not as critical as for a deformed material. In the case of deformed materials, I’ve found you need to experiment with different values to get a feel for the best choice. However, for recrystallized material using the default value of 5° generally works well. The next critical parameter is the choice of the minimum grain size in terms of the number of grid points. Once this value is selected the analysis software will exclude grains with less than this value from the grain size distribution.

There are several approaches to selecting a good value for the minimum grain size – I will call it Nmin for brevity. It is entirely possible that a single point in an OIM scan could be a grain. Imagine the grain structure in three dimensions; it is easy to imagine a single scan point being associated with the top or bottom tip of a grain just intersecting the sampling plane. Thus a single point in an OIM scan could represent a grain especially if that point has a high confidence index. Of course, we have also seen many cases where an individual point is located at a grain boundary with a low confidence index. This arises because the resulting pattern is a combination of two competing patterns from the two grains on either side of the grain boundary (or three at a triple point) and thus the Hough transform will find bands from all the competing patterns resulting in an incorrect indexing [3]. Another consideration that has gone in to the choice of Nmin is is how well a shape can be reconstructed from a given number of grid points. For example, consider a circle. The following figure shows how well a circle can be approximated by a given number of grid points. To approximate the area of circle with less than 5% error requires about 30 points. However, if very many grains are measured the errors in approximating a given grain will be averaged out so I personally don’t think this argument should carry much weight in the choice of Nmin. In fact, I hope by the end of these ramblings that I will have convinced you that if using the right approach, the choice of Nmin is not as important as one might presume.

Grid points in a circle

Figure 1: Approximation of the area of a circle using a square grid and a hexagonal grid.

I’ve done some experiments with a very nice set of data provided by my colleague Matt Nowell. These measurements were performed as part of a Round-Robin test conducted for the development of ISO Guidelines for the measurement of grain size using EBSD [4]. The figure below shows five data sets measured on one sample merged together. I have excluded the grains touching the edges from my analysis. On average, each field contains 750 grains. The step size is 2 microns and each scan contains almost 250,000 data points. The total number of grains analyzed was 3748 grains. Prior to any analysis a grain dilation cleanup was applied to each individual dataset using a 5° tolerance angle, two pixels for the minimum grain size and the grains were required to span multiple grid rows. The percentage of points changed in the clean-up process was only 0.7% confirming the high fidelity of the data.

Figure 2: Grain map of the merged data.

Figure 2: Grain map of the merged data.

The grain size distributions for the individual data sets and the merged data set are shown in Figure 3 using both a linear axis and a log axis for the grain diameter (the horizontal axis). The vertical axis is the usual area fraction.

Stu June3a Stu June3b
Figure 3: Log and linear grain size distributions of the individual data sets (colors) and the merged data set (black) 

The next step in such analyses is to calculate the average grain size (I will use the diameter). This is simply done by adding up the diameters of all the grains and then dividing by the total number of grains. Figure 4 shows the average grain diameter overlaid on the distribution for the merged data.

Figure 4: Area fraction grain diameter distribution for the merged data overlaid with the average diameter.

Figure 4: Area fraction grain diameter distribution for the merged data overlaid with the average diameter.

As usual, the location of the average diameter does not correlate well with the center of the distribution. I always find this disconcerting. A common response is to simply pass this off to more data being needed especially since the distribution curve is still a bit jagged even with 3748 grains. You can experiment with the number of bins used to create the distribution as well as the grain definition parameters but the average grain size is always a bit left of where you think it should be. The reason for this mismatch is that the distribution is given in area fraction but the average is calculated as a number average. If you plot the distribution as a number fraction then the number average appears to fit the data better. However, what originally approximated a Gaussian curve in the area fraction plot now becomes skewed to the left in the number fraction plot.

Figure 5: Number fraction grain diameter distribution for the merged data overlaid with the average diameter.

Figure 5: Number fraction grain diameter distribution for the merged data overlaid with the average diameter.

Another solution to overcoming this mismatch between the average and the peak in the distribution is, instead of using a number averaging approach, using an area weighted averaging approach. The area weighted average is a relatively simple calculation given by:
Equation
Where n is the number of grains, Ai is the area of grain i and di is the diameter.
The area weighted averaging leads to an average value that matches that approximated “by-eye”.

Figure 6: Area fraction grain diameter distribution for the merged data overlaid with the average diameter calculated using number averaging and area weighted averaging.

Figure 6: Area fraction grain diameter distribution for the merged data overlaid with the average diameter calculated using number averaging and area weighted averaging.

In fact, I’ve found that the weighted area average provides a very good seed to any automatic fitting of the distribution data. The advantage of the area average relative to a curve-fit determination, is that the area average is calculated from the raw grain size data independent of the binning used to create the distribution plot.

Figure 7: Gaussian distributions for the merged data grain diameter distributions.

Figure 7: Gaussian distributions for the merged data grain diameter distributions.

So why do I bring this whole area weighted averaging approach up when the accepted approach is the number averaging approach? What does it have to do with selecting an appropriate Nmin ? The reason lies in the following plot of the area and number averages versus Nmin. In this plot the area average appears less sensitive to the choice of Nmin than the number average. This observation has held up on across many different samples on which I’ve performed grains size analysis.

Plot of average grain diameter as a function of the choice of Nmin

Figure 8: Plot of average grain diameter as a function of the choice of Nmin.

The sensitivity of the area average to Nmin seems to increase in the plot at about a value of 50. If we look at this same data plotted on a log scale the increase in sensitivity at higher Nmin become more apparent. These curves start at a value of Nmin = 5 due to the fact that this was the minimum grain size I selected for the grain dilation clean-up.

Figure 9: Log plot of average grain diameter as a function of the choice of Nmin.

Figure 9: Log plot of average grain diameter as a function of the choice of Nmin

The argument among the grain size community is to select a much larger Nmin value than that typically used in the EBSD community (2 to 5 points). The ASTM standard states that the minimum grain that should be included should contain 100 points and that the average grain should contain at least 500 points [4]. This standard evolved to this methodology primarily for historical consistency with optical measurements. However, these results show that the choice of Nmin is not so critical in the determination of the average value provided it is not too large. Another way to look at this is to plot the data differently. If we change the horizontal axis to Nmin divided by the number of points corresponding to the average grain size and change the vertical axis to be the average diameter divided by the average diameter at Nmin equal to five then we get the following plot.

Figure 10: The normalized average grain size as a function of the ration of the number of points in the minimum sized grain to the number of points in the average sized grain.

Figure 10: The normalized average grain size as a function of the ration of the number of points in the minimum sized grain to the number of points in the average sized grain.

From this plot it appears that using a small number for Nmin is fine. The key is not to pick too large of a number – it should not exceed 10% of the number of points in the averaged sized grain. However, this is with the proviso that area weighted averaging is used in the analysis. The contribution of the small grains to the average is very much less for area weighted averaging as opposed to number averaging. Thus using a small number, even just 1, will lead to nearly the same result as using a larger value such as the value of 5 I used in this example. Because we (the EBSD community) can very much more definitively calculate grains of any size relative to traditional optical measurements, I believe this approach is the correct one despite its inconsistency with the historical approach.

References
[1] Wright, S. I. (2010). “A Parametric Study of Electron Backscatter Diffraction based Grain Size Measurements.” Practical Metallography 47: 16-33.
[2] Nolze, G. (2007). “Image distortions in SEM and their influences on EBSD measurements.” Ultramicroscopy 107: 172-183.
[3] Wright, S. I., M. M. Nowell, R. de Kloe and L. Chan (2014). “Orientation Precision of Electron Backscatter Diffraction Measurements Near Grain Boundaries.” Microscopy and Microanalysis: (in press but available on First View).
[4] ISO 13067: Microbeam analysis – Electron backscatter diffraction – Measurement of average grain size.
[5] ASTM E2627-10: Standard practice for determining average grain size using electron backscatter diffraction (EBSD in) fully recrystallized polycrystalline materials.