Electron Backscatter Diffraction (EBSD) is mainly used in deformation applications. Can EBSD be used to measure material strain?
Strain is a bit of an ambiguous term. It can mean a lot of different things to different people. To be more specific, let's break it down into two parts: elastic strain and plastic strain. It's important to remember that elastic strain is a second rank tensor and is not simply a scalar value. Plastic strain is a tensor too, but with plastic strain, we also consider other scalar values of interest, such as stored energy and dislocation density.
When we think of plastic strain, we think of the interaction of dislocations with the crystal lattice. Dislocations can affect patterns in two different ways. First, a set of dislocations may align so to form a subgrain boundary. Second, non-aligned dislocations may not align but still cause local perturbations of the crystal lattice. They do create local misorientations but much more locally than the dislocations that form sub-grain boundaries. In fact, sometimes they can cancel each other out.
When considering the local perturbations, you can have a significant amount of dislocation density, but you could end up with a net Burgers vector of zero. We refer to these dislocations as statistically stored dislocations or SSDs. They will lead to degraded pattern quality and lower IQ values as a result of the distortion of the crystal lattice within the diffraction volume.
Suppose you do have a set of dislocations that form an ordered structure, for instance, that create changes in crystallographic orientation within the lattice within a large enough volume. In that case, you can get slightly different patterns from different areas within a microstructure. For example, two points in a deformed grain just a few nanometers apart can produce slightly different patterns due to the points having slightly different orientations. We often refer to such dislocations as Geometrically Necessary Dislocations or GNDs.
How can individual patterns be used in quantitative analysis?
Angus Wilkinson at Oxford University is a pioneer in this area. In his work, you compare two patterns. Ideally, a reference pattern for the non-strained material and a pattern for the deformed material. The goal is to quantify the differences between the two patterns. The first step is to create a set of matching regions of interest or ROIs in both patterns. Cross-correlation analysis is then applied between matching pairs of ROIs from the two patterns. Cross-correlations analysis is used to find small shifts in pixel intensities between the two ROIs. Careful analysis allows these shifts to be found at the sub-pixel range. Also, there are cross-correlations within each one of these regions of interest.
Once the shifts are determined for all ROI pairs, a displacement gradient tensor can be calculated. The tensor can be split into the elastic parts and the plastic parts. The symmetric components are the elastic tensor, and the anti-symmetric components are the plastic tensor. The plastic parts are associated with geometrically necessarily dislocations (GNDs).
The cross-correlation approach for measuring strain has been around for over a decade now, and it's becoming better accepted in the EBSD community. While this is a relative measure, because we have to compare the patterns, progress is being made to try to go towards an absolute measure incorporating simulated patterns in the analysis. This very much continues to be an active research area, but it's improving because of the emergence of dynamically simulated patterns.
Regarding what is possible with conventional indexing and learning about plastic strain, strain magnifies itself in two ways in the EBSD patterns. One way is that you have a degradation of pattern quality or slight changes in orientation, even though the pattern quality can remain relatively good, especially for small levels of plastic strain. In those cases, you only get slight changes in orientation.
This shows up in the maps in two different ways. If we focus on pattern quality, on partially recrystallized material, for instance, there may be dark regions in the strained areas and lighter regions in the recrystallized grains.
With a standard inverse pull figure (IPF) map showing the orientation, you can see that the color with reflective orientation will change quite a bit from one end of the grain to the other end in strained areas. Whereas in recrystallized grains, the color is solid. Subtle changes in color are indicative of strain.
What effects do IQ maps show up particularly well?
Plastic strain is very evident in IQ maps, but there are a lot of other things that create contrast in IQ maps. One is sample prep, and that is actually an indication to strain. IQ can also be affected by the phase of the materials. Second phases will often show up in IQ maps as lower or higher intensity due to the second phases' nature or chemical composition versus the matrix phase.
Cracks show up in IQ maps, as well as pores and grain boundaries. That's a problem because grain boundaries will appear to be strained material when it's just a grain boundary effect, and so the strain is actually a lower order effect that we would see in the patterns. Even grain size can have effects. These can be pretty subtle, and they are all effects that we can see in an IQ map.
Are there different mapping methods to characterize the distribution of local, microstructural misorientations?
There are many different methods of analyzing low angle misorientations that are characteristic of strain in the microstructure. There are kernel or window-based techniques, the most popular being the kernel average misorientation or KAM for average misorientation, but there is also the kernel orientation spread or KOS as well.
With KAM, the idea is that you have a kernel of points, and we calculate the angular deviation from a point in the kernel with respect to the orientation of the point at the center of the kernel. The average of all these deviations is the KAM value for the point at the center of the kernel. This process is repeated for all the points in the dataset. Generally, we only consider the points at the kernel's perimeter, but we're often looking at nearest neighbors, so the distinction doesn't matter.
To create a KAM map, you simply assign a color to each point in the scan area based on the KAM value.
The idea of these kernel-based metrics of misorientation can be extended to grains. One example is grain orientation spread (GOS). The first step is to group the points in the scan into grains using the standard grain reconstruction approaches, based on nearest neighbor misorientation.
The next step is to calculate the average orientation for a grain. Then, for each point in that grain, calculate the deviation in orientation from the average orientation. Then, you calculate the average of all of those deviations, which gives you the GOS value for the grain.
When you are looking at GOS, each point in the grain gets the same color, and again, this process is repeated for each grain in the dataset. This method results in a map where each grain is colored according to GOS, allowing you to see which grains have a lot of variation in orientation versus those grains that may be very clean, indicating they are free of any residual strain.
There's another method that I call grain reference orientation deviation (GROD), and in GROD, instead of each point getting the same color, we allow for some deviation. One approach to this is that you calculate an average orientation for the grain. Then you calculate the deviation at each point from the average, but instead of assigning each point that average value, you color each point according to that deviation, repeating this for every grain in the dataset.
What do GROD maps show, and how do they compare to other mapping techniques?
To explore what GROD maps can tell us, I will use some in-situ EBSD scan data from low-carbon steel undergoing uniaxial tensile deformation. We capture EBSD scans at steps of 1% strain during the in-situ tensile test out to 10% strain. In the IPF maps from this data, you'll see two effects. You see some change in the image quality, and that is somewhat due to repeatedly scanning the same area. More critical is the subtle changes in color you may see, which is what we focus on because the change color is reflective of the change in orientation, which, in turn, is reflective of the development of strain in the material.
Our repeated scans are not perfectly aligned, but we have tried to align them as best as we can. They can't be perfectly aligned because the grains are changing shape as we deform the material. This makes it difficult to do a point-by-point comparison between the scans at 10 percent and 0 percent. But we can use the idea of the GROD map.
With GROD maps, we're comparing the orientation at each point relative to a reference orientation. Within a single scan, each grain's reference orientation is generally chosen to be the average orientation for the grain. However, we can use the pre-deformation orientation of each grain from the 0% scan data for our in-situ data. We have named this a GROD0 map. The GROD0 map tends to show us the more general change in orientation. That is the independent rotation, the rigid body rotation of the material as a whole. Whereas the average grain orientation GROD map tends to emphasize the fragmentation that occurs during deformation as the material tries to maintain structural compatibility with neighboring grains, all of which are also rotating. Two models used to describe deformation in polycrystalline materials are the Taylor and Sachs models.
The Sachs model is a uniform stress model. It is assumed that each grain of material undergoes the same amount of stress during deformation. That results in that you have variable strain within the material, so you start to lose compatibility.
The Taylor approach assumes uniform-strain so that each grain has the same amount of strain in the material but variable stress. That overcomes the compatibility issue. This is well understood with slip lines and other types of analysis.
GROD0 tends to give us more of a Taylor-like view of the microstructure. The single scan GROD maps give us more of a Sachs-like view focused on the fragmentation grains undergo to satisfy compatibility while accommodating the strain. It is not a valid assumption that the points of the orientations during the reference orientation represent stationary material.
Still, it does give us an interesting picture, and it is always important to remember when looking at these types of maps on a plastic strain that they provide a description of the current state of the material but may not always provide us a historical evolutionary context of the materials as it moved towards that state.
What specific pattern challenges does EBSD present?
One challenge is that the more strain there is, the noisier the patterns are. Our indexing precision tends to drop off when we have more strain. This means we are less able to precisely locate the bands in the patterns using the Hough transform, which leads to more noise in the orientation measurement. As we increase the noise in the pattern, the precision goes down, and in KAM maps, we often see that the KAM values are higher near grain boundaries.
We were interested to see whether the increase in KAM values near grain boundaries was real due to dislocation pile up at the grain boundaries or if the increase was simply an artifact of imprecision. We have looked at this in detail. If the interaction volume contains a grain boundary, then you get a contribution from the lattice on either side of the grain map.
To use an example for real materials and the effect on the GND measurements, we added noise to the patterns artificially and then use some clean-up routines to see if we can improve the strain measurements. A simple one is Gaussian weighting, where we simply average the orientations of nearby pixels. Another one is called the Kuwahara Filter, which is a little more complex. We look at the neighboring grains, look at the median or mean and standard deviation, and replace the center of that, which is a well-known image processing technique. This filter will clean up the map, but it can create artificial sub-grain boundaries. A bilateral filter is basically a mix of these two ideas.
The Kuwahara method will bias towards sub-grain boundary creation. The Gaussian simply smooths things out, and bilateral is a mix between the two. If you play with a bilateral and all of its different parameters, you can get it to either match the Kuwahara or the Gaussian.
A new technique we've pioneered in recent years is called NPAR, where we look at the patterns of neighboring points and calculate an average pattern. Essentially, the NPAR technique provides spatial averaging of patterns as opposed to temporal averaging as you get with frame averaging or longer exposure times. NPAR can be very effective in improving the pattern quality. The higher pattern quality improves the orientation precision of pattern indexing, so we can use NPAR to filter and improve the orientation precision and is done with the Gaussian and Kuwahara filters.
How does EBSD compare to other imaging techniques? Are there trends seeing research favor alternative methods?
More and more people are using multiple techniques to try to get as complete a picture as possible. As a complement to EBSD, there are five important alternatives: transmission electron microscopy (TEM), electron channeling contrast imaging (ECCI), digital image correlation (DIC), or high-resolution digital image correlation (HRDIC), and high energy x-ray diffraction microscopy (HEDM).
I'm seeing EBSD studies on strain coupled with ECCI much more in papers and at conferences. It is natural, as ECCI is also an SEM-based technique. You have the BSE detector mounted below the pole piece, and you lightly tilt the sample into a two-beam condition, and you start to see the evidence for individual dislocations.
DIC is another method that I think is exciting, and I'm seeing more and more. If you think in the macro sense, you apply some markers on your material, you strain it, and you watch and see how those markers move. That's a well-known way to get an idea of strength fields. High-Resolution DIC can be achieved now using SEM imaging. This is convenient as it allows direct comparison with EBSD results providing more information on how deformation is accommodated in the microstructure.
With all of these SEM and TEM based techniques, we are always viewing planar surfaces. These characterization techniques are very much valuable, but sometimes it is critical to look below the free surface and probe the volume. High Energy X-Ray Diffraction a means of achieving this. More tools for studying the evolution of texture and micro-texture are being developed making it possible to couple EBSD measurements with such techniques for increased understanding
About Dr. Stuart Wright
Stuart's Ph.D. thesis research focused on automating the EBSD technique, which led to the first fully automated EBSD scans in 1991. Stuart then joined Los Alamos national lab and continued work in micro-texture and texture analysis using both the OIM technique and conventional x-ray diffraction.
He then joined the start-up company TSL commercializing the OIM technique working primarily on software development, and has continued in this role through the purchase of TSL by EDAX. Stuart is closely involved in the continued development of the technique as well as in working with scientists all over the world to apply the technique to materials research.
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