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?

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

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.

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.

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.

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.

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

EBSD Analysis Between a Rock and a Hard Place

Travis Rampton, Applications Engineer EBSD

As an applications engineer at EDAX, I have the opportunity to work with many different people on a regular basis. Each person I meet has his or her own unique reason for using our microanalysis systems. At one recent event I was able to work with Dr. Nigel Kelly, an assistant professor from Colorado School of Mines. Besides bringing his great Australian accent he also brought an interesting geological specimen to study via EBSD: a single embedded Zircon grain. While this might not seem exciting to someone with a background dealing with polycrystalline metals, the remainder of this post will use EBSD data to demonstrate otherwise.

To begin understanding why the Zircon specimen was fascinating enough to deserve its own blog post, I will provide a brief background on the sample. Before being extracted, mounted, and polished, the observed grain (BSE and IPF image shown above) was subjected to the presence of Uranium by natural causes. The exposure to radiation caused crystallographic changes in the grain which were manifested as deformation within the grain. Crystallographic deformation has long been observable by EBSD and so this particular specimen seemed well suited for the technique.

EBSD offers many metrics for measuring and quantifying deformation in a crystalline material. Research has shown the usefulness of both image quality (IQ) and local measures of misorientation (kernel average misorientation (KAM), grain average misorientation, etc.) in obtaining this information via EBSD. Each of these metrics is important depending on the magnitude and length scale of the deformation present in a specimen.
Image quality is a metric that looks at the intensity of the Kikuchi bands in an EBSD pattern at each point in a scan. Mathematically it is defined as:

where N is the number of measured Kikuchi bands used and H is the value of the Hough transform located at peak (p_i,θ_i). Typically maps of IQ are used like images obtained from traditional metallographic etching under a light microscope to reveal grain structure (see below).

The darkest areas are indicative of grain boundaries. This occurs due to mixing of patterns at grain boundaries which causes a reduction in the intensity of all reflected Kikuchi bands. While this phenomenon is manifested at grain boundaries it can also happen for other reasons. Those causes are generally on the length scale of the electron interaction volume, so anything that affects the crystal structure with a ~100 nm radius of the scan point could manifest itself in the IQ map. Below is the IQ map of just the Zircon grain coupled with a few EBSD patterns (96 x 96 pixels) from indicated regions.

Conversations with Dr. Kelly revealed that the variations in image quality in this sample point to metamictization within the grain. Metamictization occurs in the grain due to the presence of Uranium which causes the crystal to become amorphous. As the crystal structure degrades so do the EBSD patterns and associated IQ which can be seen above.

The metamictization seen via the IQ maps is not the only detectable deformation mechanism that is present in this specimen. Other measures of local misorientation show subtle changes in orientation at discrete zones in the grain. For this specimen two conventional measures were used along with one novel metric. The first misorientation map below shows the KAM which has been a traditional measure of plastic deformation in crystals since the early days of EBSD (i.e. before my time). In the KAM map there are a few distinct regions of higher values which indicate subtle changes in crystallographic orientation often associated with increased dislocation content. The second maps show the grain reference orientation deviation (GROD) angle which is displays the misorientation angle of a point from the grain’s average orientation. With this map we get a different perspective of the deformation in the sample. Additionally, the misorientation angles are all less than two degrees so the visible plastic deformation is really quite small. Finally, the new metric used on this sample was a GROD axis plot. Previously, deformation only focused on the angle of misorientation since these measures could be readily correlated to % plastic strain values. However, the addition of mapping the axis reveals the deformation zoning in a sample which might not otherwise be visible with traditional measures.

While the KAM and GROD angle maps provide quantitative values on the degree of deformation in the Zircon grain the GROD axis map shows the subgrain structure. In the words of Dr. Kelly, “The GROD maps show nicely the sub-grain rotation that is occurring. But what I find cool is that it is radial – the higher U core compared with rim causes differential expansion of the two domains, the core expanding greater than the rim causing radial fractures” (now reread that in your mind with an Australian accent for better effect). These radial fractures can be best seen in the BSE image at the beginning of this blog and the GROD axis map.

The maps used in this blog to show various modes of deformation are a subset of all possible measures. PRIAS imaging was also used on this sample and showed several types of information including compositional difference, topography, and orientation/deformation contrast (see below). With all of the types of deformation that can occur in a sample it is nice to know that EBSD provides several metrics for extracting each bit of that information.