#### 1. Introduction

Starting in 1988, Electron Backscatter Diffraction or EBSD revolutionized the way that materials scientists were able to view the microstructure of crystalline solids. Now there’s a new revolution in strain measurement: **High Angular Resolution EBSD** (HR EBSD). The properties of materials are heavily affected by the strain state of their microstructure.

HR EBSD makes it possible to measure residual strain states of materials at a resolution and sensitivity suitable for investigating the interplay between microstructure and the strain state. With 80 times more misorientation sensitivity than traditional EBSD analysis, HR EBSD enables scientists to view microstructural properties that have traditionally been invisible—and to make measurements of strain distributions that were once mere theory.

###### Data courtesy of Dr Ben Britton

#### 2. Background: The relationship between micro-texture and strain

Standard SEM based EBSD primarily provides maps of the spatial distribution of crystal orientation, i.e. crystallographic texture, and nearest neighbor disorientation, i.e. meso structure. It is well known that both factors contribute to the mechanical, properties of polycrystalline materials and it is understood that this arises from the orientation relationship between the internal stress state and the crystal slip systems. The Taylor and Schmidt models have been the standard methods of estimating the likely consequences. However, such models are necessarily very approximate because the details of the internal stress state is very poorly known, particularly in the more anisotropic materials and where loading conditions other than simple uniaxial tension apply.

## Accurate knowledge of the internal stress state is important in understanding and controlling the recrystallization process, the precursor to determining texture.

This is further compounded when we are dealing with materials with multiple phase and high degrees of precipitation.

**3. Conventional EBSD: Missing the complete picture **

The need to assess a material’s internal stress state is clearly necessary and many attempts have been made using conventional EBSD. These attempts have been indirect and have only produced qualitative results. This is because of the relatively poor angular resolution possible in conventional EBSD, 0.5 degrees as determined using the Hough Kikuchi band detection algorithm. Secondly because distortions within individual patterns, which occur because of elastic strain, are completely inaccessible. Thus although the spatial resolution of the technique is capable of detecting crystallographic changes within individual grains, the measurements are of insufficient precision to be able to interpret them in terms of the residual stress or dislocation density. The best that has been achieved so far has been the mapping of EBSD pattern quality and an assessment of the average disorientation between an individual point within a grain with its next nearest neighbors, the latter giving rise to the metric termed **Kernel Average**. *Kernel Average Maps *(**KAM**) have become the norm for assessing internal strain. As you will see below-

## There are inaccuracies with the conventional KAM approach to assessing strain primarily because of its low precision and artifacts of the Hough transform.

#### 4. Filling The Gap: HR EBSD for a better measure of strain

Now that we have established the need to better understand the strain and stress components of a material, in contrast to traditional EBSD methods the technique of **High Angular Resolution EBSD** or HR EBSD provides a rigorous quantitative measure of residual strain. Ranging from the elastic strains as small as 0.01% to the measurement of dislocation density distributions over the GND range 1x1012m-2 to 1014m-2.

The method is based on a **cross correlation procedure **or** XCF** between an EBSD pattern recorded from a reference region within a grain, (normally that with the lowest KAM value as measured using conventional EBSD) and all other points within the grain. This well documented and tested procedure leads to the determination of the full strain tensor and thence, through the generalized Young’s modulus, i.e. complete elastic stiffness tensor, to a measure of the stresses and on to the energy density distribution/von Misses stress metric. For example, it is possible to correlate slip line observations to shear stresses acting along them, to tensile stress concentrations at grain boundaries and to relate both to a set of sample reference axes or to the three reference axes defining the crystal orientation. A good example of this is shown in **Figure 1**.

#### 5. High Angular Resolution: Revealing inaccuracies in conventional EBSD

The HR EBSD technique improves the angular resolution to 0.0006˚ which leads to the KAM values being of far greater quality than otherwise possible. **Figure 2** illustrates a striking example of just how misleading the normal KAM map can be.

But much more valuable is the fact that the higher angular resolution also permits an analysis that reveals the distribution of the residual geometrically necessary dislocation density. These are the dislocations that are required to account for the measured disorientations. The analysis provides for the separate contributions from edge and screw dislocation components as well as the total GND density as shown in Figure 1(g). Such measurements are based on the Nye dislocation tensor and as such are dependent on the criterion of minimum residual energy. The result is also a lower bound case as the disorientations in the direction normal to the surface which cannot be measured without serial sectioning, are set to zero.

#### 6. Engineering Measures: The Von Misses Stress

It is often argued that a simpler metric might be invoked at times to assimilate all the information contained in the 9 component stress tensor as measured by the HR EBSD technique. One is that of principle stresses which are those commonly used in mechanics to define the set of orthogonal directions parallel to the axes that remain unchanged in direction under the imposed strain condition. Another is the Von Misses stress, which is a scalar stress which signifies a critical internal energy density which when exceeded will cause the material to yield plastically. HR EBSD provides the means through which both the principle stresses and the **Von Misses** stress can be mapped. No other electron diffraction based technique, which is used because of its high special resolution can provide this data. See the examples in **Figure 3**.

#### 7. Conclusion: A big step forward in Microstructural Characterization

HR EBSD provides a new dimension to EBSD. It is an advanced tool that moves us one step further in properly understanding the role of crystal orientation and neighbor disorientation in determining the mechanical properties and recrystallization processes. It is the next logical development to EBSD and without it the huge step forward in microstructural characterization provided by EBSD would be very much poorer.