Tutorial A: General procedure – using CrossCourt to collect High Resolution EBSD Data
CrossCourt uses cross-correlation based techniques to measure the relative shifts between EBSD patterns caused by small lattice rotations or elastic strains. Comparisons are made between a reference pattern, representing a point of zero strain and a number of patterns taken from the area of interest. There are 4 stages of analysis:
1. Calibration and Preparation
It is very important to note that good quality data leads to good quality results and time needs to be spent optimising the pattern collection. Please refer to the separate manuals issued by EDAX, Oxford Instruments and Bruker for the necessary data collection steps.
2. Measurement of Pattern Shifts
The EBSD patterns are transferred from the data collection software used, i.e. OIM_DC, Aztec or CrystAlign, and imported into CrossCourt4. The software then measures the relative shifts of small, selected Regions of Interest (ROI) between each pattern and another selected as a reference pattern; the ROIs can be selected either automatically or manually and the shifts are measured in pixels. Results are displayed graphically and can be exported to a BLG Project File (based on an Excel worksheet).
3. Calculation of Infinitesimal Relative Distortion Tensor
To calculate the distortion tensor a minimum of 4 ROIs is needed. Normally, the best fit distortion tensor is calculated by oversampling with 20 or more ROIs. Alternatively, an iteratively weighted least squares’ solution to the distortion tensor can be calculated.
The pattern centre values and specimen to screen distance values, read from the data collection project files, are used to calculate the distortion tensor in the reference axes of the sample surface. Then, applying infinitesimal strain theory, the lattice distortion matrix is split to provide the Strain tensor (normal and shear strains) and Rotation tensor (rigid body rotations).
The stress tensor is calculated with this further information about the material’s crystal orientation and elastics constants.
4. Calculation of the Finite Relative Distortion Tensor
In the case of finite strain, infinitesimal strain theory breaks down, and finite strain theory must be considered.
Where the elements of the rotation tensor, as calculated above, are substantially bigger than the elements of the elastic strain tensor finite strain becomes relevant.
Crosscourt4’s approach is to remap the EBSD patterns to remove the rotations, as measured in stage 3 above, by back rotating them around the pattern centre. Then, these remapped patterns are cross-correlated with the original reference pattern allowing the actual elastic strains to be measured without influence from the large rotational components. Lastly, these measurements are recombined with the initial rotation tensor to create the Finite Distortion Matrix which then allows more accurate Elastic Strains and Stresses to be extracted.