Many crystal structures belong to one crystallographic symmetry group but share many characteristics with a group of higher symmetry. For example, the mineral quartz (SiO2) is trigonal but has a structure that is close to being hexagonal. This is known as pseudosymmetry and can cause significant problems for Electron Backscatter Diffraction (EBSD) analyses. Keeping with the quartz example, the images show a typical low resolution EBSP from quartz, and 2 possible solutions, rotated 60° about the <0001> axis relative to each other.
These systematic indexing errors can usually be avoided by careful optimisation of the experimental parameters, including:
Typical low resolution EBSD pattern from Quartz (SiO2), with a correct (top) and incorrect (bottom) solution. The incorrect solution is rotated 60° about the <0001> axis relative to the correct solution (i.e. the <m> axis is in the place of the <a> axis) Note the presence of certain Kikuchi bands (marked with red arrows) that distinguish the correct solution from its pseudosymmetric equivalent.
Orientation map showing some ilmenite (FeTiO3) grains in a rock sample. The checkerboard / speckled appearance in some grains is caused by the pseudosymmetry of ilmenite: it is low trigonal (Laue group -3), but very close to high trigonal (-3m).
For materials such as quartz, the Tru-I class indexing algorithm will successfully resolve the trigonal symmetry of the material, minimising any systematic misindexing. However, for some materials, the pseudosymmetry can result in errors, even with optimisation of the experimental parameters, and this will lead to orientation maps that have a “checkerboard” appearance, as shown on the left.
There are 2 ways to solve these problems (unless you resort to time-consuming pattern matching techniques), and these are highlighted in the following tabs.
Within AZtecHKL, there is an optional module (“Pseudosymmetry”) that utilises pre-knowledge about potential pseudosymmetric problems to ensure correct indexing. This tool is best used with good quality EBSPs and works as follows:
There are limitations to this approach: the EBSP quality cannot be too poor (as the differences between the pseudosymmetric equivalents needs to be resolved), and the difference between the structures has to be sufficient: typically at least 1-2% difference.
The efficacy of this approach is shown in the following example. The phase γ-TiAl is tetragonal, but the c:a ratio is only 1.018, so it is very close to having a cubic structure. With conventional indexing (the left-hand image), the orientation map has the characteristic checkerboard or speckled appearance, indicating that the indexing algorithm struggles to differentiate between 2 or more solutions. When the Pseudosymmetry tool is enabled within AZtec in conjunction with the refined accuracy indexing mode (using a 3-fold relationship close to the <111> axis), as shown in the right image, the indexing is far more robust, and the detailed structures of the twins in this material are fully resolved.
Example orientation maps from γ-TiAl collected using standard indexing (left) and with a combination of refined accuracy and pseudosymmetry definitions in AZtec (right)
Further details about this application can be read in our detailed application note, available here.
In many cases the degree of pseudosymmetry-related misindexing is relatively minor, and only becomes apparent once the data collection has been completed. In this situation it is possible to clean up the pseudosymmetric errors during the data analysis process.
This process can be carried out using AZtecCrystal and follows these steps:
This process is demonstrated in the following dataset from a quartz rock, showing how isolated pseudosymmetry errors can be removed whilst retaining genuine twin boundaries with the same crystallographic relationship.
The raw data shows that some grains contain isolated indexing errors caused by the pseudo-hexagonal structure of quartz. These are shown as isolated pixels or groups of pixels with red borders (denoting a 60° rotation about <0001>). However, also present are “Dauphiné Twins” that have the same crystallographic relationship.
The IPF map shows the data after cleaning to remove pseudosymmetric errors but retaining any twin domains >10 pixels in area. This process will then enable a more accurate analysis of the quartz boundary populations and the extent of Dauphiné Twinning in the sample.