In EBSD a common believe exists which claims that cubic phases are easier to index than phases of lower symmetry. Since only the (pre calculated) interplanar angles are used - except of the optional band widths which remarkably reduces the indexing speed - why an indexing should be more complicated for low-symmetry phases? On the other hand, for cubic phases many angles are equal. Is a discrimination of the concerned planes even more problematic for cubic phases which causes the well-known pseudo-symmetric orientation solutions?
Dear Gert, I suggest you get hold of a crystallography textbook or have a go at indexing a diffraction pattern yourself "by hand" (rather than automatically in a computer). You will find that indexing a cubic pattern is straightforward because there is only one variable, the cell parameter "a". All unit cell lengths are the same, and all inter-axial angles are 90˚. There is therefore a high degree of degeneracy. Compare this with a triclinic crystal where there are six variables and reciprocal lattice vectors are much more independent of each other.
Dear Simon, I don't talk about identification or lattice parameter determination. There you are (probably) right. In EBSD you KNOW the phases (better: you need to know), so that the calculation of any angle might take a bit longer but you need to do it only once...before the measurement. Therefore my question: What should be more difficult since the entire indexing is only based on the comparison of experimentally extracted angles and theoretically calculated derived from the phase description? Nevertheless thanks for your answer.
It really is as simple as Simon stated. With the same number of data points it is much easier to fit one variable than six. This is not just for the lattice constants but for the orientation as well since fitting the orientation of a cubic structure involves using a much smaller part of orientation space than less symmetric structures. So to answer your question, not only are cubic structures assumed to be more easily indexed than lower symmetry structure they are actually in practice easier to index both in terms of the amount of data needed to get a quality fit but also by the actual computation necessary to do the indexing. This has been widely known and verified for almost a century, so again I have to agree with Simon and suggest you brush up on your crystallography by reading a good introduction (for example Warren or Cullity if you don't want to a rigorous mathematical approach from first principles but just want to know the relevant mathematics needed without seeing how they are derived.
I am not sure whether we are talking about the same topic. If you start indexing an EBSD patterns you simply see the bands which define together with the pattern center (incl. detector distance) undetermined planes which are assumed to correspond to lattice planes of a single-crystalline volume (which is not correct along grain or phase boundaries. Moreover, "faked" bands complicates this business dramatically.). From these planes you only derive the interplanar angles, so that you have a matrix describing any possible angle combination. Until now you don't know anything about symmetry, reduced orientation space etc. The indexing procedure itself is using in different ways (depends on the company which developed the algorithm) a comparison of derived angles with theoretical angles between planes calculated from one or more phases. There it doesn't matter which size these angles have (i.e. which symmetry). From my (present) point of view you also cannot reduce the set of possible angles simply because it is a cubic phase, since you need to consider in any case the half hemisphere to cosider e.g. each of the dodecahedron planes which shows a different angle to a specific band represented by a general (hkl). If you change the cubic lattice into a slightly distorted all {110} planes have to split into independent crystallographic planes {hkl}_i which practically have the same position in space, i.e. a more or less unchanged angle table. But in any case you need all planes, anyway which symmetry your lattice has.
A reduction of the Euler angles in to a fundamental sector or zone happens later: see e.g.
Article Euler angles and crystal symmetry
If you asking whether this particular software you are using to index the images cares about the symmetry then you are asking a question you already the know the answer to. I was discussing the fact that cubic structures are easier to index if the software you are using is optimized to take the possible symmetries in orientation space into account. I think the problem is that your software is fitting in Euler space, which is not well suited for indexing orientations. If you transform to Rodriguez space then points in reciprocal space (scattering vectors) become lines. The point of intersection of a number of lines defines the orientation. In this space it becomes much easier to index multiple orientations in the same measured area. Symmetry considerations allow optimization is the order in which sub-volumes of Rodriguez space are searched for intersections of lines (this back projection approach is much faster than using a matrix of interplanar angles since that matrix would have to be inverted in order to find the orientation solutions and therefore does not take advantage of higher symmetry solutions). Cubic orientations need a much smaller volume of Rodriguez space to be searched for intersecting lines than low symmetries. This, I believe, meets the requirements for being easier to index.
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