In texture analysis the data are often symmetrized in order to increase the statistical significance assuming an expected symmetry. To this aim terms like triclinic, monoclinic and orthorhombic have been introduced which practically results in a reduction of the first Euler angle, and an adaptation of the second and the third. Unfortunately, these term are already used for the classification of crystal systems which is at least irritating but also misunderstanding since often it is not clear that the assumed (sample or process) symmetry required a well-aligned sample before application of this symmetry. Is there any reason why one uses these terms, and who introduced them? Is it still necessary to "symmetrize" data since the detection techniques have been strongly improved?
Thanks for refering the Texture book (Kocks et al.). I guess it is a very good recommendation to use in future the terms "plane symmetry" and "orthotropic symmetry".
Just adding to the discussion...
If you do have a rather rare book by Matthies, Vinel & Helming "Standard distributions in texture analysis", you may consult the chapter 5.
Sample symmetry definitely reduces the fundamental region of the orientation space, which contains non-redundant ODF information. Sample symmetry may be quite exotic, meaning, with extra symmetry elements when compared to possible set of crystal symmetries; e.g., five-fold axis... or infinite axis, leading to a fiber texture. Personally, I prefer not to enforce any sample symmetry unless the dataset is largely insufficient to completely cover the orientation space, e.g., if one performs diffraction experiment in high pressure cell with uniaxial stress, there is no possibility to collect necessary amount of data, but logically one expects a fiber texture to form in the sample. Or, if one works with the same samples, e.g., rolled sheets, over and over, there is no need to make extra measurements (and experimental time) in sample directions that are physically indistinguishable from those already probed. In diffraction, pole figure grid has some angular step, and detectors do see a certain finite solid angle; thus some sample misalignment (within the instrumental angular resolution) could be tolerated.
It's a good question/observation (a terminology designed to confuse ? :-) ).
One of my mentors on this general topic, Prof. Tony Rollett advocates using a combination of crystal and sample symmetries to describe symmetry of any particular case, i.e. crystal-sample, e.g. cubic-orthorhombic, or hexagonal-triclinic.
I see from your question you already appreciate probably all of what follows, but for anybody else who wants a lead into the general issues, I thought it might be helpful to them to lay some of it out & add a source or two to the discussion. Going to Tony's webpages is also recommended for a good introduction to texture. http://neon.mems.cmu.edu/rollett/27750/27750.html
For a known crystal structure that you can enforce its crystal symmetry on the data is the general assumption (perhaps there are esoteric crystal cases where this is not the done thing ? ). Having symmetries present reduces the size of Euler space required to fully describe the texture of a sample, as shown in Table 2.2 of 'Introduction to Texture Analysis, Macrotexture, Microtexture & Orientation Mapping' by V. Randle and O. Engler. Crystal symmetry on one hand affects the range of PHI and phi2 required for a full texture description. Sample symmetry on the other hand affects the range of phi1 required to fully describe the texture of a sample (see Table in book).
Sample symmetry unlike crystal symmetry is only a statistical symmetry, if it actually appears in your data, (with the expected symmetry for the sample reference frame (say deformation mode) investigated), then it is because with respect to the mirror/symmetry plane involved you have sampled enough material on either side of that reflection plane to satisfy the statistical requirements.
On the other hand you may decide this or that sample symmetry will be present and simply enforce the requisite symmetry on your data.
The question then arises when is it appropriate to enforce the sample symmetry ?
That really depends upon the question you were trying to answer in the first place with your investigation, and its affect on the data (i.e. that of sample symmetry) depends upon the influence of the processes that created the texture in your sample, and the practicalities of how you went about investigating your sample, technique, exact location sampled & size of area examined, accuracy of sampling plane alignment etc. etc. I guess it is quite a fundamental/basic thing in such investiagtions to make sure you are doing the right things to get the answer you were after.
As another poster noted, in the various software suites there is often a function to tweak (rotate) the 'raw' data (typically pole figures) to symmetry before processing it, if the alignment was a bit off.
Hopes this helps in some way.
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