It depends what do you want to show. Euler maps display - as you already mentioned - all non-equivalent orientations with another color, although the resolution is not that big as for IPF coloring. The biggest disadvantage is, that color jumps may appear in grains if the orientation is close to the fundamental sector, e.g. one Euler angle is described with 359°...and the next pixel by an angle 0.5°. Then the color jumps from a very dark to a bright color. Therefore, IPF have are commonly better (at least for m3m, 4/mmm, 6/mmm and mmm). In this case grains with practically the same orientation do not show color jumps anymore. The disadvantage: The color only displays the crystallographic encoding of a single reference direction, i.e. not the orientation. Even if you use IPF maps for all reference orientations X, Y, and Z, identically colored crystals do not automatically represent the same orientation. For cubic phases the same color is used by 8 different and non-equivalent orientations.

IPF coloring has, however, another application. The coloring of a reference direction is not useless since often a loading direction or thermal gradient etc. is connected to this directions, and then only this crystallographic direction is of special importance and not the orientation. Then and only then you should use IPF coloring.

The problems of color jumps is also for IPF coloring not solved since all other symmetries show them as well (except the above listed). To get a better impression about this problem, and to see a possible solution I recommend the following article:

Article Orientations - Perfectly colored

Hi,

Nice answer Gert! I was not aware of the coloring problem.

Please correct my if I am wrong, but I am not sure whether they show "all non-equivalent orientations" isn't the multiplicity of the Eulerspace a big problem for the quantification of all non-equivalent orientations - see, e.g. HJ Bunge - Texture analysis in materials science: mathematical methods -- or "Hansen - Tables for texture analysis in cubic crystals".

Kind regards

Dear Manuel, if I understand your remark correctly, then the multiplicity of the Euler space for cubic materials is 3? Then follows that 72 orientation descriptions are absolutely identical.What I man is something additional. It only looks like from the colors. In your case all are really identical or three times described. The case I point out is that for cubic phases 8 really different orientations are described by the same IPF colors. In this paper I only selected s example the 24 Kurdjumov-Sachs variants since it should be well-accepted that they are different. If moved (rotated) into the highest symmetric position it hopefully becomes visible that all orientations in a map occupying arbitrarily these orientations are non-equivalent but colored by the same colors.

Thank you very much Gert for your detailed answer. I was not aware of these problems on IPF-colour maps, and it comes as a surprise to me as so many researchers use IPF-colour maps reluctantly without being aware of these problems. Are you considering to follow a similar approach (as in the paper attached) for the Euler maps as well?