Crystal orientation maps, e.g. derived by EBSD, are often displayed in so-called inverse pole figure (IPF) coloring. Do these maps (often three maps are displayed for reference direction X, Y and Z) really reflect the locally discovered orientation, or do they insert additional symmetries which reflect a higher symmetry and therefore perhaps another not-symmetry-equivalent crystal orientation?
> Crystal orientation maps, e.g. derived by EBSD, are often
> displayed in so-called inverse pole figure (IPF) coloring.
> Do these maps (often three maps are displayed for reference
> direction X, Y and Z) really reflect the locally discovered orientation, or
> do the insert additional symmetries which reflect a higher symmetry?
While a pole figure represents a crystal direction or plane normal of a material within the sample reference system, an inverse pole figure displays a specific sample direction within the crystal system. Due to the symmetry of the crystal system in most cases, the inverse pole figure can be reduced (for example standard triangle in the case of cubic materials).
Thus, IPF coloring of automated orientation imaging microscopy data shows which crystal direction is parallel to the sample direction to which the IPF is assigned to.
Using the common color-code for cubic materials means:
- red point: [001] of the crystal is parallel to the assigned sample direction
- blue point: [111] of the crystal system is parallel to the assigned sample direction
- green point: [101] of the crystal system is parallel to the assigned sample direction
Best regards, Alex
If you have 3 inverse pole figures then you have the complete orientation for each sampled point in the sample (unless the material is a quasi-crystal, in which case I guess you would need 6?). There are no assumptions made with respect to symmetry, only that it can be described by 3 basis vectors.
I have to admit that this was also my believe for many years. However, I think I was wrong. Look the attached IPF-colored pole figure from a transformation microstructure bcc->fcc. I only show a subset of 8 of the possible 24 variants. They all have different orientations, but in IPF colors they are identical. Or where do I do a mistake?
That's because this is just the {100} projection. They only way to show the full orientation symmetry is by creating an orientation distribution map (ODF), which you can do if you have 3 full pole figures.
Well, I am not sure we are talking about the same. Let me explain again: If I have grains which are displayed with the same color in all IPFs (i.e. X, Y and Z) I thought they have the same orientation. The transformation pole figures however display that there are much more orientations which are displayed be the same colors (in case of this very specific alignment for the fcc-bcc transformation). Why should I need more pole figures to display this effect?
My major topic was: is there a unmistakable correlation between crystal orientation and IPF colouring (even under the aspect of using 3 IPF-colored maps). My opinion is now: No.
> Crystal orientation maps, e.g. derived by EBSD, are often
> displayed in so-called inverse pole figure (IPF) coloring.
> Do these maps (often three maps are displayed for reference
> direction X, Y and Z) really reflect the locally discovered orientation, or
> do the insert additional symmetries which reflect a higher symmetry?
While a pole figure represents a crystal direction or plane normal of a material within the sample reference system, an inverse pole figure displays a specific sample direction within the crystal system. Due to the symmetry of the crystal system in most cases, the inverse pole figure can be reduced (for example standard triangle in the case of cubic materials).
Thus, IPF coloring of automated orientation imaging microscopy data shows which crystal direction is parallel to the sample direction to which the IPF is assigned to.
Using the common color-code for cubic materials means:
- red point: [001] of the crystal is parallel to the assigned sample direction
- blue point: [111] of the crystal system is parallel to the assigned sample direction
- green point: [101] of the crystal system is parallel to the assigned sample direction
Best regards, Alex
Well described Alex, but again: if you have two grains with the same colors for X, for Y and for Z (i.e. for each direction they can or actually must be different except of some specific cases) , does it mean that these two grains have the same orientation? As far as I understood the IPF concept, it claims this...what is actuallly the reason why this presentation is mainly used to display orientation maps in publications.
I know that this is actually not a direct conclusion since the definition of IPF colors is as you described. It defines the crystallographic description of a reference direction, but does not tell anything dierctly about the crystal orientation. Nevertheless, I have the impression that IPF coloring is used to present orientations instead of Euler coloring or anything else, simply because it seems to be easy to interprete.
> what is actuallly the reason why this presentation is mainly used to display
> orientation maps in publications.
I assume that it's simply the most colorful one ; ) - in many publications it's used without a special reference to texture - scientifically this is arguable.
I usually prefer to use a color-code which is somehow related to the texture components expected in the material. For uniaxial production methods (casting, directional solidification, swaging, uniaxial tensile & compression test, etc.) fibre textures are usually observed. In this case the IPF map of the corresponding sample direction directly shows the distribution of the different fibre texture components within the material.
> if you have two grains with the same colors for X, for Y and for Z
> (i.e. for each direction they can or actually must be different
> except of some specific cases), does it mean that these two grains
> have the same orientation?
This is only valid for triclinic materials. In the case of higher symmetry the relation is not biunique - for example: a grain with X || [100], Y || [010] & Z || [001] would produce the same color-coding as X || [010], Y || [-100] & Z || [001] and all other crystallgraphically equivalent orientations. Within other descriptions of orientation these can clearly be distinguished.
Best regards, Alex
You are obviously not surprized that the generated (colorized) map displays a higher symmetry than the data actually reflect. The virtually visible symmetry is even higher than any "sample" symmetry you can additionally apply....although this is then really considered in texture analysis whereas the IPF coloring is obviously only an visualization effect.
>This is only valid for triclinic materials. In the case of higher symmetry the relation is >not biunique - for example: a grain with X || [100], Y || [010] & Z || [001] would produce >the same color-coding as X || [010], Y || [-100] & Z || [001] and all other >crystallgraphically equivalent orientations. Within other descriptions of orientation >these can clearly be distinguished.
This effect is BTW something else since it does not change the orientation of the grain, only the description. Look again the upper pole figures! Your symmetry-equivalence describes the intrinsic symmetry of a crystal and would never generate the above shown pole figure. I guess you have to think about it again. It is not the same as I described in
Article Euler angles and crystal symmetry
Dear Gert,
very interesting mind twister indeed... just wondering what the PFs would look like with a color code obtained from the X and Y IPFs - Here you show only the Z IPF color code, which in the case of your 24 variants is always very near . I'm actually surprised that you get some orange gradated colors : I would have assumed that it would give roughly the same reddish shade.
Dear Claire, you are right...the slightly reddish is coming from a not well-aligned sample. The correct K-S or N-W relationship shows exactly the identical color.
The other PFs show...as you can imagine...green :-). There are then two possible options with a very near color, cf. the attached image. It shows each variant as one point in a 6x4 map for all variants at the same time and for all reference directions.
Dear Gert, I meet this problem in IPF coloring recently. I found even the colors for TD, RD, ND for two grains are same, the orientation could be different. That is due to the coloring algorithm where they mapping all the direction to the unit triangle. Here are two gains in cubic system for example.
Grain 1
Euler; ZXZ convention
295.4 51.6 176.6
Orientation matrix (Mechanical to crytal)
-0.3949 0.91755 0.04648
-0.58556 -0.21239 -0.78231
-0.70794 -0.33615 0.62115
Grain 2
Euler; ZXZ convention
64.6 51.6 3.4
Orientation matrix (Mechanical to crytal)
0.3949 0.91755 0.04648
-0.58556 0.21239 0.78231
0.70794 -0.33615 0.62115
As you can see from the orientation matrix, the RD, TD, ND directions (column value in the matrix) are crystallographically equivalent for two grains, so the color key for these directions should be the same. However, they are different orientation, the misorientation angle is about 108 deg. Therefore, judging misorientation just from the color could be wrong. Am I right?
Hello,
For the FCC I came across the case when the "normal" crystal and one of its sigma3 twins give exactly the same colors in the three inverse pole figures.
This happens when the [111] twinning axis is along X, Y or Z.
This is because the orientation matrix used for calculating the color for the x axis is rotated so as to bring either x or -x in the first stereo triangle. (using only rotations x will not always fall in the first triangle)
NB : if somebody could tell me where to find the calculation for the orientation colors for the monoclinic it would help me a lot.
Thanks
Best regards
Odile
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