1
The four frames
An orientation is a relation between two coordinate systems, so it is meaningless until both are named. In an EBSD experiment there are four in the chain, and the software reports a relation between the last two while silently assuming things about the first two.
| Frame | Set by | Where it bites |
|---|---|---|
| The detector frame | The phosphor screen, the pattern centre and the detector distance | Indexing happens here. A wrong pattern centre distorts orientations by degrees, systematically across the map, and it looks like a real gradient. |
| The microscope frame | The chamber: the beam along one axis, the stage tilt about another | The 70° tilt lives here. Whether the software has already taken it out is the first thing to establish, because applying it twice is as wrong as not applying it. |
| The scan or map frame | The scan generator: which way x runs across the map, and which way y runs down it | The handedness problem. If the map y runs down the image while the stage y runs up, the map and the orientations disagree by a mirror. |
| The specimen frame, RD, TD and ND | You, when you cut the sample | Nobody but you knows how the rolling direction sits relative to the scan. If you do not write it down and mark it, it is not recoverable afterwards. |
A vendor file can use one specimen frame for the map positions and a different one for the Euler angles. That is not a bug; it is a historical convention, and the reader has to know which pair the file uses. MTEX documents this explicitly, offers numbered settings for EDAX files and notes that Oxford and Bruker present the same problem with different alignments, and it enforces one invariant of its own: after import, the Euler angles refer to the map frame, so the map x and z axes are exactly the axes the Bunge rotations are defined about. The correction is applied at import rather than at plotting, which is the right place: fix the data once and every later figure inherits it.
The Euler angles themselves carry a second convention. Bunge (φ1, Φ, φ2) is a Z-X-Z sequence and is what nearly everything uses today. Roe and Matthies use Z-Y-Z, and Kocks differs again in the sense of the last rotation. Three numbers in a text file do not say which. Reading a Roe triple as if it were Bunge shifts the first and last angles by 90° each, which is not a small error and not a visible one.
And there is a third: whether the reported matrix takes crystal coordinates to sample coordinates or the other way round. The two are transposes, both are called "the orientation matrix" in print, and substituting one for the other leaves every misorientation angle unchanged while sending every axis somewhere else. The switch board below has all of these.
2
Flip a convention, watch the map
One synthetic rolled sheet, measured once. The grains are elongated along RD because that is what rolling does, and the texture is the ordinary face-centred-cubic rolling texture: copper, S and brass. Everything below is the same data read under different conventions.
Watch two things rather than one. The map carries the grain shapes, which are set by the processing and cannot lie. The short black bars are the in-plane trace of each grain's crystal [100], which comes from the orientation. When the frames agree, the bars sit at a consistent angle to the elongation. When they do not, the bars turn or mirror against grain shapes that have not moved, and that disagreement is the only visible symptom there is.
What the switches actually do to the numbers
The mirror. Reversing the sense of one specimen axis is a reflection, and a reflection is not a rotation. So the orientations you read out are not a rotated version of the truth; they are the truth's mirror image, which for a chiral texture is a different texture. The give-away is that the pole figure keeps its shape and reverses its handedness, and every plot still looks completely normal. This is the single most common frame error and the hardest to see.
The swap. Putting RD along the other map axis is an honest 90° rotation of the specimen frame, so it is recoverable: apply the rotation and the data is correct again. A rolling texture read this way looks like a sample that was cut across the rolling direction, which is exactly the mistake you would make from it.
The transpose. Using the crystal-to-sample matrix where the sample-to-crystal one is wanted inverts every orientation. Misorientation angles survive untouched, because the angle of a rotation equals the angle of its inverse, so a grain boundary distribution looks perfect. The axes do not survive: a 60° twin still reads 60°, but about the wrong direction, and every pole figure is wrong in a way that has no simple description.
The Euler convention. Roe (ψ, θ, φ) is Z-Y-Z; Bunge (φ1, Φ, φ2) is Z-X-Z. The two are related by φ1 = ψ + 90° and φ2 = φ − 90°, so reading one triple as the other rotates everything by 90° twice, about different axes. The result is a plausible but unrelated texture. This one bites when a text file changes hands, which is most of the time.
The pole figure layout. This one is only a plotting choice and changes no data, but it is worth a switch because half the confusion when comparing with a published figure is that the paper drew RD up and your software drew it to the right. Compare shapes, not positions, until you have checked which is which.
A note on the projection hemisphere, which people expect to be a switch and is not, for cubic {111}: the pole set is centrosymmetric, so the upper and lower hemispheres carry the same figure. Hemisphere choice matters for a non-centrosymmetric pole set and for a direction that is genuinely one-sided, such as a plotted sample direction on an inverse pole figure.
3
What each mistake looks like
Sorted by how often it happens rather than how bad it is, because the common ones are the quiet ones.
| Mistake | In the map | In the pole figure | What survives it | The check |
|---|---|---|---|---|
| Map and Euler frames mirrored relative to each other | Crystal traces lean the wrong way against unchanged grain shapes | The right shape with the wrong handedness | Every misorientation angle, every grain size, every phase fraction | A fiducial with a known handedness, or a known texture |
| RD assigned to the wrong map axis | Grains elongated along the axis you are calling TD | Rotated by 90°, and it looks like a cross-rolled or transverse sample | Everything except the direction labels | Mark the rolling direction on the specimen before it goes in |
| Orientation matrix transposed | Traces uncorrelated with grain shape | An unrelated but plausible texture | Misorientation angles and the boundary distribution | Check a known twin: 60° is not enough, the axis must be <111> |
| Euler triple read under the wrong convention | Traces uncorrelated with grain shape | An unrelated but plausible texture | Nothing about direction; angles between grains are also wrong | Re-import from the vendor file rather than from a text export, or ask what the exporter wrote |
| Pattern centre wrong | A smooth orientation gradient across the map that is not in the material | Components smeared along an arc | Nothing, quantitatively; the map is still qualitatively right | Calibrate on a strain-free single crystal and check the fit residual across the field |
| The 70° tilt applied twice, or not at all | Everything rotated by 70° about the tilt axis | Whole texture rotated by 70° | Misorientation angles | A cube-textured or single-crystal standard indexed with a known orientation |
Look at the "what survives it" column. Misorientation angles survive almost everything, which is exactly why a clean grain-boundary-misorientation distribution is not evidence that the frames are right. Anything you compute from angles alone (grain size, boundary fractions, a KAM map, a Σ3 count) will look correct in a completely mis-framed dataset. Everything you compute from directions (a texture component, a Schmid factor, a slip trace analysis, a boundary plane, a lift-out direction) will be wrong and will not tell you.
4
How to settle it, once
This is an afternoon, done once per instrument and software version, and it retires the question. Everything after that is bookkeeping.
- Put a handed mark on a sample. An L-shaped scratch, an asymmetric array of microindents, a FIB-milled letter: anything whose mirror image is distinguishable from itself. A square or a cross will not do, and neither will a single scratch, because both are their own mirror images. Map it. If the mark comes out mirrored in the image the map frame is flipped; if it comes out correct, the image is right and the orientations may still not be.
- Use a specimen whose texture you already know. A heavily rolled sheet of a common face-centred-cubic metal is ideal, because its {111} pole figure is a textbook picture and it is chiral, so a mirror is visible at a glance. A single crystal cut on a known plane is better still if you can get one. Compare your pole figure to the published one including its handedness, not just its shape.
- Check a twin. In an annealed face-centred-cubic metal, the coherent twin boundaries must come out at 60° about <111>. The 60° part survives a transposed matrix, so the <111> part is the test that matters. If the angle is right and the axis is not, the matrix sense is wrong.
- Cross-check the same file in a second package. Import once in the vendor software and once in MTEX or another reader, plot the same pole figure, and confirm they agree. If they do not, one import setting is wrong and the disagreement tells you which axis it is on.
- Write the answer down where the data lives. The import setting, the Euler convention, the matrix sense, which map axis is RD, and the date. Put it in the folder with the datasets, not in your head. Software versions change defaults, and a note in the folder is the only thing that survives the change.
Label RD and TD on the figure itself. Say which projection and which hemisphere. Say the software and version that made it. Four extra words in a caption make the figure re-usable by someone who does not share your defaults, and they make your own future re-analysis possible. Most published pole figures do not carry them, which is why so much time gets spent guessing.
Sources
Show the references
- MTEX documentation, Reference Frame Alignment (mtex-toolbox.github.io): the statement that a vendor file may use one specimen frame for map positions and another for Euler angles, the numbered EDAX settings, the note that Oxford and Bruker present the same problem with different alignments, and the rule that the correction belongs at import rather than at plotting.
- H.-J. Bunge, Texture Analysis in Materials Science, Butterworths (1982): the Z-X-Z Euler convention used throughout this page, and its relation to the Roe angles.
- A. J. Schwartz, M. Kumar, B. L. Adams, D. P. Field (eds.), Electron Backscatter Diffraction in Materials Science, 2nd ed., Springer (2009): the detector, microscope and specimen frames and the tilt correction between them.
- U. F. Kocks, C. N. Tomé, H.-R. Wenk, Texture and Anisotropy, Cambridge (1998): the rolling texture components used in the simulation (copper, S and brass) and the convention comparison.