Hi,

Misorientation is the difference in crystallographic orientation between two crystallites in a polycrystalline material.

In crystalline materials, the orientation of a crystallite is defined by a transformation from a sample reference frame (i.e. defined by the direction of a rolling or extrusion process and two orthogonal directions) to the local reference frame of the crystalline lattice, as defined by the basis of the unit cell. In the same way, misorientation is the transformation necessary to move from one local crystal frame to some other crystal frame. That is, it is the distance in orientation space between two distinct orientations. If the orientations are specified in terms of matrices of direction cosines gA and gB, then the misorientation operator ∆gAB going from A to B can be defined as follows:

gB = Delta gAB*gA

Delta gAB = gB / gA

where the term gA−1 is the reverse operation of gA, that is, transformation from crystal frame A back to the sample frame. This provides an alternate description of misorientation as the successive operation of transforming from the first crystal frame (A) back to the sample frame and subsequently to the new crystal frame (B).

Various methods can be used to represent this transformation operation, such as: Euler angles, Rodrigues vectors, axis/angle (where the axis is specified as a crystallographic direction), or unit quaternions.

Disorientation is the opposite of orientation. It is a cognitive disability in which the senses of time, direction, and recognition of items (things), people and places become difficult to distinguish/identify.

With my best regards!

Dr. Adel OUESLATI

As in case of martensite (phase or not?), the answer depends on definitions (conventions). However, unlike martensite, there is no even more or less established rules. So, the definite rule that is still waited will depend on frequency of one or another term in further publications. In my opinion, based on the current publication statistics, MISORIENTATION is most often applied to interfaces (local sense), whereas DISORIENTATIONS characterize BOTH adjacent AND remote crystal elements.

It is interesting to see that the two terms are sometimes used interchangeably, or as Prof. Zisman points out, for different kinds of measurements.

My understanding was that disorientation is a subset of misorientation, while talking about orientation difference between two crystals in terms of rotation angle/rotation pairs. Different pairs of rotation axis-rotation angles can be used to bring one crystal to the orientation of the other (number of pairs would depend on the symmetry of the crystals). All the pairs represent misorientations. Of these, the pair with the smallest angle is the disorientation. Hence, disorientation becomes a subset of misorientation.

This definition is applied to FCC in the link below; there must would be similar examples for other crystal structures:Article Statistical Analysis of Misorientation Distributions From Gr...

I would be very keen to hear any other definitions/differences of these terms.

So, it means that intergrain orientation variations are preferred misorientations (small angles, low-angle boundaries) whereas intragrain orientations are better called disorientation (high-angle boundaries)?

I havn't seen it under this aspect but sounds reasonable. :-)

I think that the terms 'misorientation' and 'disorientation' refer to the same phenomenon.

Orientation (g): The orientation of the crystal lattice with respect to some reference frame; usual a frame defined by the processing or sample geometry.

Misorientation (∆g): The orientation of one crystal lattice with respect to another. Some times termed the orientation difference or disorientation.

Regards

The intra/inter granular difference is quite interesting, because it suggests a measurement-based classification (rather than a fundamental crystallographic difference). Yet, I don't find this difference in common EBSD based terminology- commonly used parameters like GAM (intergranular) and KAM/LAM (intragranular) all use the term 'misorientation'. One exception seems to be the ATOM package, where misorientation, disorientation, disinclination are all used.

Interestingly, a tiny note in the MTEX documentation seems instead to reference the crystallographic difference between misorientation/disorientation:

" different disorientation, i.e., a different but symmetrically equivalent misorientation has a smaller misorientation angle. "

https://mtex-toolbox.github.io/files/doc/BoundaryMisorientations.html

Dear Aaashranth B.!

The term ''misorientation", when related to the so called KAM or GAM, have quite different sense than we discussed above. Specifically, they express an AVERAGED magnitude of numerous mis( or dis-)orientation angles of certain ensemble (the former- over indicated /n-th/ coordination shell of neighbors at a EBSD point; the latter -within a domain delimited by a boundary with a misorientation angle > certain "tolerance angle"). To sum up, KAM and GAM are simplified measures of crystal CURVATURE (orientation gradient) rather than a relative rotation angle for a COUPLE of measurement points. By the way, in the paper you mentioned the authors say about misorientation/disorientation use rather softly (...sometimes termed..) and in no way recommend a certain of these two terms. As to attempts to base the rule on difference between inter- and intra-granular boundaries, they only dis-(or mis-) orient people. Indeed, deformation-induced fragments within constituent grains of a deformed polycrystal gradually (eventually) become dis- (mis-)oriented by high angles (15 degs and more), whereas the famous random distribution of inter-grain misorientations in polycrystals contains a notable part of 5-15deg angles. /// As to selecting the least misorientation angle among crystallographically equivalent variants (due to symmetry), it is for long a commonly accepted routine, in particular when treating EBSD data.

@ A.A. Zisman: If I understand you correctly (sorry if I don't), from your point of view there is no clear differentiation between misorientation and disorientation? I assume that the majority of people know that the accumulated misorientation within grains can become quite big. In meteorites 25 degrees are not rare, but the grain detection algorithm still recognize them as grain as long as the maximal misorientation angle is properly (whatever this means) selected. In this relation, the use of disorientation as measure between different grains would define a term which enables a qualitative discussion about two difference phenomena, which are of course for strongly deformed materials very close to each other. However, it is not the size of the rotation angle which is under discussion.

I also guess that mainly all readers know that the reference orientation which needs to be used for the calculation of the mis- or disorientation can be a single orientation or an averaged orientation, or even an averaged angle only. Here, GAM, LAM, KAM, GOS, GRD, IGM etc are often used but I am not sure how many people really know the correct equations used and which information is finally used.

misorientation correspond to all angles that bring a grain to the same orientation as its neighbor (depending on the crystal symmetry) while disoriontation is usually assigned the the smalest angle of all misorientation angles.

Dear Gert,

I would not discuss on therminology. However mis- or disorientation, when applied to a relative rotation vector betwen two points (crystal domains) of certain "uniform" orientations, is essentially the same indeed. Remarks that classification may base on selecting the minimum angle among several ones admitted by symmetry do not seem of great use. Anyway, they are not at all commonly accepted as an imperative rule. /// When the previously uniform grains get high-angle substructures (e.g. deformation-induced fragmentation or a lot of martensite blocks within a common parent /austenite/ grain), it is hard to differentiate the "true" grains and their interiors in terms of disorientation only. Moreover, as in case of martensite, special means are necessary to reconstruct the former grains on the backgrond high-angle substructure elements (say, blocks). //// More confusion is possible since the disorientation term is sometimes used to express the degree of orientation non-uniformity within some domain RATHER THAN a relative ritation whether across a boundary or in comparison of two remote points. In this case such terms, as GND density by HR EBSD, etc, should rely indeed on an appropriate reference lattice (orientation). However this is not the case for the usual means concerning a RELATIVE rotation of two crystal domains.

Dear Prof. Zisman,

Thanks for your explanation! Indeed, KAM/GAM/other measures represent orientation gradients, rather than a single rotation angle. My objective in bringing up this was that the common use of terms like misorientation/disorientation in these applications can add to confusion, and perhaps the nomenclature should be less ambiguous. Also, as Prof. Nolze points out, the formulae used in these measures are often considerably more complex than a simple arithmetic average that one may imagine. No wonder that, in your humorous words, people could easily be dis-oriented.

Coming back to the crystallographic difference between misorientation/disorientation, I searched around a bit and found some sources that are hopefully more satisfactory. Slides 6 and 18 of lecture notes [1] define this term, but also point us further to 'some texts', which are not specified. The much cited paper [2] clearly specifies this disorientation/misorientation difference as being a convention (Introduction), but also says that the terms are interchangeable. I suppose once the lowest angle is selected as a matter of routine, the terms become interchangeable and redundant.

[1] http://pajarito.materials.cmu.edu/rollett/27750/L13-Grain_Bndries_RFspace-15Mar16.pdf

[2] Article Grain boundary misorientation distributions