I agree with Gert Nolze , that the 15° misorientation as a fixed value for the separation of low and high angle grain boundaries should be critically reviewed with respect to specific observations.

Nevertheless, this value is not chosen in a completely arbitrary way. If you plot the grain boundary energy as a function of the misorientation angle (at least for metals), it increases up to an misorientation angle of about 15° and stays approximately constant for larger misorientation angles (except deep energy minima of the CSL / "sigma" grain boundaries). To my knowledge, this can be explained with the dislocation model of grain boundaries, in which the distance of adjacent dislocations becomes so small for misorientation angles >15° that the strain fields heavily overlap and the structures have been considered as completely unordered / amorphous for a long time.

Whereas choosing another transition angle might be useful to explain specific observation, an unified value simplifies comparison of different studies. In my opinion, providing the grain boundary misorientation distribution as a graph is a suitable way to address both issues and to provide a more detailed view of the results. Since modern experimental systems give access to the data of many grain boundaries in reasonable time, putting them into only two bins (low and high angle GB) can be considered as waste of existing data.

As far as I remember the software packages use as default value for a high angle grain boundary 5°. My interpretation is that this is simply a number in order to find some correlation between (mechanical) properties and observed misorientations. It makes no real sense that 15° is a high angle boundary and 14.9° is not. However, this is exactly the way software works. It derives the misorientation angle and if it is bigger that x° it is high-angle...and if smaller than x° it is low-angle (or however you denote the value x and related angles). I don't think that this a clever way, but I do not see a better (or more simple) approach which is easy to interpret.

In consequence it means that you have to adapt this angle with respect to your experimental observation. It will be only a correlation which does not mean that between the misorientation angle and your observation is any relationship. Here we are in general too often too optimistic! It might happen that a correlation you used for years finally turns out as misinterpretation.

This misorienation angle changes since the chemical/physical forces are different from crystal structure to crystal structure, and since our understanding of these deeper forces is rudimentary we are often speculating and claiming instead of knowing it. On reason is that the misorientation is not all. You have to consider also the misorientation axis, quite easy to understand that a misorientation angle of 60° in fcc does not mean that all these grains are in twin relationship.

The next influence is the habit plane, i.e. the really existing interface between adjacent grains. An there are other effects like "contamination" along the interface like precipitates etc.

I agree with Gert Nolze , that the 15° misorientation as a fixed value for the separation of low and high angle grain boundaries should be critically reviewed with respect to specific observations.

Nevertheless, this value is not chosen in a completely arbitrary way. If you plot the grain boundary energy as a function of the misorientation angle (at least for metals), it increases up to an misorientation angle of about 15° and stays approximately constant for larger misorientation angles (except deep energy minima of the CSL / "sigma" grain boundaries). To my knowledge, this can be explained with the dislocation model of grain boundaries, in which the distance of adjacent dislocations becomes so small for misorientation angles >15° that the strain fields heavily overlap and the structures have been considered as completely unordered / amorphous for a long time.

Whereas choosing another transition angle might be useful to explain specific observation, an unified value simplifies comparison of different studies. In my opinion, providing the grain boundary misorientation distribution as a graph is a suitable way to address both issues and to provide a more detailed view of the results. Since modern experimental systems give access to the data of many grain boundaries in reasonable time, putting them into only two bins (low and high angle GB) can be considered as waste of existing data.

Thanks, Timo Müller. Only one "question": I guess you agree when I point out that you are talking about "easy" metals like fcc, bcc, hcp. However, there are many other alloys with much more complicated structures and the huge amount of non-metals where everything seems to be even more complicated. I never calculated grain boundary energies so that this is only my expectation...

Thank you Gert and Timo,

I can only recommend your answers. But I really want to add the following comment:

Why did we decide that there should be low and high angles? It was initially because we had observed boundaries between some structure elements (grains or structure fragments) and a structure inside of these grains (substructure). It was extremely important to mention whether the high- and low-angle boundary limits you can choose are really help in distinguishing the structure and substructure boundaries (in other words, the grain boundaries between structure elements and some boundary network inside a big grain).

May be it has a theoretical background, but it is obviously not strict correlation. That is why there is always a possibility to adjust it in any software to what you see. Nevertheless, I should admit, that in most cases 15 degrees are ok and fit into the above mentioned structure/substructure framework. Our Tomsk scientific school of physics of metals and materials science has lot of experience in these questions.

Regards,

Anton

@ Anton: You mentioned a lot of experience. Could you give some examples or papers which demonstrate that the finding of 15° does or does not fit to different metals and alloys? How is the structural relationship?

Dear Anton:

I agree with Timo. In general, the definition of the angle " transition from low angle GB to high angle GB " means that the dislocation model fails to describe the grain boundary strucutre from the primary preferred state (In this state, the Burgers vectors for boundary dislocation are the translation vectors of the crystal structure).

Take symmetric tilt grain boundary (lowe angle GB) of the simple cubic structure for example, the dislocation sapcing is D ~ b/theta, where b is the Burgers vector, and theta is the misorientation angle. If misorientation angle theta increases, D decreases. At extreme cases, the dislocations will be too close, and their core structure will be superimposed with each other, that means the definition of the dislocation is physically meaningless. Suppose the dislocation core size of 2b, thus D = 4b be the extreme case, theta ~ 0.25 rad ~ 14 deg. Of course, as Gert said the angle should be adapted for specific cases.

Dear Gert,

Unfortunately, I did not study many other materials except Zr and its alloys. Here you would probably have much better experience. Concerning the Tomsk school. All works were performed 1970-2010th using TEM. There was often a discussion concerning structure and substructure elements. Low angle boundaries were geometrically necessary boundaries that allow the material to deform without braking its grain structure. Material that accommodated some strain should have it. In most cases it did not exceed approx 5-7 degrees in one grain. Grain with substructure looked deformed; it had some small boundaries inside, but it was still a grain with "almost" same orientation in space. In other cases it is higer than 15 degrees and these were grain boundaries. May be it is a specific case - not general. But in fact Gert mentioned that "some software uses this angle". It would be interesting to learn why did they do it, right? Probably the works of E. V. Kozlov and N. A. Koneva will help you in these questions. There were many published papers. One of the books published can be found under the link https://doi.org/10.1002/3527602461.ch6f

When I started investigations of Zr using EBSD I also tried to take around 5-7. But let's say in case of annealed material mostly 60 and 90 degrees boundaries were present. It was not necessary. Material was not deformed (but not dislocation free).

Later in Germany using EBSD I studied hydrogenated Zr. I figured out that in the case of two-phase materials there are phase boundaries between Zr and ZrH1,66 in the range of 1-9 degrees. These are not substructure boundaries it was a phase boundary and I don't really know whether "the dislocation model fails to describe..." I do not doubt the Brandon's criterion [David Brandon [ 1966: "The structure of high-angle grain boundaries”, Acta metallurgica 14: 1479-1484] originated a criterion for proximity to a CSL structure. vm = v0Σ-1/2 where the proportionality constant, v0, is generally taken to be 15°, based on the low-to-high angle transition (quoted from here http://pajarito.materials.cmu.edu/rollett/27750/L14-CSL_Theory_GBE-17Mar16.pdf)]. But it has its own limits to be applied to. It is not applicable to deformed structure or multiphase materials, i think. How about paired Schottky splitted dislocations in hcp metals? What should be minimum angle in this case? Everyone can learn and describe the cubic lattice, but how many materials in the nature do have this cubic lattice?

That is why as Gert has already said: "In consequence it means that you have to adapt this angle with respect to your experimental observation". Fully agree.

Regards,

Anton

Timo and Xinfu are right in saying that the transition angle is taken as that at which the individual dislocations that make up a low angle boundary are so close together that their 'cores' overlap (so the individual dislocations can't be resolved as such in TEM images) and that this core width depends on the type of bonding in the material but Timo is very out of date in saying that the structures of high angle grain boundaries in metals 'have been considered as completely unordered / amorphous for a long time'. Since the 1970s, field ion microscopy and high resolution TEM have confirmed the results of computer simulations of high angle grain boundary structure in metals that they are made up of regular repeating patterns of structural units. There may be amorphous films at the grain boundaries of some minerals and ceramics but high angle grain boundaries in metals all have orderly structures (which, as Gert has intimated, depend on the misorientation, grain boundary plane and impurities present).

I have myself long wondered why the default transition angle for LAGB/HAGB is set in some software at such an low angle as 5deg. when GB energy vs misorientation plots and TEM evidence suggest about 15deg for metals and I think perhaps 10-12deg. for minerals and ceramics

Thanks everyone for spending your precious time and providing valuable discussion to this questions. It is true that software packages are provided with some default value, but they also facilitates the user defined values for more accurate calculation.

Timo Müller can you please point out some of the best (according to you, as there are many) research papers which provide some data (on how to calculate or model) on grain boundary energy wrt. misorientation angle.

Orientations of 15 degrees or less across a boundary means that the boundary is a twin boundary. The orientation variation across a grain boundary is much higher, more like 60 degrees, as I recall from our EBSD work. This enables EBSD to identify twins in FCC metals and delete them from the image to permit accurate grain area measurements use to calculate the ASTM grain size number.

An experimental evidence of extreme physical importance of low-angle 5 degrees and lower boundaries can be found in the following paper Article Microtexture and Microstructure Evolution during Necking in ...

Low-angle boundaries have been chosen to be from 2 to 15 degrees as it was suggested by software. In the Fig.4 one can see, that after deformation of Zr alloy not much happened in range 5 - 15 degrees. In contrast, the fraction of boundaries lower than 5 degrees together with formation of small-sized fragmented substructure increased significantly.

Here 15 degrees of misorientation does not play any significant role in understanding because it does not reflect the physical process of structure developement.

In my opinion it is a good example when 15 degrees does not fit the concept.

And I bet the "grain boundary energy as a function of the misorientation angle" will be different in different lattice types.

@G.F. Vander Voort: You are starting your contribution with "Orientations" but don't you mean "Misorientations" (MO)? MO lower than 15° are usually no twins, at least quite unusual for cubic materials (I would not exclude them per se since as far as I understand twins they are related to the crystal structure and for a complex structure I could imagine even such cases). In contrast, for lower symmetries and huge lattice parameter ratios, superstructures etc. it might happen but apart from these special cases I don't think you will find many phases where twins have smaller MO angles than 15°. BTW: The maximum MO angle for fcc materials (symmetry: m3m) is slightly over 60° (in fact 61°) as shown in the Mackenzie plot. It shows how the distribution of MO angles is when you do not have any texture, i.e. an isotropic orientation distribution.

On the other hand, EBSD is able to differentiate any misorientation higher than the precision limit, i.e. about 0.1° (in case of Si and high-binned patterns). For standard interpretation this minimal value is more in the scale of 0.5...1°. The question is, what does a MO smaller that 15° really means (topic of this question here).

Moreover, whether a twin "removement" by postprocessing is useful or not depends on the assumed model. For TWIP steels it might be not a good idea to remove them, for Cu interconnects it is useful since the conductivity is not affected by Sigma3 boundaries.

A careful construction of grain boundary (gb) with an array of dislocations can lead to a maximum gb misorientation of about 18 degrees (calculated) in case of cubic structures. So, gb's with misorientation < 18 degrees are termed low angle grain boundaries. However, for the sake of simplicity, 15 degrees is being used to demarcate low and high angle gb's. This observation in case of low symmetry materials is slightly greyish but again for simplicity 15 degrees can be used as criteria for demarcation.

Do you have a reference for the 18 degrees?

Dear Sir,

It should be approximately 18 degrees. I have read it a year back, shall find out the reference ASAP and post it. Thanks

As rightly pointed out by Mr. Hamed, the identification of recrystallized grains becomes subjective in terms of grain boundary misorientation angle. Observations made by several researchers related to the instability of boundaries formed by dislocation arrays could be used as a point to distinguish the recrystallized structure w.r.t deformed. On the conservative side 15 degrees is being used as demarcation rather than 10 degrees. This can keep things simpler.

See our recent paper on dDRX in alpha-Zr

10.1016/j.msea.2018.01.117

Do you prefer now 15 or 18 degrees?

Can anyone point out any research work on the generalised model to calculate GBE vs. misorientation for various crystal systems.

Dear all,

with respect to all participants please do not mix important things:

a) ....15 degrees for high angle grain boundaries should be critically reviewed with respect to particular observations... I agree

b) ... there is a general agreement of critical misorientation angle of 15 degrees.... I disagree

There is obviously no general agreement, as we have here very huge discussion on this problem. In the case of materials other than iron fcc things can be more complicated. Many of us already mentioned different angles during experimental and theoretical results. But if 5 or 15 or 10 or 18 degrees really reflect the physical process in your material, you are very welcome to use it in your paper, but please provide evidence or a physical explanation, why.

There is no such thing as a 15 degree misorientation across grain boundaries. Twin boundaries are distinguished from grain boundaries by EBSD because the misorientation across a twin boundary is ~15 degrees while the misorientation across a grain boundary is ~60 degrees.

Dear George, I think there is a misunderstanding, or we use different terms. A misorientation practically always exist between two measurements (of the same or different positions). You multiply the orientation matrix form measurement A with the inverse matrix from B. From the resulting matrix the diagonal elements define the misorientation angle. What we are doing with this angle is a question of our definition. We can use it als criterion for the definition of different grains or the number of dislocations which would explain the observer rotation. The problem is that all these calculations do not consider the atomic arrangement within the volumes which are he real player and not our mathematical translation lattice.

Twins are very special grain boundaries only which result in certain properties.

A twin is either linked via a rotation around a two-fold axis (180°!) or a mirror plane (which is a two-fold rotation followed by an inversion). For your fcc twin the two-fold rotation axis is parallel which already has a 120° symmetry so that this specific configuration results in a 60° misorientation angle. Twin boundaries have been measured already before the discovery of x-rays and electrons, simply by microscopy. And even now twins are more often analyzed by other techniques than EBSD. Twin boundaries are simply perfect since they do not generate any mismatch along the twinning plane.

Twinning generated by mirror planes is quite irritating for EBSD since it changes a right-handed into a left-handed coordinate system. In other words, there is no rotation which can transfer the crystal in its twin, i.e. also no Euler rotation. I am not sure how EBSD systems deal with this problem. For fcc it is easy since two fold axis as well as mirror plane can be used...

1º High-angle boundaries can change the crack growth direction by acting as strength barriers because they have different crystallographic orientation;

2º "The boundaries between grains having different orientations of 15º or higer are high-angle boundaries, and these grains are generally considered to be effective ones [24]" - Article Effects of acicular ferrite on charpy impact properties in h...

3º "Several packets separated by different boundaries can have a similar crystallographic orientation. This leads to the definition of two types of packets: morphological packets, defined by OM or SEM as areas enclosed by different boundaries; and crystallographic packets (grains), defined by EBSD as exhibiting crystallographic misorientation. The relevantmicrostructural unit controlling cleavage crack propagation is the crystallographic packet, since only high angle bainite packet boundaries (misorientation >40◦) can efficiently stop the propagation of brittle cleavage microcracks, whereas a 10◦ misorientation never achieves any noticeable deviation of a cleavage crack [6,7] . Other authors have reported that a misorientation of more than 10–15◦ between {100} cleavage planes corresponding to two adjacent bainite packets can markedly deflect brittle crack propagation" Article Measurement of bainite packet size and its influence on clea...