It is seen in literature that Sigma-3 CSL boundaries are usually taken as twin boundaries and more importantly coherent twin boundaries. I am asking this since I am getting significantly different fractions of coherent twin boundaries when I use the criteria of reconstructed twin boundaries for finding coherent twins and when I use Sigma-3 CSL boundaries as coherent twins. Please advice which is more correct way to find coherent twin fractions using TSL-OIM software. I am asking this relating to FCC structure of copper which shows (111) twins.
As far as I can say this Sigma3 are only in fact twin boundaries. You need to take care on the misorientation criterion (Brandon) used as reliability criterion. Twins are extremely exact boundaries,, i.e. only the incorrect orientation determination of EBSD limits the accuracy. Twins are absolutely exact boundaries. The Brandon criterion allows a bigger deviation since it should classify boundaries only "roughly". I do not have the exact deviation angle in mind but i believe it was in the scale of 8 degrees. From this follows you will always found more Sigma3 than twin boundaries.
How OIM this handles I don't know exactly. But I am sure that you can either dit the misorientation angle. If you replace the 8 degrees by 1 degree you will get a better coincidence.
Sigma 3 results from (special) misorientation only, whereas to be coherent at that the boundary should have a certain orientation of its plane in the crystal basis. Thus, if we take a good long twin, the rectilinear parallel boundary parts are both sigma 3 and coherent, however the curved (frontal) boundary is not coherent though still sigma 3. Naturally, fraction of coherent among all sigma 3 is less than unity.
Thanks Zisman for that incredible insightful answer. I think I got the logic. Correct me if I'm wrong, it seems that the TSL takes the mobile growing incoherent boundary along the breadth of a rectangular twin as a twin boundary. But reconstructed boundaries looks only at coherency hence the mobile boundaries are neglected to give smaller fractions.
To be honest, I do not think that any software looks for coherent or mobile boundaries derived from the image of a microstructure. The uncertainties like drift are non-predictable so that a general definition would be difficult. Moreover, not all twin boundaries are straight lines. For fcc materials this might be OK but for many other materials it is not.
Thank Gert for that additional info as well. I'll try use both EBSD as well as TEM to characterise these boundaries.
The CSL option in TSL only calculates the the misorientation between the two (average orientations of the) grains, and considers the boundary as a Sigma3 as long as the misorientation is within the Brandon criterion. In other words, we are still missing information on the grain boundary plane.
Using the reconstructed twin boundaries is still only a "guess". This is because we don't know the inclination of the grain boundary in the bulk. The deviation between the reconstructed line segment and the plane trace of the {111} (in both grains) is calculated. If the two fall within some angular deviation (preset 5° maybe?), the boundary is considered a coherent twin by the the software.
Generally this works, especially in the FCC materials that show lamellar twins. The reconstructed twin boundaries should highlight both sides of the twinned grain. But of course as Gert mentioned, not all twin boundaries are straight (generally your incoherent twin boundaries), and drift and etc. can also alter this.
I fully agree with Brian Lin. For the decision whether a Sigma3 boundary is a coherent or an incoherent one we need additional information concerning the inclination of the boundary plane within the sample. There is a method proposed by V. Randle (Crystallographic characterization of planes in the scanning electron microscope. Mater. Charact. 34 (1), 29-34, doi: 10.1016/1044-5803(94)00047-O (1995)) how to get this information by EBSD investigations on two surface planes of the sample.
Agree with all above. Be careful about your calculations. Absolute numbers might not be that accurate in EBSD as partly mentioned by Gert. But for comparison you are completely fine.
It is a bit easier to distinguish twins in FCC. I am having hard time for HCP metals ...
Nice question, what I have seen from TSL OIM software is that we can specify angular deviation. Better if we are giving Brandon Criterion. By default it is different. But in the same software, if we are selecting ZIgma 3, automatically Brandon Criteria is imposed. We will get different result if we are using ZIgma criteria or Twin criteria
Dear Arun,
I think the deviation for twin matching using brandon criterion is much higher by default and hence gives much more density of twins. But the twin boundary criterion gives a much lesser density. I currently use sigma 3 as the condition since it matches well the twins that are visually identited in the IQ maps as well.
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