On the Representation of Different Orientation Relations: Assumption Conjecture K-S, N-W, GT

[wanghaijian217]

Hello Frank and Azdiar
I want to carry out G-T or N-W based variant graph reconstruction, can you provide the corresponding method, I have detailed variant corresponding orientation relationship, I want to input them, and then reconstruct, but I do not know how to start, if you can provide help I would appreciate it!

[AzdiarGazder]

Hi @wanghaijian217,

Using ORTools_example07 as a template, please replace lines 59 to 76 with the following:

%% Define and refine parent-to-child orientation relationship
screenPrint('SegmentStart','Define and refine parent-to-child OR');
% Define 'Gamma" as the parent and 'AlphaP' as the child phase
job = setParentGrainReconstructor(ebsd,grains,Ini.cifPath);

%--- Define the theoretical planes and directions of the Bain OR
% fcc theoretical plane and direction
hklP = Miller(0,1,0,job.csParent); uvwP = Miller(0,0,1,job.csParent);
% bcc theoretical plane and direction
hklC = Miller(0,1,0,job.csChild); uvwC = Miller(1,0,1,job.csChild);
B = orientation.map(hklP,hklC,uvwP,uvwC);
%---

%--- Define the theoretical planes and directions of the Kurdjumov-Sachs OR
% % REF: https://doi.org/10.1016/j.actamat.2014.03.059
% fcc theoretical plane and direction
hklP = Miller(1,1,1,job.csParent); uvwP = Miller(-1,0,1,job.csParent);
% bcc theoretical plane and direction
hklC = Miller(0,1,1,job.csChild); uvwC = Miller(-1,-1,1,job.csChild);
KS = orientation.map(hklP,hklC,uvwP,uvwC);
%---

%--- Define the theoretical planes and directions of the Nishiyama-Wassermann OR
% % REF: https://doi.org/10.1016/j.actamat.2014.03.059
% fcc theoretical plane and direction
hklP = Miller(1,1,1,job.csParent); uvwP = Miller(1,1,-2,job.csParent);
% bcc theoretical plane and direction
hklC = Miller(0,1,1,job.csChild); uvwC = Miller(0,-1,1,job.csChild);
NW = orientation.map(hklP,hklC,uvwP,uvwC);
%---

%--- Define the theoretical planes and directions of the Pitsch OR
% (also known as inverse Nishiyama-Wassermann)
% % REF: https://doi.org/10.1016/j.actamat.2014.03.059
% fcc theoretical plane and direction
hklP = Miller(0,1,0,job.csParent); uvwP = Miller(-1,0,1,job.csParent);
% bcc theoretical plane and direction
hklC = Miller(1,-1,0,job.csChild); uvwC = Miller(-1,-1,1,job.csChild);
P = orientation.map(hklP,hklC,uvwP,uvwC);
%---

%--- Define the theoretical planes and directions of the Greninger-Troiano OR
% % REF: https://doi.org/10.1016/j.actamat.2014.03.059
% fcc theoretical plane and direction
hklP = Miller(1,1,1,job.csParent); uvwP = Miller(5,12,-17,job.csParent);
% bcc theoretical plane and direction
hklC = Miller(0,1,1,job.csChild); uvwC = Miller(7,-17,17,job.csChild);
GT = orientation.map(hklP,hklC,uvwP,uvwC);
%---

%--- Define the theoretical planes and directions of the inverse Greninger-Troiano OR
% % REF: https://doi.org/10.1016/j.actamat.2014.03.059
% fcc theoretical plane and direction
hklP = Miller(17,7,17,job.csParent); uvwP = Miller(-1,0,1,job.csParent);
% bcc theoretical plane and direction
hklC = Miller(5,12,17,job.csChild); uvwC = Miller(-1,-1,1,job.csChild);
iGT = orientation.map(hklP,hklC,uvwP,uvwC);
%---

%--- Define the theoretical planes and directions of the Headley-Brooks OR
% % REF: https://link.springer.com/article/10.1007/s11661-002-0001-0
% fcc theoretical plane and direction
hklP = Miller(1,1,1,job.csParent); uvwP = Miller(-1,1,0,job.csParent);
% bcc theoretical plane and direction
hklC = Miller(1,1,0,job.csChild); uvwC = Miller(-1,1,0,job.csChild);
HB = orientation.map(hklP,hklC,uvwP,uvwC);
%---

% Give an initial guess for the optimal OR by choosing any one of the 
% above defined theoretical ORs
job.p2c = GT;
... and refine it based on the fit with boundary misorientations
job.calcParent2Child;

% Let us check the disorientation and compare it with all ORs
% (The disorientation is the misfit between the grain misorientations
% and an OR's theoretical misorientation)
plotHist_OR_misfit(job,[B,KS,NW,P,GT,iGT,HB],'legend',{'B OR','K-S OR','N-W OR','iN-W(P) OR','G-T OR','iG-T OR','H-B OR'});

% Plot information about the OR
ORinfo(job.p2c);

Hope this helps.

Warm regards,
Azdi

[AzdiarGazder]

Hi @wanghaijian217,

The rational, geometrically perfect N-W OR has 12 variants caused by degeneracy (i.e. - an overlap of certain crystal symmetries).
As soon as you deviate away from the exact N-W OR the degeneracy is lost and you have 24 variants again.
Have a look at Section 2 in this paper for a detailed explanation.

Please note that K-S, N-W, G-T etc. are all rational, geometrically perfect ORs based on a set of perfectly parallel planes and directions.
However, in the real-world, polycrystalline materials do not exactly follow any of these theoretical rational ORs - they are close to them but never exact.

So, after you have provided an initial guess using a theoretical OR (such as N-W with its degeneracy), the command "job.calcParent2Child" returns the optimally refined OR based on your EBSD map data (where the degeneracy is lost).

The above method has been applied in almost all of the ORTools example scripts.

Warm regards,
Azdi