Burgers relationship between BCC-HCP

[Shuang Xie]

Hi,

When I calculating the variant selection during BCC to HCP, I am facing a strange question. The codes is as follows, in which I have picked up the 12 particular symmetry operation matrix S1-S12.

cs=crystalSymmetry('cubic'); 

ss=crystalSymmetry('triclinic'); 

d=rotation('Euler', 135*degree, 90*degree, 354.736*degree,'Bunge'); %d is the burgers relationship 

phi_medio=54.74;

theta_medio=45;

psi_medio=0;

rot=rotation('Euler',phi_medio*degree, theta_medio*degree, psi_medio*degree, 'Bunge'); 

ori_beta=orientation(rot,cs,ss); % orientation reconstructed beta  

s=symmetrise(ori_beta); 

for i=1:24

        var(i)=s(2*i-1)*d;  

end 

   

          cs=crystalSymmetry('hexagonal'); 

          ss=crystalSymmetry('triclinic'); 

% 12 theoretical variants from reconstructed beta  

      or(1)= orientation(var(1), cs,ss); 

          or(2)= orientation(var(3), cs,ss); 

         or(3)= orientation(var(5), cs,ss); 

         or(4)= orientation(var(7), cs,ss); 

         or(5)= orientation(var(8), cs,ss); 

        or(6)= orientation(var(9), cs,ss); 

         or(7)= orientation(var(11), cs,ss); 

 

        or(8)= orientation(var(12), cs,ss); 

     or(9)= orientation(var(13), cs,ss); 

      or(10)= orientation(var(14), cs,ss); 

       or(11)= orientation(var(18), cs,ss); 

       or(12)= orientation(var(19), cs,ss);  

I have two questions:

1. For one particular BCC texture component, for example, (-1-12)<111>, there are 4 sets of equivalent  Euler angles (54.7/234.7 45 0) and (144.7/324.7  90  45 ). However, through the SAME symmetry operation, let's say var1=E, which also means the same orientation relationship between bcc and hcp, different euler angles are leading to NOT equivalent HCP orientation, why this happen?

2. Could someone tell me how to deduce the symmetry operation matrix from miller index orientation relationship, like in literature referred as" (101)beta//(0001)alpha [-111]beta//[11-20]alpha" meaning symmetry operation E=[100

                                                                                    010

                                                                                    001 ]

and the other 11 rest relationship?

Best regards,

Shuang Xie

[Thomas Simm]

Hi,

There's a few recentish posts on similar things you may want to have a quick look through, but

For (2) for FCC->BCC and look in the literature for the OR:

    aa=PFCC(n);bb=PBCC(n);cc=DFCC(n);dd=DBCC(n);%D = direction, P=plane

    KCO(n)=orientation('map',cc,dd,aa,bb);%the rotation matrix of each of 

For (1) I'm not sure exactly what you mean, MTEX should take account of different equivalent orientation when you give the crystal structure. Are the angles equivalent in the Bunge convention of MTEX? You could check this by looking for the misorientation between them given the CS

Tom 

[Thomas Simm]

https://groups.google.com/forum/#!topic/mtexmail/Zc2t9qWeiys

https://groups.google.com/forum/#!topic/mtexmail/MK_Yup7afB4