Identify a orientation on a ODF

[Camilo Garzón]

Hi,

I've been trying to identifing the orientations of certain points on a ODF of a Titanium Alloy in each of their phases (alpha=hcp, and beta=bcc).

What I would like is to get the orientation in Miller's Indices notation (hkl)[uvw] and (hkuil)[uvtw]  using the Euler angles of the ODF.

Something like the nomograms that I attached (for hexagonal), I compare my results with them, without success in the hcp.

Someone could help me? or  could give me an advice with it?

I tryed with the next codes:

For hexagonal system 1:

 function [hkil,uvtw] = euler2millhx(q1,q,q2,c,a)

%This function becomes a Orientation in euler angles in the Bunge convention to Orientation in the Miller Index

%Degree to Radians

q1 = degtorad(q1)

q = degtorad(q)

q2 = degtorad(q2)

%According to this article: https://bit.ly/2H9I8AS

h1 = [sqrt(3)/2, -1/2, 0;0,1,0;-sqrt(3)/2,-1/2,0;0,0,c/a]

h2 = [sin(q2)*sin(q);cos(q2)*sin(q);cos(q)]

u1 = [2/3, -1/3, 0;0,2/3,0;-2/3,-1/3,0;0,0,c/a]

u2 = [cos(q1)*cos(q2)-sin(q1)*sin(q2)*cos(q);-cos(q1)*sin(q2)-sin(q1)*cos(q2)*cos(q);sin(q1)*sin(q)]

%plane

hkil = h1*h2 

%direction

uvtw = u1*u2

end

For hexagonal system 2: 

function [hkil,uvtw] = euler2millhx2(q1,q,q2,c,a)

%This function becomes a Orientation in euler angles in the Bunge convention to Orientation in the Miller Index using the symetry matrix L (for hcp system)

%Degree to Radians

    q1 = degtorad(q1)

    q = degtorad(q)

    q2 = degtorad(q2)

    

%Matrix construction

    z1 = [cos(q1), sin(q1), 0; -sin(q1), cos(q1), 0; 0,0,1]

    z2 = [cos(q2), sin(q2), 0; -sin(q2), cos(q2), 0; 0, 0, 1]

    X = [1, 0, 0; 0, cos(q), sin(q); 0, -sin(q), cos(q)]

%Matrix with notation with 3 indices    

    A = z2*X*z1

    

%Symmetry Matrix

    L = [a, -a/2, 0; 0, a*sqrt(3)/2, 0; 0, 0, c]

    

%Columns of A

uvw = A(:,1)

t_column = A(:,2)

hkl = A(:,3)

% Cubic to Hexagonal

g = L*A

%vectores en sistema de 4 ejes

hkil = [(2*hkl(1)- hkl(2))/3; (hkl(2)-hkl(1))/3;-(hkl(1)+hkl(2))/3; hkl(3)]

uvtw = [(2*uvw(1)- uvw(2))/3; (uvw(2)-uvw(1))/3;-(uvw(1)+uvw(2))/3; uvw(3)]

end

For cubic system result fine testing diferent fiber values.

For cubic system code: 

function [hkl,uvw] = euler2millcb(q1,q,q2)

%This function becomes a Orientation in euler angles in the Bunge convention to Orientation in the Miller Index (for cubic systems)

%Degrees to Radians

    q1 = degtorad(q1)

    q = degtorad(q)

    q2 = degtorad(q2)

%Components of Matrix

    z1 = [cos(q1), sin(q1), 0; -sin(q1), cos(q1), 0; 0,0,1]

    z2 = [cos(q2), sin(q2), 0; -sin(q2), cos(q2), 0; 0, 0, 1]

    X = [1, 0, 0; 0, cos(q), sin(q); 0, -sin(q), cos(q)]

%Matrix

    A = z2*X*z1

    

  

%Miller Index

uvw = A(:,1)

hkl = A(:,3)

end

[Rüdiger Kilian]

Hi,
I think round2Miller does what you are looking for.
Hope this helps.
Cheers,
Rüdiger
________________________________________
From: mtex...@googlegroups.com <mtex...@googlegroups.com> on behalf of Camilo Garzón <scga...@gmail.com>
Sent: Saturday, March 9, 2019 8:31:31 AM
To: MTEX
Subject: {MTEX} Identify a orientation on a ODF

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[Camilo Garzón]

Thanks, that exactly what I need.

Best Regards

Camilo

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