{0 0 1} pole figure doesn't make any sense

[falloutrangerlol]

I tried to plot some pole figures with Euler angles in Kocks convention (psi, theta, phi). Most of them are correct, such as {0 0 1}, {1 1 0} and {1 1 1} pole figures. However, when it comes to {0 0 1} pole figure, it seems to me that the plot I got doesn't make any sense. There should be four dots forming a square, since the crystallographic orientations of the data are [1 1 1], [-1 1 1], [-1 -1 1] and [1 -1 1]. So viewing from [0 0 1] direction, there should be four dots that form a square shape. However, the plot I got showed only one dot, as shown in the figure attached. 

The symmetry I used was triclinic. When I changed the symmetry to m-3m cubic, there are six dots forming a hexagon. That doesn't make any sense, either, since there are only four crystallographic directions, so there should be 4 dots, not 6.

The texture, represented by the Euler angle sets, is as follows:

0 54.73561032 45

0 125.26438968 -135

0 54.73561032 135

0 125.26438968 -45

0 54.73561032 135

0 125.26438968 45

0 54.73561032 -135

0 54.73561032 -45

[Ralf Hielscher]

Dear falloutrangerlol,

First of all I think there is a mistake in you orientation data as the 3. and 5. row are identical. 

I corrected to this

psi = zeros(1,8);
theta = [54.7356 125.264 125.264 125.264 54.7356 125.264 54.7356 54.7356] * degree;
phi = [45, -135, 135, -45, 135, 45, -135, -45] * degree;

ori = orientation('Euler',psi,theta,phi,'Kocks')

and got the same result you got

However, I think the result is perfectly fine. According the Kocks angles the spots in the (001) pole figure has to be on the x-axis and close to the spots in the (111) pole figure. Maybe you forgot that you look only at the upper hemisphere and that no antipodal symmetry is included?

Set the option 'antipodal' to include antipodal symmetry in your plots, i.e.,

plotpdf(ori,[Miller(0,0,1),Miller(1,1,0),Miller(1,1,1)],'antipodal')

gives

I you are still wondering about the result - compute each orientation for its own, i.e.

ori(1) * Miller(0,0,1)

or plot it by

plotpdf(ori(1),Miller(0,0,1))

I hope this helps,

Ralf.

[falloutrangerlol]

Hi Dr. Hielscher,

You are right the data sets (Euler angles) provided in the original post were wrong.

Could you tell me why the spots in the (001) pole figure have to be on the x-axis, please? That's what I really don't understand ...

And even if I only look at the upper hemisphere, shouldn't there still be 4 spots, since 4 of the 8 data sets represent crystallographic directions of [1 1 1], [-1 1 1], [-1 -1 1] and [1 -1 1]? When the 4 directions are projected onto the (0 0 1) plane, there are four spots at 45, 135, 225 and 315 degree angles?

Thank you so much!

P.S. The correct data are:

0 54.73561032 45

0 125.26438968 -135

0 54.73561032 135

0 125.26438968 -45

0 125.26438968 45

0 54.73561032 -135

0 54.73561032 -45

0 125.26438968 135

[Ralf Hielscher]

The spots in the (001) pole figure have to be on the x-axis because

* (001) is first rotated about phi + something about the z-Axis -> nothing changes

* (001) is then rotated about theta + something about the y-Axis -> hence it stays perpendicular to the y-Axis and hence in the projection on the x-Axis

* the result is then rotated about psi = 0 degree about something -> nothing changes

I'm very sorry, but I do not understand your arguments. Your data are orientations and can not "correspond" to directions.

Ralf.