calculating plane normal - old question but I did not find an answer in this forum. Thanks.

[Raju Kada]

Hi,

Schmid factor calculations in mtex is well developed but my question is related to calculation of plane normal to define load direction.

If i am not wrong, r=vector3d(1,0,1) defines the load direction to [ 1 0 1 ]. For instance, in the cubic system this is ok, as [ 1 0 1 ] is perpendicular to (1 0 1). This is however not true for hexagonal system. 

I want to define a plane and want mtex to automatically calculate the plane normal which should be defined as the load direction.

The r in the following code should work fine as a direction, but in order to simulate the transmission X-ray diffraction, the load direction is along the (hkil) plane normal. For example, the (10-11) reflection during in-situ transmission XRD has actually (10-11) plane normal along the load direction. If I define r = vector3d(1,0,1) this takes the [1 0 -1 1] direction which is not normal to (10-11) plane. Please help me in calculating the plane normal.

CS = crystalSymmetry('6/mmm', [2.95 2.95 4.686], 'X||a*', 'Y||b', 'Z||c*','mineral', 'Titanium');
%CS = crystalSymmetry('cubic',[3.523,3.523,3.523],'mineral','Nickel')


n = Miller(h,k,l,CS,'hkl')
d = Miller(u,v,w,CS,'uvw')
r=zvector;
sS = slipSystem(d,n)
sSAll=sS.symmetrise%('antipodal')

% define the load directions

% The r below should work fine as a direction, but in order 
% to simulate the transmission X-ray diffraction, the load direction is
% along the hkl plane normals

r = [vector3d(1,0,0) vector3d(0,0,1) vector3d(1,0,1) vector3d(1,0,2) vector3d(1,1,0)] % The question belongs to this line
tau = sSAll.SchmidFactor(r)

Thanks in advance.

Raju

[ruediger Kilian]

Hi Raju,
as far as I understand, the loading direction is one external direction (vector3d).
Could you explain what you mean with “… r=vector3d(1,0,1) defines the load direction to [ 1 0 1 ]. “ and, if I understand correctly why you want have multiple loading directions?

Wrt your normals: o*m gives the pole to the crystal plane m (=Miller(…cs,'hkl')) in a crystal with orientation o

Cheers,
Rüdiger

[Raju Kada]

Hi Rudiger,

Thanks for the prompt reply.

In an in-situ deformation transmission X-ray diffraction experiment, the load direction is along the scattering vector. This means that unlike in the case of conventional reflection measurements, in the case of transmission X-ray diffraction, the load is acting along all the hkil's observed. For example, in the attached picture, you can see in the (0002) pole figure that the fibers indicated by solid arrows are the ones which are diffracting, with their plane normals along the applied load (Ydirection). 

So, I need to calculate the plane normal of {10-11} and {10-13} fibers and not the orientation 'o'. But may be if I define one of the slip sytem in the orientation 'o' and do a cross product, can this be the plane normal I can use to define in vector3d?

 This is the reason I want to extract the fiber orientations from EBSD (in my other post) to compare with the XRD data.

Regards

Raju

[ruediger Kilian]

Hi Raju,
I guess I still do not understand exactly why each crystal plane has an external loading direction normal to it and apparently you’d like to calculate the Schmid factor for something different than the load direction indicated in your figure.
In any case, for example vector3d(symmetrise(Miller(1,0,-1,3,cs,'hkl'))) will give you all the directions of poles to the Miller in external coordinates - however totally unrelated to any orientation you might have measured, hence it is simply a function of crystal coordinate system convention - but maybe this is already what you need?
Cheers,
Rüdiger