I need to distribute random points in a pole figure, showing a random texture. After distributing 100 points inside 24 regions of pole figure, what's the simplest way to name them in the form of hkl?
Is there any rule for hkl digits in a region of pole figure? for example for the primary slip triangle?
If you define R=[uvw] and H=(hkl) the respective Cartesian coordinates of vector V are defined by
V = AT*R = R*A
V = A-1*H
Thus, form Cartesian coordinates crystal lattice or reciprocal lattice vectors can be derived by:
R = (A-1)T*V = V*A-1
H = A*V
A is the crystal matrix which describes the metric of the crystal lattice. The general form is
a11 = a
a12 = a13 = a23 = 0
a21 = b*cos(gamma)
a22 = b * sin(gamma)
a31 = c * cos(beta)
a32 = c/sin(gamma) * [cos(alpha)-cos(beta)*cos(gamma)]
a33 = c/sin(gamma) * sqrt[1+2*cos(alpha)*cos(beta)*cos(gamma)-[cos²(alpha)+cos²(beta)+cos²(gamma)]
The last term is a bit longer but once introduced in Excel or any program it is applicable for any crystal symmetry, using a,b,c and alpha, beta and gamma as lattice parameters.
Please dont forget to transfer degrees in radiants.
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