DRAFT: Diffraction model with intragranular misorientation

[MACarlsen]

Hi All,

I was reading a very nice paper-draft this wednesday, which was using this package to simulate diffraction from deformed microstructures. But I couldn't help to thing that there must be a better way to make such a simulation. So I tried to implement a concept where the sample consists of a collection of gaussian-shaped "grains" with a narrow anisotropic gaussian ODF each.

If you make a the right approximations, the diffraction peaks produced by such a grain is also a "gaussian" in the detector coordinates, so you can use some concept from "gaussian splatting" to do fast evaluation. Since this package already has a few different model for rendering diffraction peaks, I figured why not add another one.

There is still a lot of work to be done testing and optimizing, but if you are interested and can give me some pointers about how to implement it, I would try to do it.

The model is also fully differentiable, so one can dream about doing proper gaussian-splatting fitting...

In the jupyternotebook from the front-page of the documentation you can run this:

from xrd_simulator.gaussian_crystal_model import GaussianGrainish, GaussianPolycrystal
import torch

def make_random_tensor(axis_1, axis_2):
    random_direction = np.random.normal(size=3)
    random_direction = random_direction/np.linalg.norm(random_direction)
    tensor = axis_1**2 * np.eye(3) + (axis_2**2-axis_1**2) * np.outer(random_direction, random_direction)
    return tensor

N = mesh.number_of_elements
orientation = R.random(mesh.number_of_elements).as_matrix()

grain_list = []
for ii in range(N):

    shape_tensor = torch.eye(3) * mesh.eradius[ii]**2

    misorientation_tensor = make_random_tensor(
        np.random.uniform(0.002, 0.0005),
        np.random.uniform(0.002, 0.0005),
    )

    grain = GaussianGrainish(
        phase=quartz, #  For now it assumes all gaussians are the same phase, but it just needs a wrapper for multiphase
        position=mesh.espherecentroids[ii], # 3 vector centroid real-space position
        shape_tensor=shape_tensor, # 3-by-3 symmetric shape tensor where the eigenvalues are the radii-squared.
        orientation=orientation[ii], # 3-by-3 rotation matrix.
        misorientation_tensor=misorientation_tensor, # 3-by-3 misorientation tensor where the eigenvalues are the misorientaion spread in radians squared.
                                                     # misorientation vectors live in laboratory coordinates.
        strain_tensor=polycrystal.strain_lab[ii] # 3-by-3 symmetric strain tensor.
    )

    grain_list.append(grain)

gauss_polycrystal = GaussianPolycrystal(grain_list)

f = gauss_polycrystal.render_detector_frame(
    detector=detector,    
    xray_propagation_direction=np.array([1.0, 0.0, 0.0]),
    wavelength=0.28523,
    max_misorientation=np.radians(1.0),
    sample_rotation_during_exposure = np.array([0, 1 / np.sqrt(2), -1 / np.sqrt(2)])*np.radians(1.0), # This is of course with a gaussian time-window
)

fig, ax = plt.subplots(1, 1, figsize=(12, 12))
ax.imshow(f, cmap="gray", vmax=100000)
plt.show()