Strain Mapping

Strain mapping in pyxem is done by fitting a DisplacementGradientMap to the data. This can be thought of as image distortion around some central point.

from pyxem.data import simulated_strain
import hyperspy.api as hs

In this example we will create a simulated strain map using the simulated_strain() function. This just creates a simulated diffraction pattern and applies a simple “strain” to it. In this case using simulated data is slightly easier for demonstration purposes. If you want to use real data the zrnb_precipitate() dataset is a good example of strain from a precipitate.

strained_signal = simulated_strain(
    navigation_shape=(32, 32),
    signal_shape=(512, 512),
    disk_radius=20,
    num_electrons=1e5,
    strain_matrix=None,
    lazy=True,
)

The first thing we want to do is to find peaks within the diffraction pattern. I’d recommend using the get_diffraction_vectors() method

strained_signal.calibration.center = (
    None  # First set the center to be (256, 256) or the center of the signal
)
template_matched = strained_signal.template_match_disk(disk_r=20, subtract_min=False)
template_matched.plot(vmin=0.4)

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Plotting the template matched signal and setting vmin is a good way to see what threshold you should use for the get_diffraction_vectors() method.

diffraction_vectors = template_matched.get_diffraction_vectors(
    threshold_abs=0.4, min_distance=5
)

markers = diffraction_vectors.to_markers(color="w", sizes=5, alpha=0.5)
strained_signal.plot()
strained_signal.add_marker(markers)

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Determining the Strain

We can just use the first ring of the diffraction pattern to determine the strain. We can do this by using the filter_magnitude() method. You can also look at the filtering vectors example to see how to select which vectors you want to use more generally. You can also just manually input the un-strained vectors or use simulated/ rotated vectors as well.

first_ring_vectors = diffraction_vectors.filter_magnitude(
    min_magnitude=0.1,
    max_magnitude=1,
)
unstrained_vectors = first_ring_vectors.inav[0, 0]

strain_maps = first_ring_vectors.get_strain_maps(
    unstrained_vectors=unstrained_vectors, return_residuals=False
)

strain_maps.plot()

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[<Axes: title={'center': 'e11'}, xlabel='x axis (nm)', ylabel='y axis (nm)'>, <Axes: title={'center': 'e22'}, xlabel='x axis (nm)', ylabel='y axis (nm)'>, <Axes: title={'center': 'e12'}, xlabel='x axis (nm)', ylabel='y axis (nm)'>, <Axes: title={'center': 'theta'}, xlabel='x axis (nm)', ylabel='y axis (nm)'>]

Some final notes about strain mapping. In general, you want to use as many pixels as possible. 512 x 512 is a good place to start. You can do strain mapping with fewer pixels, but the results will be less accurate. Precession also helps improve the results as does having a thinner sample both of which reduce the effects of dynamical diffraction.

sphinx_gallery_thumbnail_number = 5