Plot Lattice Structure Maps

The temul.topotem.polarisation module allows one to easily visualise various lattice structure characteristics, such as strain, rotation of atoms along atom planes, and the c/a ratio in an atomic resolution image. In this tutorial, we will use a dummy dataset to show the different ways each map can be created. In future, tutorials on published experimental data will also be available.

Prepare and Plot the dummy dataset

>>> import temul.api as tml
>>> from temul.dummy_data import get_polarisation_dummy_dataset
>>> atom_lattice = get_polarisation_dummy_dataset(image_noise=True)
>>> sublatticeA = atom_lattice.sublattice_list[0]
>>> sublatticeB = atom_lattice.sublattice_list[1]
>>> sublatticeA.construct_zone_axes()
>>> sublatticeB.construct_zone_axes()
>>> sampling = 0.1  # example of 0.1 nm/pix
>>> units = 'nm'
>>> sublatticeB.plot()

Plot the Lattice Strain Map

By inputting the calculated or theoretical atom plane separation distance as the theoretical_value parameter in temul.topotem.polarisation.get_strain_map() below, we can plot a strain map. The distance l is calculated as the distance between each atom plane in the given zone axis. More details on this can be found on the Atomap website.

>>> theor_val = 1.9
>>> strain_map = tml.get_strain_map(sublatticeB, zone_axis_index=0,
...            units=units, sampling=sampling, theoretical_value=theor_val)

The outputted strain_map is a Hyperspy Signal2D. To learn more what can be done with Hyperspy, read their documentation!

Setting the filename parameter to any string will save the outputted plot and the .hspy signal (Hyperspy’s hdf5 format). This applies to all structure maps discussed in this tutorial.

Setting return_x_y_z=False will return the strain map along with the x and y coordinates along with their corresponding strain values. One can then use these values externally, e.g., create a matplotlib tricontour plot). This applies to all structure maps discussed in this tutorial.

Plot the Lattice Atom Rotation Map

The temul.topotem.polarisation.rotation_of_atom_planes() function calculates the angle between successive atoms and the horizontal for all atoms in the given zone axis. See Atomap for other options.

>>> degrees=True
>>> rotation_map = tml.rotation_of_atom_planes(sublatticeB, 0,
...                     units=units, sampling=sampling, degrees=degrees)

'''
Use `angle_offset` to effectively change the angle of the horizontal axis
when calculating angles. Useful when the zone is not perfectly on the horizontal.
'''

>>> angle_offset = 45
>>> rotation_map = tml.rotation_of_atom_planes(sublatticeB, 0,
...                     units=units, sampling=sampling, degrees=degrees,
...                     angle_offset=angle_offset, title='Offset of 45, Index')

Plot the c/a Ratio

Using the temul.topotem.polarisation.ratio_of_lattice_spacings() function, we can visualise the ratio of two sublattice zone axes. Useful for plotting the c/a Ratio.

>>> ratio_map = tml.ratio_of_lattice_spacings(sublatticeB, 0, 1,
...                 units=units, sampling=sampling)

One can also use ideal_ratio_one=False to view the direction of tetragonality.