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%config InlineBackend.rc = {"figure.dpi": 72, "figure.figsize": (6.0, 4.0)}
%matplotlib inline

import abtem
import ase
import matplotlib.pyplot as plt
import numpy as np

HRTEM quickstart

This notebook demonstrates a basic HRTEM simulation of a double-walled carbon nanotube.

Configuration

We start by (optionally) setting our configuration. See documentation for details.

abtem.config.set({"device": "cpu", "fft": "fftw"})

<abtem.core.config.set at 0x1feb74ad7e0>

Atomic model

In this section we create the atomic model. See our walkthough or our tutorial on atomic models.

We create two nanotubes with different radii using the nanotube function from ASE.

tube1 = ase.build.nanotube(10, 0, length=5)

tube2 = ase.build.nanotube(16, 0, length=5)

# combine the two nanotubes into a single structure
tubes = tube1 + tube2

# add vacuum in the x- and y-direction
tubes.center(vacuum=4.0, axis=(0, 1))

abtem.show_atoms(tubes, plane="xy", title="Beam view");

We rotate the nanotubes such the beam travels perpendicular to the length of the nanotubes.

rotated_tubes = tubes.copy()

# rotate cell and atoms by 90 degrees around y
rotated_tubes.rotate("y", 90, rotate_cell=True)

# standardize unit cell (done automatically in an abTEM simulation)
rotated_tubes = abtem.standardize_cell(rotated_tubes)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 4))
abtem.show_atoms(rotated_tubes, plane="xy", ax=ax1, title="Beam view")
abtem.show_atoms(rotated_tubes, plane="yz", ax=ax2, title="Side view");

Potential

We create an ensemble of potentials using the frozen phonon model. See our walkthrough on frozen phonons.

frozen_phonons = abtem.FrozenPhonons(rotated_tubes, 16, sigmas=0.1)

We create a potential from the frozen phonons model, see walkthrough on potentials.

potential = abtem.Potential(
    frozen_phonons,
    sampling=0.05,
    projection="infinite",
    slice_thickness=1,
)

Wave function

We create a plane wave function at an energy of 100 keV. See our walkthrough on wave functions.

wave = abtem.PlaneWave(energy=100e3)

Multislice

We run the multislice algorithm to calculate the exit waves, see our walkthrough on multislice.

exit_wave = wave.multislice(potential)

exit_wave.compute()

[########################################] | 100% Completed | 4.17 ss

<abtem.waves.Waves object at 0x000001FEC2E8A800>

Contrast transfer function

We create a contrast transfer function of the objective lens, see our walkthrough on the contrast transfer function

Cs = -8e-6 * 1e10  # spherical aberration (-8 um)

ctf = abtem.CTF(Cs=Cs, energy=wave.energy, defocus="scherzer", semiangle_cutoff=45)

print(f"defocus = {ctf.defocus:.2f} Å")

defocus = -66.65 Å

We include partial coherence in the quasi-coherent approximation. For more accurate descriptions of partial coherence, see our tutorial on partial coherence.

Cc = 1.0e-3 * 1e10  # chromatic aberration (1.2 mm)
energy_spread = 0.35  # standard deviation energy spread (0.35 eV)

focal_spread = Cc * energy_spread / exit_wave.energy

incoherent_ctf = ctf.copy()
incoherent_ctf.focal_spread = focal_spread

We show a profiles of the contrast transfer functions.

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 5))
ctf.profiles().show(ax=ax1)
incoherent_ctf.profiles().show(ax=ax2, legend=True);

We apply the contrast transfer function, then calculate the intensities of the wave functions.

measurement_ensemble = exit_wave.apply_ctf(incoherent_ctf).intensity()

measurement_ensemble.shape

(16, 426, 411)

The result is an ensemble of images, one for each frozen phonon, we average the ensemble to obtain the final image.

measurement = measurement_ensemble.mean(0)

measurement.show();

Postprocessing

Many tasks requires additional post-processing steps. Below we apply Poisson noise to simulate the shot noise of a given finite electron dose.

noisy_measurement = measurement.poisson_noise(dose_per_area=1e4)

noisy_measurement.show()

<abtem.visualize.MeasurementVisualization2D at 0x1feea6d4490>

Showing the results as a line profile often provides a better sense of relative intensities.

start = (0, 0)
end = (0, potential.extent[1])

measurement.interpolate_line(start, end).show();

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# this cell produces a thumbnail for the online documentation

visualization = measurement.show()
visualization.axis_off(spines=False)
plt.savefig("../thumbnails/hrtem_quickstart.png", bbox_inches="tight", pad_inches=0)