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

import ase
import matplotlib.pyplot as plt
import numpy as np
from ase.build import bulk

import abtem

CBED quickstart

This notebook demonstrates a basic CBED simulation of silicon in the \((111)\) zone axis.

Configuration

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

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

<abtem.core.config.set at 0x22d18f4ff70>

Atomic model

We create the atomic model. See our walkthough or our tutorial on atomic models.

We create an atomic model of silicon using the bulk function from ASE.

silicon = bulk("Si", crystalstructure="diamond")

abtem.show_atoms(silicon, plane="xy");

We can choose the \((111)\) zone axis to be a propagation direction using the surface function.

silicon_111 = ase.build.surface(
    silicon, (1, 1, 1), layers=3, periodic=True
)  # create surface structure in the (111) direction

silicon_111_orthogonal = abtem.orthogonalize_cell(silicon_111)  # make cell orthogonal

abtem.show_atoms(silicon_111_orthogonal);

Finally we repeat the structure in \(x\) and \(y\), this will improve the reciprocal space resolution. We also repeat the structure in \(z\), thus simulating a thicker sample.

atoms = silicon_111_orthogonal * (13, 8, 60)

fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(12, 6))
abtem.show_atoms(atoms, ax=ax1, title="Beam view")
abtem.show_atoms(atoms, ax=ax2, plane="xz", title="Side view", linewidth=0.0);

Potential

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

frozen_phonons = abtem.FrozenPhonons(atoms, 8, {"Si": 0.078})

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

potential = abtem.Potential(
    frozen_phonons,
    sampling=0.2,
    projection="infinite",
    slice_thickness=2,
    exit_planes=80,
)

Wave function

We create a probe wave function at an energy of 100 keV with a convergence semiangle of \(9.4 \ \mathrm{mrad}\). See our walkthrough on wave functions.

Partial temporal coherence is neglected here, see our tutorial on partial coherence if you want to include this in your simulation..

wave = abtem.Probe(energy=100e3, semiangle_cutoff=9.4)
wave.grid.match(potential)

wave.profiles().show();

[########################################] | 100% Completed | 224.81 ms

Multislice

We run the multislice algorithm and calculate the diffraction patterns, see our walkthrough on multislice.

measurement = wave.multislice(potential).diffraction_patterns(max_angle=30)

We take the mean across the frozen phonons axis, and compute the result.

measurement = measurement.mean(0)

measurement.compute()

[########################################] | 100% Completed | 11.78 ss

<abtem.measurements.DiffractionPatterns object at 0x0000022D1D471090>

Visualize results

We show the thickness series as an exploded plot.

visualization = measurement.show(
    explode=True,
    figsize=(16, 5),
)